15848_LMECE407_2

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ECE407 : Unified electronics lab V

1 Implementation of delta modulation and demodulation and observe effect of slope Overload using matlab/simulink

2 Implementation of pulse data coding techniques for various formats using matlab/simulink..

3 Implementation of Data decoding techniques for various formats using matlab/simulink..

4 Implementation of amplitude shift keying modulator and demodulator using matlab/simulink...

5 Implementation of Time Division Multiplexing system using matlab/simulink. 6 Implementation of pulse code modulation and demodulation using

matlab/simulink.

7 Study of microwave components and instruments 8 Measurement of klystron characteristics and Measurement of VSWR 9 Measurement of Directivity and coupling coefficient of a directional coupler. 10 Determination of the phase-shift of a phase shifter. 11 Implementation of frequency shift keying modulator and demodulator using

matlab/simulink.. 12 Implementation of phase shift keying modulator and demodulator using

matlab/simulink.

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PRACTICAL NO 1 OBJECT Implementation of delta modulation and demodulation and observe effect of slope Overload using matlab/simulink

THEORY Delta Modulation: Delta modulation (DM or Δ-modulation) is an analog-to-digital and digital-to-analog signal conversion technique used for transmission of voice information where quality is not of primary importance. DM is the simplest form of differential pulse-code modulation (DPCM) where the difference between successive samples is encoded into n-bit data streams. In delta modulation, the transmitted data is reduced to a 1-bit data stream.

This scheme sends only the difference between pulses, if the pulse at time tn+1 is higher in amplitude value than the pulse at time tn, then a single bit, say a ―1‖, is used to indicate the positive value.

If the pulse is lower in value, resulting in a negative value, a ―0‖ is used. This scheme works well for small changes in signal values between samples. If changes in amplitude are large, this will result in large errors.

Figure 1.1 the process of delta modulation

Figure 1.2 Delta modulation components

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Figure 1.3 Delta demodulation components

Mtalb Code: % *** Function for Delta Modulation*********** % (deltamod.m) function s_DMout=deltamod(sig_in,Delta,td,ts) % usage % s_DMout=deltamod(xsig,Delta,td,ts) % Delta-step size % sig_in-input signal vector % td-original signal sampling period of sig_in % NOTE: td*fs must be a positive integer; % S_DMout -DM sampled output % ts-new sampling period if (rem(ts/td,1)==0) nfac=round(ts/td); p_zoh=ones(1,nfac); s_down=downsample(sig_in,nfac); Num_it=length(s_down); s_DMout(1)=Delta/2; for k=2:Num_it xvar=s_DMout(k-1); s_DMout(k)=xvar+Delta*sign(s_down(k-1)-xvar); end s_DMout=kron(s_DMout,p_zoh); else warning('Error! ts/t is not an integer!'); s_DMout=[]; end end

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%********Delta Modulation **********************************% % togenerate DM signals with different step sizes, % Delta1=0.2,Delta2=Delta1,Delta3=Delta4 clc; clear; clf; td=0.002; % original sampling rate rate 500 hz t=[0:td:1.]; % time interval of 1 sec xsig=sin(2*pi*t)-sin(6*pi*t); % 1hz +3 hz sinusoidals Lsig=length(xsig); ts=0.02; % new sampling rate =50 hz Nfact=ts/td; % send the signal through a 16-level uniform quantiser Delta1=0.2; s_DMout1=deltamod(xsig,Delta1,td,ts); % obtaind the DM signal % plot the original signal and DM signal in time domain figrue(1); figure(1); subplot(311); sfig1=plot(t,xsig,'k',t,s_DMout1(1:Lsig),'b'); set(sfig1,'Linewidth',2); title('Signal {\it g}({{\it t}) and its DM signal') xlabel('time(sec.)'); axis([0 1 -2.2 2.2]); % Apply DM again by doubling the Delta Delta2=2*Delta1; s_DMout2=deltamod(xsig,Delta2,td,ts); subplot(312); sfig2=plot(t,xsig,'k',t,s_DMout2(1:Lsig),'b'); set(sfig2,'Linewidth',2); title('Signal {\it g}({\it t}) and DM signal with doubled stepsize') xlabel('time(sec.)'); axis([0 1 -2.2 2.2]); %*********** Delta3=2*Delta2; s_DMout3=deltamod(xsig,Delta3,td,ts); subplot(313); sfig3=plot(t,xsig,'k',t,s_DMout3(1:Lsig),'b'); set(sfig3,'Linewidth',2); title('Signal {\it g}({\it t}) and DM signal with quadrupled stepsize') xlabel('time(sec.)'); axis([0 1 -2.2 2.2]);

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Results:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-2

-1

0

1

2

Signal {\it g}({{\it t}) and its DM signal

time(sec.)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-2

-1

0

1

2

Signal g( t) and DM signal with doubled stepsize

time(sec.)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-2

-1

0

1

2

Signal g( t) and DM signal with quadrupled stepsize

time(sec.)

