free space optics for antenna beamforming

Table of Contents

Abstract..........................................................................................................................iList of Tables...............................................................................................................iiiList of Figures..............................................................................................................ivChapter I. Introduction..................................................................................................1

1.1. Background........................................................................................................11.2. Purpose and Scope.............................................................................................2

Chapter II. Theoretical Review.....................................................................................32.1. Previous Works..................................................................................................32.2. Review of Theory..............................................................................................5

2.2.1. Beam Scanning of Uniform Array..............................................................52.2.2. Beam Squinting..........................................................................................92.2.3. Free-space Method for Time-delay..........................................................112.2.4. Phase Shift in Fiber Optics.......................................................................13

Chapter III. System Overview....................................................................................153.1. Introduction......................................................................................................153.2. System Specification.......................................................................................153.3. Prototype..........................................................................................................173.4. Analysis and Discussion..................................................................................18

3.4.1. Reference Channel Delay.........................................................................183.4.2. Coaxial Delay Line Cable.........................................................................193.4.3. Collimator.................................................................................................21

3.5. Summary..........................................................................................................22Chapter IV. Source and Detector................................................................................23

4.1. Introduction......................................................................................................234.2. Laser Diode......................................................................................................24

4.2.1. Connection and Characteristics................................................................244.2.2. Biasing of Laser Diode.............................................................................26

4.3. RF Spectrum Measurement.............................................................................274.3.1. Methods....................................................................................................284.3.2. Results and Discussions............................................................................29

4.4. Summary..........................................................................................................31Chapter V. True Time-Delay Units............................................................................32

5.1. Introduction......................................................................................................325.2. Design Steps....................................................................................................325.3. Design Calculation...........................................................................................33

5.3.1. Maximum Time Delay..............................................................................335.3.2. Required Time Delays..............................................................................35

5.3.2.1. Analysis.............................................................................................365.3.3. Configurations and Dimensions...............................................................37

5.3.3.1. Configuration One.............................................................................385.3.3.2. Configuration Two.............................................................................395.3.3.3. Configuration Three...........................................................................405.3.3.4. Analysis.............................................................................................415.3.3.5. Design................................................................................................44

5.3.4. Generating Time Delays...........................................................................465.4. Summary..........................................................................................................51

Chapter VI. Experiments............................................................................................53

i

6.1. Introduction......................................................................................................536.2. Prototype Setup................................................................................................53

6.2.1. Components Alignment............................................................................55Finding Polarizer and Half-Wave Plate Axes.................................................56TTD Units Alignment.....................................................................................58

6.2.2. Discussions...............................................................................................596.3. RF Signal Measurements.................................................................................61

6.3.1. Introduction...............................................................................................616.3.2. Methods....................................................................................................626.3.3. Results and Discussions............................................................................636.3.4. Modifications............................................................................................63

6.4. Time Delay Measurements..............................................................................656.4.1. Introduction...............................................................................................656.4.2. Methods....................................................................................................666.4.3. Results and Discussions............................................................................68

6.5. Summary and Recommendation......................................................................74Chapter VII. Simulations............................................................................................76

7.1. Introduction......................................................................................................767.2. Simulation on Design Values..........................................................................76

7.2.1. Beam Pattern for 0Δτ................................................................................797.2.2. Beam Pattern for 1Δτ................................................................................827.2.3. Beam Pattern for 2Δτ and 3Δτ..................................................................84

7.3. Simulations on Measured Delays....................................................................857.4. Summary and Recommendation......................................................................90

Chapter VIII. Conclusion............................................................................................91References...................................................................................................................93Appendix A. Matlab Source Code.......................................................................94Appendix B. Simulation Results........................................................................101Appendix C. PCAAD v.2.1................................................................................117Appendix D. Laser Diode Datasheets................................................................119Appendix E. List of Components.......................................................................121Appendix F. Setup Photos.................................................................................122

ii

AbstractPhased array antennas have been increasingly gaining interest in

communication systems. The advantage of using phased array antennas is that the

radiation pattern can be controlled electronically. By controlling the radiation

pattern, power transmitted can have high gain and high efficiency at the direction of

interest. The process of controlling the radiation pattern is also known as

beamforming or beam scanning. Beam formation can be easily achieved by inserting

a phase shift or time delays between array elements. The later approach is preferred

since it eliminates beam squint problem. True-time delays methods to do

beamforming also allow phased array antennas to be applicable for wide band

applications.

The purpose of the project was to design and build a true-time delay system

using switched free-space section method to demonstrate beamforming capabilities.

The project implemented 2-bit true-time delay system to scan the beam in four

discrete angles from -45º to +45º. Experiments were carried out to measure the time

delays generated by the units that were built. The measured time delays were then

simulated under Matlab to show the beam scanning capabilities.

Time delay measurements and simulations indicate that the system can scan

the beam in four discrete angles. There were some deviations in the simulated beam

patterns compared to the designed beam patterns. These deviations were mostly

caused by the errors in the time delays generated. Time delays errors were calculated

and they were about 2ps to 11ps (5.7% error).

Small errors in beam angles will be significant as distance increases.

Therefore, high accuracy in beam pattern design is a necessity for long distance

application. This accuracy can be achieved by increasing the accuracy of time delays

generated by the system. To increase time delays accuracy, high precision of optical

devices dimensions and high accuracy in assembling the time delay units would be

required.

Further investigations need to be done on system bandwidth and system

linearity. Measurements of the beamforming capabilities using real antenna and

testing the system at the receiver side will help to investigate the system performance

further.

i

AcknowledgementThe author would like to thank Prof. Alphones for his guidance and support

throughout the project. His deep knowledge in communication system has helped the

author to overcome many problems encountered during the project. The author is

also indebted to Mr. Joseph Lasante and Dr. Zhao Zhiqiang from Thales Technology

Centre Singapore. Mr. Joseph Lasante has been thoroughly given his guidance in

managing the project and also given his help so that the project can be funded by

Thales. A special thank should also be rewarded to Dr. Zhao who has guided the

author and his partner to complete the project successfully. His training and

supervision have been done in a very intensive way. This has helped the author to

have a deep understanding in the topic and to be able to overcome many difficulties

in the project.

ii

List of TablesTable 1 System Specification.....................................................................................16Table 2 Laser Diode Measurement.............................................................................27Table 3 Required Four Time Delays..........................................................................36Table 4 Time Delays and Their Respective Beam Angles.........................................37Table 5 Summary of True Time-delay Configurations Analysis...............................43Table 6 States of True Time-delay Units....................................................................44Table 7 Half Wave Plate Light Polarization...............................................................50Table 8 Summary in Generating Time Delays...........................................................51Table 9 Power Measurements during Collimator Alignment.....................................55Table 10 Measurements to Find Polarizer Axes.........................................................56Table 11 Measurements to Find Half-Wave Plate Axes............................................57Table 12 Power Measurements with TTD Units........................................................59Table 13 Spectrum Measurement with Free-space Section Included.........................63Table 14 Modification on Laser Diode Bias...............................................................64Table 15 Phase Shift on TTD Units Measurement.....................................................71Table 16 Measured Time Delay.................................................................................71Table 17 Beam Angle Measurements.........................................................................72Table 18 Summary of Beam Angle Deviation...........................................................73Table 19 Simulated Beam Angle Deviations..............................................................89

iii

List of FiguresFigure 1 Far-field Geometry of 3 Element Array.........................................................6Figure 2 Planar Array...................................................................................................8Figure 3 Beam Squint...................................................................................................9Figure 4 Polarization Beam Splitter...........................................................................12Figure 5 Delay Element of True Time-delay Network...............................................13Figure 6 Overall System.............................................................................................15Figure 7 Maximum Beam Angle................................................................................16Figure 8 Prototype True Time-delay System..............................................................17Figure 9 Beam Divergance.........................................................................................21Figure 10 Thales Optical Link....................................................................................23Figure 11 Block Diagram of Thales Optical Link......................................................24Figure 12 Bias Connection for Laser Diode...............................................................25Figure 13 Laser Diode Characteristics.......................................................................25Figure 14 Laser Diode Modulation.............................................................................26Figure 15 RF Spectrum at the Output of SMA Cable................................................29Figure 16 RF Spectrum when Transmitter Connected Directly to Receiver..............29Figure 17 First Configuration.....................................................................................38Figure 18 Dimension for First Configuration.............................................................38Figure 19 Configuration Two with Dimensions.........................................................39Figure 20 Third Configuration with Dimensions.......................................................40Figure 21 True Time-delay Configuration for S0.......................................................45Figure 22 True Time-delay Configuration for S1.......................................................46Figure 23 the Working of PBS...................................................................................47Figure 24 True Time-delay System............................................................................47Figure 25 Polarization State before Linear Polarizer.................................................48Figure 26 Output of Linear Polarization. (a) When it is set to pass through y-axis

component. (b) When it is set to pass through x-axis components....................48Figure 27 Reflected Light in PBS...............................................................................49Figure 28 Half Wave Plate.........................................................................................50Figure 29 Prototype True Time-delay System............................................................53Figure 30 Top View of the Prototype Layout.............................................................54Figure 31 Side View of the Prototype Layout............................................................54Figure 32 Linear Polarizer Axis.................................................................................57Figure 33 Half-wave Plate Axis.................................................................................58Figure 34 Losses due to PBS......................................................................................61Figure 35 RF Spectrum with Free-space Section Included........................................65Figure 36 Phase Shift for 0Δτ.....................................................................................68Figure 37 Time Delay Measurement Using Network Analyzer.................................69Figure 38 Phase Shift as TTD S0 Generates Time Delay..........................................70Figure 39 Phase Shift as TTD S1 Generates Time Delay..........................................70Figure 40 Phase Shift as Both TTD Generate Time Delays.......................................70Figure 41 (a) Electric Field of a single element. (b) Array Factor of a two-element

linear array..........................................................................................................78Figure 42 Radiation Pattern of a Two-element Linear Array.....................................78Figure 43 Array Factor for 0Δτ in Polar.....................................................................79Figure 44 Array Factor for 0Δτ with respect to Angle...............................................80

iv

Figure 45 Radiation Pattern for 0Δτ in Polar..............................................................80Figure 46 Radiation Pattern for 0Δτ with respect to Angle........................................81Figure 47 Radiation Pattern for 0Δτ (n=8).................................................................82Figure 48 Array Factor for 1Δτ...................................................................................83Figure 49 Radiation Pattern for 1Δτ...........................................................................83Figure 50 Array Factor for 2Δτ...................................................................................84Figure 51 Array Factor for 3Δτ...................................................................................84Figure 52 Array Factors for (a) 0Δτ, (b) 1Δτ, (c) 2Δτ, (d) 3Δτ..................................86Figure 53 Array Factors for (a) 0Δτ, (b) 1Δτ, (c) 2Δτ, (d) 3Δτ w.r.t Angle...............86Figure 54 Radiation Patterns in Polar for (a) 0Δτ, (b) 1Δτ, (c) 2Δτ, (d) 3Δτ.............88Figure 55 Radiation Patterns for (a) 0Δτ, (b) 1Δτ, (c) 2Δτ, (d) 3Δτ w.r.t Angle........88

v

Chapter I. Introduction

I.1. BackgroundCommunication systems have become important parts of many engineering

applications. The need for communication services has been growing in capacity and

quality. Examples of applications that require high quality and capacity of

communication services are new generation satellite, radar, and personal

communication services. In these kinds of applications, the communication distance

is long and therefore there is a necessity to design antennas with very directive

characteristics. In other words, the antennas should have a very high gain that can

radiate maximum power at a direction of interest. This can only be accomplished by

increasing the electrical size of the antenna. To do this, the dimension of a single

element antenna can be enlarged. Another approach is to enlarge the dimension of

the antenna by forming an array.

The advantage of using an array is that the beam or the radiation pattern of

the antenna can be controlled. High gain and maximum power can be obtained if the

beam can be directed to the desired direction. This beam forming can be controlled

electronically when array antennas are used. The advantages of controlling the beam

electronically rather than mechanically include speed, reliability and graceful

degradation. Therefore, array antennas are useful for compensating platform

movement, beam shaping, providing graceful degradation, and improving reliability

[1].

The beam can be directed to a specific angle by shifting the phase of the

signals or by inserting delays. Inserting delay (true time-delay) is preferred since it

overcomes the “squint” problem in phase shifting methods [2, 3]. The effect of beam

squinting is even more pronounced if the wide-band characteristic is to be exploited

and phased arrays in more than one frequency band use the same beam forming

network. True time-delay (TTD) methods make phased array antennas to be

applicable for wideband applications since the beam steering allows for a wide

instantaneous bandwidth.

1

I.2. Purpose and ScopeThe purpose of this project was to design a true time-delay beam forming

network based on free-space method. Digital true-time delay network was to be

designed and the prototype was then to be built to show the beam forming

capabilities.

This project designed 2-bit free-space time-delay units to show the beam

scanning from -45˚ to +45˚. The beam scanning was limited to one dimension only

for simplicity. Experiments were carried out to measure the time delay produced by

the units. Another constraint in the project was the measurement equipments. Due to

the difficulties to measure the radiation pattern with the complete system, the beam

forming capabilities was verified using computer simulation. However, an antenna

was designed for the field test of the complete system in future works.

2

Chapter II. Theoretical Review

II.1. Previous WorksIn the past, true time-delay was generated electronically using different length

of electrical waveguide or cable. However, this approach can be bulky and costly.

Using electrical waveguide also results in higher loss at high frequency and more

susceptible to electro-magnetic interference. Another approach is to use optical

components to generate true time-delay. The interest in using optical processing for

RF phased arrays began about the time when G. A. Koepf proposed the free-space

heterodyne optical beamformer [4]. In optical beam forming systems, excited signals

are converted to the optical band, transmitted via optical fibers and/or free space, and

reconverted back to the microwave band at the antennas.

Different optical methods have been proposed to generate true time-delay.

These proposed methods are either based on switched path delay lines or on variable

dispersive time delays. Many researches have been done on variable dispersive time

delays [1, 5, 6, 7, 8, 9], which is able to provide a continuously variable time delay.

Among the first approaches is the use of fiber with chromatic dispersion property [5,

10]. Soref and Esman (1992), in two different researches, used fibers that have same

length and in which the dispersion property of the fiber is used together with

wavelength-tunable laser-diode source (TLD). In this method the time delay is

proportional to the electrically induced wavelength shift of the laser, Δτ = DLΔλ,

which in turn is proportional to the dc electrical bias applied to the TLD. In the

formula, D is the total chromatic dispersion per nanometer of wavelength shift per

kilometer of fiber; L is the length of fiber.

The disadvantage of using dispersion property proposed by Soref and Esman

is that the required length of fiber is very long. Soref, in his paper [10], mentioned

that the length of the fiber-optic transmission lines is about 1-2 km for the case of

dispersion-shifted fiber. In 1995, Molony [11] suggested an alternative approaches

using fiber Bragg grating. Fiber Bragg TTD element is a single length of fiber with

equally spaced, high reflectivity Bragg gratings, of different centre wavelengths,

distributed along its length. This approach gives discrete time delays where the

3

maximum number of discrete time delays is determined by the tuning range of the

source and by the optical bandwidth of Bragg reflection. His experiment showed

some discrepancy between the experimental results and the theoretical calculation.

These discrepancies are attributed to uncertainties in the precision of the positioning

of the gratings during fabrication of the delay lines.

The most current researches on variable dispersive methods are based on

fiber-optic prism reported by Esman [6, 7]. In this method, the optical carrier is split

onto numerous optical fibers each having the same nominal group delay but with

slightly different net dispersion. It can be easily made by connecting varying

amounts of dispersive and non-dispersive fiber.

The apparent limitation of the dispersion-based beamformers is the dispersion

itself. Dispersion of the modulated optical signal can distort the microwave signal at

higher frequencies [1]. Esman in his paper showed that dispersion limits the

frequency over beamwidth ratio. Another limitation is the complexity of tunable σ-

laser [8]. This type of laser is needed to tune the wavelength of the laser source to

produce the desired time delay. The complexity of the tunable σ-laser should be

reduced before it can find widespread practical applications.

Besides variable dispersion methods, optical approach to produce true time-

delay can be achieved using a switched path delay lines, which is simpler. Switched

path delay lines can be done either on free space or guided optics. The latter case is

usually achieved by switching the optical signal through the appropriate length of

optical fiber [12]. The method realizes variable optical delay by preparing a bank of

optical fibers of the appropriate lengths and choosing the desired one by switching.

However, the main concern of the method is the switching method. If the beam

forming network contains N delay lines, one laser is switched on and N-1 must be

switched off at an instant. To reduce microwave loss, optical switch rather than an

electrical switch was proposed by Jemison [13]. However, the use of different

lengths of optical waveguides might result in a quite long fiber. This can be

overcome by using free-space method.

