LabMan_VTU_2.1.2010

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©-2010, GB Technology [email protected]

1

Advanced Communication Laboratory B.E Degree Course in Electronics & Communication Engineering

Laboratory Manual for

Microwave Experiments

GB Technology e mail: [email protected]

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2

Intellectual Property Rights (IPRs) Notice

This manuscript may be protected by one or more of Indian Copyright Registrations (Pending)

by GB Technology

GB Technology restricts the use, in any form, of the information, in part or full, contained in this manuscript ONLY on written permission of GB Technology.

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3

Contents Introduction 5

1. Prerequisite for Experiments 6

1.1 Instruments- Main Features 6 1.2 Measurement Principle and General Instructions 7 1.3 Basics of Stripline 9 1.4 Basics of Microstrip line 11

2. Experiment I: Measurement of Directivity and Gain of Antennas: Printed dipole, Microstrip Patch antenna, Printed Yagi antenna 17

2.1 Theory 17

2.1.1 Introduction to planar antennas 17 2.1.2 Directivity and gain - Definitions and formulas 18 2.1.3 Printed dipole 21 2.1.4 Microstrip patch antenna 23 2.1.5 Printed Yagi antenna 26 2.1.6 Pattern measurement 28 2.1.7 Absolute gain measurement 28 2.1.8 Relative gain measurement 30

2.2 Experiment 30

2.2.1 Measurement of directivity 30 2.2.2 Measurement of gain 35 2.2.3 Write-up 38

3. Experiment II: Determination of Coupling and Isolation Characteristics of Microstrip Directional Couplers 39

3.1 Theory 39

3.1.1 Basic parameters of directional couplers 39 3.1.2 Branchline directional coupler 41 3.1.3 Parallel coupled directional coupler 43

3.2 Experiment 46

3.2.1 Measurement of coupling and isolation 46 3.2.2 Write-up 48

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4. Experiment IIIA Measurement of Resonance Characteristics of Microstrip Ring Resonator and Determination of Dielectric Constant of the Substrate 51

4.1 Theory of Ring Resonator 51

4.2 Experiment 53 4.2.1 Measurement of resonant frequency 53 4.2.2 Write-up 54

5. Experiment IIIB Measurement of Power Division and Isolation Characteristics of a Microstrip 3dB Power Divider 55

5.1 Theory of Power Divider 55

5.2 Experiment 59

5.2.1 Measurement of power division and isolation 59 5.2.2 Write-up 61 References 63

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5

Introduction This manual describes a total of four laboratory experiments in the area of Microwave Integrated Circuits (MICs). The first experiment is on planar antennas; namely printed Yagi antenna, printed dipole and rectangular patch antenna; all fed by microstrip. The experiment involves basic antenna measurement techniques for far field radiation pattern, directivity and gain. The other three experiments deal with the characterization of MIC components realized in microstrip. The components are directional couplers, ring resonator and power divider; all in microstrip configuration.

All the four experiments are designed for operation within the frequency range 2.2 -3.0 GHz. The instruments required for all the experiments are common; one is a microwave signal source and the other is a VSWR meter which is to be used in conjunction with a coaxial detector.

Chapter1 presents essential background material for the experiments. Section 1.1 covers some salient features of the source, VSWR meter and the detector. Section 1.2 provides the principle behind the measurement technique and general instructions.

Sections 1.3 and 1.4 of Chapter 1 cover the theory of the two basic planar transmission lines used in MICs; namely the stripline and the microstrip line. Since all the antennas and components provided for the experiments are microstrip based, microstrip is covered in more detail (Sec.1.4). Also, the theory of the coupled microstrip is included so that the principle of operation of parallel coupled directional coupler (based on coupled microstrip) can be understood.

Chapters 2 to 5 are devoted to the four experiments. Each chapter is divided into two parts. The first part covers the theory of the devices (antennas or MIC components) on which the experiment is to be conducted. The second part contains the procedure to conduct the experiment, document the results, and also prepare the report.

It is recommended that the students go through Chapter 1, particularly sections 1.1 and 1.2 before starting the experiment. Also going through the theoretical aspects of the devices provided in each chapter would help in better understanding of the experiments. For any additional theoretical information, students may refer the books listed at the end of the manual.

GB Technology

Mysore

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6

Prerequisite for Experiments

1.1 Instruments – Main Features The instruments required for all the experiments are common; one is a microwave signal source and the other is a VSWR meter which is to be used in conjunction with a coaxial detector. Microwave Signal Source

The microwave signal source has an operating frequency range from 2.2 to 3GHz. It is a compact source with a minimum power output of 10mW over this frequency range. It has a built-in modulation facility, provision for varying the frequency and RF power output, and a digital display for frequency readout on the front panel. The source has a built-in 1KHz AM preset mode so that standard VSWR meters can be used as test instruments for making measurements.

Coaxial Detector

The coaxial detector incorporates a nonlinear non-reciprocal device (Schottky barrier diode). The nonlinearity of the diode is used to demodulate the 1KHz amplitude modulated microwave signal. The desired demodulated output at 1KHz is filtered out in the detector. The amplitude of the corresponding current in the diode is proportional to the RF power of the input signal; i.e, square of the RF voltage. This square-law range is the desired operating range of the detector and hence the detector is referred to as a square-law detector.

Figure 1.1 shows typical characteristic of a diode detector where the detector output voltage is plotted in log scale as a function of input power in dBm. It can be seen that square-law response of the detector is available over a restricted range of power input; typically below about -10dBm. VSWR Meter

The measuring instrument for all the experiments is a VSWR meter, the input to which is the detected output from the coaxial detector. The VSWR meter is basically a high gain low noise audio amplifier tuned to a mean frequency of 1KHz. On the front panel is a display meter that is square-law calibrated to read the SWR directly and relative power levels in dB. It has a RANGE SWITCH covering 0 to 60dB in steps of 10dB and a GAIN CONTROL knob that provides continuous variation over about 10dB. In your experiments, there is no requirement to read SWR directly; you only need to read the relative power levels on the dB scale.

1

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7

10

-30 -20 -10 -0 10

0.1

100

1.0

-400.01

noise level

square law region

saturation

Input power (dBm)

De

tect

or

volta

ge(m

V) 10

-30 -20 -10 -0 10

0.1

100

1.0

-400.01

noise level

square law region

saturation

Input power (dBm)

De

tect

or

volta

ge(m

V)

1.2 Measurement Principle and General Instructions

Principle of Measurement

In all the experiments, you will be using the microwave signal source with 1KHz amplitude modulation. Hence the input to the MIC component (or transmit antenna in antenna experiment) is the microwave carrier modulated with 1KHz square wave. The output signal from the component (or receive antenna) is fed to the coaxial detector. The detector demodulates this modulated microwave signal and produces an output which is the 1KHz modulation envelope. The output of the detector is fed to the VSWR meter which is square-law calibrated to read (relative) power levels in dB with respect to the maximum (i.e., VSWR =1 or 0dB).

As discussed in section 1.1, detectors offer square-law response over a restricted range of input powers. In order to enable correct measurements over a larger range of input power levels, the calibration curve that is provided with the coaxial detector is to be used.

Calibration Graph to correct the readings of the VSWR meter during measurements

Figure 1.2 is a typical Calibration Graph for the detector cum VSWR meter. The actual readings of the VSWR meter in dB(minus) are marked on the x-axis and the corrected values after taking into account any deviation from square law response of the detector, are marked on the y-axis. Please note that markings on the VSWR meter in dB are positive because they represent the VSWR values in dB i.e., 20log10(VSWR). The same dB numbers can be used to represent

Fig.1.1 Typical theoretical characteristic of a detector

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relative input signal power in dB with a negative sign. For example, the relative input power level denoted by 50dB on the VSWR meter is to be read as -50dB relative signal power.

Note:

All VSWR meter readings are to be recorded as minus dB. No correction is required for readings in the range from -70dB to -60dB because the graph is linear (the detector response is square law). Deviation from square law increases with an increase in the input power level above approximately -60dB. For readings above -60dB locate the point corresponding to the VSWR meter reading (minus value) on the x- axis and then read the correct value on the y-axis Example:

Supposing the VSWR meter reads 48dB, locate -48dB point on the x-axis and read the correct value on the y-axis as shown in the graph. The corrected value here is -49.5dB.

Cor

rect

ed v

alue

(dB

)

VSWR meter reading (dB)

Fig. 1.2 Typical Calibration Graph Corrected value in dB versus the actual reading of the VSWR meter in dB(minus).

-75

-70

-65

-60

-55

-50

-45

-40

-75 -70 -65 -60 -55 -50 -45 -40

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1.3 Basics of Stripline Stripline is a basic planar transmission line and can be considered as a flattened version of the coaxial line. There are many types of planar transmission lines. In general, they are made of flat metallic conductors that lie entirely in the same plane or in parallel planes. Planar transmission lines form the transmission media for realizing Microwave Integrated Circuits; popularly known as MICs. A microwave integrated circuit represents an extension of integrated circuit technology to microwave frequencies. The technology involves printing the circuit on a metallized dielectric substrate using the photolithographic technique, and then mounting the semiconductor and other passive devices onto the circuit using either the soldering or bonding technique. The final circuit is then packaged in a shielding enclosure.

It is important to recognize that a MIC is different from a conventional printed circuit card used at low frequencies. In a low frequency printed circuit card, the printed conductors serve only as conducting paths. In a MIC, the dimensions of the conducting paths as well as the parameters of the dielectric substrate are part of the design and hence the widths and lengths of conductors will have to be realized (etched out of a metallized substrate) with precision.

A strip transmission line consists of a central strip conductor placed in between two large ground planes with the intervening medium completely filled with a homogeneous dielectric. Practical striplines are constructed from two dielectric substrates, having the same thickness and dielectric constant. Figure 1.3a illustrates the geometry of a stripline. The lower substrate of height b/2 has the printed strip conductor of width w and thickness t (t<<w) on its top surface and complete metallization on its lower surface. The top substrate, also of height b/2, has no metallization on its lower side but its top surface is fully metallized. The two substrates are sandwiched to form a homogeneous medium in between the two outer conducting surfaces that serve as ground planes.

A stripline, because of its homogeneous medium, supports a pure transverse electromagnetic mode (TEM mode) as in a coaxial line. Figure 1.3b shows the typical electric and magnetic field lines of this dominant mode. As illustrated, the field lines lie entirely in the transverse plane with no component along the direction of propagation (z-direction in Fig.1.3b). These fields get concentrated essentially near the strip conductor. The electric field lines terminate on the top and bottom ground planes and the magnetic field lines form closed loops around the strip. The fields

Fig. 1.3 (a) Basic structure of stripline (b) Typical TEM mode fields in the cross sectional plane

(b)

εr

E lines H lines

x

y

b

(a) w

Ground planes

Strip conductor

εr

t

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decay rapidly in the lateral direction (x direction) on either side of the strip conductor. Therefore, at sufficient distance from the strip conductor, the structure can be terminated with side metallic walls without affecting the propagation characteristics. As in the case of any TEM line, the phase velocity vph, guide wavelength λg and the characteristic impedance Z0 for a stripline are given by

( )1100

00 .Z

Z,,v

vr

a

rg

rph εε

λλε

===

where, v0 and λ0 denote the velocity of propagation and wavelength, respectively in free space, εr

is the relative dielectric constant of the dielectric medium. The parameteraZ0 is the characteristic

impedance of the same stripline with the medium replaced by air (εr =1) and it is a function of the dimensional parameter w/b.

Figure 1.4 shows the variation of normalized characteristic impedance rZ ε0 of stripline as a

function of strip width w/b. It can be seen that for fixed values of εr and b, the characteristic impedance reduces with an increase in the width of the strip conductor. Striplines are generally used for the realization of passive components such as filters and directional couplers.