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PRACTICAL NO 2 OBJECT Implementation of pulse data coding techniques for various formats using matlab/simulink.

THEORY Data Encoding Methods: We can roughly divide line coding schemes into five broad categories, as shown in figure: 2.1.

Figure 2.1 line coding scheme

Non-Return to Zero (NRZ):

Figure 2.2 NRZ

• It is called NRZ because the signal does not return to zero at the middle of the bit • NRZ is the simplest representation of digital signals • One bit of data is transmitted per clock cycle • Bit values of 1and 0 are represented by high and low voltage signals, respectively

NRZ-L (NRZ-Level), NRZ-I (NRZ-Invert):

Figure 2.3 NRZ-L (NRZ-Level), NRZ-I (NRZ-Invert)

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In NRZ-L the level of the voltage determines the value of the bit.

In NRZ-I the inversion or the lack of inversion determines the value of the bit

Polar RZ: Return-to-Zero scheme:

Polar biphase: Manchester and differential Manchester schemes:

In Manchester and differential Manchester encoding, the transition at the middle of the bit

is used for synchronization

The minimum bandwidth of Manchester and differential Manchester is 2 times that of NRZ

Bipolar Schemes: sometimes called multilevel binary

Three voltage levels: positive, negative, and zero

Two variations of bipolar encoding o AMI (alternate mark inversion)

0: neutral zero voltage 1: alternating positive and negative voltages

o Pseudoternary 1: neutral zero voltage 0: alternating positive and negative voltages

• AMI (alternate mark inversion) – The work mark comes from telegraphy and means 1. – AMI means alternate 1 inversion

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– The neutral zero voltage represents binary 0. – Binary 1s are represented by alternating positive and negative voltages.

• Pesudotenary : – Same as AMI, but 1 bit is encoded as a zero voltage and the 0 bit is encoded as

alternating positive and negative voltages.

Multilevel Schemes:

• The desire to increase the data speed or decrease the required bandwidth has resulted in the creation of many schemes.

• The goal is to increase the number of bits per baud by encoding a pattern of m data elements into a pattern of n signal elements.

• Different types of signal elements can be allowing different signal levels. • If we have L different levels, then we can produce L

n combinations of signal patterns.

• The data element and signal element relation is • mBnL coding, where m is the length of the binary pattern, B means binary data, n is the

length of the signal pattern, and L is the number of levels in the signaling. • B (binary, L=2), T (tenary, L=3), and Q (quaternary, L=4). • In mBnL schemes, a pattern of m data elements is encoded as a pattern of n signal

elements in which 2m ≤ L

n

2B1Q (two binary, one quaternary) – m=2, n=1, and L=4 – The signal rate (baud rate)

2B1Q is used in DSL (digital subscriber line) technology to provide a high-speed connection to the Internet by using subscriber telephone lines

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8B6T:

• Eight binary, six ternary (8B6T) – This code is used with 100BASE-4T cable. – Encode a pattern of 8 bits as a pattern of 6 signal elements, where the signal has

three levels (ternary). – 2

8=256 different data patterns and 3

6=478 different signal patterns. (The mapping

is shown in Appendix D.) – There are 478-256=222 redundant signal elements that provide synchronization

and error detection. – Part of the redundancy is also used to provide DC (direct-current) balance.

• + (positive signal), - (negative signal), and 0 (lack of signal) notation. • To make whole stream DC-balanced, the sender keeps track of the weight

4D-PAM5 :

• Four-dimensional five-level pulse amplitude modulation (4D-PAM5) – 4D means that data is sent over four wires at the same time. – It uses five voltage levels, such as -2, -1, 0, 1, and 2. – The level 0 is used only for forward error detection. – If we assume that the code is just one-dimensional, the four levels create

something similar to 8B4Q. – The worst signal rate for this imaginary one-dimensional version is Nx4/8, or N/2. – 4D-PAM5 sends data over four channels (four wires). This means the signal rate

can be reduced to N/8. – All 8 bits can be fed into a wire simultaneously and sent by using one signal

element. – Gigabit Ethernet use this technique to send 1-Gbps data over four copper cables

that can handle 1Gbps/8 = 125Mbaud –

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Multiline Transmission: MLT-3: • The multiline transmission, three level (MLT-3) • Three levels (+V, 0, and –V) and three transition rules to move the levels

– If the next bit is 0, there is no transition – If the next bit is 1 and the current level is not 0, the next level is 0. – If the next bit is 1 and the current level is 0, the next level is the opposite of the

last nonzero level. • Why do we need to use MLT-3?

– The signal rate for MLT-3 is one-fourth the bit rate (N/4). – This makes MLT-3 a suitable choice when we need to send 100 Mbps on a

copper wire that cannot support more than 32 MHz (frequencies above this level create electromagnetic emission).