For free-space method, time delay is generated through the switching of free-

space sections of variable lengths [14]. The microwave signals is converted to optical

signal which is then transmitted through free-space. The optical signal in free-space

4

passes through time delay unit that causes the signal to have longer optical path. The

signal is then converted back to microwave signal using a photodetector. Dolfi

proposed the time delay network consisting of analog phase shifter network and a

digital time delay network. The analog phase shifter is used to control the

polarization of the optical signal which will pass through digital time delay network.

The time delay network produces delays of binary increasing in magnitude (τ, 2 τ,

…, N τ). The time delay unit forwards or reflects the signal based on its polarization.

The reflected signal passes through longer optical path which results in a delayed

signal.

Chazelas [15] showed that time delay as small as 6.4ps (6-18GHz operating

frequency) can be produced using free-space method (5 bits true time delay module).

The prototype used 5 nematic liquid crystal Spatial Light Modulators to control the

polarization of light on each stage of true time-delay units.

In this report, the project is based on free-space methods as described by

Dolfi and Chazelas. Prisms and polarization beam splitters were used to implement

true time-delay unit. Differ from the two researches above, this project did not use

spatial light modulators to control light polarization. It used linear polarizer and half-

wave plate to perform the same task.

II.2. Review of Theory

II.2.1. Beam Scanning of Uniform ArrayOne advantage of using array antennas is that the beam can be directed to

a specific angle. This capability is usually referred to as beam scanning or beam

forming. From antenna theory it can be proved that the radiation pattern of an

array antenna is the product of the field of a single element, at a selected reference

point, and the array factor of that array. This is referred to as pattern

multiplication for arrays of identical elements [16].

E(total) = [ E(single element at reference point)] x [ array factor]

5

The array factor is a function of the geometry of the array and the

excitation phase. The characteristics of the array factor can be controlled by

varying the separation between each elements and/or the phase between the

elements. The change in the array factor will result in the change in the total field.

It is easier to vary the phase between the elements rather than varying the

separation distance. Therefore, the beam in the radiation pattern can be controlled

by varying the phase between the elements.

For linear array with N elements, the array factor can be derived by

considering the elements to be point sources. This derivation assumes identical

elements with uniform amplitude and spacing. An array of identical elements all

of identical magnitude and each with a progressive phase is referred to as a

uniform array. The array factor is given by

Equation 1

N Number of elements

k Wavelength number

d Separation distance between elements

θ Angle as shown in Figure 1

β Progressive phase lead current excitation

Figure 1 Far-field Geometry of 3 Element Array

6

The array factor in Equation 1 can be expressed in an alternate, compact

and closed form as shown in Equation 2. This equation assumes that the reference

point is the physical centre of the array. The maximum value of Equation 2 is

equal to N. To normalize the array factors so that the maximum value of each is

equal to unity, the equation can be rewritten as shown in Equation 3.

Equation 2

Equation 3

In case of planar array, the pattern of a rectangular array is the product of

array factors in the x- and y-directions. The normalized form is shown in Equation

4.

Equation 4

Where

Equation 5

Equation 6

M Number of elements in x direction

N Number of elements in y direction

θ and φ Angles as shown in Figure 2

7

Figure 2 Planar Array

The phase of βx and βy are independent of each other and they can be

adjusted so that the main beam of due to x elements is not the same as that of y

elements. However, in most application it is required that the conical main beams

intersect and their maxima be directed toward the same direction. If the main

beam is to be directed along θ = θo and φ = φo, the progressive phase shift between

the elements must be equal to

Equation 7

Equation 8

The two equations above show that we can find the required phase shifts

between elements if the beam direction is known. If the beam is only directed in

one dimension only, it means that one of the progressive phase shifts will be zero.

For example if the beam is to be scanned in the z-y plane, Equation 7 will result in

zero since there is no phase different between elements in x direction. On the

other hand, Equation 8 will become as shown in Equation 9. This is because as φ

= 90˚, the term sin(φ) becomes one. Note that Equation 9 agrees with Equation 1

for linear array.

Equation 9

8

II.2.2. Beam SquintingThe previous section has shown that the angle of the beam can be

controlled by shifting the phase between elements. Assuming the beam is scanned

only in one direction; the angle can be derived from Equation 9 and is shown

below.

Equation 10

In the equation above, k is the wavelength number which is equal to

(2π/λc). If frequency rather than wavelength is substituted (λc = c/fc ), Equation 10

becomes

Equation 11

Equation 11 shows that changing the frequency results in the change of θ.

This becomes a problem in wide-band signals. In wide-band application, the

signal will be “squinted”. In other words, components of different frequency will

be radiated in different directions. The peak angle of the beam is reduced for

frequencies above the design frequency and increased for frequencies below the

design frequency. This is shown in Figure 3.

Figure 3 Beam Squint

9

This phenomenon also affects the bandwidth of the system. If the

bandwidth is defined by the frequency limits at which the gain is reduced to half

power, the resulting fractional bandwidth for linear array is given by

Equation 12

Where

θ3 Beamwidth

Bb Beam broadening factor,

equals to unity for uniformly illuminated array

L Length of array, equals to (N x dy) for N number of elements

Equation 12 shows that the bandwidth becomes smaller as the scan angle

is increased. Therefore, for wide-band application scanning the beam using phase

shifting method results in a poor performance. This problem can be overcome by

using time-delay approaches. By using true time-delay approaches, each

frequency component will be radiated in the same direction. Time delay is defined

as shown below.

Equation 13

If Equation 13 is substituted into Equation 11, it will result in equation

shown below.

Equation 14

Equation 14 can be simplified since the frequency terms in the numerator

and denominator cancel one another. The resulting equation (Equation 15) shows

that if the time delay is set to a fix value, the angle of the beam will not change

even though the frequency changes. This overcomes the problem of beam

squinting in phase-shifting method.

10

Equation 15

In this equation, angle teta only depends on the time delay and the distance

between elements. Thus, it does not depend on the frequency like the shown when

using phase shifting.

II.2.3. Free-space Method for Time-delayAs has been discussed in the two previous sections, beam scanning can be

achieved by introducing time delay between elements instead of phase-shift.

There are many approaches to generate true time-delay; the one that is described

in this section uses different length of optical path in free-space.

Elementary physics defined velocity as distance divided by time.

Rearranging the terms will result in Equation 16. Where t is time, d is the distance

traveled, and v is the velocity.

Equation 16

In case of free-space, the velocity equals to the speed of light divided by

the refractive index of the medium. The above equation can be rewritten as

Equation 17

Where

t Time taken for light to travel

d Distance traveled

n Refractive index of medium. n equals to unity for

air. In other medium, , where v is the speed

of light at that medium.c Speed of light, equals to 2.998x108 m/s

11

Since time taken by the light will increase with longer distance, time delay

between two signals can be obtained by making the path of one optical signal

longer than the other one. To do this, one signal needs to be forwarded while the

other one has to change its direction. One solution is to use polarizing beam

splitter (PBS). The working of PBS is shown in the figure below.

Figure 4 Polarization Beam Splitter

The reflected signal can be directed to undergo longer path which results

in a delayed signal. To make sure one signal is forwarded while the other one is

reflected, the polarization of optical signals must be controlled. Therefore, an

optical device that can change the polarization state of a signal is needed. Some

devices fall into this category such as half-wave plate and Spatial Light

Modulators (SLM).

One configuration to generate true time delay is shown in the figure

below. This configuration uses two prisms, two PBSs, and SLM.

12

Figure 5 Delay Element of True Time-delay Network

Once the dimension of the delay element is known, Equation 17 can be

used to calculate the time delay generated. In this case, time taken for both paths

must be calculated and time delay is the difference between the times of the two

signals.

II.2.4. Phase Shift in Fiber OpticsOne method to study the propagation characteristics of light in an optical

fiber is ray-tracing approach. This method gives a good approximation when the

ratio of the fiber radius to the wavelength is large [20]. For a step-index fiber

structure (the refractive index of the core is uniform throughout and undergoes an

abrupt change at the cladding boundary), the electromagnetic energy at optical

frequencies is made to propagate along the fiber waveguide through internal

reflection at the core-cladding interface.

Light propagating inside fiber optic lines experiences a phase shift. As a

wave travels through the material, it undergoes a phase shift β given by

Equation 18

Where

n1 Refractive index of the core of fiber.

kFree-space propagation constant

d Distance the wave has traveled in the material

In addition, when light is internally reflected, a phase change δ (Equation

19) occurs in the reflected wave. The phase change depends on the incident angle

θ1 (θc<θ1<π/2-θc, where θc is the critical angle) according to the relationships

13

Equation 19

In the above equations, δN and δp are the phase shift of the electric-field

wave components normal and parallel to the plane of incidence, and n is the ratio

between core’s refractive index and cladding’s refractive index.

Equation 18 and Equation 19 shows that the phase shift inside the fiber

optic depends on the length of the fiber as well as the how the light is reflected

inside the fiber. How the light is reflected inside the fiber is determined by the

angle when light enters the fiber and also the bending of the fiber lines.

14

Chapter III. System Overview

III.1. IntroductionThe proposed block diagram of the overall system for two elements array is

shown in Figure 6. The input of the system is RF signal which modulates the laser

source. The optical signal carries the information signal and passes through some

true time-delay units. The optical signal is then converted back to RF signal using

photodetectors. After some amplification, the RF signal is then transmitted through

the array antennas.

Figure 6 Overall System

The above figure shows the basic building block of the system. It consists of

laser source and photo detector at each ends, true-time delay units, and antenna as the

transmitter. The focus on this project was to design the true-time delay units to scan

the beam of the antenna radiation.

The following sections in this chapter elaborate the overall system. Detail

descriptions on true time-delay units are given in the following chapter while

descriptions on antenna design are presented in [18].

III.2. System SpecificationThe system was designed to show the ability of antenna beam forming using

free-space switched delay lines method. The specification of the prototype system

depends on many constraints such as budget, time limitation, equipments and

15

components availability. Based on these limitations, the design specification of the

system is shown in Table 1.

Table 1 System Specification

Parameters Value

Maximum angle 45

Time delay units 2-bit (4 beam positions)

Antenna array elements 2x2

RF signal frequency 3.6GHz

The first parameter specifies that the system should be able to scan the beam

from -45 to +45 as shown in Figure 7. Thus, the maximum change in angle that is

produced by the true time-delay unit is 90. Since the true time-delay unit is 2-bit,

there are four beam positions that the system can scan the angle. Ideally the four

positions are to be in -45˚, -15˚, +15˚, and +45˚.

Figure 7 Maximum Beam Angle

The specification for the number of array elements shows that there are four

channels of RF signal that go to antenna. This means that the beam should be able to

be controlled in two dimensions (planar) instead of one dimension only. However,

due to limitation of budget and components, the prototype in this project only

scanned the beam in one dimension, which utilized only two array elements. Choice

of the number of elements is mainly based on simplicity reason.

The centre frequency for the system is specified based on the operating

frequency region of Thales Optical Link. Thales Optical Link comprises of laser

diode, two power amplifier, and photodetector. The specification manual [19] given

by Thales specified that the optical link is to be operated in the range of 1.5 to

3.7GHz. Thus, 3.6GHz was chosen as the operating frequency of the system to be

designed.

16

III.3. Prototype Due to limitation in time, budget and equipments, the proposed system shown

in Figure 6 was modified to produce a simplified representative prototype system.

For simplicity, the true time-delay system was narrowed down to two channels only

instead of four. With this, the capability of beam scanning would still be possible to

be demonstrated. Another simplification in the prototype was on the signal paths. In

the proposed system all signals go through free space where they pass through some

true time-delay units. To reduce the optical components complexity, one signal path

was connected directly to antenna using coaxial cable as shown in the Figure below.

This however creates another problem as the cable has delay. Discussion on this

matter is presented in the following section. The prototype system is shown in Figure

8.

Figure 8 Prototype True Time-delay System

Figure 8 shows that the RF Signal is split into two paths, one signal

modulates an optical signal and passes through true time-delay units while the other

one goes directly to antenna. With this simplification, the optical components only

need to handle one optical signal instead of two. The prototype signal uses one laser

diode, no power splitter, and one collimator at the transmitting end; at the receiving

end it only uses one photodetector instead of two.

III.4. Analysis and Discussion

17

III.4.1. Reference Channel DelayFigure 6 shows the actual proposed system for the project. All designs of

the system are based on the system shown in that Figure. In the specification, it is

stated that the beam scanning angle should go from -45º to +45º. For

simplification, beam scanning of the system would be linear instead of planar.

This would require a minimum of two signal channels. There are two signal

channels in the proposed system: one is the reference channel and the other is the

optical signal channel to be delayed. The reference channel should be passed

through without any delay in the free-space while the other channel is passed

through some true time-delay units.

The specification required the beam to scan from -45º to +45º. In other

words, the system should direct the beam at angle -45º when true time-delay is set

to zero while it should direct the beam at +45º when the time delay is set to

maximum.

Equation 9 in Chapter Two describes the required amount of phase shift

between elements when the beam is to be directed at certain angle. If the number

of elements is limited to two as in the case of the proposed system, Equation 9

specifies the phase lead of the second element (with respect to the reference

element) needed to scan the beam.

For angle = -45º

Substituting

θo = -45º

k = 24π

=

where

dy = 4.15x10-2 m (Refer [17, 18] for detail calculation)

Result in

18

The calculation shows that the optical channel needs to be phase shifted by

2.2126 rad (lead) with respect to the reference channel. Another way to see this is

that the reference channel should be phase shifted by 2.2126 rad lagging. This

phase shift is equal to time delay of 97.82ps. The calculation is shown below

using Equation 13.

The above value is the required time delay to be inserted into the reference

channel in order to scan the beam at -45º. In this case the other optical signal

channel undergoes zero true time-delay.

Therefore, to have a system that scan the beam start from -45º, the delay of

the reference channel should be fixed to 97.82ps. Thus, the time delay to be

inserted into the other channel will be dependent onto this amount of delay.

III.4.2. Coaxial Delay Line CableFigure 8 shows the modified true time-delay system to be demonstrated.

This prototype system should be able to demonstrate the beam scanning

capabilities as specified in Table 1 System Specification. The prototype system

proposed two signal channels where one is the reference channel and the other is

the optical channel to be delayed.

The prototype system suggests that one channel is connected directly to

antenna and the other one would pass through some true time-delay units. This

scheme, however, creates some problem. The problem arises since the coaxial

cable, that is used to connect directly to antenna, has a fixed amount of delay.

Thus, it is necessary to design the system carefully so that it can perform the beam

scanning to meet the specification.

The specification requires the beam to be directed from -45º to +45º.

Taking the coaxial delay line cable as the reference channel, the amount of phase

shift required to scan the beam can be calculated using Equation 9.

For Angle = +45º

19

The previous section has calculated the value for -45º which is 2.2126 rad.

For +45º, the phase shift required is -2.2126 rad. The negative sign means that the

optical channel should be phase shifted by 2.2126 rad lagging with respect to the

reference channel. The amount of time delay to be inserted has been calculated as

well which is 97.82ps. 97.82ps is the required time delay to be inserted to the

optical channel when the reference channel has zero delay. However, reference

channel has non-zero delay. The delay in the reference channel can not be ignored

as in the previous section since the two signal paths are not identical. In other

words, the delay to scan the beam to +45º is no longer 97.82ps but 97.82ps plus

the delay of the reference channel. In the proposed system shown in Figure 6, the

two signals pass through identical paths (fiber and then free-space). In the

prototype system (Figure 8), one signal passes through fiber and free-space

(optical domain) while the other passes through coaxial cable (electrical RF

signal).

For angle = -45º

Section III.4.1 has calculated the required phase shift to scan the beam at -

45º, which is +2.2126 rad. The calculated value shows that the signal of the

optical channel should lead the signal in reference channel by 2.2126rad. This

amount of phase shift equals to 97.82ps as shown in the previous calculation. If

the optical channel has zero delay, the reference channel must be delayed by

97.82ps in order to scan the beam to -45º. However, the optical channel has non-

zero delay and therefore the reference channel must be delayed by

τactual = 97.82ps + delay of optical channel Equation 20

It is important to note that delay of optical channel in Equation 20 is the

delay of the channel when the true time-delay units are set to generate zero delay.

In this case the delay is caused by the fiber line, distance of free-space path for

zero delay, and other delays from the circuits and components.

Thus, it is necessary to measure the delay of the optical channel (when true

time-delay units are set to generate zero delay) in order to design the coaxial cable

of the reference channel. The coaxial cable must be chosen to provide the

required delay time. When the coaxial cable for reference channel has delay that

satisfies Equation 20 and the true time delay units are set to generate zero delay,

20

the beam should be directed at -45º. The amount of delay in Equation 20

determines the design of true time delay units. In other words, the design of time

delay generated by the units would depend on the delay of the coaxial cable.