Fig. 1.4 Z0√εr as a function of w/b for symmetrical stripline

0

50

100

150

200

250

0 0.2 0.5 0.7 1 1.25 1.5

Z0√

ε r (

ohm

s)

w/b

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11

1.4 Basics of Microstrip line The microstrip line, also referred simply as the microstrip, consists of a strip conductor on a flat dielectric substrate, the reverse side of which is metallized to form the ground plane (Fig. 1.5a). Geometrically, a stripline with the top substrate removed results in a microstrip. Unlike the stripline, the microstrip is an inhomogeneous transmission line. Figure 1.5b shows the approximate field distribution for the dominant mode. The electric and magnetic fields lie partly inside the substrate and partly in the air medium above the substrate. At the air-dielectric boundary, the tangential component of the displacement density D

r

becomes discontinuous. From Maxwell’s equations, it can be shown that there must exist a longitudinal component of H

r

in order to satisfy the boundary conditions. That means, a pure TEM mode cannot exist in a microstrip. In most practical applications, the dielectric substrate is electrically very thin (h << wavelength in microstrip) and the dielectric constant is much higher than that of air. Hence, a major portion of the electric field is concentrated inside the substrate beneath the strip conductor and the electric flux crossing the interface is very small. Higher the dielectric constant of the substrate, larger is the concentration of energy inside the substrate and less in the air region. Since the longitudinal components of the field lines are negligible in comparison with the transverse components, the fields closely resemble the TEM mode. The dominant mode in a microstrip is therefore termed as quasi-TEM and for most of the circuit design applications, it is treated as TEM. The main advantage of the microstrip over the stripline is that its top surface is accessible for mounting discrete devices. Also minor adjustments can be made after the circuit is fabricated. The circuit must however be shielded to minimize radiation loss or interference due to nearby objects. Figure 1.6 shows the cross section of a shielded microstrip. The side walls and the top wall must be sufficiently away from the strip conductor so as to have negligible effect on the

propagation. The side wall effects can be made insignificant by choosing c/w ≳ 10. In order to avoid the propagation of waveguide modes while keeping the top wall effect negligible, the distance b from the strip conductor to the top wall is kept approximately equal to 5h.

Fig. 1.5 (a) Basic structure of microstrip line (b) Typical quasi - TEM mode field lines

εr h

w Ground plane

Dielectric substrate

Strip conductor

y

x

(b) z

εr

Air

H lines

E lines

(a)

t

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12

Effective Dielectric Constant, Guide Wavelength and Characteristic Impedance

Since the field lines in a microstrip are partially in the dielectric substrate and partially in air, the phase velocity of the propagating wave lies in between that of air and the dielectric medium.

Under the TEM approximation, the phase velocity vph, the guide wavelength λg and the characteristic impedance Z0 for a microstrip are given by

( )2100

00 .Z

Z,,v

vef

a

efg

efph εε

λλε

===

where εef is the effective (relative) dielectric constant of the microstrip. εef satisfies the condition

1 < εef < εr. The parameteraZ0 is the characteristic impedance of the microstrip with the dielectric

replaced by air (εr =1). The effective dielectric constant can be interpreted as the dielectric constant of a homogeneous medium that replaces the dielectric and air regions of the microstrip with the dimensional parameters retained as such. For practical designs, the following empirical formulas for calculating the effective dielectric constant and characteristic impedance are quite adequate.

The effective dielectric constant is given approximately by

The guide wavelength in microstrip can be obtained using (1.2) and (1.3). Given the dimensions of the microstrip, the characteristic impedance Z0 can be determined using,

Fig. 1.6 Microstrip in a shielding enclosure

w

b

h

c

εr

air

( )3110

12

1

2

1 21

.w

h /rr

ef

−

+

−+

+=

εεε

( )41

144416670391120

14

860

10 .

h

wfor.

h

wln..

h

w

h

wfor

h

w

w

hln

Z

ef

ef

≥

+++

≤

+

=−

επ

ε

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13

For a given characteristic impedance Z0 and substrate parameters εr and h, the width of the strip conductor can be calculated using the expression,

( )

( ) ( )( )51

2610

39012

1121

2

228122

.

h

wfor

..BlnBlnB

h

wforee

h

w

rr

r

AA

>

−+−−

+−−−

<−

=

−

εεε

π

where

The above quasi-static formulas are valid for an infinitely thin strip conductor and the error in the values of impedances is reported to be within about 1%.

Typical Characteristics

Figure 1.7 illustrates typical variation in the effective dielectric constant εef of a microstrip as a function of the ratio w/h. As expected, for a fixed substrate thickness, εef increases gradually with an increase in w and tends to saturate to the value of εr.

( )

( )b.Z

B

a..

.Z

A

r

rr

rr

6160

61110

2301

1

2

1

60

0

2

0

επ

εεεε

=

+

+−

++

=

0

2

4

6

8

0 0.5 1 1.5 2 2.5 3

εr = 9.8

εr =3.2

w/h

ε ef

Fig.1.7 Variation in the effective dielectric constant of a microstrip (Fig. 1.5) as a function of w/h

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14

Figure 1.8 shows typical variation in the characteristic impedance Z0 of a microstrip as a function of w/h for two different values of the dielectric constant of the substrate (εr = 3.2 and 9.8). As in the case of a stripline, Z0 decreases with an increase in the strip conductor width. Secondly, for the same w/h ratio, larger the value of εr, smaller is the characteristic impedance. It may be noted that practical values of Z0 used in microstrip circuits, lie in the approximate range 20Ω to 100Ω.

Coupled Microstrip line Coupled transmission lines are commonly used for designing directional couplers and filters. The most important type is the coupled microstrip line. In this section we consider a coupled microstrip line in which two strip conductors of equal width w run parallel to each other along the direction of propagation (Fig. 1.9). The spacing between the conductors is s and their thickness is t. This configuration is called parallel coupled or edge coupled microstrip line. In practical circuits t is so small in comparison with s and w that it can be neglected.

As in the case of a single microstrip, the dominant mode of propagation in a parallel coupled microstrip is quasi-TEM. When one of the strip conductors is excited, power is transferred to the other conductor due to coupling of fields. Smaller the spacing s, stronger is the coupling.

The coupled structure has a vertical plane of symmetry passing midway between the two strip conductors. In view of this symmetry, any general excitation of the coupled line can be considered as a superposition of two simpler types of excitations; namely, the even-mode and the odd-mode. Figure 1.10 illustrates how an excitation voltage V at one end of a strip conductor (say, strip 1) can be decomposed into even- and odd-mode excitations. In the even-mode, each of

Fig. 1.8 Variation in the characteristic impedance of a microstrip (Fig. 1.5) as a function of w/h

0

2 5

5 0

7 5

1 0 0

1 2 5

1 5 0

0 0 .5 1 1 .5 2 2 .5 3

εr = 3.2

9.8

w/h

Z0

(Ohm

s)

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15

the two conductors is excited in a voltage V/2; that is, the voltages at the two strips are equal in magnitude and in phase (both positive with respect to the ground). In the odd-mode, the two strips 1 and 2 are excited in voltages V/2 and –V/2, respectively; that is, the voltages are equal in magnitude but opposite in phase (one positive and the other negative with respect to ground). The superposition of these two normal mode excitations results in the original excitation.

Figure 1.10 also shows typical electric and magnetic field lines for the even- and odd- modes. We note that at the plane of symmetry, marked PP′, the normal component of the electric field is zero for the even-mode excitation, whereas the tangential component is zero for the odd-mode excitation. This is equivalent to placing at PP′, a ‘magnetic wall’ for the even-mode and an ‘electric wall’ (or perfect conductor) for the odd-mode.

In a coupled microstrip, the relative proportion of fields shared between the dielectric substrate and air for the even- mode is different from that for the odd-mode. Corresponding to the even- and odd- modes, we therefore define two different effective dielectric constants (εef e and εef o), phase velocities (vph e and vph o) and characteristic impedances (Zoe and Zoo), where the last subscript ‘e’ in each parameter refers to even- mode and ‘o’ refers to odd- mode.

The concentration of the electric field lines within the substrate for the even-mode is larger than that for the odd-mode and hence εef e > εef o. Consequently, the phase velocity for the even-mode is less than that for the odd- mode (vph,e < vph o). However, under the TEM approximation, which is valid for most practical purposes, we can treat the phase velocities to be equal. But the characteristic impedances for the two modes are quite different since they are strongly dependent on the dimensional parameters.

Figure 1.11 shows typical variation in the even- and odd- mode characteristic impedances (Zoe and Zoo) of a microstrip as a function of the strip width w normalized with respect to the substrate height h. Plots are shown for different values of the normalized spacing (s/h). It can be seen that for a fixed set of values of w/h and s/h, the even- mode impedance is always greater than the odd-mode impedance. Furthermore, as the spacing between the strip conductors increases, the even- mode impedance decreases and the odd- mode impedance increases, and in the limit when the strip conductors are decoupled, the two impedances reduce to the characteristic impedance of a single microstrip (shown by the dotted line in Fig. 1.11).

Fig. 1.9 Schematic of coupled microstrip

εr h

w

Ground plane

Dielectric substrate

Strip conductors

w s

t

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Strip 1 Strip 2 Excitation V 0 Even mode V/2 V/2 Odd mode V/2 - V/2

P′

Even mode

εr

P′

P + -

Odd mode

Strip 1

εr

P

+ +

Strip 2

H lines

E lines

Fig. 1.10 Fields in a coupled microstrip for even- and odd-mode excitations

0

20

40

60

80

100

120

140

0 0.5 1 1.5 2 2.5w/h

Zo

e , Z

oo (

Ohm

s)

even

odd

s/h

0.128

0.128

1.28

1.28

∞

Fig. 1.11 Variation in the even- and odd- mode impedances of a coupled microstrip (see Fig. 1.10) as a function of normalized width of the strip conductor (εr = 9.8 )

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17

Experiment I

Measurement of Directivity and Gain of Antennas [Printed Yagi, Printed dipole and Microstrip patch antenna]

2.1 Theory

2.1.1 Introduction to Planar Antennas The antennas provided for the experiment are in planar form. The printed dipole is a planar version of the conventional dipole and the Yagi antenna is a planar form of the conventional Yagi that is commonly made of conducting rods or tubes. The microstrip patch antenna is a basic antenna belonging to a class of planar antennas based on microstrip techniques. The antenna that is provided has a rectangular shaped conducting patch fed by a microstrip. The function of an antenna is to transform guided electromagnetic energy in a transmission line into free space radiated energy and vice versa. In the first case, the antenna functions as a transmitting antenna and in the second case it functions as a receiving antenna. Antenna forms an essential part of any system required to either transmit or receive electromagnetic energy. The basic parameters of an antenna remain the same whether it is used for transmission or reception. Antennas can be broadly classified into the following four categories- wire antennas such as the dipoles and loops; aperture antennas such as the open ended waveguides and horns; reflector antennas such as the parabolic dishes with feeds; and planar antennas. Among these different types, planar antennas are relatively new. Advantages of Planar Antennas Planar antennas in the form of printed antennas offer several advantages over the conventional antennas mentioned above. They are lightweight, low profile antennas and can be made conformal with the use of flexible substrates. These features make them well suited for aerospace applications such as for aircraft, missiles and satellites and also for land mobile systems. Microstrip patch antennas in particular are thin and flat, and hence are ideal for mounting in the interior of a vehicle, a cellular mobile phone system and portable manpack radars.

2

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18

2.1.2 Directivity and Gain – Definitions and Formulas Directivity and Gain are two important parameters of any antenna. Before defining these parameters, we need to understand certain other characteristics of the antenna; namely, radiation pattern, far field region, E- and H- plane half-power beam widths, and radiation intensity.