–

Summary of line coding schemes:

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Matlab code: function [U P B M S]=nrz(a) % 'a' is input data sequence, % U = Unipolar, P=Polar, B=Bipolar, M=Mark and S=Space %Wave formatting, %Unipolar U=a; n= length(a); %POLAR P=a; for k=1:n; if a(k)==0 P(k)=-1; end end %Bipolar B=a; f = -1; for k=1:n; if B(k)==1; if f==-1; B(k)=1; f=1; else B(k)=-1; f=-1; end end end %Mark M(1)=1; for k=1:n; M(k+1)=xor(M(k), a(k)); end %Space S(1)=1; for k=1:n S(k+1)=not(xor(S(k), a(k))); end %Plotting Waves subplot(5, 1, 1); stairs(U) axis([1 n+2 -2 2]) title('Unipolar NRZ') grid on subplot(5, 1, 2); stairs(P) axis([1 n+2 -2 2]) title('Polar NRZ') grid on subplot(5, 1, 3); stairs(B) axis([1 n+2 -2 2]) title('Bipolar NRZ') grid on subplot(5, 1, 4); stairs(M) axis([1 n+2 -2 2]) title('NRZ-Mark') grid on subplot(5, 1, 5); stairs(S) axis([1 n+2 -2 2]) title('NRZ-Space') grid on

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Input a=[1 0 0 1 1] a = 1 0 0 1 1 [U P B M S]=nrz(a) Output wavform

1 2 3 4 5 6 7-2

0

2Unipolar NRZ

1 2 3 4 5 6 7-2

0

2Polar NRZ

1 2 3 4 5 6 7-2

0

2Bipolar NRZ

1 2 3 4 5 6 7-2

0

2NRZ-Mark

1 2 3 4 5 6 7-2

0

2NRZ-Space

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RACTICAL NO 3 OBJECT Implementation of Data decoding techniques for various formats using matlab/simulink Matlab Code: function [Ur Pr Br Mr Sr]=nrzRx(U,P,B,M,S)

% 'a' is input data sequence

% U = Unipolar, P=Polar, B=Bipolar, M=Mark and S=Space

%Wave formatting

%Unipolar

Ur=U;

n= length(P);

%POLAR

Pr=P;

l=find(Pr<0);

Pr(l)=0

%Bipolar

n= length(B);

Br=B;

l=find(Br<0);

Br(l)=1;

%Mark

n= length(M);

for k=1:n-1;

Mr(k)=xor(M(k), M(k+1));

end

%Space

n= length(S);

S(1)=1;

for k=1:n-1

Sr(k)=not(xor(S(k), S(k+1)));

end

%Plotting Waves

n= length(Ur);

subplot(5, 1, 1); stairs(Ur)

axis([1 n+2 -2 2])

title('Unipolar NRZ Decoded')

grid on

n= length(P);

subplot(5, 1, 2); stairs(P)

axis([1 n+2 -2 2])

title('Polar NRZ Decoded')

grid on

n= length(Br);

subplot(5, 1, 3); stairs(B)

axis([1 n+2 -2 2])

title('Bipolar NRZ Decoded')

grid on

n= length(Mr);

subplot(5, 1, 4); stairs(M)

axis([1 n+2 -2 2])

title('NRZ-Mark Decoded')

grid on

n= length(Sr);

subplot(5, 1, 5); stairs(S)

axis([1 n+2 -2 2])

title('NRZ-Space Decoded')

grid on

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*******************************end***********************************

Input

U =

1 0 0 1 1

P =

1 -1 -1 1 1

B =

1 0 0 -1 1

M =

1 0 0 0 1 0

S =

1 1 0 1 1 1

Call [Ur Pr Br Mr Sr]=nrzRx(U,P,B,M,S)

Output

Pr =

1 0 0 1 1

Ur =

1 0 0 1 1

Pr =

1 0 0 1 1

Br =

1 0 0 1 1

Mr =

1 0 0 1 1

Sr =

1 0 0 1 1

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PRACTICAL NO 4 OBJECT Implementation of amplitude shift keying modulator and demodulator using matlab/simulink.

THEORY ASK (amplitude shift keying) modulator: Amplitude-shift keying (ASK) is a form of modulation that represents digital data as variations in the amplitude of a carrier wave. The amplitude of an analog carrier signal varies in accordance with the bit stream (modulating signal), keeping frequency and phase constant. The level of amplitude can be used to represent binary logic 0s and 1s. We can think of a carrier signal as an ON or OFF switch. In the modulated signal, logic 0 is represented by the absence of a carrier, thus giving OFF/ON keying operation and hence the name given

ASK is implemented by changing the amplitude of a carrier signal to reflect amplitude levels in the digital signal.