III.4.3. CollimatorPrototype system shown in Figure 8 has a collimator to interface between

the fiber optic and the free-space. A collimator is needed in the system since

output light from fiber diverges. Collimator helps to collimate the output light

from fiber to free-space.

There are some devices that can be used to collimate light. Chazelas [15]

in his project used microlens to collimate the output light from fiber. This

microlens, however, is very small and difficult to handle. Another choice is to use

GRIN (Gradient Index) lens as a collimator. This project used GRIN lens in its

prototype. The data sheet specifies that the beam diameter of this GRIN lens is

less than 0.5mm. The beam divergence half angle of the lens is specified to be less

than 0.25º. The beam divergence is shown in the following figure.

Figure 9 Beam Divergance

For 500mm distance the beam diameter becomes (2 X 2.18 + 0.5)mm,

which is 4.86mm. The error is about 872%, which is very big. Since the aperture

of the collimator is 2mm, a lot of power will not be detected. This contributes to

losses. The divergence issue limits the dimension of the free-space section of the

true time-delay system. The optical free-space path should not be designed to be

too long. And hence, the maximum delay to be designed is also limited by this

maximum distance.

III.5. SummaryA proposed system is presented in Figure 6 to demonstrate beam scanning

capabilities using switched free-space sections method. The specifications of the

system require the scanning angle from -45º to +45º. The beam scanning of the

21

system was implemented linearly instead of planar. For linear beam scanning the

system needs at least two signal channels. True time-delay units are inserted in one

of the channels in order to delay the signal.

Analysis on the system shown in Figure 6 suggests that the reference channel

should be inserted a fixed amount of delay to make the system scan the beam start

from -45º. The amount of the time delay is 97.82ps. This fixed amount of delay is

important in the design of the true time-delay units since the delay to be designed

should refer to this reference value.

Due to limitation in time and budget, the prototype of the system (Figure 8) to

be built was simplified. This simplification does not reduce the capability of the

system to demonstrate beam scanning. The simplified prototype is presented in

Figure 8. In this scheme one signal channel is connected directly to the antenna

without modulating an optical signal to change into the optical domain. The

prototype system requires that the coaxial cable has a delay of 97.82ps plus the delay

of the optical channel when it is set to generate zero true time-delay. This is

important to make the system scans the beam from -45º. Another consideration is the

use of collimator to interface between fiber and free-space. Collimator is needed to

collimate the output light from fiber. It is necessary due to the divergence property of

light. Without collimator the light can only travels a short distance before the

divergence effect is too dominant. This limits the maximum distance of free-space

sections the system can have, which also limits the maximum true time delay the

system can generate.

This Chapter has discussed the overall design consideration of the true time-

delay system that was built. The following chapter elaborates the components that

were used for the source and detector in the prototype system. Chapter V discusses

the design of true time-delay units of the system.

22

Chapter IV. Source and Detector

IV.1. IntroductionThis project used Thales Optical Link (Figure 10) for its laser source and

optical detector. This section describes the overview of the optical link provided by

Thales Airborne System.

Thales optical link has one RF input, three bias inputs (+10V, -10V, and

GND), and one RF output. The RF input is to be fed by RF signal that will modulate

the optical carrier. Inside the optical link, there is one photodetector to convert the

optical signal back to RF signal. This RF signal appears at the output of the optical

link. The ±10V bias voltages are converted to provide bias voltage for the power

amplifiers inside both the transmitter and receiver modules and to provide bias

current for the laser diode. Inside this converter, there are three potentiometers to

adjust the output DC voltage and output DC current. The block diagram of this

optical link is shown in Figure 11.

Figure 10 Thales Optical Link

23

Figure 11 Block Diagram of Thales Optical Link

The block diagram shows that the RF signal modulates the laser which is

connected to fiber optic. The fiber is then connected back to the receiver circuit

which converts back the optical signal to RF signal. The fiber line of the transmitter

and receiver is connected using a converter since the transmitting end is a FC

connector and the receiving end is ST connector.

The optical link was used as the source by disconnecting the fiber connection

and feeding the fiber (from transmitter) to free-space. After the optical signal passes

through time delay units, it goes back to fiber and is received by the optical link

receiver module.

IV.2. Laser Diode

IV.2.1. Connection and CharacteristicsThe laser diode inside optical link would be used as the laser source to

carry the RF signal that was to be transmitted through free-space. The laser diode

is biased with the circuitry inside the transmitter module. The anode pin is

connected to the ground plane and the cathode is connected to a negative voltage.

The connection to bias the laser diode is shown in the following figure.

24

Figure 12 Bias Connection for Laser Diode

The negative supply controls the biasing current of the laser diode. This

bias current at the end determines the output power of the laser. The bias current

is supplied from the DC converter inside Optical Link. This DC converter has a

potentiometer to adjust the amount of current supplied to this negative voltage

pin. It provides a constant current source to the laser diode. The relationship

between bias current and output power is given from the data sheet of the laser

diode and is shown in Figure 13.

Figure 13 Laser Diode Characteristics

25

The left vertical axis in Figure 13 shows the output power in mW while

the bottom horizontal axis shows the biasing current needed to obtain the desired

output power. Appendix D shows the summary of the laser diode characteristics.

It is stated that the rated output power is 2.50mW and the rated current at 25ºC is

31.2mA. The datasheet also specified that the threshold current at 25ºC is 9.6mA.

This is the current that is needed for the laser diode to turn on.

Another observation made from Figure 13 is that a small increase in

voltage results in a large increase in the current. Therefore, it is not advisable to

bias the laser diode using a constant voltage source. Rather, a constant current

source should be used to bias the laser. The current that pass through the laser

diode must be limited below the rated current specified in the data sheet.

IV.2.2. Biasing of Laser DiodeThe laser diode must be biased to deliver some amount of output power.

The choice of the biasing point might depend on some consideration. In this

project the laser diode would be modulated by RF signal. The modulation inside

the transmitter module of Thales Optical Link was done by connecting the

negative bias of the laser diode to the output of power amplifier through a

capacitor as shown in the figure below.

Figure 14 Laser Diode Modulation

Therefore, a middle bias point was chosen so as to allow maximum swing

laser diode modulation. Figure 13 shows that a bias point can be chosen at the mid

point between 15mA and 30mA. To decide the bias point, power measurement

was done so that a bias point that delivers power at about -3dBm can be chosen.

To do the measurement, the DC converter box was opened up. The bias

current that go through the laser diode was adjusted directly through the

26

potentiometer. The output fiber from transmitter module was connected directly to

the optical power meter. Then, the Optical Link was connected to ±10V and then

was powered on. The current was adjusted to start at 9mA (threshold current is

9.6mA) and then it was increased in step. The optical power was measured as the

current increased. The measurement results are tabulated in Table 2.

Table 2 Laser Diode Measurement

Bias Current

(mA)

Output Power

(μW)

Bias Current

(mA)

Output Power

(μW)

09 1.05 19 509.1

10 10.3 20 561.2

11 64.5 21 622.4

12 119.1 22 676.4

13 173.2 23 731.1

14 227.0 24 788.5

15 284.4 25 843.1

16 339.7 26 900.0

17 395.1 27 954.5

18 453.8 28 1011.0

Table 2 shows that output power of -3dBm (500μW) was obtained when

the laser diode was biased at approximately 19mA. Therefore, 19mA was chosen

as the bias point of the laser diode in this project. It would deliver output power

approximately -3dBm. This DC bias point also allowes large swing for laser diode

modulation.

Laser diode DC bias = 19mA

IV.3. RF Spectrum MeasurementThales Optical Link was to be used to change the information into optical

domain and to convert back the optical signal to RF signal. Therefore, the Optical

Link output RF spectrum was measured to determine its performance. The

27

measurement was done using a spectrum analyzer. The following equipment was

used in the experiment.

- Agilent E4407B ESA-E Series Spectrum Analyzer

- Anritsu 68347C Synthesized Signal Generator

- Two SMA cables

- Two dual DC power supplies

IV.3.1. MethodsTable 1 specifies that the input RF signal was 3.6GHz continuous wave.

This RF signal was provided by Anritsu signal generator. The signal generator

was set to deliver continuous wave with frequency 3.6GHz. The output RF

spectrum was measured using Agilent spectrum analyzer. The reading was taken

from 3GHz up to 4GHz.

Before any measurement was done, losses of the SMA cables were

measured so as to get more accurate reading on the RF measurements. One end of

the SMA cable was connected to the signal generator and the other one directly to

the input of the spectrum analyzer. As the signal generator was turned on,

spectrum analyzer displayed the RF signal spectrum on the screen. The peak value

of the spectrum was recorded. The power spectrum at the output of the cable

should be about the same with the input power injected by signal generator at the

input of the cable.

After SMA cable measurement, the output of signal generator was

connected to the transmitter module and the output of the receiver module was

connected to the spectrum analyzer using SMA cable. The optical link was

connected to ±10V. This voltage was converted by a DC converter inside the

Optical Link to provide +7V bias to power amplifier (in both receiver and

transmitter modules) and 19mA current to laser diode.

Once all had been setup, the optical link was powered on and the signal

generator was turned on to deliver RF signal. Reading was taken on the RF signal

when the transmitter fiber was directly connected to the receiver fiber. Under this

condition, RF spectrum was recorded.

28

IV.3.2. Results and DiscussionsThe output spectrum when the signal generator was connected directly to

the input of spectrum analyzer is shown below.

Figure 15 RF Spectrum at the Output of SMA Cable

The figure showed that the peak was -6.351dBm when the input power

pumped in by the signal generator was -3dBm. The result indicates that each SMA

cable seems to introduce some losses during measurements. The loss on each

cable is about -3dBm, which is not negligible.

The next measurement was taken with the transmitter fiber connected

directly to the receiver fiber. The spectrum at the receiver module is displayed in

the figure below.

Figure 16 RF Spectrum when Transmitter Connected Directly to Receiver

29

The result shows that the peak of RF signal was about -19dBm. There

seems to be a significant loss in the system. It is possible that the losses include

the SMA cable loss which is about -6dB and the loss at optical link. The loss of

the optical link was about 10dB. This loss is quite high. The losses inside optical

link can be seen by analyzing the path of the signal.

In this experiment the RF signal modulated the optical signal by

modulating the bias current of the laser diode. It was then transmitted through a

fiber with length about 1.5m before it reached the adaptor. After the adapter the

signal went through a fiber with the same length and then converted back by the

photodiode inside the receiver module. This RF signal was then amplified before

it reached the RF Out pin of the optical link.

There may be losses due to the circuitry of the transmitter and the receiver.

This is mostly caused by the mismatches and the reflection. The other losses may

be caused by the length of fiber. Since the optical signal went through a fiber with

length of 3m. The signal appears to be attenuated slightly along the line. Another

possible source of losses is the connector between the transmitter fiber and the

receiver fiber. Thales Optical Link used ST connector at the receiving side and FC

connector at the transmitting side. These two different connectors requires an

adaptor ST-FC. This connector might also cause losses in the system.

Since the attenuation is quite significant, some amplification might need to

be introduced to amplify the detected signal. This is necessary since the signal

would undergo the free-space section. Losses in the free-space section can cause

more attenuation on the signal.

30

IV.4. SummaryThales optical link as shown in Figure 10 was used as source and detector of

the true time-delay system. The optical link has a laser diode without temperature

control and one photodetector. The laser diode was biased to give output power at

about -3dBm. Experiments were done to detect the RF spectrum at the output of the

receiver module.

Laser diode data sheet and some power measurement suggest that the laser

diode should be biased at 19mA bias current. This DC bias was needed to obtain

output power at about -3dBm. This bias point also allowed a maximum swing when

the laser diode is modulated.

RF spectrum measurement was then done at the output of the receiver

module. There seem to be losses introduced by SMA cable and by the optical link

itself. The optical link appears to introduce loss of about 10dB. This loss is quite

large and some amplification might be needed, especially when it is to be integrated

with the free-space section.

The results of the experiments show that the performance of the optical link is

quite poor. This can affect the performance of the overall system. However, the

optical link can still be used as source and detector in the system as long as the signal

can be detected. This is because the purpose of the prototype was to only

demonstrate the beam scanning capabilities. To perform beam scanning, the phase

shift or time delay of the signal becomes important.

31

Chapter V. True Time-Delay Units

V.1. IntroductionBeam scanning can be performed either by phase-shifting method or true

time-delay method. The prototype of the system was built to do beam scanning using

true time-delay method. To insert true time-delay into the signal, a switched free-

space sections method was chosen. In this method the optical signal is passed

through longer path in order to create a delay.

The system specification states that the true time-delay is a two-bit time delay

system. With two-bit true time-delay, the system can scan the beam in four discrete

positions. The four beam positions are results from four discrete time delay, which is

0Δτ, 1Δτ, 2Δτ, and 3Δτ.

This chapter elaborates the design of the true time-delay units to generate the

required time delays. Most of the theory has been covered in Chapter II. The

following section starts directly with the design.

V.2. Design StepsThe purpose of the design was to propose true time-delay units that can

generate the required delay. The design comprises of choosing true time-delay units

configuration, designing their dimensions, and designing the methods to generate the

required delay using the units.

The design started by getting the specification of the system (Table 1). The

most important information from the specification was the beam angle coverage.

This information was needed to know the maximum angle the system is able to scan,

which is 90º (from -45º to +45º) in this case. With this information, the maximum

time delay that the system should generate was then calculated.

Other information needed was the angle positions of the beam. Since the

system specification states that the time delay is two-bit system, the beam can scan in

four discrete positions. With this, four time delays needed to scan the beam were

calculated.

32

After all the values had been obtained, two configurations were chosen for

the two-bit time delay system. Once a configuration was chosen, the dimensions for

the components were then calculated.

When the two units had been designed, a method to generate the required

delay was designed. The constraint in this state was the available components that

could be used in the true time-delay systems.

The design finished with the three steps concluded. A detail layout of the

designed time delay units is presented at the end of this chapter. Experiments to test

the work and performance of the system are described in the following Chapter.

V.3. Design Calculation

V.3.1. Maximum Time DelayTable 1 states that the system should be able to scan from -45º to +45º. In

other words, the system should be able to insert a delay that will result in 90º

change in the beam direction.

Note that when the system is set to zero true time-delay, the beam should

be directed at -45º. Thus, when the system is set to maximum true time-delay, the

beam should be directed at +45º. The maximum time delay can be calculated

using Equation 9 by substituting +45º as θo. The calculation is shown below.

Equation 21

Equation 22

To obtain a directivity pattern with minimum sidelobes, the distance between

array elements was set to half wavelength [17].

Equation 23

Equation 24

33

Using Equation 13 to get the time delay

Equation 25

Equation 24 shows that to get +45º the phase of the optical channel should

lag the phase of the reference channel by 2.2126 rad. Converting to time shows

the amount of time delay that should be inserted in the optical channel. Equation

25 suggests that the optical channel should generate a delay of 97.82ps with

respect to the reference channel. This is shown in the diagram below.

However, Chapter III shows that the reference channel should be inserted

a fixed amount of delay to make the beam start at -45º. In this case the reference

channel is delayed by 97.82ps or is phase shifted by 2.2126 rad lag. This is shown

in the diagram below.

Thus, it is obvious that the delay channel should be phase shifted by 2 X

2.2126 rad, which is 4.4252 rad. This amount of phase shift can be converted to

time delay by using Equation 13. The resulting time delay is 195.64ps. The detail

calculation is shown below.

Equation 26

This is the maximum time delay that the system should be able to

generate. The angle of the beam can be recalculated to verify the result.

34

Time delay of the reference channel, τo = 97.82ps

Maximum time delay of the optical delay channel, τ1 = 195.64ps

Time delay of the delay optical channel with respect to the reference channel is

This amount of time delay is the same as a phase shift of

Since the delay of the optical delay channel is larger than the reference

channel, the phase shift of the optical delay channel lags the reference channel. If

the reference channel is assumed at zero phase shift, the phase shift of the optical

delay channel is -2.2126. A negative sign is put to show that the phase is lagging.

When the phase shift between elements is known, the beam direction can be

calculated using Equation 10.

The above calculation verified that the maximum time delay of 195.64ps

would result in the maximum beam scan angle which is +45º. This calculation

result is important since it determines the other time delays that the system should

generate. The calculation for the other time delays is presented in the following

chapter.

V.3.2. Required Time DelaysThe previous section has calculated that the maximum time delay is

195.64ps. This time delay can be achieved using several time delay units. Table 1

presents the system specification which requires the system to be two-bit time

delay system. With two-bit time delay system, the beam can be scanned at four

discrete angle locations. These four positions correspond to four time delays; they

are 0Δτ, 1Δτ, 2Δτ, and 3Δτ. Therefore, it is necessary to design two units of time

delay that can generate the four required time delays.