Radiation Pattern: Practical antennas do not radiate uniformly in all the directions. Every antenna has a radiation pattern. It is a graphical representation of the distribution of radiated energy as a function of angle about the antenna in the three-dimensional space. The radiation pattern is generally measured in the far field region.

Far Field Region: The far field region is defined as that region of space where the angular field distribution of the antenna is essentially independent of the distance from the antenna. If the maximum overall dimension of the antenna is D, then the far field region is commonly taken to exist at distances greater than 2D2/λ0 from the antenna where λ0 is the free space wavelength.

The strength of radiation is usually measured in terms of field strength relative to some reference level, and this reference level is usually the peak of the main beam. Radiation pattern plots, however, can be shown in terms of field strength or power density or decibels (dB). Thus a complete radiation pattern gives relative power radiated (or field strength) at all angles of θ and φ in spherical coordinate system (Fig. 2.1) and requires a 3-dimensional presentation. However, in practice, it is common to present cross sections of the radiation pattern in two principal planes of interest. For linearly polarized antennas, these planes are the E- and H- planes.

E-plane: The E-plane is the plane passing through the antenna in the direction of the beam maximum and parallel to the far-field E -vector.

H-plane: The H-plane is the plane passing through the antenna in the direction of the beam maximum and parallel to the far-field H -vector.

Beam Width: The radiation pattern of a typical antenna consists of a main beam and a few minor lobes. Minor lobes usually represent radiation in the undesired directions. The beam width is a measure of sharpness of the main radiated beam. The 3dB beam width is the angular width of a pattern between the half-power points; that is, -3dB points with respect to the maximum field strength. In the electric field intensity pattern, it is the angular width between points that are 1/√2 times the maximum intensity (Fig. 2.2).

Radiation Intensity: Radiation intensity in a given direction is defined as the power radiated by the antenna per unit solid angle. It is obtained by multiplying the power density in the far field region by the square of the radial distance from the antenna. If U denotes the radiation intensity in W/unit solid angle (steradian or square degree) and Srad denotes the power density in W/m2, then we can write

where R is the distance from the antenna to the far field point of observation. It may be noted that in the far zone, the power density Srad depends on the radial distance from the antenna, but the radiation intensity U is independent of the distance.

( )122 .SRU rad=

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19

Directivity

The directivity D of an antenna is defined as the ratio of maximum radiation intensity (Umax) to the average radiation intensity (Uav).

where S is the radiated power density (or the Poynting vector); Sav is the average value over a sphere and Smax is the maximum value. The average power density over a sphere is given by

( ) ( )324

1

0

2

0.d,SSav Ω∫∫=

ππφθ

π

Thus the directivity D can be written as

( )( ) ( )( )

( )424

4

11

4

11

.d,Pd

,S

,SD

An

max

Ω=

Ω∫∫

=Ω∫∫

= π

φθπφθ

φθπ

where Pn(θ ,φ) is the normalized power pattern and ΩA is the beam solid angle.

For an isotropic antenna, the radiation is uniform in all the directions. Hence, Pn(θ ,φ) =1 for all angles of θ and φ, ΩA = 4π, and D = 1. Approximate Formula for Directivity

The radiation pattern of a practical antenna generally includes minor lobes. If we neglect the effect of minor lobes, then the directivity can be calculated from the approximate formula

where ∆θ E and ∆θ H are the half power beam widths in radians in the of E- plane and H- plane,

respectively, of the antenna; and oEθ∆ and oHθ∆ denote the same beam widths in degrees.

In practice, the directivity is calculated from the measured E-plane and H-plane radiation patterns. Therefore, we need to take into account the power lost in the minor lobes. An approximate formula that is commonly used for directivity in practice is

The directivity expressions given in (2.2), (2.4) and (2.5) are dimensionless. In decibels, the directivity given by

For example, directivity D =100 is 20dBi; that is 20dB above the isotropic radiator.

( ) ( ) ( )22.S

,S

U

,UD

av

max

av

max φθφθ==

( )a.DoH

oEHE

52410004

θθθθπ

∆∆≈

∆∆=

( ) ( ) ( )6210 10 .DlogdBiD =

( )b.DoH

oE

5232400

θθ ∆∆≈

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20

Gain The gain G of an antenna is defined as the product of its directivity and radiation efficiency.

where ηrad is the radiation efficiency of the antenna and is defined as

where Prad is the power radiated by the antenna, and Pacepted is the power accepted by the antenna at its input terminals. Pacepted is equal to the sum of the power radiated and power dissipated (Pdis) in the antenna. The power dissipated includes the conductor loss as well as the dielectric loss in the antenna.

( )82.PP

P

P

P

disrad

rad

accepted

radrad +

==η

( )72.DG radη=

z (θ = 0o)

θ

(φ = 0o)

x

y

P (θ , φ )

φ

Antenna at the origin

Fig. 2.1 Coordinate system for antenna pattern

Fig. 2.2 Typical normalized radiation patterns ∆θ is the half power beam width

EN 1

z

Minor lobes

θ

0.707

(a) Field pattern

∆θ

PN 1

z

Minor lobes

θ

(b) Power pattern

0.5

∆θ

------------------------------------------------------------------------------------------------------------------


21

2.1.3 Printed Dipole

The simplest type of antenna and one of the most commonly used is the center fed half wave (λ0/2) dipole, where λ0 is the free space wavelength. For a thin wire dipole (diameter less than about λ0/100), the current distribution is approximately sinusoidal. Figure 2.3a shows the approximate current distribution on a thin centre fed λ0/2 dipole.

In the far zone, the only nonzero field components are Eθ and Hφ, and they are related by the expression Hφ = Eθ/η0 where η0 is the intrinsic impedance of free space. The expression for Eθ is given by

Figure 2.3(b) shows the variation of Eθ in the E- and H- planes. The 3dB beam width is about 90o in the E-plane. In the H-plane, the pattern is omni-directional. The directivity of the λ0/2 dipole is D =1.643 or 2.16 dBi.

Dipoles are generally constructed from conducting cylindrical rods. The length l of the dipole for its first resonance is in the range 0.47λ0 to 0.48λ0 depending on the diameter of the wire. The fatter the dipole, shorter is its resonant length.

Figure 2.4a shows a dipole realized in planar form. The dipole arms are printed as strip conductors on one side of a dielectric substrate. This makes the cross section of the printed dipole arms a rectangle of width w and thickness t. It is possible to theoretically derive an equivalent circular cross section that gives a cylindrical dipole of the same performance. If a is the radius of the cylindrical rod, then the equivalence is, a = (w + t)/4. With this equivalence, the theoretical formulas available for a cylindrical dipole can be used to predict the characteristics of the corresponding planar dipole. Since the dipole arms are printed, the thickness t of the conductor pattern is negligibly small as compared with the width w. Further, the presence of the dielectric substrate affects the effective resonant length of the dipole, although to a small extent.

The center fed wire dipole as shown in Fig. 2.3a has a balanced input in the form of a two-wire line. The printed dipole has a 50Ω coaxial connector at the input end which is an unbalanced input. We therefore need an unbalanced to balanced line converter (balun) plus an impedance transformer to excite the printed dipole. A microstrip feed which incorporates both these features is printed on the reverse side of the same substrate. The substrate containing the entire printed pattern is mounted on a ground plane with a suitable bracket.

The microstrip feedline has a quarter- wave transformer and a stub line exciting the resonant slot, which in turn excites the dipole. The dimensions are chosen so as to achieve an input impedance of 50Ω at the connector point. The conductor plate on which the printed dipole is mounted serves as a reflector. The reflector allows radiation only in the forward direction and thus enhances the directivity of the dipole. Thus, the pattern of the dipole is different from that of the simple dipole in free space. Another advantage of the printed dipole is its enhanced return loss bandwidth over the dipole in free space. This is accomplished in view of its decrease in the length to width ratio.

( )92θ

θ2

π

θ .sin

coscos

E

=

------------------------------------------------------------------------------------------------------------------


22

Radiation pattern : The field patterns of the printed dipole in the E- and H- planes are shown in Fig. 2.4b. The 3dB beamwidth is approximately 78o in the E- plane, and 190o in the H- plane.

Directivity: The theoretical directivity of the printed dipole is 4.6dBi which is higher than that of a wire dipole. The bandwidth corresponding 10dB return loss for the printed dipole is ~ 29%.

(b)

Fig.2.4 (a) Printed dipole with microstrip feed (b) E - and H- plane far field patterns

y

z

H-plane (φ =90o)

θ

E-plane (φ =0o)

z

θ

x

(a)

Ground plane

Metallization on the backside

x

Coaxial input

Shorting pin

Substrate

Microstrip

Slit on the backside

z

Fig.2.3 (a) Centre fed dipole with sinusoidal current distribution, (b) E- and H- plane far field patterns

z θ = 0o

E-plane

θ

90o - 90o

zx

y

H- plane (b)

θ

yz

(a)

λ0/2

------------------------------------------------------------------------------------------------------------------


23

2.1.4 Microstrip Patch Antenna A microstrip patch antenna basically consists of a conducting patch on a grounded dielectric substrate. The radiation and impedance characteristics of the patch antenna depend on the shape and size of the patch and the feeding arrangement. The patch may be of various shapes; rectangular, square, circular, triangular etc, and it may be excited at one or more feed points from the edge of the patch or through the ground plane. Of the various shapes, the most popularly used one is the rectangular shape. In the following we shall consider the theory of the rectangular patch. Radiation Mechanism of Rectangular Patch Antenna In order to understand the radiation mechanism in a rectangular microstrip patch, consider a linearly polarized radiating patch fed by a microstrip as shown in Fig. 2.5a. The substrate is electrically thin (typically about 0.02λ0, where λ0 is the free space wavelength) such that the electric field between the patch and the ground plane is essentially x-directed and independent of the x- coordinate. At resonance, the length L of the patch is approximately half wavelength (λg/2) in the microstrip medium. The input impedance of the patch is mainly governed by the patch width W and this width is generally chosen to be between 0.5 to 2 times the length L, but much larger than the strip width of the microstrip line feeding it. The larger the patch width, the smaller is the input impedance and larger is the bandwidth. The width W should however be kept less than 2L in order to avoid higher order modes.

Since the patch length is approximately λg/2, the electric field lines (Fig. 2.5a) at each of the two edges of width W are out of phase. The fringing fields at these two edges can be resolved into normal and tangential components with respect to the ground plane. The normal components are oppositely directed because the patch is nearly λg/2 long; and therefore the far fields produced by them cancel in the broadside direction (normal to the surface of the patch). On the other hand, the far fields due to the tangential components that are parallel to the ground plane (see Fig. 2.5b) add in phase to give a maximum in the broadside direction. The patch antenna can therefore be treated as two radiating slots separated by a distance L. It may be noted that the fringing fields at the other two edges, each of length L do not contribute to radiation. This is apparent from the reversal of electric field lines at the edge as shown in Fig. 2.5c.

Resonance Frequency

Because of the fringing fields, the effective size of the patch is slightly larger than its physical size. The end correction ∆l at each of the two radiating slots accounts for the capacitive susceptance of the fringing fields. The effective length of the patch, denoted as Lef is given by

The end correction ∆l is a function of the effective dielectric constant εef of the microstrip patch and the ratio W/h where h is the height of the substrate. The expressions for ∆l, εef , and the resonant frequency fr are given by ,

( )1022 .LLef l∆+=

------------------------------------------------------------------------------------------------------------------


24

( )

( )( )112

2580ε80

30ε26404120

∆.

.h

W.

.h

W.