For example: a digital ―1‖ could not affect the signal, whereas a digital ―0‖ would, by making it zero.

The line encoding will determine the values of the analog waveform to reflect the digital data being carried.

Fig. 4.1 Ask modulator

Fig. 4.1 Ask signal

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Matlab Code : % program for amplitude shift keying % clc; clear all; close all; s= [1 0 1 0]; f1=20; a=length (s); for i=1:a f=f1*s (1,i); for t=(i-1)*100+1:i*100 x(t)=sin(2*pi*f*t/1000); end end plot(x); xlabel('time in secs'); ylabel('amplitude in volts'); title('ASK') grid on; Results:

0 50 100 150 200 250 300 350 400-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time in secs

ampl

itude

in v

olts

ASK

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PRACTICAL NO 5 OBJECT Implementation of Time Division Multiplexing system using matlab/simulink

THEORY Time-division multiplexing (TDM) is a type of digital or (rarely) analog multiplexing in which two or more signals or bit streams are transferred apparently simultaneously as sub-channels in one communication channel, but are physically taking turns on the channel. The time domain is divided into several recurrent timeslots of fixed length, one for each sub-channel. A sample byte or data block of sub-channel 1 is transmitted during timeslot 1, sub-channel 2 during timeslot 2, etc. One TDM frame consists of one timeslot per sub-channel plus a synchronization channel and sometimes error correction channel before the synchronization. After the last sub-channel, error correction, and synchronization, the cycle starts all over again with a new frame, starting with the second sample, byte or data block from sub-channel 1, etc For multiple signals to share one medium, the medium must somehow be divided, giving each signal a portion of the total bandwidth. The current techniques that can accomplish this include

Frequency division multiplexing (FDM)

Time division multiplexing (TDM)-Synchronous vs statistical1

Wavelength division multiplexing (WDM)

Code division multiplexing (CDM)

Multiplexing: Two or more simultaneous transmissions on a single circuit

Figure 5 Multiplexing Multiplexor (MUX) Demultiplexor (DEMUX)

Time Division Multiplexing: Sharing of the signal is accomplished by dividing available transmission time on a medium among users. Digital signaling is used exclusively. Time division multiplexing comes in two basic forms: 1. Synchronous time division multiplexing, and 2. Statistical, or asynchronous time division multiplexing.

Synchronous Time Division Multiplexing: The original time division multiplexing, the multiplexor accepts input from attached devices in a round-robin fashion and transmits the data in a never ending pattern. T-1 and ISDN telephone lines are common examples of synchronous time division multiplexing. If one device generates data at a faster rate than other devices, then the multiplexor must either sample the incoming data stream from that device more often than it samples the other devices, or buffer the faster incoming stream. If a device has nothing to transmit, the multiplexor must still insert a piece of data from that device

into the multiplexed stream. So that the receiver may stay synchronized with the incoming data stream, the transmitting multiplexor can insert alternating 1s and 0s into the data stream. Three types popular today of Synchronous Time Division Multiplexing:

• T-1 multiplexing (the classic)

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• ISDN multiplexing • SONET (Synchronous Optical NETwork)

The T1 (1.54 Mbps) multiplexor stream is a continuous series of frames of both digitized data and voice channels. The ISDN multiplexor stream is also a continuous stream of frames. Each frame contains various control and sync info SONET – massive data rates Statistical Time Division Multiplexing: A statistical multiplexor transmits only the data from active workstations (or why works when you don’t have to). If a workstation is not active, no space is wasted on the multiplexed stream. A statistical multiplexor accepts the incoming data streams and creates a frame containing only the data to be transmitted. To identify each piece of data, an address is included. If the data is of variable size, a length is also included. More precisely, the transmitted frame contains a collection of data groups. A statistical multiplexor does not require a line over as high a speed line as synchronous time division multiplexing since STDM does not assume all sources will transmit all of the time! Good for low bandwidth lines (used for LANs) Much more efficient use of bandwidth!

Matlab code for TDM: % *********** Matlab code for Time Division Multiplexing ************* clc; close all; clear all; % Signal generation x=0:.5:4*pi; % siganal taken upto 4pi sig1=8*sin(x); % generate 1st sinusoidal signal l=length(sig1); sig2=8*triang(l); % Generate 2nd traingular Sigal % Display of Both Signal subplot(2,2,1); plot(sig1); title('Sinusoidal Signal'); ylabel('Amplitude--->'); xlabel('Time--->'); subplot(2,2,2); plot(sig2); title('Triangular Signal'); ylabel('Amplitude--->'); xlabel('Time--->'); % Display of Both Sampled Signal subplot(2,2,3); stem(sig1); title('Sampled Sinusoidal Signal'); ylabel('Amplitude--->'); xlabel('Time--->'); subplot(2,2,4); stem(sig2); title('Sampled Triangular Signal'); ylabel('Amplitude--->'); xlabel('Time--->'); l1=length(sig1); l2=length(sig2); for i=1:l1 sig(1,i)=sig1(i); % Making Both row vector to a matrix sig(2,i)=sig2(i); end