To calculate each time delay that is required, the maximum time delay was

divided by three. This is due to four states of time delays with one of them is 0

second delays.

35

Table 3 Required Four Time Delays

States Time delays

0Δτ 0 ps

1Δτ 65.21 ps

2Δτ 130.43 ps

3Δτ 195.64 ps

Table 3 shows the four required time delays needed to scan the beam into

four discrete angle positions. These four delays are achieved using two units of

time delay. The configurations to generate the time delays are elaborated in the

next section.

V.3.2.1. Analysis

The beam angle that is produced by the four time delays shown in Table 3

must be recalculated. This is due to the non-linear relationship between the time

delay and the angle. The relationship between time delay inserted and the beam

angle is a sine function.

Using Equation 9, the four beam angles was recalculated and is shown in

the following table. In this calculation, all the inserted time delay is subtracted by

the time delay of the reference channel before it is put into Equation 9.

Table 4 Time Delays and Their Respective Beam Angles

Time delay Effective Time delay Angle

0ps 97.82ps -45º

65.21ps 32.61ps -13.6º

130.43ps -32.61ps +13.6º

36

195.64ps -97.82ps +45º

This calculation shows that the system could not achieve angle -15º and

+15º. In other words, the step angle does not increase linearly. This is caused by

the digital switching method that is used by the system. In this system, it is the

time delay that is increasing linearly.

An increase in the number of bit of the time delay system might improve

the precision of the beam angles. This is because the step angle is getting smaller

and there are more discrete beam angles.

V.3.3. Configurations and DimensionsThis section discusses the design of the true time-delay units based on

free-space sections switched method. The design started with the proposed

configuration to generate true time-delay. Analysis was done on the proposed

configuration to choose the appropriate configuration for the project. The design

ended with the calculation of the dimension in order to produce the required

delay.

The idea behind this method is to control the path that the optical signal

passes through. The delay is inserted by making the distance that the signal passes

through longer than the one without delay. To switch the free-space sections, an

optical device is needed to change the direction of the optical signal. In this case

Polarizing Beam Splitter (PBS) performs the required function. The working of

PBS has been described in the Chapter II.

V.3.3.1. Configuration One

Frigyes [2] in his paper showed one configuration to generate time delay

using free-space sections switched method. The proposed configuration is

shown in the figure below.

37

Figure 17 First Configuration

The above figure shows one possibility to generate time delay. In this

method, PBS was used to reflect the delayed signal or pass through the non-

delayed signal. Whether PBS forwards the signal or it passes the signal depends

on the polarization of the optical signal. Therefore, it is necessary to control the

polarization of the optical signal in order to control the delay units.

In this configuration the delay produced depends on the dimensions of

PBS, prisms, and the space between them. Assuming the same dimension for

PBS and prisms, the time delay is calculated as shown below.

Figure 18 Dimension for First Configuration

Recalling Equation 17, the time taken by the non delayed signal in

second is given below.

Where 2a is the distance (horizontal path in Figure 17), n is the

refractive index of the glass, and c is the speed of light. And the time taken by

the delayed signal is

Where d is the distance between prisms and PBS. In the equation above

the distance is the summation of the horizontal path (first term : 2an) with the

38

vertical path (second term : 2(d+an) ). The time delay is the difference between

the two equations.

Equation 27

V.3.3.2. Configuration Two

The second configuration quite different in principle with the first one

and is shown in the Figure below. In this configuration the delay is inserted by

changing the speed of the optical signal. When a glass is inserted, the speed of

light in that medium is decreased and therefore the optical signal is delayed.

Figure 19 Configuration Two with Dimensions

The above figure shows that the two signals undergo the same length of

optical paths. The difference is that the delayed signal is passed through a glass

with distance d while the non-delayed signal passes through air. Thus, the

difference between this refractive index of glass and the air refractive index

give the delay value between the two paths per unit length.

Since the lengths of the two paths are equal, the time delay for this

configuration can be calculated by considering only d sections where one is air

and the other one is glass. The time for the non-delayed signal is can be

calculated using Equation 17.

The time taken by the delayed signal is given by

39

Where d is the distance, n is the refractive index of glass, and c is the

speed of light. The time delay is therefore the difference between these two

equations.

Equation 28

V.3.3.3. Configuration Three

The third configuration that is proposed in this project was to combine

the concepts in the first two approaches. The configuration is shown in the

figure below.

Figure 20 Third Configuration with Dimensions

In this configuration the two signals undergo different lengths and

different refractive index with distance d. To determine the time delay in this

configuration, each optical path needs to be examined carefully. The time taken

by the non-delayed signal is given below.

While the time taken by the delays signal is expressed in the equation below.

The first term in the above equation refers to the horizontal path inside

the glass while the second term refers to the vertical path inside the glass. The

last term (d) is put to take into account the free-space section with length d.

Once the two equations are known, the time delay can be calculated as shown in

Equation 29.

40

Equation 29

V.3.3.4. Analysis

The three proposed configuration has their own features in generating

the required time delays and in space efficiency. This section tries to analyze

the three configurations in term of the time delay they can provide and the

amount of space they might occupy.

In the analysis, a dimension for prisms and PBS was chosen.

Investigations on popular optic suppliers’ catalogues showed that 10mm

dimension is common for prisms and PBS. The analysis in this section uses

10mm dimension as its reference.

Equation 27 shows that the time delay in the first configuration can be

varied by varying either the optical device dimensions, the refractive index of

the glass, or the space between the prisms and PBS (Figure 18). Since the

optical devices dimensions are fixed to 10mm (a = 10mm) and it is more

difficult to design the refractive index of the glass, the easier way to vary the

time delay is by changing the space between prisms and PBS. The smallest time

delay using this configuration is obtained by setting the space d to zero. Thus,

the minimum time delay is

Substituting the values of a, n, and c, results in

This shows that configuration one can provide delay of 100.07ps or

larger. However, section V.3.2 shows that the minimum delay required is

41

65.21ps. And thus, this configuration can not be used for this minimum time

delay. The first configuration is appropriate to generate long delays.

The amount of space taken by this configuration depends on the space

between the prisms and PBS. However, the smallest amount of space it takes is

2a multiplied by 2a, which is 4a2. If a is 10mm, then the smallest amount of

space for this configuration is 400mm2.

The time delay generated by the second configuration can be varied by

changing the space d or the refractive index of the glass. The choice falls to

designing the length d. Substituting the value of n = 1.5 into Equation 28 results

in

Where the unit of d is in meter.

However, the dimension for d normally is a few millimeter only. The

above equation also shows that the time delay is equal to zero when d is zero.

Thus, this configuration can be used for short delays by designing the

dimension of d to be small. Therefore, the second configuration is more

appropriate in generating short and accurate delays.

The amount of space needed for the second configuration depends on

the space d as well. To give some insight, dimension for minimum delay of

65.21ps is calculated below.

With this dimension, the total amount of space will be

The calculation shows that it would take quite a large space to generate

a delay of 65.21ps. Smaller amount of space is preferred due to mounting and

light dispersion reasons.

The analysis on the last configuration is the same with the other two.

The time delay is designed by choosing the dimension for d instead of changing

42

the refractive index (Figure 20). Substituting a equals to 10mm and n equals to

1.5 into Equation 29 results in

Where the unit for d is in meter.

The above equation shows that the maximum delay it can generate is

100.07ps (when d = 0). This third configuration is also appropriate for short

time delays. The maximum length of d is 60mm which is the length that would

make the delay equals to zero. Thus, this configuration has an advantage in size

compared to the second one.

To give more insight on the amount of space it is needed, the dimension

to generate a time delay of 65.21ps is calculated.

The total amount of space it occupies is

The above calculation confirms the fact that the last configuration has an

advantage in the amount of space it occupies. It takes only 409mm2 compared

with 1181mm2 when using the second configuration. The table below presents

summary of the analysis for a 10mm dimension of the optical components.

Table 5 Summary of True Time-delay Configurations Analysis

First Configuration Second Configuration Third Configuration

Suitable for long delays Suitable for short and

accurate delays

Suitable for short delays

Able to generate delay of

100.07ps or larger

Maximum delay depends

on the length of d

Able to generate delay

smaller or equal to

100.07ps

Total dimension larger or

equal to 400mm2

Total dimension is quite

large (1181mm2 for

65.21ps time delay)

Total dimension is

reasonable (409mm2 for

65.21ps time delay)

43

V.3.3.5. Design

The design of true time-delay units was to choose the correct

configurations with their dimensions in order to generate the required delays as

specified in V.3.2. The choice of true time-delay configurations is presented the

previous section.

Section V.3.2 has calculated the required four time delays. These four

time delays can be generated using two true time-delay units. Table 3 is

presented again below.

Table 3. Required Time Delays

States Time delays

0Δτ 0 ps

1Δτ 65.21 ps

2Δτ 130.43 ps

3Δτ 195.64 ps

The true time-delay units behave similar to binary system and thus it has

four states that correspond to four time delays it generates. The binary

representation of the states is given in Table 6.

Table 6 States of True Time-delay Units

States S0 S1 Time delays

0Δτ 0 0 0 ps

1Δτ 1 0 65.21 ps

2Δτ 0 1 130.43 ps

3Δτ 1 1 195.64 ps

The value of zeros and ones in the table shows whether the units are set

to insert a delay or not. For example, true time-delay unit S0 is turned on and

unit S1 is turned off to generate time delay of 65.21ps. The above information

suggests that unit S0 is in charge to generate the minimum delay which is

65.21ps while S1 is in charge to generate time delay of 130.43ps. The

44

maximum delay is generated by turning on both true time delay units (65.21ps

+ 130.43ps = 195.64ps).

Designing True Time-Delay Unit S0

Table 6 shows that unit S0 has to generate a time delay of 65.21ps. This

amount of delay is too small for configuration one as discussed in V.3.3.4.

Therefore, the choice falls into either the second or the third configuration.

However, the third configuration is preferred since the amount of space it takes

is less than the second configuration. The third configuration was then chosen

for unit S0. The design of unit S0 was based on the following values.

a = 10 mm (Dimension of prisms and PBS)

n = 1.5 (Refractive index of glass)

Equation 29 gives the formula to calculate the time delay for this

configuration. Therefore, the only unknown value in this equation would have

been distance d. The calculation of d is shown below.

Since the value of d has been obtained, all dimension in true time-delay

units are known. Figure 21 shows the configuration for unit S0 with its

dimension.

Figure 21 True Time-delay Configuration for S0

45

Designing True Time-Delay Unit S1

Unit S1 was designed to generate a time delay of 130.43ps. As has been

described in the Analysis section, the first true time-delay unit configuration is

suitable for long delays. Therefore, unit S1 was designed using configuration

one as shown in Figure 17. The design calculation was based on the following

values.

a = 10 mm (Dimension of prisms and PBS)

n = 1.5 (Refractive index of glass)

The value that needed to be calculated was the distance between prisms

and PBS. This value can be obtained using Equation 27 as given below.

With value of d was known, all the dimensions for this configuration

had been obtained. Figure 22 shows the true time-delay configuration for unit

S1.

Figure 22 True Time-delay Configuration for S1

V.3.4. Generating Time DelaysOnce the true time-delay units have been designed, the system is able to

generate delays. However, the system must have the ability to turn on or off the

delay as shown in Table 6. A delay is set when the optical signal is passed through

46

the delay path. In order to control the path that the signal should take, PBS and

other optical components to control the polarization are needed.

As shown in the true time-delay configurations, all true time-delay units

have PBS. PBS is transparent or total-reflective according to the polarization. The

working of PBS is described in Figure 4 and is presented back in the figure below.

Figure 23 the Working of PBS

The circles and the small vertical lines represent two different polarization

states that are orthogonal to one another. Therefore, if the polarization state of the

light can be controlled, then PBS can be used to change the direction of the light.

With two-bit true time-delay units, the system must have two components

to control the polarization. Each true time-delay unit must have one polarization

controller before it.

Figure 24 True Time-delay System

The choice of linear polarizer and half wave plate was mainly because

they are common optical devices. Frigyes and Chazelas in their project used

Spatial Light Modulator (SLM) to control the polarization on each stage.

Linear polarizer is used to subject one of the two orthogonal polarizations

to strong absorption. Thus, if the incoming light has a polarization state at angle

45º, then the linear polarizer can be used to choose the x axis or y axis

polarization of the light.

Half wave plate is used to rotate the light polarization. When the half wave

plate is rotated to angle θ, the light polarization will be rotated by 2θ. Therefore,

this component can be used to change the state of polarization of the optical

signal.

The following section describes the polarization changes in each stage of

Figure 24.

47

Stage Linear Polarizer

The polarization state before the linear polarizer is unknown. Polarization

controller, however, helps the output polarization from the fiber to be more linear.

Nevertheless, the angle of the polarization is unknown. Linear polarizer is used to

control the angle of the polarization state θ.

The polarization state before and after the polarizer is shown in the two

figures below.

Figure 25 Polarization State before Linear Polarizer

Figure 26 Output of Linear Polarization. (a) When it is set to pass through y-axis component. (b) When it is set to pass through x-axis components.

Figure 25 shows the polarization state that is assumed at certain angle θ.

When the polarizer is set to absorb the x-axis component, the result is shown in

Figure 26(a). Figure 26(b) shows the other case when the polarizer is set to absorb

the y-axis components. Thus, the input light of the next stage can be controlled

either in two polarization states as shown in the above figure.

Stage True Time-delay Unit S0

The incoming light into stage S0 has two possibilities as are shown in

Figure 26. The true time-delay is inserted in this stage. Whether a delay is inserted

or not depends on the polarization of the incoming light that comes into PBS. This

is described more clearly in the figure below.

48

Figure 27 Reflected Light in PBS

Based on this picture it is obvious that if the polarization is on the y-axis,

then the light will be reflected. On the other hand, the light is forwarded directly

to the output of PBS when the polarization is on the x-axis.

Figure 17 on page 38 shows that the delayed signal is the one that is

reflected by PBS. Therefore, the incoming light to stage S0 should be set to have a

polarization on the y-axis in order to insert a delay. If stage S0 is to be set not to

insert a delay, then the incoming light should be set to have polarization on the x-

axis. This control of light polarization is done on the previous stage.

The output light from stage S0 has the same polarization with its input. In

other words, if the incoming light has polarization on the y-axis, then the outgoing

light from the true time-delay unit will have polarization on the y-axis as well.

Thus, there are two possibilities of light polarization at the output of stage S0

which are the same as the one shown in Figure 26.

Stage Half Wave Plate (λ/2 plate)

The previous part has discussed that the output of stage S0 has two

possibilities of light polarization, which are either in y-axis or in x-axis. This state

of polarization is to be changed in this stage in order to insert the second delay.

49

The working of half wave plate is shown in the figure below. This picture

shows that when the half wave plate is rotated at angle θ, then the light

polarization will be rotated by 2θ.

Figure 28 Half Wave Plate

All possibilities of outgoing light from half wave plate is presented in the

table below.

Table 7 Half Wave Plate Light Polarization

Incoming Polarization Outgoing Polarization Half Wave Plate

Not rotated

Rotated by 45º

Not rotated

Rotated by 45º

Stage True Time-delay Unit S1

50

Light polarization state from half wave plate determines whether stage unit

S1 should insert delay or not. The principle of this stage is the same as stage unit

S0. When light polarization is on the y-axis then the signal will be delayed. And if

the light polarization is on the x-axis the unit does not insert any delay.

All the stages in generating time delays can be summed up in the

following table.

Table 8 Summary in Generating Time Delays

Delay S0 S1 Polarizer rotation

from vertical axis

λ/2 plate

0Δτ 0 0 90º (x-axis) Not rotated

1Δτ 1 0 0º (y-axis) Rotated 45º

2Δτ 0 1 90º (x-axis) Not rotated

3Δτ 1 1 0º (y-axis) Rotated 45º

V.4. SummaryThis chapter elaborates the design of true time-delay units and their

mechanism to generate delays. A two-bit true time-delay system has been designed

to demonstrate beam scanning capability that is able to scan the beam from -45º to

+45º.

The design started by examining the required specification. Maximum time

delays and the four required delays to be generated were calculated. Based on this

specification, three true time-delay units were proposed. Analyses on the three

configurations were done and two out of three proposed configurations were chosen

to be used in the system. The choice of the configuration was based on their ability to

generate the required time delays and the amount of space they takes.

The next step was to calculate the dimensions of the two configurations so

that a correct time delay may be produced. Once the dimensions had been calculated,

the design of the units was done. However, a mechanism to produce time delays

using these units should be designed. Table 8 summarizes the mechanism to generate

time delays using linear polarizer and half wave plate.