.h

ef

ef

−

+

+

+=l

Radiation Pattern: The radiated field is linearly polarized with its electric field vector lying parallel to the patch length. If the patch is assumed to lie in the y-z plane as shown in Fig. 2.6a, then the E-plane pattern lies in the x-y plane and the H-plane pattern lies in the x-z plane. Because of the ground plane on one side, the radiation of the patch is one sided. The expressions for the electric field Eφ in these two principal planes are given below: E-Plane (θ = 90o , 0 ≤ φ ≤ 90o and 270o ≤ φ ≤ 360o )

H-Plane (φ = 0o , 0 ≤ θ ≤ 180o )

where k0 = 2π/λ0. The angle θ is measured from the z-axis and φ is measured from the x-axis.

Figure 2.6b shows the theoretical E- and H- plane far field patterns. The 3dB beamwidth is around 75o in the E- plane and 82o in the H- plane.

Directivity

Since the radiation of the patch is one sided, it has a larger directivity than a simple dipole. Directivity of the order of 6 to 7dBi is achievable with the patch antenna. The bandwidth of the patch antenna is inherently narrow (~2.5%).

( )1422

2

2 0

0

0

.sinLk

coscos

hk

coshk

sin

Eef

= φφ

φφ

( )152θ

2

θ2

2

2

0

0

0

0

.cos

Wk

cosWk

sin

sinhk

sinhk

sin

sinE

=θ

θθφ

( )132ε2

00 .velocityspacefreev,

L

vf

efefr ==

( )1221012

1ε

2

1 21

.W

hrref

−

+

−+

+=

εε

------------------------------------------------------------------------------------------------------------------


25

Excitation of the patch: The input impedance of the patch antenna at the edge is generally high. The input impedance varies approximately as cos2θL from the centre of one radiating edge to the other, where θL is the electrical length from the edge. We can locate a point on the patch where the input impedance is 50Ω and feed the patch directly at this point using a 50Ω coaxial connector fitted from the ground plane side. In the rectangular patch antenna provided for the experiment, a λg/4 (where λg is the wavelength in microstrip) impedance transformer is used to transform the patch impedance to 50Ω. A coaxial connector is fitted from the ground plane side with its centre pin piercing through the substrate and making contact with the other end of the microstrip (2.6a).

Fig. 2.5 Rectangular microstrip patch antenna fed by microstrip, (b) End correction due to fringing fields, (c) E- field lines at the non-radiating edges

(c)

Fig. 2.6 (a) Rectangular patch with coordinate system (b) Theoretical E- and H- plane far field patterns

E- Plane

x

y

φ

x H- Plane

z

θ

(b)

z

θ θ = 0 φ

φ = 0

φ = 90o y

x

L

(a)

εr

Contact with centre pin of coaxial input

L

h εr

L

W

h

Fringing E –field at radiating edge 1

Fringing E- field at radiating edge 2

(a) Ground plane

x

εr

W

∆l ∆l (b)

L

------------------------------------------------------------------------------------------------------------------


26

2.1.5 Printed Yagi Antenna Principle of Operation

The Yagi antenna consists of one excited dipole, one reflector and several parasitic directors. Figure 2.7 shows the basic geometry of a 5-element Yagi antenna. Parasitic elements are shorted dipoles that are not directly excited, but carry induced currents due to proximity coupling. By adjusting the lengths and spacings of the parasitic elements with respect to the main excited dipole we can control the amplitude and phase of the induced currents in the parasitic element.

If the length of the parasitic element is longer than the resonant length λ0/2, the induced current lags the voltage as in an inductor, and if the length is less than λ0/2, the current leads the voltage as in a capacitor. The reflector is a parasitic element with a lagging current and the directors are parasitic elements with leading current. Yagi antenna is essentially an array supporting a travelling wave, and its performance is determined by the current distribution in each element and the phase velocity of the traveling wave.

The Yagi antenna produces a highly directive unidirectional radiation pattern. The field intensity is maximum along the line of the array and towards the directors. The directivity is a function of the number of directors or the length of the array. Normally only one reflector is used since increasing the number of reflectors does not improve the directivity significantly. With five elements (one reflector, one dipole and three directors) we can get a directivity of about 10dBi in the forward direction (in the direction of the directors). The positions and lengths of the parasitic elements strongly affect the input impedance of the Yagi antenna, and the feed network has to be appropriately designed taking into consideration these effects.

As shown in Fig. 2.7, the excited dipole and the directors are of width w. The lengths and spacings of the various elements as marked in the figure form the design parameters. The Yagi antenna radiates an endfire beam with nearly the same beamwidth in both the E- and H- planes.

Printed 5-Element Yagi Array

Fig. 2.8a shows the geometry of a 5-element printed Yagi antenna. It uses a printed dipole with the addition of printed parasitic elements on a dielectric substrate. The printed dipole configuration is the same as that described in section 2.1.3. All the five elements are located on one side of the substrate and the microstrip feed is on the reverse side of the substrate.

Radiation Pattern: Figure 2.8b shows typical field patterns of a Yagi array. The half-power beamwidth is 52o in the E-plane and 64o in the H-plane.

Directivity: The antenna offers a directivity of about 10dBi. The bandwidth corresponding to 10dB return loss is approximately 10%.

------------------------------------------------------------------------------------------------------------------


27

Microstrip conductor on backside

z

y

Substrate Printed pattern on front side of the substrate

(a)

(b)

y

z

E-plane

y

x

H-plane

Fig. 2.8(a) Geometry of the five-element printed Yagi antenna with microstrip feed, (b) Typical far field patterns

Fig. 2.7 Basic configuration of a 5-element Yagi antenna

y

Reflector Directors

λ0/2

s1 s3 s2

L1 L3 L2 L4

z

------------------------------------------------------------------------------------------------------------------


28

2.1.6 Pattern Measurement

As defined earlier, antenna pattern is a plot of radiated power distribution as a function of the angle around the antenna kept in free space. This definition suggests the measurement procedure. We go around the antenna and measure the radiated power density as a function of the angle. In order to ensure that we measure only the radiated power, the following conditions must be satisfied.

1. The surrounding space should be free of reflecting objects. Ideal environment is open free space, but is difficult to obtain inside a laboratory. The laboratory walls and the instruments around will reflect RF energy and perturb the measured pattern. This point should be kept in mind while interpreting the measured pattern which may not conform to the theoretical pattern. 2. Measurement should be done in the far field region, i.e., the distance between the two antennas must be greater than 2D2/λ0 of both transmitting and receiving antennas. 3. The detector must be operated in the square law region, so that the reading is proportional to the received power. For readings outside the square law region of the detector, use the Calibration Graph provided to you.

In a practical pattern measurement, instead of going around the antenna to measure the radiated power, the antenna whose pattern is to be measured is rotated around its axis keeping the other antenna in a fixed position. It is common practice to connect the receiver (the detector- VSWR meter combination) to the antenna on a rotating stand and keep the transmit antenna on a fixed stand. The measured pattern is that of the antenna mounted on the rotating stand. In this arrangement we are actually measuring the receive pattern. Since the radiation and receive patterns are the same for an antenna, the positions of the transmitter and receiver can be interchanged without affecting the measurement.

2.1.7 Absolute Gain Measurement The power input to the antenna can be split into three parts, namely, power radiated into the free space, power dissipated on the antenna and the power reflected back to the source. If the antenna input is perfectly matched to the source impedance then the reflection coefficient is zero. The power dissipated in the antenna cannot be made zero in most cases. Hence not all the power input to the antenna is radiated. This is taken into account by the efficiency factor. The gain is a product of the directivity and efficiency. The absolute gain measurement procedure includes all the losses. The only assumption made is that the two antennas are identical in all respects. In the following we obtain an expression for antenna gain in terms of measurable parameters.

Let Pt be the power input to the transmit antenna. The power density St at a distance R is equal to the power density due to an isotropic source having the same input power multiplied by the gain Gt of the transmitting antenna.

If an antenna having an effective aperture area Ar is used to receive the signal, then the power received Pr by it at the distance R is given by

.16)2(π4 2R

GPS tt

t =

------------------------------------------------------------------------------------------------------------------


29

The aperture area of the receiving antenna is related to its gain Gr by the expression

where λ0 is the free space wavelength. Substituting for St and Ar from (2.16) and (2.18) respectively, in (2.17) we obtain

or

If the two antennas are identical, then Gr = Gt = G. The gain of the antennas is given by,

or

In decibels, equation (2.21) can be expressed as

( ) ( ) ( ) ( )2324

202

1

010 .

RlogdBPdBPdBG tr

+−=

λπ

This is the simplified principle of absolute gain measurement. The last term in (2.23) gives the path loss.

For a given operating frequency, the free space wavelength λ0 is known, Thus, if we measure the distance R between the two antennas, the power input Pt to the transmit antenna, and the received power Pr by the receive antenna, with the two antennas aligned for gain maximum and polarization matched, we can calculate the gain of the antenna.

A far more accurate method of determining the gain at a specified frequency is to measure Pt and

Pr for three or four values of R (all lying in the far field zone) and then plot rt PP as a

function of R. From (2.22), we note that the slope of the graph gives the value of ( )G04 λπ . By

substituting for λ0, we can calculate the gain G. In decibels, the gain is 10log10G.

.18)2(π4

λ20 r

rG

A =

( )192π4

λ2

0 .R

GGPP rttr

=

( )172.ASP rtr =

( )202λ

π42

0.

R

P

PGG

t

rtr

=

( )2124

0.

R

P

PG

t

r

=

λπ

( )2224

0.R

GP

P

r

t

=

λπ

------------------------------------------------------------------------------------------------------------------


30

2.1.8 Relative Gain Measurement Gain can also be measured with respect to a reference antenna whose gain has been measured by other means. With a fixed transmit antenna, first use the reference antenna as the receiving antenna and note the power received as Pref. Next, simply replace the reference antenna by the test antenna and note the power received as Ptest. The gain of the test antenna is then given by

where Gref is the gain of the reference antenna with respect to the isotropic source.

In this method, it is assumed that both the reference and test antennas are perfectly matched. Therefore, the accuracy of the measured gain depends on the extent to which the two antennas are matched.

2.2 Experiment Three types of planar antennas are provided: printed Yagi antenna, printed dipole and microstrip rectangular patch antenna. All are designed to operate within the S-band with a centre frequency around 2.4 GHz. The experiment involves

1. Measurement of E- and H- plane patterns and calculation of directivity 2. Measurement of gain –Absolute gain method and Comparison method

Note: Measurement of Gain: The Absolute Gain method is more accurate than the Comparison method. The Absolute Gain method requires two identical antennas, and Comparison method requires a reference antenna with known gain.

Use Absolute Gain method to measure the gain of the rectangular patch antenna (since its bandwidth is inherently very narrow). Two Yagi antennas are also provided so that the gain of the Yagi can also be measured using the Absolute Gain method. You can then use the Yagi antenna with known (high)gain as a reference antenna to measure the gain of the printed dipole by Comparison method

The experimental procedure is written by considering the Yagi antenna as an example. The measurement procedure given is common to all the antennas.

2.2.1 Measurement of Directivity

Objective: (a) To measure the E- and H- plane radiation patterns of an antenna (b) To determine the half-power beamwidths in the principal planes and calculate the directivity of the antenna

Equipment/Components

1. Microwave signal source (2.2 -3 GHz) 2. VSWR meter

( ) ( ) ( ) ( )[ ] ( )242.dBPdBPdBGdBG reftestref −+=

------------------------------------------------------------------------------------------------------------------


31

3. Coaxial detector 4. N(m) to SMA(F) adapter 5. Attenuator pad (3dB) 6. BNC/SMA connector fitted cables 7. Antenna stands 8. Planar antennas: Yagi antennas, printed dipole, microstrip rectangular patch antennas.

As an example, consider measuring the radiation pattern of Yagi antenna. Use the two identical Yagi antennas ; one for transmission and the other for reception. Procedure 1. Assemble the set up as shown in Fig. 2.9. Mount the two (identical) Yagi antennas on the

two stands.