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% TDM of both quantize signal tdmsig=reshape(sig,1,2*l1); % Display of TDM Signal figure stem(tdmsig); title('TDM Signal'); ylabel('Amplitude--->'); xlabel('Time--->'); % Demultiplexing of TDM Signal demux=reshape(tdmsig,2,l1); for i=1:l1 sig3(i)=demux(1,i); % Converting The matrix into row vectors sig4(i)=demux(2,i); end % display of demultiplexed signal figure subplot(2,1,1) plot(sig3); title('Recovered Sinusoidal Signal'); ylabel('Amplitude--->'); xlabel('Time--->'); subplot(2,1,2) plot(sig4); title('Recovered Triangular Signal'); ylabel('Amplitude--->'); xlabel('Time--->');

Results:

0 10 20 30-10

-5

0

5

10Sinusoidal Signal

Am

plit

ude--

->

Time--->

0 10 20 300

2

4

6

8Triangular Signal

Am

plit

ude--

->

Time--->

0 10 20 30-10

-5

0

5

10Sampled Sinusoidal Signal

Am

plit

ude--

->

Time--->

0 10 20 300

2

4

6

8Sampled Triangular Signal

Am

plit

ude--

->

Time--->

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0 10 20 30 40 50 60-8

-6

-4

-2

0

2

4

6

8TDM Signal

Am

plit

ude--

->

Time--->

0 5 10 15 20 25 30-10

-5

0

5

10Recovered Sinusoidal Signal

Am

plit

ude--

->

Time--->

0 5 10 15 20 25 300

2

4

6

8Recovered Triangular Signal

Am

plit

ude--

->

Time--->

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PRACTICAL NO 6 OBJECT Implementation of pulse code modulation and demodulation using matlab/simulink

THEORY ANALOG-TO-DIGITAL CONVERSION: A digital signal is superior to an analog signal because it is more robust to noise and can easily be recovered, corrected and amplified. For this reason, the tendency today is to change an analog signal to digital data. In this section we describe two techniques, pulse code modulation and delta modulation Pulse code Modulation (PCM): Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals, which was invented by Alec Reeves in 1937. It is the standard form for digital audio in computers and various Blu-ray, Compact Disc and DVD formats, as well as other uses such as digital telephone systems. A PCM stream is a digital representation of an analog signal, in which the magnitude of the analogue signal is sampled regularly at uniform intervals, with each sample being quantized to the nearest value within a range of digital steps. PCM consists of three steps to digitize an analog signal:

1. Sampling 2. Quantization 3. Binary encoding

Before we sample, we have to filter the signal to limit the maximum frequency of the signal as it affects the sampling rate.

Filtering should ensure that we do not distort the signal, ie remove high frequency components that affect the signal shape.

Figure 6.1 Components of PCM encoder

Sampling:

Analog signal is sampled every TS secs. Ts is referred to as the sampling interval. fs = 1/Ts is called the sampling rate or sampling frequency. There are 3 sampling methods:

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– Ideal - an impulse at each sampling instant – Natural - a pulse of short width with varying amplitude – Flattop - sample and hold, like natural but with single amplitude value

The process is referred to as pulse amplitude modulation PAM and the outcome is a signal with analog (non integer) values

According to the Nyquist theorem, the sampling rate must be at least 2 times the highest frequency contained in the signal.

Quantization: Sampling results in a series of pulses of varying amplitude values ranging between two

limits: a min and a max. The amplitude values are infinite between the two limits. We need to map the infinite amplitude values onto a finite set of known values. This is achieved by dividing the distance between min and max into L zones, each of

height

= (max - min)/L

Quantization Levels: The midpoint of each zone is assigned a value from 0 to L-1 (resulting in L values) Each sample falling in a zone is then approximated to the value of the midpoint.

Quantization Error:

When a signal is quantized, we introduce an error - the coded signal is an approximation of the actual amplitude value.

The difference between actual and coded value (midpoint) is referred to as the quantization error.

The more zones, the smaller which results in smaller errors. BUT, the more zones the more bits required to encode the samples -> higher bit rate

Quantization Error and SNQR: Signals with lower amplitude values will suffer more from quantization error as the error

range: /2, is fixed for all signal levels. Non linear quantization is used to alleviate this problem. Goal is to keep SNQR fixed for

all sample values. Two approaches:

The quantization levels follow a logarithmic curve. Smaller ’s at lower

amplitudes and larger ’s at higher amplitudes. Companding: The sample values are compressed at the sender into logarithmic

zones, and then expanded at the receiver. The zones are fixed in height.