51

In summary, a two-bit true time-delay system has been designed to generate

the required time delays. This true time-delay system is to be integrated with the

other components such as source and detector in order to build a complete system for

beam scanning demonstration.

52

Chapter VI. Experiments

VI.1. IntroductionPrevious chapter has presented the design true time delay system. Last

chapter showed that the designed true-time delay units should give the appropriate

time delay as shown in Table 3. When the prototype was built, it faced some

problems such as the availability of the components, losses in the electrical and

photonic components, electrical coupling, etc. Therefore, experiments were set up to

measure the time delay that was produced by the system that had been designed.

This chapter elaborates the setup of the prototype and the experiments to

measure the time delay it can generate. The first section will discuss the setup of the

prototype and any modification made. The second part will present the experimental

setup together with its collected measurement on the time delay that was generated.

VI.2. Prototype SetupThe prototype that was to be built has been discussed in Section III.3. The

system is shown again in the figure below. The components list for this system is

given in Appendix E.

Figure 29 Prototype True Time-delay System

The first step in setting up the prototype was to design the layout of

component on the optical platform. This prototype was setup on 60cm x 60cm

Newport optical platform. The optical components that are shown in Figure 29 were

to be mounted on 3 inch posts. The collimator was to be mounted on a compact

kinematics mount. This helped the collimator to be adjusted for alignment. True

53

time-delay units were to be mounted on 50mm x 50mm kinematics platform mount.

The linear polarizer and half-wave plate had their own mount that can be rotated. The

fiber line from the transmitter was fed into a polarization controller before it went

into free-space. The layout of the prototype is shown in the two figures below.

Figure 30 Top View of the Prototype Layout

Figure 31 Side View of the Prototype Layout

54

VI.2.1. Components AlignmentOnce the layout is done, the components needed to be aligned before it

could function. The first alignment was done from the transmitting collimator to

the receiving collimator. To do this alignment, all other optical components

between the two collimators were taken out. The optical link was connected to

±10V. These voltages were then converted to deliver +7V voltage to the power

amp and 19mA current to bias the laser diode. Before the alignment was done, the

output power of the transmitter was measured. To do this, the fiber output from

the transmitter was connected to an optical power meter. The reading showed that

the power was -2.97dBm. This output power can be adjusted by adjusting the bias

current of the laser diode. To deliver output power of about -3dB, a bias current of

19mA was needed. The amount of bias current needed can be checked in the laser

diode’s datasheet.

After the reading was done, the fiber output from the transmitter was

connected back to the fiber from the transmitting collimator. The power meter

was connected to the fiber of the receiving collimator. The two collimators were

aligned so as to get a maximum power reading. Once the reading was a maximum

value, the polarization controller was adjusted to get the maximum power. The

maximum power reading measured was -10.83dBm.

After the two collimators were aligned, the two true time-delay units were

assembled and mounted on top of the 50mm x 50mm kinematics platform mount.

The mounts were than put into the 3inch posts. The two units were also aligned by

measuring the power detected on receiving collimator.

Table 9 Power Measurements during Collimator Alignment

Measurements Power (dBm) Power (μW)

Output power from transmitter -2.97 504.1

Power detected from collimator to

collimator (no components between)

-10.83 82.60

55

Finding Polarizer and Half-Wave Plate Axes

Linear polarizer and half-wave plate was used in the process of TTD units

alignment. Before these two components could be used, they were tested so as to

know the axes of the components. This was necessary since there could be error

when the polarizer and half-wave plate were mounted onto the rotation mounts.

To get the axis of the polarizer, two PBSs were used in the measurement.

Linear polarizer was on the post after the transmitting collimator. After the

polarizer, a 50x50mm kinematics mount was put on. The two PBSs were put on

top of it so as the horizontal light polarization would pass through and the vertical

light polarization would be reflected. After these components were placed, the

polarizer was set at 0º on its rotation mount. The laser diode was turned on and

optical power was detected at the other end. The rotation mount of polarizer was

then rotated in step of 10º from 0º to 180º. Power measurements for each angle

were recorded and are tabulated in Table 10.

Table 10 Measurements to Find Polarizer Axes

Rotation Mount Angle

Power Detected(dBm)

Rotation Mount Angle

Power Detected(dBm)

0º -39.47 100º -21.02

10º -46.22 110º -20.64

20º -67.71 120º -21.09

30º -48.26 130º -21.88

40º -39.20 140º -23.01

50º -32.73 150º -25.47

60º -28.40 160º -27.49

70º -25.52 170º -32.67

80º -23.17 180º -38.11

90º -21.73

Table 10 shows that the maximum power detected was when the rotation

mount rotated to angle 110° and the minimum was when it was at 20°. Further

tuning on the rotation mount showed that 108° had the maximum power detected

while 18° had the minimum power detected. This result suggests that light

56

polarization is vertical at 18° angle on the rotation mount. On the other hand, the

light polarization at 108° is horizontal. This result is reasonable since the PBS

only passes through horizontal light polarization. That is why the maximum

power detected was at 108° and the minimum was at 90° different, which was

18°. With this, the polarizer can be used to pass through certain angle of light

polarization by rotating the rotation mount from 18° up to 198°. The dotted line in

Figure 32 shows the axis where light polarization can pass through; the axis is at

angle 18º on the rotation mount.

Figure 32 Linear Polarizer Axis

To find out the axes of half-wave plate, a similar procedure was adopted.

The half-wave plate was placed after the first stage of two PBSs. Linear polarizer

was rotated to angle 108° so as the outgoing light had horizontal polarization.

With this polarization state, all light would be passed through on the first stage of

the two PBSs. The incoming light to the wave-plate would have horizontal

polarization. Another two PBSs were then placed onto the kinematic mounts and

was positioned after half-wave plate. Power was detected from the receiving

collimator and the wave-plate was rotated. The power was measured as the wave-

plate’s rotation mount was rotated from 0° to 180°. The maximum and minimum

power detected was recorded and are shown in Table 11.

Table 11 Measurements to Find Half-Wave Plate Axes

Half-Wave Plate Rotation Mount Angle Power Detected

11° -30.8dBm

56° -59.1dBm

The result showed that the minimum power detected was at angle 56° of

the rotation mount and the maximum was at 11°. The result suggests that if the

57

rotation mount is at 11°, half-wave plate does not change the polarization state.

The maximum power was detected at 11° since the wave plate does not change

the horizontal light polarization from the previous stage. The minimum power

detected was due to all light was reflected by PBS. This is due to the wave plate

was rotated by 45° (11° + 45°). This would cause the light polarization changed

by 90°. Since the polarization was vertical, light was reflected. The measurements

indicate that the 0º axis is at 11º angle on the rotation mount as is shown in Figure

33.

Figure 33 Half-wave Plate Axis

TTD Units Alignment

To align and mount the TTD units, the following methods were done. TTD

unit S0 was set up first. The two PBSs were placed on the kinematics mount and

then the linear polarizer was put before unit S0. The polarizer was set to block the

vertical polarization. In other words, only the horizontal polarization could pass

through. To do this, the polarizer was set at 108º or light polarization on

horizontal axis. In this polarization state, all light would be forwarded through as

it reached PBS. The two PBS were aligned so as to get a maximum power reading

at the detector. Once the PBSs were aligned, the polarizer was set to block the

horizontal polarization (polarizer was set at 18º). In this case, light would undergo

the reflected path in the TTD unit. The two prisms were then aligned to get the

maximum power reading.

To align and mount the second TTD unit, the half-wave plate was put

before TTD unit S1. Linear polarizer (before state S0) was set to block vertical

polarization so as light will not be reflected as it went through PBSs. Wave plate

was then set at 11º so as not to rotate the incoming polarization. With these

58

configurations of polarizer and wave plate, the incoming light to PBS unit S1 will

have horizontal polarization. With this condition, the two PBSs were aligned.

Once it was aligned, the half-wave plate was set at 56º (or 45º angle) so as to

rotate the incoming polarization by 90º. With this condition, all incoming light

would be reflected by PBS. With this setup, the two prisms were then aligned.

After the setup was done, power readings were taken for four possible

cases as shown in Table 8. The first reading was taken with the linear polarizer set

to 108º and half-wave plate set to 11º. In this case, all light was passed through

PBS. In other words, this was the setup for no delay. After the reading was taken,

the polarizer was changed to 18º. This is the case for generating delay in the two

units. Next, the half-wave plate was rotated to 56º. With this configuration, the

light would be delayed in the first unit only. The next measurement was taken

with linear polarizer at 108º and the half-wave plate was still at 56º. The

measurement results are shown in the table below.

Table 12 Power Measurements with TTD Units

Polarizer Half-wave Plate Power (dBm) Delay

108º 11º -30.33 0Δτ

18º 11º -20.99 1Δτ

18º 56º -25.09 2Δτ

108º 56º -37.70 3Δτ

VI.2.2. DiscussionsMeasurement of the system showed that the output power from the

transmitter was about -3dBm. This output power was set by adjusting the bias

current of the laser diode. This power was then transmitted through free-space

with length about 127mm. The detected power at the end of free-space section

was -10.83dBm. It showed that the loss of the free-space section was about 8dB.

However, due to small aperture of receiving collimator, there may be loss due to

misalignment and loss due to inability of the receiving collimator to capture wider

incident light (caused by dispersion property of light). These losses are included

in that 8dB loss.

59

For length of 127mm, the beam diameter at the end of the free-space

section, excluding any components in between, is (2 x 0.55 + 0.5)mm, which is

about 1.61mm. This beam diameter is still smaller than the aperture of the

receiving collimator. However, when light is reflected (by prisms or PBS) and the

reflection surface has some elevation, the beam diameter seems to be even

broader. When the beam diameter is bigger than the diameter of the receiving

collimator, some power is not detected. This contributes to some losses.

When TTD units, polarizer, and half-wave plate were placed between the

two collimators, more losses occurred in the system. Each component seems to

contribute to losses. Moreover, every stage is likely contributes to light deflection.

This may cause the system to be adjusted again after every alignment of each

stage.

Losses from TTD units can be explained by considering the reflections at

every interface between air and glass. Another possible cause of loss seems to be

the polarization beam splitter (Figure 27 Reflected Light in PBS).

The equation to calculate light reflection between glass and air is shown in

Equation 30. Where n is the refractive index of the glass, Pr is the reflected power,

and Pin is the incident power.

Equation 30

If 1.5 is used as the refractive index of the glass, the reflection can be

calculated as shown below.

The result suggests that 4% of the incident power is reflected as the light

passes through the interfaces between glass and air. Note, however, that the

refractive index of the actual components might not be exactly 1.5.

The other possible cause of losses may be due to polarization beam

splitter. Figure 27 shows that when the light is reflected by PBS, practically there

is some amount of light that is not reflected. The percentage is less than 2%. The

possible losses due to PBS are shown in the dotted line in the figure below.

60

Figure 34 Losses due to PBS

Figure 34 shows that ideally the losses due to PBS might occur only in

two paths (two vertical dotted lines). The dotted line in horizontal path shows the

leakage that is in the same path with the delayed signal. This leakage light,

however, will be reflected again when it meets the second PBS. Therefore, the

total loss due to imperfection in PBS is about 4%.

Another point to note is about polarization controller. Polarization

controller that was placed before the transmitting collimator affected the output

power transmitted. The polarization controller needed to be adjusted again so as

the outgoing light from linear polarizer was high enough for both states (vertical

and horizontal polarization.

The detected power at the receiving collimator varied from -20dBm to -

37dBm. This power was very weak. More losses would reduce this detected

power as it is transmitted to the photodiode and receiver module. In order to

detect the RF signal, some amplification might be needed. A semiconductor

optical amplifier can be used to amplify the optical signal from the receiving

collimator to the photodiode.

VI.3. RF Signal Measurements

VI.3.1. IntroductionOnce the prototype was ready, measurement to detect the RF signal was

done. The purpose was to detect back the transmitted RF signal at 3.6GHz. The

RF signal was used to modulate the optical signal from laser source. This optical

signal was then transmitted through free-space. This optical signal was then

converted back to RF signal using a photodiode. Measurement was done to check

61

the spectrum of the received RF signal. To do this measurement, the following

components were used.

- Agilent E4407B ESA-E Series Spectrum Analyzer

- Anritsu 68347C Synthesized Signal Generator

- Two SMA cables

- Two dual DC power supplies

VI.3.2. MethodsThe input RF signal was 3.6GHz continuous wave. This RF signal was

provided by Anritsu signal generator. The signal generator was set to deliver

continuous wave with frequency 3.6GHz. The output power level was then set at -

3dBm. RF spectrum measurement was done using Agilent spectrum analyzer. The

spectrum analyzer was set to capture signal from frequency 3GHz up to 4GHz.

The output of signal generator was connected to the transmitter module

and the output of the receiver module was connected to the spectrum analyzer

using SMA cable. The optical link was connected to ±10V. This voltage was

converted by a DC converter inside the Optical Link to provide +7V bias to power

amplifier (in both receiver and transmitter modules) and 19mA current to laser

diode.

The linear polarizer and wave plate was set to allow forward transmission

of light. To do this, the polarizer was set at 108º and the wave plate was set at 11º.

With this setup, light would not be reflected by PBS.

Once all had been setup, the optical link was powered on and the signal

generator was turned on to deliver RF signal. The readings were taken with free-

space section included. The transmitter fiber was connected to the transmitting

collimator. The RF signal would undergo free-space section and then back to fiber

before it was detected by the photodiode. The RF output RF spectrum from the

receiver module was measured. After this reading was taken, the free-space

section was blocked so as not to allow any light coming to the receiving

collimator. Reading was taken again from the spectrum analyzer under this

condition.

62

VI.3.3. Results and DiscussionsMeasurements on the losses of SMA cable and optical was done on

Chapter IV. The experiment results discussed in this chapter included TTD and

free-space section. When the free-space section was not blocked, a continuous

wave signal spectrum appeared in the analyzer. The reading showed that the peak

of the signal spectrum was about -37dBm. However, when the free-space section

was blocked, the spectrum in the analyzer was still the same.

Table 13 Spectrum Measurement with Free-space Section Included

Condition Peak Value (dBm)

Light forwarded in the free-space -37

Light was blocked -37

A possible explanation for this result can be the coupling signal from the

transmitter to the receiver modules. The circuit inside Thales Optical Link used

the same DC converter to power up the receiver module and the transmitter

module. Both DC supplies to the transmitter and receiver shared the same ground

point. This can be the cause of the coupling signal.

VI.3.4. ModificationsTo overcome this problem, some modifications were made on Thales

Optical Link. The transmitter was separated and put on some distance from the

receiver. The DC supply for the transmitter was connected directly a separate DC

power supply. This would help to isolate the coupling through the ground wires.

The wires to bias the transmitter module from the power supply were also

shielded. This can help to reduce the coupling through radiation.

The bias to the transmitter module consists of +7V to bias the power

amplifier and 19mA to bias the laser diode. In the Optical Link, the bias for the

laser diode was done by controlling the current. Since then the transmitter was

connected to DC power supply which supplies constant voltage, a resistor was

added in the laser diode bias path. A resistor of 390Ω was connected between a

63

negative power supply and the bias of the laser diode to limit the current from the

constant voltage source.

As the modification was made, the negative power supply for the laser

diode was set to deliver current of 18mA. With this set of bias, power

measurement was taken again to get the output power from the transmitter fiber.

The transmitter fiber was connected to the optical power meter and the optical

power was measured when 18mA current was delivered to the laser diode. With

this bias configuration the output power was -2.416dBm (573.67μW).

Table 14 Modification on Laser Diode Bias

Bias current Optical Output Power (dBm) Optical Output Power (μW)

18mA -2.416 573.67

With this set of modifications, the last two measurements were repeated.

The fiber from transmitter was connected to the transmitting collimator and the

RF spectrum was measured from the receiver module. The peak of the spectrum

signal was about -51dBm. This output signal was very weak and very near to the

noise floor.

To be able to detect the signal, some amplification was needed. A

semiconductor optical amplifier (SOA) was used to provide this amplification.

SOA was introduced in the system and connected between the output of receiving

collimator and the input fiber of the receiving module. Opto-Link SOA (SOA-

1310-A) was used in this project.

Opto-Link SOA has one optical input and one optical output with a knob

to adjust the amplification gain. The output from the receiving collimator was

connected to the optical input of the SOA and the receiver module fiber was

connected to the output of the SOA. Additional fiber of 2m was used to connect

the output of SOA to the input of the receiver fiber. This may cause the reference

delay in the optical channel increase and a required delay for the coaxial delay

cable may need to be recalculated.

The same measurement was repeated again with SOA included in the

system. Before the measurement started, amplification gain of SOA was set to its

minimum value. The system was then powered on the reading was taken from the

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receiver module. Amplification gain of SOA was increased slowly to its

maximum allowable value. The output spectrum detected at the receiver module

with a maximum amplification from SOA is shown in Figure 35.