Do not switch ‘ON’ the signal source or the VSWR meter until you read the instructions given at Sl. Nos. 2 and 3 below.

[In general, when the two antennas are not identical, the antenna whose pattern is to be measured must be mounted on the stand which has provision for rotation as a function of angle. You may consider this as the receiving antenna. The other antenna on the fixed stand will then be the transmitting antenna.]

2. Procedure for switching ‘ON’ the Microwave Signal Source

(a) Before switching ‘ON’ the signal source, rotate the RF power level knob on the front panel anti-clockwise to minimum position (lowest power output). Connect a 3dB attenuator pad at the RF output port as shown in the diagram.

The RF power should not be switched ‘ON’ without a load (attenuator pad or antenna) connected to avoid damage to the RF circuits inside the source.

(b) Switch on the signal source in the following sequence: First Power Switch to ‘ON’ position and then RF Power Switch to ‘ON’ position. Set modulation switch to AM and modulation frequency to the 1KHz preset position (click at extreme left).

Before making any change in the setup, i.e., changing cable connections, device or attenuator, ensure that there is at least a 3dB attenuator pad at the RF output port of the source. Alternatively, you can switch ‘OFF’ the RF power while making any changes.

3. Procedure for switching ‘ON’ the VSWR meter

The VSWR meter is to be used in conjunction with the coaxial detector. Keep the Range Switch in the 40dB position and the Variable Gain Knob to maximum.

The choice of 40dB range initially, is to avoid the meter needle from kicking in case the input power is high.

Switch ‘ON’ the VSWR meter. Then change the Range setting to 50dB, 60dB till the meter needle is within the reading range. You can vary the source RF power to get reading in one of these ranges.

------------------------------------------------------------------------------------------------------------------


32

4. How to record VSWR meter readings

Take all VSWR meter readings on the dB scale and record them as ‘minus’ dB. Positive dB numbers that you read refer to the VSWR meter gain, but for the input signal, it is negative dB.

For example, if the Range Switch is in 40dB position and the needle on the meter points to 6dB on the dB scale, then note down the reading as – (40+6) = - 46dB.

5. Keep the receiving antenna in the far zone of the transmitting antenna. That is, the distance R between the two antennas must satisfy the relation R > 2D2/λ0, where D is the maximum size of the antenna(s), and λ0 is the free space wavelength. Calculate this value for the given antennas and make sure that the distance between the antennas is greater than this R.

6. For E-plane Pattern: Align the two Yagi antennas along their main beam peaks (boresight direction) and for horizontal polarization. Set the pointer on the receiving antenna stand to read 0o.

7. Set the frequency of the source near 2.4GHz and vary frequency around this value to get maximum reading on the VSWR meter. [When the frequency of the source is set to the center frequency of the antennas, the VSWR meter will show maximum reading.]

8. With the antennas properly aligned and the pointer on the rotating stand set at 0o, adjust the power output of the source to indicate high power in dB on the VSWR meter (say, - 46dB). This is the reference value at the peak of the beam.

9. Next, rotate the antenna clockwise in steps of 5o at a time till 90o (or till the meter reading falls to -70dB). Record the angles in column 1 and VSWR meter readings as ‘minus’ dB in column 2 of Table 2.1.

10. Return to 0o position. The VSWR meter needle should return to the reference level (-46dB). In case of any minor deviation (which can occur due to power fluctuation), adjust the gain on the VSWR meter slightly to read the same reference value. Repeat measurements by rotating the antenna anticlockwise in steps of 5o till -90o (or till the meter reading falls to -70dB). Record the angle and VSWR meter readings at every step in columns 5 and 6, respectively.

This completes the measurement in the E-plane.

11. For H-plane Pattern: Now turn both the antennas by 90o and mount them for vertical polarization. Align the antennas for maximum reading on the VSWR meter.

Follow the same procedure as given above in steps 8 to 10 and tabulate the readings in Table 2.2 in the respective columns (as in Table 2.1).

This completes the measurement in the H-plane.

------------------------------------------------------------------------------------------------------------------


33

Worksheet 1: Table 2.1 : Measured Data for E-plane Pattern Frequency =

Angle

(degrees)

Relative power level

Angle

(degrees)

Relative power level VSWR meter

reading (dB)

Corrected

value (dB)

Norma- lized value (dB)

VSWR meter

reading (dB)

Corrected

value (dB)


0

5

10

:

:

x (ref)

y 0

:

:

:

0

-5

-10

:

:

0

:

:

:

Fig.2.9 Antenna test set up for measurement of radiation pattern and gain

Attenuatorpad

Signal source2.2 –3GHz

1KHz AM

Transmitting antenna

Detector

Test antenna (rotatable)

R

VSWR meter

------------------------------------------------------------------------------------------------------------------


34

Table 2.2 : Measured Data for H-plane Pattern Frequency =

Angle

(degrees)

Relative power level

Angle

(degrees)

Relative power level VSWR meter

reading (dB)

Corrected

value (dB)


VSWR meter

reading (dB)

Corrected

value (dB)


0

5

10

:

:

0

:

:

:

0

-5

-10

:

:

0

:

:

:

1. Refer to the Calibration Graph that is provided with the detector and VSWR meter. Locate the VSWR meter readings of columns 2 and 6 on the x-axis of the graph. Read the corrected values on the y-axis and record them in columns 3 and 7, respectively. [See Fig. 1.2 for an example. In Fig. 1.2, if x = -48dB, the corrected value y is -49.5dB]

2. Normalize all the readings by taking the reference value as 0dB. [For example, if the corrected reference value is y = -49.5dB, then add 49.5dB to all the readings of column 3 and 7 and enter the normalized values in the respective adjacent columns. Plot the E- and H- plane patterns on a polar plot showing normalized values in dB versus the angle.

3. For both the patterns, locate the -3dB points on either side of the peak (0dB) and note the angle between them. This gives the -3dB beam widths ∆θ E

o and ∆θ Ho), in the E- and H-

planes, respectively.

4. The pattern directivity D can be calculated using the approximate formula given in (2.5b).

( )

( ) ( )262θθ

4003210

252θθ

40032

oH

oE

10

oH

oE

.,

logdBiD

or

.,

D

∆∆=

∆∆=

------------------------------------------------------------------------------------------------------------------


35

2.2.2 Measurement of Gain

Objective

(a) To measure the absolute gain of an antenna using two identical antennas (b) To measure the gain of a given antenna using a reference antenna with known gain.

(comparison method)

Equipment/Components

1. Microwave signal source (2.2 -3GHz) 2. VSWR meter 3. Coaxial detector 4. Attenuator pads (3dB, 6 dB, 10dB) 5. N(m) to SMA(F)Adapter 6. BNC/ SMA cables 7. Antenna stands 8. Planar antennas: Yagi antennas -2, printed dipole, microstrip rectangular patch antenna.

(a) Measurement of Absolute Gain of an Antenna using Two Identical Antennas

The absolute gain of an antenna can be measured if we have two identical antennas. For making this measurement, two identical printed Yagi antennas are provided.

This experiment involves measurement of RF power input to the transmit antenna and the power received at the receive antenna.

Procedure

1. Measure RF power input to the transmit antenna.

First we set the transmit power level. Connect all the three attenuator pads (3dB+6dB+10dB) at the source output and then connect the detector and VSWR meter.

2. Switch ‘ON’ the RF power with source in AM 1KHz modulation and frequency 2.4 GHz. Set the VSWR range switch to 40dB range and variable gain knob to maximum.

Increase the RF power so that the VSWR meter shows reading in the 40dB range. This is the reference power level. If the needle is at 46dB, then note this reference reading as Pref (dB) = -46dB. Do not vary RF power setting on the source throughout the gain measurement.

3. Now, switch ‘OFF’ the RF power output without disturbing the power level setting of the source. Disconnect the detector and VSWR meter from the source.

4. Connect the equipment as in the experimental arrangement shown in Fig.2.9. Mount the two identical Yagi antennas on the two antenna stands. The distance between the two antennas must satisfy the far zone criterion.

------------------------------------------------------------------------------------------------------------------


36

5 Align the two antennas for the same polarization (say vertical). Start with a minimum distance R that satisfies the far zone criterion.

6. Switch ‘ON’ the RF power. If the VSWR meter does not show any reading, increase the transmit power by removing one or two of the attenuator pads. The VSWR meter gives the received power level Prec (dB) at distance R.

7. Record R (cm), Pref (dB) (minus), value of attenuator pad(s) removed as A(dB)(plus) and the received power level Prec (dB) (minus) in columns 1 , 2, 4 and 6, respectively, of Table 2.3.

8. Increase the distance R by 10cm at a time and record the VSWR meter readings. Do not change the RF power level setting at the source. You may remove the attenuator pads to increase the power to the transmit antenna. Record Prec(dB) and A(dB) for four different values of R in Table 2.3.

9. The experiment can be repeated at other frequencies to obtain gain versus frequency plot.

Worksheet 2

1. Refer to the Calibration Graph that is provided to you. Locate the readings of column 2 on the x-axis of the graph. Read the corrected values on the y-axis and record them in column 3 as P’

ref(dB). Similarly get the corrected values for Prec (column 6) from the User Graph and record them as Pr(dB) in column 7.

2. The power input PtdB) to the transmit antenna is calculated by adding the value of the attenuator pad(s) removed to the corrected reference value P’

ref(dB).

For example, if P’ref (dB) = -49.5dB, and one 10dB pad has been removed, then

Pt(dB) = (-49.5 + 10)dB = -39.5dB.

Record Pt(dB) in column 5 of Table 2.3.

3. For each value of R, calculate (Pt - Pr )dB and enter at column 8. Calculate the power ratio (Pt / Pr ) using the following formula.

Calculate rt PP and enter at column 9 of Table 2.3.

3. Plot a graph with R (cm) along the x-axis and the power ratio rt PP along the y- axis.

4. From the graph, find the slope which is equal to 4π/(λ0G). The derivation of the relevant formula is given in section 2.1.7. Determine λ0 (in cm) from the frequency setting of the source and then calculate the gain G. In decibels, the absolute gain is 10log10G.

( ) ( ) ( )2721010 .

dBPdBPloganti

P

P rt

r

t

−=

------------------------------------------------------------------------------------------------------------------


37

Table 2.3: Absolute Gain Measurement – Measured data Frequency =

(c) To Measure the Gain of an Antenna using a Reference Antenna This is a comparison method. An antenna with known gain is used as a reference to measure the gain of a given antenna.

Procedure 1. Use the experimental arrangement as shown in Fig.2.9. The reference antenna with known

gain is used as the receiving antenna. Adjust the distance between the two antennas to satisfy the far -field criterion.

2. Align the two antennas for the same polarization and for maximum reception along the main beam peaks. Note the VSWR meter reading as Pref(dB). Refer to the Calibration graph and get the corrected value. Let P’ref (dB) denote the corrected value.

3. Remove the reference antenna and connect the ‘Test Antenna’ (whose gain is to be determined) in its place and orient the antenna for the same polarization.

4. Note the VSWR meter reading as Ptest(dB). From the Calibration Graph, get the corrected value and record it as P’test (dB).

5. Repeat measurements at different frequency settings if gain versus frequency is required.

Worksheet 3

1. Calculate the absolute Gain G of the ‘Test Antenna’ using the formula

where Gref is the absolute gain of the reference antenna.

For example, if P’test = -50dB and P’ref = -55dB, then the relative gain of the test antenna with respect to the reference antenna is +5 dB, and its absolute gain is (Gref + 5)dB.