Bit rate and bandwidth requirements of PCM: The bit rate of a PCM signal can be calculated form the number of bits per sample x the

sampling rate Bit rate = nb x fs The bandwidth required to transmit this signal depends on the type of line encoding used.

Refer to previous section for discussion and formulas. A digitized signal will always need more bandwidth than the original analog signal. Price

we pay for robustness and other features of digital transmission.

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PCM Decoder: To recover an analog signal from a digitized signal we follow the following steps:

We use a hold circuit that holds the amplitude value of a pulse till the next pulse arrives.

We pass this signal through a low pass filter with a cutoff frequency that is equal to the highest frequency in the pre-sampled signal.

The higher the value of L, the less distorted a signal is recovered.

Matlab code of PCM: %********PCM************************************************** %the uniform quantization of an analog signal using L quantizaton levels% %****implemented by uniquan.m function of matlab %(uniquan.m) function [q_out,Delta,SQNR]=uniquan(sig_in,L) %usage % [q_out,Delta ,SQNR]=uniquan(sig_in,L) % L-number ofuniform quantization levels % sig_in-input signalvector % function output: % q_out-quantized output % Delta-quantization interval % SQNR- actual signal to quantization ratio sig_pmax=max(sig_in); % finding the +ve peak sig_nmax=min(sig_in); % finding the -ve peak Delta=(sig_pmax-sig_nmax)/L; % quantization interval q_level=sig_nmax+Delta/2:Delta:sig_pmax-Delta/2; %define Q-levels L_sig=length(sig_in); % find signal length sigp=(sig_in-sig_nmax)/Delta+1/2; % convert int to 1/2 to L+1/2 range qindex=round(sigp); % round to 1,2,.....L levels qindex=min(qindex,L); % eliminate L+1 as a rare possibility q_out=q_level(qindex); % use index vector to generate output SQNR=20*log10(norm(sig_in)/norm(sig_in-q_out)); % actual SQNR value end

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% sampandquant.m function executes both sampling and uniform quantization %sampandquant.m function [s_out,sq_out,sqh_out,Delta,SQNR]=sampandquant(sig_in,L,td,ts) % usage % [s_out,sq_out,sqh_out,Delta,SQNR]=sampandquant(sig_in,L,td,ts) % L-no. of uniform quantization levels % sig_in-input signal vector % td-original signal sampling period of sig_in % ts- new sampling period % NOTE: td*fs must be +ve integef % function outputs: % s_out-sampled output % sq_out-sample and quantized output % sqh_out-sample, quantized and hold output % Delta- quantization interval % SQNR-actual signal to quantization ratio if rem(ts/td,1)==0 nfac=round(ts/td); p_zoh=ones(1,nfac); s_out=downsample(sig_in,nfac); [sq_out,Delta,SQNR]=uniquan(s_out,L); s_out=upsample(s_out,nfac); sqh_out=upsample(sq_out,nfac); else warning('Error! ts/td is not an integer!'); s_out=[]; sq_out=[]; sqh_out=[]; Delta=[]; SQNR=[]; end end %********generation of PCM *****************************% clc; clear; clf; td=0.002; % original sampling rate rate 500 hz t=[0:td:1.]; %time interval of 1 sec xsig=sin(2*pi*t)-sin(6*pi*t); %n1hz +3 hz sinusoidals Lsig=length(xsig); Lfft=2^ceil(log2(Lsig)+1); Xsig=fftshift(fft(xsig,Lfft)); Fmax=1/(2*td); Faxis=linspace(-Fmax,Fmax,Lfft); ts=0.02; % new sampling rate =50 hz Nfact=ts/td; % send the signal through a 16-level uniform quantiser [s_out,sq_out,sqh_out1,Delta,SQRN]=sampandquant(xsig,16,td,ts); % obtaind the signal which is % - sampled,quantiser,and zero-order hold signal sqh_out % plot the original signal and PCM signal in time domain figrue(1); figure(1); subplot(211); sfig1=plot(t,xsig,'k',t,sqh_out1(1:Lsig),'b'); set(sfig1,'Linewidth',2); title('Signal {\it g}({{\it t}) and its 16 level PCM signal') xlabel('time(sec.)');