Figure 35 RF Spectrum with Free-space Section Included

The result showed that the peak RF spectrum was -31.61dBm. This output

was higher compared to the previous configuration (-51dBm). When the light path

was blocked, spectrum analyzer showed no signal. This indicates that the coupling

had been eliminated from the system and the detected signal of about -32dBm was

the signal from the receiver module alone. Even though the signal was not high,

yet it was adequate to measure true-time delay in the system.

VI.4. Time Delay Measurements

VI.4.1. IntroductionThe purpose of this measurement was to verify the time delays generated

by the system. To do this, four measurements that represented the four states of

time delay were taken. A network analyzer was used in these measurements.

Network Analyzer is capable to measure the phase shift or time delay from input

65

port to output port. Below is the list of components and equipments that were used

in the experiment.

- HP 8753C Network Analyzer with HP 85047A S-parameter Test Set

- Calibration kit HP85033D 3.5mm

- Two Dual output DC power supplies

- Two SMA cables

VI.4.2. MethodsBefore the network analyzer could be used for measurements, it needed to

be calibrated. The calibration was done using 3.5mm calibration tool kit provided

by Hewlett-Packard. The analyzer was calibrated using Full 2-Port calibration. It

consists of three calibrations, namely reflection coefficient, transmission

coefficient, and isolation. Reflection coefficient was calibrated for short, open,

and 50Ω load termination. It was done for port one and port two of the analyzer.

Transmission coefficient was calculated by the analyzer with the two port

connected using a thru connection. The last calibration, which is isolation, was

omitted. The calibration was done for frequency range of 3.5GHz to 3.7GHz.

After the analyzer had been calibrated, port one was connected to the transmitter

module using a SMA cable and port two was connected to the output from

receiver module.

Since the experiment was to measure the time delay introduced by the

TTD units, the fiber output from transmitter module was connected to the

transmitting collimator. In this case, the signal would be transmitted through free-

space where it would be processed by TTD units.

The receiver module was powered up using ±10V which was then

converted to +7V to bias the power amplifier. The transmitter module after

modification was connected directly to a separate dual output power supply. One

output was to provide +7V for transmitter module power amplifier and the other

output was to provide 18mA current to bias the laser diode. A resistor of 390Ω

was used to limit the current from the power supply as has been discussed in the

previous section.

66

In this measurement, SOA was used to amplify the detected signal at the

receiving collimator. The input of SOA was connected to the output of receiving

collimator and the output of SOA was connected to the input of receiver fiber

using another 2m single mode fiber. The SOA was powered on with the

amplification gain set to minimum value.

The first reading was to measure the delay or phase shift introduced by the

system when the TTD units did not generate any delay. To measure this, linear

polarizer was set to 108º angle in the rotation mount to allow horizontal light

polarization to pass through. The half-wave plate was set to 11º angle in its

rotation mount so that it would not rotate the polarization of the incoming light.

Under this configuration, the light would not be reflected by PBS and it would be

forwarded through until the end of free-space section.

After everything was ready, network analyzer was set measure the S21

parameter of the device under test. The format measurement was Logarithmic

Magnitude. With this display on the network analyzer screen, SOA gain was

increased steadily until its maximum value or the network analyzer able to detect

the signal. Polarization controller can be adjusted to increase the signal power

detected.

Once the signal detected had reached its maximum value the analyzer

could detect, the format measurement was changed to Phase. The output display

of the analyzer was printed and recorded. Note, however, the value was a phase

shift from input port to output port expressed in degree. The time delay was

recorded by changing the format measurement to Delay. However, when

measuring under this format, an exact time delay could not be accurately obtained.

Therefore, all readings were taken from Phase format or phase shift which then

converted back to time delay.

The next measurement was to get the phase shift introduced by the first

TTD units. The linear polarizer was then set to 18º angle in rotation mount to

allow vertical polarization to pass through and the half-wave plate was set to 56º

angle to change the polarization back to horizontal. Under this setup, the light

would only be reflected in the first TTD unit. Same measurement method was

done to get the delay from input port to output port.

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The third measurement was to get the delay generated by the second TTD

unit. Before the reading was taken, linear polarizer was set back to 108º angle and

the half-wave plate was set to 56º. Thus, the light would only be reflected in the

second TTD units. The delay was then measured using the same approach as

before.

The last measurement was to get the delay generated by both TTD units.

In order to do this, light was to be reflected in both stages. Therefore, linear

polarizer was set to 18º angle and the half-wave plate was set to 11º. Thus, delay

from input to output could be measured using the same approach.

The readings from the last three measurements did not represent the true-

time delay introduced by the TTD units. Rather, it showed the delay from the

input port to the output port. Therefore, the phase delay readings must be

subtracted with the first reading to obtain 1Δτ, 2Δτ, and 3Δτ.

VI.4.3. Results and DiscussionsThe phase shift from input to output when light was not delayed is

displayed in the following figure.

Figure 36 Phase Shift for 0Δτ

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The phase shift from input to output when TTD units did not introduce any

delay was 30.499º or +0.5323 rad. However, since the phase is leading, the actual

phase shift is (0.5323rad - 2π) rad, which is -5.7509rad. This was the amount of

phase shift introduced by the optical and electrical system which includes

transmitter module, fiber lines, free-space section, and finally receiver module.

This phase shift can be converted to time delay using Equation 13.

This amount of delay is important to determine the delay of coaxial delay

line cable. As has been mentioned in Equation 20, the delay of coaxial cable has

to be 97.82ps plus the delay of this channel.

τactual = 97.82ps + 254.24ps = 352.06ps

This amount of time delay is a phase shift of -1.6803rad. This means the

coaxial delay must introduce a phase shift of -1.6803rad in order the beam can

start at -45º.

Another conclusion is about the difference between phase shift and time

delays to scan the beam. Figure 36 shows that the phase shift is very sensitive

with the frequency. As the frequency changes, the phase shift also changes

significantly. Therefore, if the beam scanning is done by shifting the phase, the

beam angles would be affected as the frequency changes or as the signal

transmitted is a wide band. Whereas if true-time delay is inserted, the time delays

between elements are quite constant for a range of frequency span. This can be

seen from Figure 37. This figure shows the time delay measurement using

network analyzer for state 0Δτ. It can be seen that the time delay constitutes

almost a straight line.

Figure 37 Time Delay Measurement Using Network Analyzer

69

The results for other phase shift measurements are shown in the three

figures below.

Figure 38 Phase Shift as TTD S0 Generates Time Delay

Figure 39 Phase Shift as TTD S1 Generates Time Delay

Figure 40 Phase Shift as Both TTD Generate Time Delays

Measurements results showed that the phase shifts introduced for the last

three measurements were -56.96º, -147.65º, and 122.39º. From these values, a

phase shift in radian can be calculated. These phase shift in radian are shown in

Table 15.

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Table 15 Phase Shift on TTD Units Measurement

Unit Delay Phase Shift Phase shift

No delay +30.499º +0.5323rad

TTD S0 -56.96º -0.9941rad

TTD S1 -147.65º -2.5770rad

TTD S0 and S1 +122.39º +2.1361rad

These values, however, are not the phase shift introduced by TTD units.

These values simply represent the phase shift introduced from the input port to the

output port. Therefore, to obtain the true-time delay generated by TTD units, these

values must be subtracted with the phase shift for 0Δτ. This concept is explained

in the following diagram.

The diagram shows that the phase different when the system introduced no

delay and when TTD S0 introduced delay was 1.5264rad. This value is the phase

delay with 0.5323rad as its reference, or in other words it is obtained from

0.5323rad subtracted by -0.9941rad. This value when converted back to time

delay (Equation 13) is about 67.48ps. This measured time delay is about the same

with the designed time delay specified in Table 6. The following table lists the

difference between time delay measurements and the designed value.

Table 16 Measured Time Delay

Measured Phase Shift

Phase Shift State 0Δτ

Phase Difference

Measured Time Delay

Designed Time Delay

Error

-0.9941rad +0.5323rad 1.5264rad 67.48ps 65.21ps 2.27ps

-2.5770rad +0.5323rad 3.1093rad 137.46ps 130.43ps 7.03ps

+2.1361rad +0.5323rad 4.6794rad 206.87ps 195.64ps 11.23ps

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Table 16 also shows the errors in the actual time delay generated

compared to the designed values. The errors were about 2ps to 11ps. These errors

may result in more deviation on beam angles. The actual beam angles generated

can be calculated with assumption that the coaxial delay line is able to provide a

phase shift of -1.6803rad (Refer to previous discussion). With this assumption, the

phase difference can be calculated as shown in the diagram below.

The diagram shows that the phase difference between reference channel

and with the one when TTD S0 generate delay was 0.6862. This value was then

substituted to Equation 10 to obtain the beam angle.

The calculation shows that the deviation of the beam angle from the

designed value was about 1º. The other beam angles were calculated in the same

way as above. The results are shown in the following table.

Table 17 Beam Angle Measurements

Measured

Phase Shift

Reference

Phase Shift

Phase

Difference

Beam

Angle

Designed

Beam Angle

|Error|

-0.9941rad -1.6803rad +0.6862rad -12.7º -13.6º 0.9º

-2.5770rad -1.6803rad -0.8967rad +16.7º +13.6º 3.1º

+2.1361rad -1.6803rad -2.4668rad +52.0º +45.0º 7.0º

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Table 18 Summary of Beam Angle Deviation

Delay Beam Angle Designed Beam Angle

0Δτ -45º -45.0º

1Δτ -12.7º -13.6º

2Δτ +16.7º +13.6º

3Δτ +52.0º +45.0º

Table 17 and Table 18 show that the errors in beam angles were below

7.0º. This amount of error comes with the assumption that the reference channel

has an exact value of -1.6803rad phase shift. Inaccuracy in the phase shift of

reference channel may result in more errors in the measured beam angles.

Beam accuracy becomes more important as the target distance increases.

A small error in beam angle can cause inefficient power delivered or even

undetectable power at the target direction.

Another problem in the demonstrated system was that the phase shifts

measured using network analyzer changed when the fiber optic layout was

changed. However, the phase differences remained the same which means that the

time delays generated by the TTD units do not change. The change of phase shifts

seems to occur in the fiber optic lines. It seems that if the bending of fiber optic

lines is changed, the phase shift of light from input to output can change. This is

reasonable since the phase shift inside the fiber also depends on how the light is

reflected internally (Section II.2.4 and [20]). And this can change when the layout

or the bending of fiber is changed. The effect seems to get worse when the length

of fiber is not short.

This problem affects the prototype system directly since coaxial delay line

is to be designed according to the phase shift of the optical channel. This optical

channel, however, might change when the fiber lines are interrupted. Thus, in the

demonstrated system, a fixed coaxial delay line could not be introduced. If the

coaxial delay line must be used in the system, the length of the fiber must be kept

short and there should be no interruption in the layout of the fiber. In other words,

the fiber must be fixed and should not be moved.

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Previous discussions suggest that accurate phase difference is necessary

for an accurate beam scanning. Accuracy in phase differences between elements

depends on the accuracy of time delays generated by TTD units and the accuracy

of the reference delay. Each TTD would have some errors in its true-time delay.

This can cause the beam angle radiated would deviate from the designed value. As

the number of channels increases, the demand for accurate time delays also

increases.

VI.5. Summary and RecommendationThis chapter elaborates the experimental setup and measurements of the

prototype system that was built. It starts with the prototype setup, continued with RF

spectrum measurements, and ends with time delay measurements.

During the setup, the optical components were aligned so that the optical

signal could be detected at the end of free-space section using the receiving

collimator. PBS, linear polarizer, and half-wave plate was utilized in the process of

alignment. Before linear polarizer and PBS could be used, their axes were to be

found out. Measurements were done to determine the axes of linear polarizer and

half-wave plate.

Once the setup was done, optical power measurements were done for the four

states of time delays. Measurement results showed that the detected power at the

receiving collimator was about -20dBm to -30dBm, which was very low. Losses

seem occurred in every stages of the system. Most of the losses seem to be

introduced in the free-space section. Losses in free-space section occurred due to

reflection at interfaces between glass and air, imperfection of PBS, misalignment,

and small aperture of the receiving collimator. These losses can be compensated by

amplifying the detected optical signal using semiconductor optical amplifier.

The problem of alignment difficulty due to imperfection of optical devices’

dimension can be overcome by using high precision optical devices. The reflection

losses can be reduced by using anti-reflection coating at the interfaces. Another

approach to reduce some loss is to reduce the beam divergence. To reduce the

74

divergence, optical device with smaller beam divergence should be chosen. All these

approaches might help to reduce the loss in the free-space section.

RF measurements were done on several stages in the system to obtain the

detected RF spectrum. During this measurement, coupling problem was discovered

in the system. Therefore, some modifications were done on the biasing of transmitter

modules and receiver modules. The detected RF spectrum had a peak value of about

-31dBm. This value was taken with an SOA introduced between the receiving

collimator and the receiver module.

Time delay measurements were done using a network analyzer. The phase

shifts of four states were measured and converted to time delay. The time delay

results are shown in Table 16. The errors of time delay measured with respect to the

designed value were about 2ps to 11ps. These inaccuracies seem to contribute to

deviations of beam angles from their designed values. These deviations are shown in

Table 18. The errors were less than 7º. This amount of error, however, becomes

significant as it travels away from the antenna. Therefore, accurate time delay is

necessary for beam scanning accuracy.

Another problem encountered is that the phase shift of the system changed

when the fiber layout was changed or even when the fiber was moved slightly. Yet,

the phase differences remain the same which suggests that the time delay inserted by

TTD units do not change. This problem makes the coaxial delay cable with a fixed

time delay seems not feasible in the prototype system. When a coaxial delay coble is

to be used, the fiber should be fixed and should not be moved to reduce the phase

change of the system.

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Chapter VII. Simulations

VII.1. IntroductionDesigns on antenna beam forming system and its true time-delay systems

have been described in the previous chapters. This chapter discusses software

simulations to demonstrate the functionality of the system.

There are two simulations that were done in this project. This chapter

elaborates beam scanning simulation using Matlab. This simulation tried to simulate

the changes in beam pattern as a certain value of time delay was inserted in the

system. This simulation demonstrates the beam scanning capabilities. The other

simulation which is elaborated in detail in [18] was to check the two-bit true time-

delay system of the project. The simulation tried to build a representatives building

block to generate true time-delays. The outputs of the simulations were the generated

time delays by the system.

The beam scanning simulation used Matlab to simulate the beam scanning

capabilities of the system. This chapter only describes the simulations process and

their results without elaborating on how to use the software.

VII.2. Simulation on Design ValuesThe purpose of this simulation was to check the array factor and radiation

pattern of the array antenna when certain time delay is inserted. The simulation

plotted the array factor and radiation pattern of the linear array antenna. The input of

this simulation is the time delay between elements and the number of array elements.

This section shows two different plots of pattern. The first plots the changes of array

factor in polar coordinates. The second one, which shows the same information, plots

the array factor with respect to sine function of angle (sinθ). The radiation patterns

were also plotted in these two formats. Simulations that are described here take

Figure 6 as the system to be simulated. This is because the design value was based on

this system.

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Antenna theories suggest that the radiation pattern of an array antenna

follows multiplication rules. This means that the total radiation pattern is a

multiplication of a single element radiation pattern with the array factor of the

antenna. The array factor of the antenna is determined by the geometry and the

phase shift between elements. Thus, the changes in phase shift would affect the

array factor of the array antenna, which at the end would affect the radiation

pattern of the antenna. The beam scanning capabilities of an array antenna could

be examined by observing this array factor and its electric field radiation pattern.

The array factor of a linear array was computed using Matlab in this

simulation. The simulated array factor used Equation 3 to compute the array

factor of a linear array. The equation is presented again here for ease of reference.

Where

This equation is the normalized array factor of a uniform linear array. As

can be seen from the above equation, the input parameters are the number of array

elements (N) and the phase shift between elements (β). These two inputs were set

manually in the m-file.

The normalized array factor was then multiplied by the electric field of a

single element array. To do this operation a “.*” was used in Matlab to multiply

every element in the matrix.

The multiplication rule can be shown as follow. Figure 41 shows the

electric field of a single element and the array factor of a two-element linear array.

The array factor in this figure has zero phase shifts between its elements.

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(a) (b)

Figure 41 (a) Electric Field of a single element. (b) Array Factor of a two-element linear array

The multiplication of the two pattern results in the radiation pattern of a

two-element linear array. In this case, the radiation pattern of a single element is

always the same, while the array factor might change if the number of element or

the phase shift between elements is changed. The resulting pattern is shown

below.