R

(cm)

Pref

(dB)

P’ref

(dB)

Att. pads removed A(dB)

Pt

(dB)

Prec

(dB)

Pr

(dB)

(Pt - Pr)

(dB) rt PP

:

:

:

:

( ) ( ) ( ) ( )[ ] ( )282.dBPdBPdBGdBG 'ref

'testref −+=

------------------------------------------------------------------------------------------------------------------


38

2.2.3 Write-up

1. Prepare a report by combining the results of worksheets 1, 2 and 3.

2. Compare the measured E- and H-plane patterns with the theoretical patterns. Also compare the experimental and theoretical values of directivity. Which value is higher? Explain.

3. Compare the measured gain of the antennas with the theoretical values. Which value is higher? Explain.

4. What are the sources of error in pattern and gain measurements?

------------------------------------------------------------------------------------------------------------------


39

Experiment II

Determination of Coupling and Isolation Characteristics of Microstrip Directional Couplers

3.1 Theory A directional coupler is a 4-port reciprocal passive network. The basic function of a coupler is to sample power flowing in one direction in a transmission line and reject power flowing in the opposite direction. It also performs the function of power division but with the output signals having 90o phase difference between them. In microstrip and stripline configurations, two basic forms of directional couplers are commonly used. They are called branchline coupler and parallel-coupled directional coupler. These couplers form the basic blocks of many other microwave components, such as balanced mixers, variable attenuators and PIN diode phase shifters.

3.1.1 Basic Parameters of Directional Couplers In order to define the parameters of a directional coupler, consider the schematic of a four port network shown in Fig. 3.1. We designate ports 1, 2, 3 and 4 as the input port, direct output port, coupled port and isolated port, respectively. As marked in Fig. 3.1, let P1i be the power fed to port 1 from a matched source, P1r denote the power reflected back from the input port; and P2s , P3s and P4s denote the power outputs from the direct output port, coupled port and isolated port, respectively. These power outputs emerging out of ports 2, 3 and 4 look into matched loads so that there is no power incident back at these ports. An ideal directional coupler is defined as one in which there is no reflection of power back from the input port (P1r =0) and no power goes to the isolated port (P4s = 0). Then part of the input power P1i comes out of the coupled port and the remaining power comes out of the direct coupled port.

3

------------------------------------------------------------------------------------------------------------------


40

In a practical directional coupler, due to mismatch at the ports and losses in the circuit, the reflected power P1r at the input port and the output power P4s at the isolated port are not zero. For a practical coupler, the performance is specified by the following parameters:

where

S31 = Voltage transmission coefficient from the port 1 (input port) to port 3 (coupled port) with ports 2 and 4 match terminated.

S41 = Voltage transmission coefficient from port 1(input port) to port 4 (isolated port), with ports 2 and 3 match terminated.

S11 = Voltage reflection coefficient at port 1 with ports 2, 3 and 4 match terminated. S21 = Voltage transmission coefficient from port 1 to port 2 (direct output port) with ports 3 and

4 match terminated.

The parameters S11, S21, S31 and S41 are also called the scattering parameters of the four port network. Negative signs are used in equations (3.1) to (3.3) so that the values of coupling, isolation and return loss expressed in dB will be positive (as per the convention).

Fig. 3.1 Four port network schematic of a directional coupler

( )132010 31101

310 .Slog

P

Plog)dB(CCoupling

i

s −=

−=

( )232010 41101

410 .Slog

P

Plog)dB(ISOLIsolation

i

s −=

−=

( )332010 11101

110 .Slog

P

Plog)dB(RLLossturnRe

i

r −=

−=

Input port

P3s

Isolated port Coupled port

Directional coupler

P1i

P4s

P2s

Direct output port

P1r 1 2

34

------------------------------------------------------------------------------------------------------------------


41

3.1.2 Branchline Directional Coupler Figure 3.2 shows two typical layouts of a branchline coupler in microstrip. Basically, the coupler consists of two main transmission lines directly bridged by two shunt branches. In Fig.3.2, AA’ and BB’ can be considered as the main transmission lines shunted by branches AB and A’B’. Z0a denotes the characteristic impedance of the main lines (series branches) and Z0b that of the shunt branches. All input and output lines have the same characteristic impedance Z0. At the design frequency (f =f0), the physical length of each branch and the separation between the branches are all one- quarter wavelength (λg0/4) in the microstrip or the electrical length θ = θ 0 = π/2.

For an ideal branchline coupler, the scattering parameters are given by,

where

It can be seen that the coupling factor S31depends on the ratio of the impedances of the series and shunt branches. Irrespective of the coupling factor, the two output signals at ports 2 and 3 are always out of phase by 900.

Ideal 3-dB Coupler and its Theoretical Response

For a 3dB coupler, we need to choose S21 = -j/√2 and S31 = -1/√2 so that half of the input power goes to the coupled port (port 3) and the remaining half of the power comes out of port 2. Then

( )5311120

20

20

.ZZZ ba

−=

( )4300

031

0

0214111 .

Z

ZS,

Z

ZjS,SS

b

aa −=−===

Fig. 3.2. Two typical layouts of branchline coupler

θ

θ

2

34

B

A

B’

A’

Z0a

Z0a

Z0b Z0b

Z0 Z0

Z0 Z0

Input port

Coupled port

Direct output port

Isolated port

1 Zoa

Zoa

Z0b

Z0 Z0 1 2

34

Z0b

Z0 Z0

(a) (b)

------------------------------------------------------------------------------------------------------------------


42

from (3.4), we get Z0a = Z0 /√2 and Z0b = Z0. Since all input and output ports are matched to Z0 = 50Ω, we get, Z0a = 35.35Ω, and Z0b = 50Ω. With port 1 as the input port, power fed to this port is equally divided between ports 2 and 3 with no power going to port 4. The two output signals at ports 2 and 3 have a phase difference of 900. The coupler is completely matched at all the ports. This property, however, is valid only at the centre frequency at which the shunt arms and the spacing between them are equal to one- quarter wavelength in the medium.

Figure 3.3 shows the ideal theoretical response of a 3dB branchline coupler. The graph is shown with port 1 as the input port. We note that at the centre frequency (f = f0), the coupling is 3dB and the isolation in dB becomes infinite. These parameters deteriorate as the frequency deviates from the centre frequency.

0

4

8

12

16

20

24

0.2 0.6 1 1.4 1.8

Fig. 3.3. Theoretical characteristics of 3dB branchline coupler as a function of normalized frequency.

S11

, S 2

1, S

31,

S 41

(dB

)

S41

S31

S11

f / f0

S21

------------------------------------------------------------------------------------------------------------------


43

3.1.3 Parallel Coupled Directional Coupler The parallel coupled directional coupler is another equally important configuration that finds practical utility. While the branchline configuration is mainly used as a 3dB coupler, the parallel coupled configuration is more suitable for achieving loose coupling and hence is used popularly for sampling microwave power. Principle of Operation The propagation parameters of a coupled microstrip line are discussed in section 1.4 of chapter1. Corresponding to the even- and odd- mode property of the coupled microstrip, we designate two different characteristic impedances; Zoe for the even- mode and Zoo for the odd- mode. The two modes also travel with different phase velocities (vph,e and vpho), but under the TEM approximation, we can treat them as equal for the purpose of analysis. The parallel coupled directional coupler is essentially a section of parallel coupled transmission line of length equal to one-quarter wavelength in the propagating medium. Figure 3.4 shows a layout of the coupler in microstrip. The electrical length of the coupled line section is θ. The width of the strip conductors in the coupled section is w and the spacing between them is s. The four ports of the coupled line are decoupled at the ends to form four single microstrip lines. If one of the ports is excited, then due to the electric and magnetic field interaction, the signal gets coupled to the auxiliary line and the coupled signal travels in the direction opposite to that of the input signal. Because the coupling takes place in the backward direction, the parallel coupled line coupler is also referred as backward wave coupler.

Any one of the four ports can be chosen as the input port. With the port designations as marked, consider port 1 as the input port. The coupled signal travels backwards in the auxiliary line and appears at port 3. The remaining power comes out of port 2. Port 4 is the isolated port. The amount of coupling depends on the spacing s between the parallel coupled conductors. The

Fig. 3.4 Typical layout of a parallel coupled directional coupler

Coupledport

3

21

4

w 0

w

w s

θ

Isolated port

Inputport

Direct output port

------------------------------------------------------------------------------------------------------------------


44

voltage signals appearing at ports 2 and 3 differ in phase by 900. Further, the voltage at the coupled port 3 attains a maximum value when the electrical length θ = π/2 or the physical length L= λg0/4 where λg0 is the guide wavelength in microstrip.

Design Formulas

At the design frequency (f =f0), the electrical length θ =θ0 = π/2 and the voltage coupling coefficient of the coupler attains a maximum value. The expression for the maximum coupling factor, denoted as C0, is given by

C0 is also called the mean coupling factor at the design frequency. The characteristic impedances Zoe and Zoo are related by the expression

( )730 .ZZZ oooe=

Using (3.6) and (3.7), we can obtain Zoe and Zoo in terms of the port impedance Z0.

Equation (3.8) forms the basic design equation for a parallel coupled line coupler. In the design of the coupler, the mean coupling factor C0 and the port impedance Z0 are specified. Using (3.8), the values of Zoe and Zoo are calculated which in turn are used to determine the dimensions of the coupled line.

Frequency Response of an Ideal Coupler The expressions for the scattering parameters (voltage transmission coefficients) S21 and S31 as a function of frequency (equivalently, the electrical length θ ) are given by

( )931

1

20

20

21 .sinjcosC

CS

θθ +−

−=

( )1031 2

0

031 .

sinjcosC

sinCjS

θθ

θ

+−=

( )11304111 .SS ==

( )831

1

1

1

0

00

0

00 .

C

CZZ,

C

CZZ oooe +

−=

−+

=

( )630 .ZZ

ZZC

oooe

oooe

+−

=

------------------------------------------------------------------------------------------------------------------


45

We note that with port 1 as the input port, the amount of power coupled to port 3 at other frequencies depends both on the electrical length of the coupled section at that frequency and on the coupling factor C0 chosen in the design. Since port 1 is matched, the remaining power emerges out of the direct output port (port 2). The coupler offers perfect match and infinite directivity at all frequencies. This result is a direct consequence of the fact that the even- and odd- mode phase velocities are equal in the TEM analysis. The theoretical frequency response of the coupler can be obtained from (3.9) and (3.10). Figure 3.5 shows the variation in the coupling C in dB as a function of the normalized frequency where C is given by

The graph is shown for couplers with mean coupling C0 = 3dB, 6dB and 10dB at the centre frequency (f = f0). As can be seen, couplers with tightly coupled lines offer slightly higher bandwidth as compared with the weakly coupled lines. As compared with a branchline coupler, the parallel line coupler offers much higher bandwidth. For example, the bandwidth of a 3dB branchline coupler is approximately 10% whereas that of a 3dB parallel line coupler is around 30% for the same coupling variation.

( )12320 3110 .Slog)dB(C −=

Fig. 3.5 Theoretical variation in coupling of a parallel line directional coupler as a function of normalized frequency

0

5

10

15

20

0 0.5 1 1.5 2

f/f0

Cou

plin

g C

(dB

)

C0 (dB) = 3

10

6

------------------------------------------------------------------------------------------------------------------


46

The formulas presented above are based on the assumption that the even- and odd-modes in the coupled section propagate with the same phase velocity and hence have the same guide wavelength and same electrical length for both the modes. In a microstrip, the quasi-TEM mode fields result in different phase velocities for the even- and odd-modes. This is because the even-mode has less fringing field in the air region than the odd mode. The effective dielectric constant for the even- mode is slightly higher and consequently the phase velocity is slightly lower than for the odd-mode. Because of the unequal phase velocities, practical microstrip couplers offer poor directivity as compared with stripline couplers.