25

% send the signal through a 16-level unifrom quantiser [s_out,sq_out,sqh_out2,Delta,SQNR]=sampandquant(xsig,4,td,ts); % obtained the PCM signal which is % - sampled,quantiser,and zero_order hold signal sqh_out % plot the original signal and the PCM signal in time domain subplot(212); sfig2=plot(t,xsig,'k',t,sqh_out2(1:Lsig),'b'); set(sfig2,'Linewidth',2); title('Signal {\it g}({\it t}) and its 4 level PCM signal') xlabel('time(sec.)'); Lfft=2^ceil(log2(Lsig)+1); Fmax=1/(2*td); Faxis=linspace(-Fmax,Fmax,Lfft); SQH1=fftshift(fft(sqh_out1,Lfft)); SQH2=fftshift(fft(sqh_out2,Lfft)); % Now use LPF to filter the two PCM signal BW=10; %Bandwidth is no larger than 10Hz. H_lpf=zeros(1,Lfft);H_lpf(Lfft/2-BW:Lfft/2+BW-1)=1; %ideal LPF S1_recv=SQH1.*H_lpf; s_recv1=real(ifft(fftshift(S1_recv))); s_recv1=s_recv1(1:Lsig); S2_recv=SQH2.*H_lpf; s_recv2=real(ifft(fftshift(S2_recv))); s_recv2=s_recv2(1:Lsig); % plot the filtered signal against the original signal figure(2); subplot(211); sfig3=plot(t,xsig,'b-',t,s_recv1,'b-.'); legend('original','recovered') set(sfig3,'Linewidth',2); title('signal{\it g}({it t}) and filtered 16-level PCM signal') xlabel('time(sec.)'); subplot(212); sfig4=plot(t,xsig,'b-',t,s_recv2(1:Lsig),'b'); legend('original','recovered') set(sfig1,'Linewidth',2); title('signal{\it g}({it t}) and filtered 4-level PCM signal') xlabel('time(sec.)');

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Results:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1

0

1

2Signal {\it g}({{\it t}) and its 16 level PCM signal

time(sec.)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1

0

1

2Signal g( t) and its 4 level PCM signal

time(sec.)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1

0

1

2

time(sec.)

signal g(it t) and filtered 16-level PCM signal

original

recovered

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1

0

1

2

time(sec.)

signal g(it t) and filtered 4-level PCM signal

original

recovered

27

PRACTICAL NO 7 OBJECT Study of microwave components and instruments

THEORY Microwave Components:

Connecting Devices: – Waveguide

• Rectangular • Circular

– Microstrip line – Strip line

Junctions: – E plane – H plane – EH plane or magic tee (hybride line) – Hybride ring

Microwave Source: – Multicavity klystron – Reflex klystron – Magnetron – Travelling Wave Tube (TWT) – Crossed Field Amplifier (CFA) – Backward oscillator

Semiconductor Source: – Gunn Diode – IMPATT, IMPATT, TRAPATT – Tunnel Diode

Microwave Amplifier: – Multicavity klystron – Travelling Wave Tube (TWT) – Gunn Diode – Parametric Amplifier

Switches: – PIN Diode

Waveguides: A waveguide is a structure which guides waves, such as electromagnetic waves or sound waves. There are different types of waveguide for each type of wave. The original and most common meaning is a hollow conductive metal pipe used to carry high frequency radio waves, particularly microwaves. Waveguides differ in their geometry which can confine energy in one dimension such as in slab waveguides or two dimensions as in fiber or channel waveguides. In addition, different waveguides are needed to guide different frequencies: an optical fiber guiding light (high frequency) will not guide microwaves (which have a much lower frequency). As a rule of thumb, the width of a waveguide needs to be of the same order of magnitude as the wavelength of the guided wave.

Principal of operation: Waves in open space propagate in all directions, as spherical waves. In this way they lose their power proportionally to the square of the distance; that is, at a distance R from the source, the power is the source power divided by R

2. The waveguide confines the wave to propagation in one

dimension, so that (under ideal conditions) the wave loses no power while propagating. Waves are confined inside the waveguide due to total reflection from the waveguide wall, so that the propagation inside the waveguide can be described approximately as a "zigzag" between the walls. This description is exact for electromagnetic waves in a rectangular or circular hollow metal tube.

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Rectangular Waveguide: It consists of a rectangular hollow metallic conductor. The electromagnetic waves in (metal-pipe) waveguide may be imagined as travelling down the guide in a zig-zag path, being repeatedly reflected between opposite walls of the guide.

Need to find the fields components of the em wave inside the waveguide

– Ez Hz Ex Hx Ey Hy

We’ll find that waveguides don’t support TEM waves

Modes of propagation: TEM (Ez=Hz=0) can’t propagate.

TE (Ez=0) transverse electric – In TE mode, the electric lines of flux are perpendicular to the axis of the

waveguide – TM (Hz=0) transverse magnetic, Ez exists – In TM mode, the magnetic lines of flux are perpendicular to the axis of the

waveguide. – HE hybrid modes in which all components exists

The cutoff frequency occurs when: Dominant mode- T10

Circular waveguide: It consists of a circular hollow metallic conductor. For same cutoff frequency the cylindrical waveguide longer then rectangular waveguide in cross-sectional area so it is more bulky Dominant mode- T11

Microstrip Line: Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board [PCB] technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components such as antennas, couplers, filters, power dividers etc. can be formed

22

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2

1

2

1or

0then When

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n

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mf

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c

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from microstrip, the entire device existing as the pattern of metallization on the substrate. Microstrip is thus much less expensive than traditional waveguide technology, as well as being far lighter and more compact.