Figure 42 Radiation Pattern of a Two-element Linear Array

The above figure shows that when there is no phase shift between the two

elements, the beam is directed at 0º angle. In the system that has been designed,

however, this angle could not be achieved. This has been discussed in the

previous chapter. The source code is provided in Appendix A with file name

“plot_microstrip.m” and “plot_rp_zero.m”.

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The radiation pattern of a single element microstrip antenna is not a simple

mathematical function and one way to obtain it is to do the real measurements on

real antenna. The following simulation uses a single element microstrip radiation

pattern generated by PCAAD v.2.1, a free DOS software for antenna design. The

software was used to plot the E-plane and H-plane of a rectangular microstrip

antenna with a dimension designed in [18]. The amplitudes of E-plane plot were

then tabulated in a text file for Matlab to read. The manual to use the software is

provided in Appendix C and the source code is for this section is named

“plot_af_design.m” and “plot_rp_design.m”. The first code is to plot the array

factor while the second one is to plot the final radiation pattern after

multiplication.

VII.2.1. Beam Pattern for 0ΔτWhen zero time delay is inserted, the beam should point to -45º. In this

case, the reference channel is delayed by 97.82ps and the zero delay is inserted

into the delay channel. To simulate this, a static variable was set as a reference

phase shift (for reference channel). The phase difference between elements was

then the difference between this phase shift and the inserted phase. The reference

phase shift was set as -2.2126 radians.

Figure 43 below shows the plot of antenna’s array factor when there is no

time delay inserted into the delay channel of the system. Figure 44 shows the

array factor against the sine angle in Cartesian coordinate.

Figure 43 Array Factor for 0Δτ in Polar

79

Figure 44 Array Factor for 0Δτ with respect to Angle

The simulation result agrees with the theoretical calculation. The array

factor shows that the maximum beam is directed to angle about -45º. Figure 44

above also confirmed this result. It is shown that the maximum electric field

radiated was about at -0.7 ( sin θ = -0.7 ), which was about -45º. The theoretical

calculation has proved that when there is no time delay is inserted the phase

difference between elements is -2.2126 rad due to a fixed phase shift of the

reference channel. This phase shift between the two elements would result in

angle -45º.

Figure 43 and Figure 44 only shows the array factor of the array antenna

when there is no delay inserted. The actual beam radiation pattern depends on the

electric field radiation pattern of a single element microstrip antenna. Multiplying

Figure 43 with Figure 41(a) results in the following plots. The electric field

pattern in Figure 41(a) is a normalized value, where its maximum is at one.

Figure 45 Radiation Pattern for 0Δτ in Polar

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Figure 46 Radiation Pattern for 0Δτ with respect to Angle

The two figures show that the radiation pattern of the array antenna could

not reach -45º. The peak was about -0.53 or -32º. The result indicates that the

radiation pattern of microstrip antenna seems to limit the performance of antenna

beam scanning. One possible explanation is that the radiation pattern of a single

element microstrip antenna does not have uniform electric field amplitude in

every angle. Figure 41(a) shows that the amplitude of the electric field reduces as

the angle gets far away from 0º. The array factor, however, has its peak at 45º.

When the array factor was multiplied with this pattern, the peak of the beam

pattern shifted towards 0º.

Another observation showed that two elements array results in a very

broad beam. This is a disadvantage since the power radiated is not concentrated at

the desired direction. This poor performance can be improved by increasing the

number of array elements in the system.

This may explain why it could not reach -45º as well. As the beam gets

broader, it becomes more difficult for the antenna to scan the beam far away from

0º. When the number of element increases, the beam gets narrower. With this

narrow beam, the antenna is able to scan the beam further away from 0º. The

following figure shows the same plot for 8-element linear array.

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Figure 47 Radiation Pattern for 0Δτ (n=8)

The figure shows that the beam can be directed to angle -45º as the

number of element increases. As the number of element increases, the simulation

showed a narrower beam as has been discussed before.

The other limitation that can be observed is that the side lobe of two-

element array had significant amplitude. Increasing the number of array elements

may help to reduce the amplitude of the side lobe with the expense of the increase

of the number of side lobes. This concept can be seen from Figure 45 and Figure

47.

VII.2.2. Beam Pattern for 1ΔτThe second simulation shows the beam pattern when the system is set to

insert 1Δτ. In this simulation, the reference channel was once again set to have a

phase shift of -2.2126rad. A time delay of 65.21ps would result in a phase shift of

-1.4750rad. This value was inserted manually inside the m-file.

The phase shift between elements was then the difference between the two

phases. The array factor is shown in the two figures below.

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(a) (b)

Figure 48 Array Factor for 1Δτ

The simulation results seem to agree the theoretical calculation. The

maximum in Figure 48 is at about -0.23, which about -13º. The array factor in

polar form also suggests the same conclusion. Appendix B shows the bigger

picture for simulation results.

When this array factor is multiplied by a single element pattern, the results

are shown below.

(a) (b)

Figure 49 Radiation Pattern for 1Δτ

Observation on the side lobe showed that it had less amplitude than the

previous case. In this case, the amplitude of side lobe was about 35% of the main

lobe. The peak of the radiation pattern was at -0.17 or -9.8º. This result also shows

some shift in the peak of the beam. Same explanation can be applied here as in the

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previous case. Note that the error in beam’s peak reduces as it is directed towards

the 0º. The previous case showed 13º errors while in this case it was only 3.8º.

This is reasonable since the radiation amplitude of a single element microstrip

gets close to one as it moves towards 0º.

VII.2.3. Beam Pattern for 2Δτ and 3ΔτThe other two simulation results indicate the same results. The plots for

array factor are presented in the figures below.

(a) (b)

Figure 50 Array Factor for 2Δτ

(a) (b)

Figure 51 Array Factor for 3Δτ

Figure 50 shows that the maximum radiation of the beam was directed at

about +13º. This result agrees with the calculated value in the design of the true

time delay units. The second figure (Figure 51) also gives the same conclusion for

the case of +45º.

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As in the two cases before, radiation pattern of a single element microstrip

seems to affect the array antenna’s radiation pattern. The radiation patterns are not

shown again since it is just the mirror image of the plots in section VII.2.1 and

VII.2.2. Some errors occurred in the beam’s peak may be due to the

characteristics of the radiation pattern of microstrip antenna and due to a small

number of array element.

VII.3. Simulations on Measured DelaysPrevious section describes the simulation on beam scanning when a design

value time delay is inserted. Last chapter showed that the actual time delay generated

by the TTD units was not exactly the same as the design value. Another point is that

the previous simulations use Figure 6 as the system to be simulated. Since this

section tries to simulate the measurement result of time delays, the system that is

used is the one shown in Figure 8. This simulation takes into account the coaxial

delay cable and the non-zero delay of the optical channel. The m-files for the

following simulations are provided in Appendix A under “plot_af_measured.m” and

“plot_rp_measured.m”.

The phase shift that is introduced by the coaxial delay cable was assumed to

be ideally -1.6803rad in the simulation. By assuming this amount of delay, the non-

zero delay in the optical channel has been taken into account. The phase shift of the

coaxial cable was set as a constant in the program. The input of the simulation would

then be the phase shift that were measured and are shown in Table 15. The

simulation results for array factor are shown in the figures below.

(a) (b)

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(c) (d)

Figure 52 Array Factors for (a) 0Δτ, (b) 1Δτ, (c) 2Δτ, (d) 3Δτ

Figure 52 shows the beam scanning capabilities of the system that was built.

The beam scanning capabilities shown in this figure are about the same as the one

using design values. However, in order to get the accurate beam’s peak, the plot of

electric field with respect to the sine function of the angle can be observed. These

plots are displayed in Figure 53.

(a) (b)

(c) (d)

Figure 53 Array Factors for (a) 0Δτ, (b) 1Δτ, (c) 2Δτ, (d) 3Δτ w.r.t Angle

86

The maximum peak for 0Δτ state was about -0.7. This value corresponds to

about 45º. This result is the same as the one in Table 18. This is because, the

reference delay of -1.6803rad was calculated based on the phase shift of this state.

Thus, the result is supposed to be the same as the designed value.

The peak values for states 1Δτ, 2Δτ, and 3Δτ were at -0.22, +0.29, and +0.79

respectively (Refer to Appendix B for bigger picture on the result). These values

correspond to angle -12.7º, 16.9º, and 52.2º. The results are about the same with the

estimated beam angle tabulated in Table 18. This result suggests that the calculation

in the previous chapter is correct.

These simulations verified the calculation in the previous chapter on the beam

angle deviation. Simulation results suggest that the calculated beam angle deviations

tabulated in Table 18 are correct. Some differences between the simulation and the

calculated one may be due to inaccuracy in reading the graph plotted by the

simulation and due to the rounding effect when calculating the values manually.

Figure 52 and Figure 53 only show the array factor of the antenna. The actual

radiation pattern is multiplication of a single element radiation pattern with its array

factor. These multiplication results are shown below.

(a) (b)

87

(c) (d)

Figure 54 Radiation Patterns in Polar for (a) 0Δτ, (b) 1Δτ, (c) 2Δτ, (d) 3Δτ

(a) (b)

(c) (d)

Figure 55 Radiation Patterns for (a) 0Δτ, (b) 1Δτ, (c) 2Δτ, (d) 3Δτ w.r.t Angle

88

The simulation results showed that the maximum beam for 0Δτ was at -

0.52 or -31.3º. The peaks for the other states were -0.18 (1Δτ), +0.17 (2Δτ), +0.52

(2Δτ).These values correspond to angles -10.4º, +9.8º, and +31.3º. There are some

differences with the values tabulated in Table 18. The differences are tabulated in

the following table.

Table 19 Simulated Beam Angle Deviations

Simulated

Peak

Calculated

Peak

Design Peak |Error|

from the

calculated value

|Error|

from the design

value

-31.3º -45.0º -45.0º 13.7º 13.7º

-10.4º -12.7º -13.6º 2.3º 3.2º

+9.8º +16.7º +13.6º 6.9º 3.8º

+31.3º +52.0º +45º 20.7º 13.7º

Table 19 shows that the errors are quite large for angles far away from 0º.

For example at the desired angle +45º, the error is the largest which is 13.7º. This

can be explained by looking at the radiation pattern of a single element microstrip

antenna. Figure 41(a) shows that the electric field decreases as the angle increases

from 0º. When the array factor is multiplied by this pattern, the beam peak of the

array factor is shifted towards 0º. Another explanation that is possible is that the

beam width was too big. Wider beam reduces the performance of the beam

scanning since it can not reach angles that are far away from 0º. Narrower beam

can be achieved by increasing the number of elements. Increasing the number of

elements, however, may increase the number of side lobes in the beam pattern.

Error of 13.7º is very significant and may cause larger error when the

target distance is far away. This may result in inefficient power delivered or even

undetectable power at the desired location. Therefore, high accuracy in beam

angle design is a necessity for long distance application.

89

VII.4. Summary and RecommendationThe beam scanning simulation showed that the designed time delay would

result in the desired beam angle for array factor patterns. Since microstrip

radiation pattern decreases as the angle increases from 0º, the radiation pattern of

array antenna is likely not able to be exactly the same as the design. The beam’s

peak is shifted towards 0º. This makes the array antenna can not scan the beam to

±45º. This problem becomes more severe when the number of array elements is

small. Small number of elements results in wider beam. A solution to this problem

is to increase the number of array elements. A large number of elements, however,

may result in the increase of side lobes and the increase in system complexity.

Therefore, a trade-off must be made in the design.

This true time delay system also suffers from a significant amount of side

lobe when it is directed at ±45º. This problem can be overcome by also increasing

the number of array elements in the system.

The second simulations tried to verify the calculation of beam angle

deviations tabulated in Table 18. Simulation showed the results were the same for

array factor simulations. Some differences in the simulation values may be due to

inaccuracy in reading the graph plotted and due to the rounding effect when

calculating the values in Table 18 manually. Some errors seem to occur when the

array factor is multiplied by a single element pattern to produce the actual

radiation pattern. The results show that beam’s peaks deviate from the design. The

worse errors seem to occurr for angles far away from 0º.

Errors in beam’s peak become significant as the target location becomes

far away from the antenna. This is because the difference in beam’s peak

increases as the distance increases. Therefore, high accuracy in beam angle design

is necessary for long distance application. The errors in beam patterns can be

reduced by improving the performance of antenna, or by selecting another antenna

structure that has better radiation pattern for beam scanning, and also by

improving the TTD systems as has been recommended in the previous chapter.

90

Chapter VIII. ConclusionThe purpose of this project was to build a true-time delay system for antenna

beam formation using switched free-space section method. True-time delay units

were to be designed to allow beam scanning from -45º to +45º using two-element

linear array antenna.

The design of true-time delay units were based on the system displayed in

Figure 6. However, the system was modified in order to build the prototype. This

was because of limitations in the components availability, budget, and time. Two

units of TTD had been designed to scan the beam at discrete angles: -45º, -13.6º,

+13.6º, and +45º. Measurement on time delays generated showed that the errors were

about 2ps to 11ps. This amount of errors causes a deviation in the maximum

amplitude of the beam angle. The deviations in beam angles were calculated and they

were less than 7º.

The inaccuracy in time delays generated might be caused by the inaccuracy

of the optical devices’ dimension and the inaccuracy of air-gap dimension in TTD

unit configuration. Another possible source of errors would be the difference in the

refractive index of the glass with the value that was used in the design. Design

calculation assumes all prisms, PBSs, and spacer have a refractive index of 1.5.

There might be slight differences in the refractive index of the components used. One

example of error is the refractive index of the spacer in TTD unit S0 was 1.5168 and

the length is 20.80mm instead of 1.5 and 20.90mm length. Besides the inaccuracy in

dimension, the error seems to be caused by the non-horizontal light path. This is

because the prisms and PBS might have some elevation as it was mounted. The path

of the reflected light would deviate from the theoretical path. The theoretical path

assumes that reflected light goes through in the same horizontal plane (x-y plane).

However, the actual reflected light might come out from this plane and this would

cause the distance is longer than the theoretical one.

The accuracy of maximum beam pattern might get even worse as it is

transmitted by the microstrip path array antenna. This is indicated by the simulation

described in Chapter VII. Matlab simulations showed that the maximum beam could

not be directed to ±45º as the array factor was multiplied by the single elements

91

pattern of a microstrip array antenna. The error in beam angle became more severe

and was about 13º. The maximum error occurred at angles far away from 0º.

These results are reasonable since the amplitude of the electric field of a

single element microstrip antenna decreases as the angle increases far away from 0º.

The multiplication with array factor may cause the maximum beam to be shifted

towards 0º. That is one possible explanation why all simulated beam’s peaks were

less than the calculated values and became closer to 0º. Another possible reason why

the system could not reach ±45º can be the small number of elements. The system

with two elements has a very wide beam. As the beam width gets bigger, the ability

to scan the beam to angles far away from 0º reduces. This problem can be solved by

increasing the number of array elements in the system. Increasing the number of

elements would result in the increase number of side lobes and the increase of

system’s complexity.

Constraints in this project come from components availability, budget and

time limitation. More accurate time delays can be generated when high precision

optical devices are used. However, using high precision dimension optical devices

will cause the cost of the project to increase. Another problem in the project was due

to the poor performance of the laser source. The laser source provided inside Thales

Optical Link does not have any temperature control. Temperature of the system

increases as the operational time increases. This reduces the performance of the

optical link as the time increases.

Due to limitation in time and equipment, the system could not be integrated

and tested with the antenna that had been designed. Radiation pattern measurements

of the overall system will help to investigate the system in more detail. Time delay

measurements were done only on continuous wave RF signal due to limitation in

time. Further experiments can help to investigate the system by examining the

performance of the system for modulated RF signal. This is important since the

signal to be transmitted by an antenna usually carries information. Thus, analysis on

bandwidth performance should be done as well on the system. As in other

communication system, linearity of the system plays an important role. Therefore,

investigation on system linearity should be carried out in further research. Another

recommendation is to study the system when it is integrated in the receiver antenna.

92

References[1] Esman, Ronald D., et al, 1998, ‘New Array Capabilities by Photonic

Beamforming’, IEEE MTT-S Digest, pp 1363-1366.[2] Frigyes, Istvan, 1995,‘Optically Generated True-time Delay in Phased-Array

Antennas’, IEEE Transaction on Microwave Theory and Technique, vol 43, no. 9, p 2378-2386.

[3] Mailloux, R J, 1994, Phased Array Antenna Handbook. Norwood: Artech House, ch 1.

[4] Koepf, G.A., 1984, ’Optical Processor for Phased-Array Antenna Beam Formation’, SPIE vol. 477, p 75.

[5] Esman, R. D., et al, 1992, ‘Microwave True Time-Delay Modulator Using Fiber-Optic Dispersion’, Electronics Letters, vol. 28(20), pp 1905-1907.