3.2 Experiment

3.2.1 Measurement of Coupling and Isolation Objective: (a) To measure the coupling characteristics of a microstrip directional coupler (b) To measure the isolation characteristics of a microstrip directional coupler

Equipment/Components required

1. Microwave signal source (2.2 –3 GHz) 2. VSWR meter 3. Detector 4. N (m) to SMA(F) adaptor 5. Attenuator pads – 3dB, 6dB, 10dB 6. Matched loads (50Ω) -2 7. SMA/BNC connector fitted cables 8. Directional couplers: Microstrip branchline coupler

Microstrip parallel coupled coupler Note:

For both the couplers, the impedance of input/ouput lines is 50Ω. Choose any one coupler for your experiment. The procedure given below applies to both. Identify any one port as the input port (port 1). With respect to the input port, identify the coupled port (port 3) and the isolated port (port 4). Measurement of coupling involves measuring the transmission response between the input port (port1) and the coupled port (port 3). Similarly, measurement of isolation of the coupler involves measuring the transmission response between the input port and the isolated port (port 4). While making the measurement between any two ports, the remaining two ports will have to be terminated in 50Ω matched loads.

------------------------------------------------------------------------------------------------------------------


47

Procedure 1. Assemble the set up as shown in Fig. 3.6. Do not switch on the microwave signal source or

the VSWR meter until you read the instructions given at Sl. Nos. 2 and 3 below. 2. Procedure for switching ‘ON’ the Microwave Signal Source

Before switching on the signal source, rotate the RF power level knob on the front panel anti-clockwise to minimum position (lowest power output). Remember to connect a 6dB (or 10dB) attenuator pad at the RF output port of the source as shown in the diagram.

Switch on the signal source in the following sequence: First Power Switch to ‘ON’ position, then RF Power Switch to ‘ON’ position. Set modulation switch to AM and modulation frequency to the 1 KHZ preset position (click at extreme left).


Keep the Range Switch in the 40dB range position and the Variable Gain Knob to maximum. [Choice of 40 dB range initially is to avoid the meter needle from kicking in case the input power is high].

Switch ‘ON’ the VSWR meter.

4. To Measure the Coupling

(a) First measure reference power level by connecting the cable end at P to Q directly (Refer Fig. 3.6). Set the frequency of the source to 2.3 GHz. Increase the RF power output of the source till the VSWR meter shows a reading in the 50dB range (say 55dB). Record the frequency (in GHz) in column 1 and the VSWR meter readings as P1i dB (minus value) in column 2 of Table 3.1. Increase the frequency of the source in steps of 0.1GHz up to 2.8GHz and note the corresponding readings of the VSWR meter. Column 2 now gives the reference input power at different frequencies.

(b) Next insert the coupler (branchline or parallel coupled) between P and Q with input port (say port1) connected to P and the coupled port (port 3) to Q. Terminate ports 2 and 4 of the coupler in 50Ω matched loads. Record the readings of the VSWR meter at the above frequencies as P3s dB (minus value) in column 3 of Table 3.1.

6. To measure the Isolation

The value of isolation is generally much greater than coupling. Therefore, choose a higher reference values so that with the device connected, the meter needle does not go below 70dB.

(a) Connect the cable end at P to Q directly (Refer Fig. 3.6). Set the frequency of the source to 2.3 GHz. Increase the RF power output of the source till the VSWR meter shows reading in the 40dB range (say 48dB). Record the frequency (in GHz) in column 1 and the VSWR meter readings as P1i dB (minus value) in column 2 of Table 3.2. Increase the frequency of the source in steps of 0.1GHz up to 2.8GHz and note the corresponding readings of the VSWR meter. Column 2 now gives the reference input power at different frequencies.

------------------------------------------------------------------------------------------------------------------


48

(b) Connect the isolated port (port 4) to Q. Terminate ports 2 and 3 in matched loads. Record the readings of the VSWR meter at the same frequencies as P4s dB (minus value) in column 3 of the same Table.

3.2.2 Write-up Table 3.1 : Measured Data and Calculation of Coupling

Freq.

f (GHz)

VSWR meter readings

Coupling

C(dB) = P’1i - P

’3s P1i

(dB) P3s

(dB) P’

1i

(dB) P’

3s

(dB) 2.3 : :

2.8

Fig.3.6 Test setup for measurement of coupling and isolation of couplers

Matchedload

Detector Attenuator pad

Parallel line coupler

P Q

Source (2.2 – 3GHz)

1KHz AM Mod.

3

2

4

1

1 2

3 4

Branchline coupler

VSWR meter

------------------------------------------------------------------------------------------------------------------


49

Table 3.2 : Measured Data and Calculation of Isolation

Freq.

f (GHz)

VSWR meter readings

Isolation

Isol.(dB) = P’1i - P

’4s P1i

(dB) P4s

(dB) P’

1i

(dB) P’

4s

(dB) 2.3 : : : :

2.8

1. Determination of coupling in decibels:

Using the Calibration Graph, get the corrected values of P1i (column 2) of Table 3.1 and record them as P’1i (dB) in column 4 of the same Table. Similarly, get the corrected values of P3s (column 3) and record them as P’3s (dB) in column 5 of Table 3.1. Coupling C (dB) = P’

1i (dB) - P’3s (dB). Enter this value at column 6 of Table 3.1.

2. Determination of Isolation in decibels:

Using the Calibration graph, get the corrected values of P1i (column 2) of Table 3.2 and record them as P’1i (dB) in column 4 of the same Table. Similarly, get the corrected values of P4s (column 3) and record them as P’4s (dB) in column 5 of Table 3.1. Isol. (dB) = P’

1i (dB) - P’4s (dB). Enter this value at column 6 of Table 3.2.

3. Plot C(dB) and Isol.(dB) as a function of frequency.

Note that C(dB) = |S31| (dB) and Isol.(dB) = |S41| (dB)

Branchline Directional Coupler 4. Plot of coupling versus frequency: In the ideal case coupling is 3dB at the centre frequency.

In the actual device, because of the losses in the connectors and in the microstrip line, the measured coupling may be slightly higher. Away from the centre frequency, observe the variation in the coupling as a function of frequency. Explain the variation.

5. Plot of isolation versus frequency: In the ideal case, the isolation is infinite dB at the centre

frequency and then it deteriorates as the frequency is either increased or decreased. In a practical microstrip coupler, the isolation is finite. Observe the variation in isolation as a function of frequency. Explain the variation.

------------------------------------------------------------------------------------------------------------------


50

6. Determine the % bandwidth of the branchline coupler corresponding to (a) coupling variation

between 3 and 4.5dB and (b) 12dB isolation. Compare these two bandwidths. Which of the two parameters of the coupler limits the bandwidth?

Parallel Coupled Directional Coupler 7. Plot of coupling versus frequency: The coupling value of this coupler is provided on the

component. Observe the variation in coupling as function of frequency. Explain the variation. 8. Plot of isolation versus frequency: In the ideal case, the isolation is infinite dB at the centre

frequency and then it deteriorates as the frequency is either increased or decreased. Observe the variation in isolation as a function of frequency. Explain the variation.

9. Determine the % bandwidth of the parallel coupled directional coupler corresponding to (a) coupling variation of 1.5dB with respect to the mean value and (b) 12dB isolation. Compare the bandwidths in the two cases. Which of the two parameters of the coupler limits the bandwidth?

------------------------------------------------------------------------------------------------------------------


51

Experiment IIIA

Measurement of Resonance Characteristics of Microstrip Ring Resonator and Determination of

Dielectric Constant of the Substrate 4.1 Theory of Ring Resonator Microstrip ring resonators are commonly used in the design of MIC components such as filters, oscillators, and mixers. Microstrip ring resonator is formed by bending the strip conductor of a microstrip in the form of a ring. Figure 4.1 shows the configuration along with the input and output feed lines. The gap between the feed line and the ring determines the coupling. Smaller the gap, tighter is the coupling.

Resonance is established when the mean circumference of the ring is equal to integral multiples of guide wavelength in microstrip.

where, R is the mean radius of the ring and n is the mode number. The other symbols are,

λg = guide wavelength in the microstrip

εef = effective (relative) dielectric constant of the microstrip

v0 = free space velocity

fr = resonant frequency of the ring

The expression for εef is given in (1.3) and is repeated below:

4

( )143212 0 .,,,nfor,f

nvnR

efrg LLL===

ελπ

( )2410

12

1

2

1 21

.w

h /rr

ef

−

+

−+

+=

εεε

------------------------------------------------------------------------------------------------------------------


52

where h is the height of the dielectric substrate, and w is the width of the strip conductor in the ring. From (4.1), we note that the lowest order resonance occurs when the mean circumference is one wavelength (n =1) in the microstrip.

Ring resonator provides a simple experimental means of characterizing a microstrip substrate. For a given microstrip ring, the dimensions are R , w and the substrate height h are known. The resonant frequency of the ring is determined experimentally by measuring its transmission response and noting the frequency at which the output shows a peak. The value of εef is first calculated using (4.1). In order to calculate εr from the knowledge of εef and w/h, we can recast (4.2) in the form

It may be noted that the resonant frequency of the ring can be affected if the coupling at the gap is very strong. In the resonator provided for the experiment, the coupling is just adequate to observe the resonance peak, but not strong enough to affect the intrinsic resonant frequency of the ring.

Fig. 4.1 (a) Layout of microstrp ring resonator with input and output lines (b) Cross- section of microstrip

( )34

110

1

110

12

21

21

.

w

h

w

h

/

/

ef

r

+

+

−

++

=−

−ε

ε

w

gap

Output Input R

(a)

h ε r

(b)

------------------------------------------------------------------------------------------------------------------


53

4.2 Experiment

4.2.1 Measurement of Resonant Frequency

Objective (a) To measure the resonance characteristics of a microstrip ring resonator

(b) To calculate the (relative) dielectric constant εr of the substrate.

Equipment/Components 1. Microwave signal source (2.2 –3 GHz) 2. VSWR meter 3. Detector 4. N(m) to SMA(F) adapter 5. Attenuator pad (3dB) 6. SMA/BNC connector fitted cables 7. Microstrip ring resonator.

The microstrip ring resonator provided has its lowest order resonance (n =1) around 2.5 GHz. The following parameters are specified on the ring resonator:

Strip conductor width (in the ring) w Height of the substrate h

Mean radius of the ring R Procedure 1. Assemble the set up as shown in Fig. 4.2. Do not switch on the microwave signal source or


Before switching on the signal source, rotate the RF power level knob on the front panel anti-clockwise to minimum position (low power output). Connect a 3dB attenuator pad at the RF output port of the source as shown in the diagram.



The VSWR meter is to be used in conjunction with the coaxial detector. Keep the Range Switch in the 40dB range and the Variable Gain Knob to Maximum.

Switch ‘ON’ the VSWR meter.

------------------------------------------------------------------------------------------------------------------


54

4. Set the frequency of the source to 2.2GHz. Connect P to Q directly. Increase the power output of the source till the VSWR meter shows a reading of about 45dB.

5. Next insert the ring resonator between P and Q.

You may notice that the power output suddenly drops. The VSWR meter may not even show any indication. That is because the ring resonator offers large attenuation away from resonance.

Vary the frequency of the source slowly from 2.3GHz to 2.8GHz and observe the frequency at which the VSWR meter reading shows a sharp peak. If no peak is observed, increase the power output of the source and vary the frequency again. Note the frequency at which the VSWR meter shows a peak. This is the (first order) resonant frequency fr of the resonator.

4.2.2 Write-up 1. For the ring resonator provided in the experiment, the values of R, w and h are given on the

device. Substitute the value of the measured resonant frequency fr in (4.1) and calculate the value of εef of the microstrip. Next, substitute the value of εef in (4.3) and calculate the relative dielectric constant εr of the substrate.

Fig.4.2 Test setup for measuring the resonant response of ring resonator

VSWR meter

Detector Attenuator pad (3dB)

P Q


1KHz AM Mod.