[6] Esman, R. D., et al, 1993, ‘Fiber-optic Prism True Time-delay Antenna Feed’, IEEE Photon. Tech. Lett. 5:1347.

[7] Esman, R. D., et al, 1995, ‘True time-delay fiber-optic control of a phased-array transmitter with three-octave bandwidth’, IEEE National Telesystems Conference Proceedings, 1995, p 175-178.

[8] Frankel, M.Y., 1998, ‘A Wide-band Fiber-Optic True-Time-Steered Array Receiver Capable of Multiple Independent Simultaneous Beams’, IEEE Photonics Technology Letter, vol 10, no. 5, p722-724.

[9] Frankel, M. Y. et al, Appl Optics, vol 36, pp 9261-9268, 1997[10] Soref, R., 1992, ‘Optical Dispersion Techniquie for Time-delay Beam Steering’,

Applied Optics, vol. 31(35), pp 7395-7397.[11] Molony, A., 1995, ‘Fiber Grating Time Delay Element for Phased Array

Antennas’, Electronics Letters, vol 31(17), pp 1485-1486.[12] Walston, W. Ng, et al, ‘The First Demonstration of an Optically Steered

Microwave Phased Array’, J. Lightwave Technol., vol 9, no. 9, pp 1124-1131.[13] Jemison, W.D., 1993, ‘Acoustooptically controlled true time delays’, IEEE

Microwave and Guided Wave Letters.,vol 3, no. 3, pp 72-74.[14] Dolfi, D., et al, 1996,’ Experimental demonstration of a phased-array antenna

optically controlled with phase and time delays’, Applied Optics, vol 35, no. 36, pp5293-5300.

[15] Chazelas, et. Al, 2003, ‘8 Channels, 5 bits wideband optical beam steering up to Ku band’, MWP Workshop.

[16] Balanis, Constantine A., 1997, Antenna theory: analysis and design, 2nd ed. John Wiley & Sons, sections 6.2, 6.3, and 6.10.

[17] Cheng, David K., 1993, Fundamentals of Engineering Electromagnetics. Addison-Wesley, sections 10-5.

[18] Kananggar, Jebie, 2004,’Free Space Optics for Antenna Beamforming(A)’.[19] Breuil, 2001, ‘S Band Optical Link Application Note’, Thales Airborne System.[20] Keiser,Gerd, 2000, Optical Fiber Communication, McGraw-Hill,ch 2.[21] Soref, R., 1996, ‘Fiber Grating Prism for True Time Delay Beamsteering’, Fiber

and Integrated Optics, vol 15, pp 325-333.

93

Appendix A. Matlab Source CodeFile name: plot_microstrip.m

%% This function is to plot the radiation pattern of a single element % microstrip antenna, the following function reads angles and the % e-plane amplitude in dB and then converted to normalized amplitude% this normalized amplitude is then plotted

fp=fopen('array.txt','r'); %open file for radiation patternn=91; %number of sample datafor i=1:n, %read file angle(i)=fscanf(fp,'%f',1); %read axis, from -90 to 90deg amp(i)=fscanf(fp,'%f',1); %read amplitute in dBend

teta=angle/180*pi; %convert degrees to radianamplitude=10.^(amp/10); %convert dB to normalized amplitudepolar(teta,amplitude); %plot the amplitude in polar % coordinate

File name: plot_rp_zero.m

%% This function is to plot the radiation pattern of % a 2-element array antenna, the following function calculate the % array factor of an array antenna and then multiply it with a % single element electric field radiation pattern.% the single element radiation pattern is obtained from file % "array.txt"% fp=fopen('array.txt','r'); %open file for radiation patternn=91; %number of sample datafor i=1:n, %read file angle(i)=fscanf(fp,'%f',1); %read axis, from -90 to 90deg amp(i)=fscanf(fp,'%f',1); %read amplitute in dBend

teta=angle/180*pi; %convert degrees to radianamplitude=10.^(amp/10); %convert dB to normalized amplitude

%defining constantsc=3e+8; %speed of lightf=3.6e+9; %RF frequencylambda=c/f; %wavelengthdy=lambda/2; %distance between elements in y axisk=2*pi/lambda; %wavelength number%end of definition

%specify parametersn=2; %number of element in y axis

beta_r=0; %reference channel phase shift

94

%change the the following value if you wish to change %the angle direction of the beam by changing its phase differencebeta_d=0; %for -45deg%beta_d=-1.4750 %for -13deg%beta_d=-2.9503 %for +13deg%beta_d=-4.4252 %for +45deg

beta=beta_d-beta_r;

%computing array factorlambda_y=(k*dy*sin(teta))+beta;num=sin((n/2)*lambda_y);denum=sin(lambda_y/2);term=(1/n)*(num./denum);af=abs(term)radiation=af.*amplitude;

%plotting the radiation patternfigure(1);plot(sin(teta),radiation); %to plot with respect sin(teta)figure(3);polar(teta,radiation); %to plot in polar coordinate

File name: plot_af_design.m

%% This function is to plot the radiation pattern of an array % antenna, the following function calculate the array factor of% an array antenna and then multiply it with a single element% electric field radiation pattern.

%defining constantsc=3e+8; %speed of lightf=3.6e+9; %RF frequencylambda=c/f; %wavelengthdy=lambda/2; %distance between elements in y axisk=2*pi/lambda; %wavelength number%end of definition

%specify parametersn=2; %number of element in y axis

beta_r=-2.2126; %reference channel phase shift

%change the the following value if you wish to change %the angle direction of the beam by changin its phase differencebeta_d=0; %for -45deg%beta_d=-1.4750 %for -13deg%beta_d=-2.9503 %for +13deg%beta_d=-4.4252 %for +45deg

beta=beta_d-beta_r;

% use the following function to generate angle space with 100 elementsteta=linspace(0,2*pi); %for plot

95

%computing array factorlambda_y=(k*dy*sin(teta))+beta;num=sin((n/2)*lambda_y);denum=sin(lambda_y/2);term=(1/n)*(num./denum);af=abs(term);

%plotting the radiation patternfigure(1);plot(sin(teta),af); %to plot with respect sin(teta)figure(3);polar(teta,af); %to plot in polar coordinate

File Name: plot_rp_design.m%% This function is to plot the radiation pattern of an array % antenna, the following function calculate the array factor of% an array antenna and then multiply it with a single element% electric field radiation pattern.%% This function is to plot the radiation pattern of an array % antenna, the following function calculate the array factor of% an array antenna and then multiply it with a single element% electric field radiation pattern.fp=fopen('array.txt','r'); %open file for radiation patternn=91; %number of sample datafor i=1:n, %read file angle(i)=fscanf(fp,'%f',1); %read axis, from -90 to 90deg amp(i)=fscanf(fp,'%f',1); %read amplitute in dBend

teta=angle/180*pi; %convert degrees to radianamplitude=10.^(amp/10); %convert from dB

%defining constantsc=3e+8; %speed of lightf=3.6e+9; %RF frequencylambda=c/f; %wavelengthdy=lambda/2; %distance between elements in y axisk=2*pi/lambda; %wavelength number%end of definition

%specify parametersn=2; %number of element in y axis

beta_r=-2.2126; %reference channel phase shift

%change the the following value if you wish to change %the angle direction of the beam by changin its phase differencebeta_d=0; %for -45deg%beta_d=-1.4750 %for -13deg%beta_d=-2.9503 %for +13deg%beta_d=-4.4252 %for +45deg

beta=beta_d-beta_r;

96

%computing array factorlambda_y=(k*dy*sin(teta))+beta;num=sin((n/2)*lambda_y);denum=sin(lambda_y/2);term=(1/n)*(num./denum);af=abs(term);radiation=af.*amplitude;%plotting the radiation patternfigure(1);plot(sin(teta),radiation); %to plot with respect sin(teta)figure(3);polar(teta,radiation); %to plot in polar coordinate

File name: plot_af_measured.m% % This function is to plot the radiation pattern of an array % antenna, the following function calculate the array factor of% an array antenna and then multiply it with a single element% electric field radiation pattern.

%defining constantsc=3e+8; %speed of lightf=3.6e+9; %RF frequencylambda=c/f; % wavelengthdy=lambda/2; %distance between element in y axisk=2*pi/lambda; %wavelength number%end of definition

%specify parametersn=2; %number of element in y axis

beta_r=-1.6803; %phase shift of coaxial delay line

%change the the following value if you wish to change %the angle direction of the beam by changin its phase difference%beta_d=+0.5323; %for -50.6degbeta_d=-0.9941; %for -12.7deg%beta_d=-2.5770; %for +16.7deg%beta_d=2.1361; %for +52deg

beta=beta_d-beta_r;

% use the following function to generate angle space with 100 elementsteta=linspace(0,2*pi);

%computing array factorlambda_y=(k*dy*sin(teta))+beta;num=sin((n/2)*lambda_y);denum=sin(lambda_y/2);term=(1/n)*(num./denum);af=abs(term);

%plotting the radiation patternfigure(1);plot(sin(teta),af); %to plot with respect to sin(teta)

97

figure(3);polar(teta,af); %to plot in polar coordinate

File name: plot_rp_measured.m% % This function is to plot the radiation pattern of an array % antenna, the following function calculate the array factor of% an array antenna and then multiply it with a single element% electric field radiation pattern.fp=fopen('array.txt','r'); %open file for radiation patternn=91; %number of sample datafor i=1:n, %read file angle(i)=fscanf(fp,'%f',1); %read axis, from -90 to 90deg amp(i)=fscanf(fp,'%f',1); %read amplitute in dBend

teta=angle/180*pi; %convert from degree to radianamplitude=10.^(amp/10); %convert from dB

%defining constantsc=3e+8; %speed of lightf=3.6e+9; %RF frequencylambda=c/f; % wavelengthdy=lambda/2; %distance between element in y axisk=2*pi/lambda; %wavelength number%end of definition

%specify parametersn=2; %number of element in y axis

beta_r=-1.6803; %phase shift of coaxial delay line

%change the the following value if you wish to change %the angle direction of the beam by changin its phase differencebeta_d=+0.5323; %for -50.6deg%beta_d=-0.9941; %for -12.7deg%beta_d=-2.5770; %for +16.7deg%beta_d=2.1361; %for +52deg

beta=beta_d-beta_r;

%computing array factorlambda_y=(k*dy*sin(teta))+beta;num=sin((n/2)*lambda_y);denum=sin(lambda_y/2);term=(1/n)*(num./denum);af=abs(term)radiation=af.*amplitude;

%plotting the radiation patternfigure(1);plot(sin(teta),radiation); %to plot with respect to sin(teta)figure(3);polar(teta,radiation); %to plot in polar coordinate

File name: array.txt

98

The first column is the angle (from -90º to +90º) and the second column is the amplitude in dB. This numbers were taken using PCAAD v.2.1.-90 -1.87-88 -1.87-86 -1.86-84 -1.85-82 -1.83-80 -1.81-78 -1.79-76 -1.76-74 -1.72-72 -1.68-70 -1.64-68 -1.59-66 -1.54-64 -1.49-62 -1.44-60 -1.38-58 -1.32-56 -1.26-54 -1.19-52 -1.13-50 -1.07-48 -1.00-46 -0.94-44 -0.87-42 -0.81-40 -0.74-38 -0.68-36 -0.62-34 -0.56-32 -0.50-30 -0.44-28 -0.39-26 -0.34-24 -0.29-22 -0.25-20 -0.21-18 -0.17-16 -0.13-14 -0.10-12 -0.08-10 -0.05-08 -0.03-06 -0.02-04 -0.01-02 -0.00-00 -0.00

99

02 -0.0004 -0.0106 -0.0208 -0.0310 -0.0512 -0.0814 -0.1016 -0.1318 -0.1720 -0.2124 -0.2922 -0.2526 -0.3428 -0.3930 -0.4432 -0.5034 -0.5636 -0.6238 -0.6840 -0.7442 -0.8144 -0.8746 -0.9448 -1.0050 -1.0752 -1.1354 -1.1956 -1.2658 -1.3260 -1.3862 -1.4464 -1.4966 -1.5468 -1.5970 -1.6472 -1.6874 -1.7276 -1.7678 -1.7980 -1.8182 -1.8384 -1.8586 -1.8688 -1.8790 -1.87

100

Appendix B.Simulation Results

Figure 41(a)

Figure 41(b)

101

Figure 42

Figure 43

102

Figure 44

Figure 45

103

Figure 46

Figure 47

104

Figure 48(a)

Figure 48(b)

105

Figure 49(a)

Figure 49(b)

106

Figure 50(a)

Figure 50(b)

107

Figure 51(a)

Figure 51(b)

108

Figure 52(a)

Figure 52(b)

109

Figure 52(c)

Figure 52(d)

110

Figure 53(a)

Figure 53(b)

111

Figure 53(c)

Figure 53(d)

112

Figure 54(a)

Figure 54(b)

113

Figure 54(c)

Figure 54(d)

114

Figure 55(a)

Figure 55(b)

115

Figure 55(c)

Figure 55(d)

116

Appendix C.PCAAD v.2.1PCAAD v.2.1 is a DOS software package for the analysis and design of

antennas, including wire antennas, horn antennas, arrays, and microstrip antennas.

The software can be downloaded at:

http://rf.rfglobalnet.com/software_modeling/software/3/413.htm

This software was used in the project to obtain the radiation pattern of a

rectangular microstrip patch antenna. The amplitudes of the E-plane plotted by this

software were saved in “array.txt” file as an input file for beam scanning simulation.

To plot the radiation pattern of a microstrip patch array antenna using this software,

the following procedures can be followed.

1. Download the software from the provided link above. The file is in Zip

format. “Winzip” software is needed to extract the files from the downloaded

“pcaad21.zip”.

2. Extract the file using Winzip or other compression software.

3. Run the file named “PCAAD.EXE”. The screen of the computer will be

changed to DOS. The following menu is displayed.

***MAIN MENU***

Wire Antennas

Array Antennas

Aperture Antennas

Microstrip Antennas

Trans. Lines & Waveguides

Utilities

4. Use the arrow keys (up and down keys) to go to “Microstrip Antennas”. Press

ENTER key to select the menu. The following menu appears.

*Mictrostrip Antennas*

Rectangular Patch

Circular Patch

Aperture Coupled Patch

117

5. Select “Rectangular patch” and press ENTER. The following data must be

entered. The data provided comes from the dimension of the antenna that was

design. Detail description on antenna design is provided in [18].

Enter the patch length (cm) : 1.681

Enter the patch width (cm) : 2.204

Enter the dielectric constant : 6.15

Enter substrate thickness : 0.0635

Enter probe distance from rad. edge (cm) : 0.579

6. Press ENTER to continue when it is asked to enter the “centre frequency”.

The following screen will then be displayed.

7. Select “Plot Patterns” inside the box “Select Action”. A plot of E-plane and

H-plane will then be displayed. Press left or right keys to move the cursors

and to record down the amplitude.

118

Appendix D. Laser Diode Datasheets

119

120

Appendix E.List of Componentsno Name Model Q* Owner Supplier Remarks 

1Optical platform, 60cmx60cm   1 NTRC Newport

2 Posts   6 NTRC Newport  

3 Post holders, 3in   6 NTRC Newport   

4 Post Collar   6 NTRC Newport   

5 Screw   12 NTRC -   

6Thales Optical Link   1 Thales -

7Infrared sensitivity card   1 NTRC  

8

Fiber Polarization controller   1 Thales Fiberpro

9Connector Adapter, FC-FC   2 Thales -

10Fiber pigtailed collimators F-COL-9-13 2 Thales Newport

11Compact Kinematic mount KMS/M 2 Thales ThorLabs

to hold grin lenses 

12IR linear polarizer, 1/2" LPIR050 1 Thales ThorLabs

13Rotation stage, 1/2" diameter RSP05/M 1 Thales ThorLabs to hold polarizer

14Spanner Wrench SPW603 1 Thales ThorLabs to screw rotation stage

15

Right angle prisms 10x10mm F32-330 4 Thales Edmund

16

Kinematic platform mount 50x50mm KM100B 2 Thales ThorLabs

to hold prisms and beam splitter

17Prism mounting hardware PM1 6 Thales ThorLabs

to hold prism on platform mount

18Multi-Order wave plates

WPMH05M-1310 1 Thales ThorLabs

19Rotation Stage, 1" diameter RSP1 1 Thales ThorLabs

to hold Wave plate 

20

Polarizing cube beamsplitters 10mm 03PBS073 4 Thales MellesGriot  

Thales Optical Link Components:1. Laser diode 1310nm2. Photodetector3. Single Mode fiber optics 0.9mm diameter

*Q = Quantity

121

Appendix F. Setup Photos

Components and Equipments

True-time Delay Unit

122

True-time Delay Unit

Both TTD Units

123