21

------------------------------------------------------------------------------------------------------------------


55

Experiment IIIB

Measurement of Power Division and Isolation Characteristics of Microstrip 3dB Power Divider

The function of a power division network is to divide the input power into two or more outputs. In this experiment, we shall study the characteristics of a two-way 3 dB power divider.

5.1 Theory of Power Divider Scattering Matrix of 3 dB Power Divider Figure 5.1 shows the line diagram of Y- junction as a power divider. Let port 1 be the input port that is matched to the source; that is, input reflection coefficient S11 = 0.

As an equal-split power divider, power incident at port1 gets divided equally between the two output ports 2 and 3. Equal power division implies |S21| = |S31| = 1/√2. The phase factors of S21 and S31 can be made equal to zero (multiples of 3600) by choosing the reference planes of ports 2 and 3 symmetrical with respect to port 1. Further, the device is reciprocal. With this information, the scattering matrix can be written as

1

2

3 Input

Fig. 5.1 Schematic of an equal-split power divider.

5

------------------------------------------------------------------------------------------------------------------


56

According to the unitary property of the scattering matrix for lossless networks; we have

[ ] [ ] [ ] ( )25.USS T =∗

where [U] is a unit matrix. Applying (5.2 ) to (5.1), it can be shown that

and

( )452

1332322 .SSS ===

Equation (5.4) indicates that ports 2 and 3 are not matched and the voltage reflection coefficient at each of these ports is 1/2. Furthermore, the two output ports 2 and 3 are not mutually isolated. Equation (5.4) is consistent with the theorem that a lossless, reciprocal, three port junction cannot be matched at all the three ports. Figure 5.2 shows the layout of a power divider with standard port impedance Z0 = 50Ω at each of the three ports. The impedance Z0 of each output arm is transformed to 2Z0 at the junction via a quarter wave transformer (where λg0 is the guide wavelength in the medium) so that at the junction, looking from the input port, the two output arms appearing in parallel yield an impedance of Z0. The impedance of the quarter wave transformer is √(2 Z0× Z0) = Z0√ 2.

[ ] ( )15

2

12

12

1

2

10

3323

2322 .

SS

SSS

=

( )352322 .SS −=

Fig. 5.2 Layout of equal-split power divider

1

2

3 Z0

Z0

Z0

Z 0 √ 2 Input

λ g0 / 4

λ g0 / 4

------------------------------------------------------------------------------------------------------------------


57

The power divider considered above is reciprocal. That is, if two signals of equal amplitude and equal phase enter ports 2 and 3, they will combine and come out of port 1. However, signals that do not meet this requirement will be reflected and part of the signal will leak into the adjacent output port. That means, the two output ports are not isolated from each other.

Matched Power Divider Figure 5.3 shows a matched power divider, popularly known also as the Wilkinson power divider. It uses an isolation resistor R of value 2Z0 between ports 2 and 3. With this resistor, the device is completely matched at all the three ports, and ports 2 and 3 are isolated from each other at the centre frequency (f0).

( )5503322 .SS == Summarizing the above results and considering the symmetry of ports 2 and 3 with respect to port 1, we can write the scattering matrix of the matched power divider (Fig. 5.3) as

Theoretical Response of Matched 3dB Power Divider From (5.6), we note that when a signal is fed to port 1, the power is divided equally between ports 2 and 3. When equal-amplitude, in-phase signals are fed to ports 2 and 3, the device acts as a power combiner and the entire power appears at port 1. If power is fed only to port 2 or port 3, then half the power goes to port 1 and the other half gets dissipated in the isolation resistor. In all the cases, ports 2 and 3 are mutually isolated.

Fig. 5.3 Matched equal-split power divider in microstrip

R= 2 Z0 1

2

3

√2 Z0

Z0

Z0

Z0

√2 Z0

λg0/4

λg0/4

[ ] ( )65

001

001

110

2.

jS

−=

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58

The scattering matrix of the matched power divider as a function of frequency can be derived by considering the electrical length of the transformer section at ports 2 and 3 as θ instead of π/2. Figure 5.4 shows the theoretical response of the matched power divider as a function of frequency f normalized with respect to the centre frequency f0. Note that at f = f0, θ = π/2.

In Fig.5.4, the power division, isolation and return loss are expressed in dB using the following

This power divider offers a theoretical bandwidth of approximately 1.44:1 for input VSWR of 1.22 and an isolation of 20dB between the two output ports.

Fig.5.4 Theoretical variation in power division (S21 (dB)), isolation (S32 (dB)) and return loss (S11(dB)) of matched microstrip power divider (Fig. 5.3) as a function of normalized frequency

( ) ( )752021 211021 .Slog)dB(SporttoportdivisionPower −=

( ) ( )952032 321032 .Slog)dB(SporttoportIsolation −=

( ) ( )105201 111011 .Slog)dB(SportlossturnRe −=

0

1.25 1.0 0.75 0. 1.5

10

20

f/f0

S21

S32

S11

S21

, S 3

2, S

11(d

B)

S32

( ) ( )852031 311031 .Slog)dB(SporttoportdivisionPower −=

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59

5.2 Experiment

5.2.1 Measurement of Power Division and Isolation Objective To measure the power division and isolation characteristics of a microstrip 3dB power divider

Equipment/Components 1. Microwave signal source (2.2 -3GHz) 2. VSWR meter 3. Coaxial detector 4. Attenuator pads (6dB, 10dB) 5. Matched load 6. SMA/BNC connector fitted cables 7. Microstrip 3dB power divider

Note:

The impedance of the input/output lines of the microstrip power divider is 50Ω and the isolation resistor connected between the two output lines has a value of 100Ω.

Measuring the power division property involves measuring the transmission response between the input port (port1) and the two output ports (ports 2 and 3). Measuring the isolation property involves measuring the transmission response between ports 2 and 3.

While measuring the transmission response between any two ports, the third port has to be terminated in a matched load.

Procedure 1. Assemble the set up as shown in Fig. 5.5. Do not switch on the microwave signal source or


Before switching on the signal source, rotate the RF power level knob on the front panel anti-clockwise to minimum position. Remember to connect a 6dB (or 10dB) attenuator pad at the RF output port of the source as shown in the diagram.


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60


Keep the Range Switch in the 40dB range position and the Variable Gain Knob to Maximum. Switch ‘ON’ the VSWR meter.

4. Measure the reference power level

Connect the cable end at P to Q directly (Refer Fig. 5.5).

Set the frequency of the source to 2.3 GHz. Increase the RF power output of the source till the VSWR meter shows a reading in the 50dB range (say 55dB). Note this reading as -55dB. Increase the frequency of the source in steps of 0.1GHz up to 2.8GHz and note the corresponding readings of the VSWR meter. Record the frequencies in column 1 and the VSWR meter readings as P1i dB in column 2 of Table 5.1.

5. To measure the power division property

Insert the power divider between P and Q with input port (port1) connected to P and coupled port 2 to Q. Terminate port 3 in a matched load.

Set the frequency of the source to 2.3GHz. Record the reading of the VSWR meter as P2s dB in column 3 of Table 5.1. Next, interchange connections at port 2 and port 3. That is, connect port 3 to Q. Terminate ports 2 in matched load. Record the reading of the VSWR meter as P3s dB in column 4 of Table 5.1.

Increase the frequency in steps of 0.1 GHz and repeat the above measurements up to 2.8GHz. For every frequency setting, note P2s dB and P3s dB and record at columns 3 and 4 of Table 5.1.

6. To measure the isolation property

Remove the power divider from the set-up. Measure the reference power level again at the same frequencies by following the procedure given at Sl. No. 4 above. Since the values of isolation are much higher, you can keep the reference level slightly higher.

(a) Set the frequency of the source to 2.3 GHz. Increase the RF power output of the source till the VSWR meter shows reading in the 40dB range (say 48dB). Record the frequency (in GHz) in column 1 and the VSWR meter readings as P2i dB in column 2 of Table 5.2. Increase the frequency of the source in steps of 0.1GHz up to 2.8GHz and note the corresponding readings of the VSWR meter in column 2.

Insert the power divider between P and Q with port 2 as the input port connected to P and port 3 to Q. Terminate port 1 in a matched load. Record the readings of the VSWR meter at the same frequencies as P3s dB in column 3 of Table 5.2.

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61

5.2.2 Write-up

Table 5.1: Measured Data and Calculation of Power Division

Freq. f (GHz)

VSWR meter readings

Power division

Port1 to 2 S21(dB)

Power division

Port1 to 3 S31(dB)

P1i

(dB) P2s

(dB) P3s

(dB) P’

1i

(dB) P’

2s

(dB) P’

3s

(dB) 2.3 : : : :

2.8

Fig.5.5 Test setup for measurement of power division and isolation of microstrip power divider

Matchedload

VSWR meter

Detector Attenuator pad

Power divider

P Q


1KHz AM Mod.

1

2

3

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62

Table 5.2: Measured Data and Calculation of Isolation

Freq. f (GHz)

VSWR meter readings

Isolation

Port 2 to 3 S32(dB)

P2i

(dB) P3s

(dB) P’

2i

(dB) P’

3s

(dB) 2.3 : : :

2.8

1. Determination of Power Division

Using the Calibration Graph, get the corrected values of P1i (column 2) of Table 5.1 and record them as P’1i (dB) in column 5 of the same Table. Similarly, get the corrected values of P2s and P3s and record them as P’

2s (dB) and P’3s (dB) in columns 6 and 7, respectively of Table 5.1.

Power division (loss) from port 1 to port 2 = P’1i (dB) - P

’2s (dB) = - 20 log10|S21|. Denote this

loss as S21(dB) and enter at column 8 of the Table 5.1.

Power division (loss) from port 1 to port 3 = P’1i (dB) - P

’3s (dB) = - 20 log10|S31|. Denote this

loss as S31(dB) and enter at column 9 of the Table 5.1 2. Determination of Isolation

Using the Calibration Graph, get the corrected values of P2i (column 2) and P3s (column 3) of Table 5.2 and record them as P’2i (dB) and P’3s (dB) in columns 4 and 5, respectively, of the same Table.

Isolation (dB) = P’2i (dB) - P’

3s (dB) = - 20 log10|S32|. Denote this as S32(dB) and enter at column 6 of the Table 5.2

3. Plot power division S21(dB) and S31(dB) as a function of frequency. Ideally the values of both these should be 3dB at the centre frequency. In the actual device, because of the losses in the connectors and in the microstrip line, the measured loss will be slightly higher. Compare the variation in the loss characteristic with the ideal response given in Fig. 5.4. From the plot determine the centre frequency.

4. Plot isolation S32(dB) as a function of frequency. Compare with the ideal response and

explain the difference. 5. Calculate the magnitudes of the scattering parameters from the measured loss at the centre

frequency. Compare with the theoretical values.

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63

References For Antenna Experiment (Expt. No.I) 1. A.R. Harish and M. Sachidananda, Antennas and Wave Propagation, Oxford Univ. Press,

2007.

2. J.D. Kraus, Antennas, Tata McGraw-Hill, 2nd Edition, 1997.

3. C.A. Balanis, Antenna Theory –Analysis and Design, John Wiley & Sons, 2nd Edition, 1997.

For Microstrip Components (Expt. Nos II, IIIA and I IIB) 4. D. M. Pozar, Microwave Engineering, Edison-Wesley, 1990.

5. Bharathi Bhat and S. K. Koul, Stripline-like Transmission Lines for Microwave Integrated Circuits, Wiley Eastern Ltd., 1989.

6. K.C. Gupta, Microwaves, Wiley Eastern Ltd., 1979.

7. T. C. Edwards, Foundations for Microstrip Circuit Design, John Wiley & Sons, 1981.

LabMan_VTU_2.1.2010

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