Cross-section of microstrip geometry, Conductor (A) is separated from ground

plane (D) by dielectric substrate (C). Upper dielectric (B) is typically air. The disadvantages of microstrip compared with waveguide are the generally lower power handling capacity, and higher losses. Also, unlike waveguide, microstrip is not enclosed, and is therefore susceptible to cross-talk and unintentional radiation It is behave as a parallel wire.

Strip line: A stripline circuit uses a flat strip of metal which is sandwiched between two parallel ground planes, The insulating material of the substrate forms a dielectric. The width of the strip, the thickness of the substrate and the relative permittivity of the substrate determine the characteristic impedance of the strip which is a transmission line. As shown in the diagram, the central conductor need not be equally spaced between the ground planes. In the general case, the dielectric material may be different above and below the central conductor To prevent the propagation of unwanted modes, the two ground planes must be shorted together. This is commonly achieved by a row of vias running parallel to the strip on each side. Like coaxial cable, strip line is non-dispersive, and has no cut off frequency. Good isolation between adjacent traces can be achieved more easily than with microstrip.

Cross-section diagram of strip line geometry. Central conductor (A) is sandwiched between

ground planes (B and D). Structure is supported by dielectric (C).

Waveguide Junction:

E-type waveguide junction:

It is called an E-type T junction because the junction arm, i.e. the top of the "T" extends from the

main waveguide in the same direction as the E field. It is characterized by the fact that the

outputs of this form of waveguide junction are 180° out of phase with each other.

Waveguide E-type junction

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The basic construction of the waveguide junction shows the three port waveguide device.

Although it may be assumed that the input is the single port and the two outputs are those on the

top section of the "T", actually any port can be used as the input, the other two being outputs.

To see how the waveguide junction operates, and how the 180° phase shift occurs, it is

necessary to look at the electric field. The magnetic field is omitted from the diagram for

simplicity.

Waveguide E-type junction E fields

It can be seen from the electric field that when it approaches the T junction itself, the electric field

lines become distorted and bend. They split so that the "positive" end of the line remains with the

top side of the right hand section in the diagram, but the "negative" end of the field lines remain

with the top side of the left hand section. In this way the signals appearing at either section of the

"T" are out of phase.

These phase relationships are preserved if signals enter from either of the other ports.

H-type waveguide junction:

This type of waveguide junction is called an H-type T junction because the long axis of the main

top of the "T" arm is parallel to the plane of the magnetic lines of force in the waveguide. It is

characterized by the fact that the two outputs from the top of the "T" section in the waveguide are

in phase with each other.

Waveguide H-type junction

To see how the waveguide junction operates, the diagram below shows the electric field lines.

Like the previous diagram, only the electric field lines are shown. The electric field lines are

shown using the traditional notation - a cross indicates a line coming out of the screen, whereas a

dot indicates an electric field line going into the screen.

Waveguide H-type junction electric fields

It can be seen from the diagram that the signals at all ports are in phase. Although it is easiest to

consider signals entering from the lower section of the "T", any port can actually be used - the

phase relationships are preserved whatever entry port is ised.

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Magic T hybrid waveguide junction:

The magic-T is a combination of the H-type and E-type T junctions. The most common

application of this type of junction is as the mixer section for microwave radar receivers.

Magic T waveguide junction

The diagram above depicts a simplified version of the Magic T waveguide junction with its four

ports.

To look at the operation of the Magic T waveguide junction, take the example of whan a signal is

applied into the "E plane" arm. It will divide into two out of phase components as it passes into the

leg consisting of the "a" and "b" arms. However no signal will enter the "E plane" arm as a result

of the fact that a zero potential exists there - this occurs because of the conditions needed to

create the signals in the "a" and "b" arms. In this way, when a signal is applied to the H plane

arm, no signal appears at the "E plane" arm and the two signals appearing at the "a" and "b"

arms are 180° out of phase with each other.

Magic T waveguide junction signal directions

When a signal enters the "a" or "b" arm of the magic t waveguide junction, then a signal appears

at the E and H plane ports but not at the other "b" or "a" arm as shown.

One of the disadvantages of the Magic-T waveguide junction are that reflections arise from the

impedance mismatches that naturally occur within it. These reflections not only give rise to power

loss, but at the voltage peak points they can give rise to arcing when sued with high power

transmitters. The reflections can be reduced by using matching techniques. Normally posts or

screws are used within the E-plane and H-plane ports. While these solutions improve the

impedance matches and hence the reflections, they still reduce the power handling capacity.

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Hybrid ring waveguide junction:

This form of waveguide junction overcomes the power limitation of the magic-T waveguide

junction.

A hybrid ring waveguide junction is a further development of the magic T. It is constructed from a

circular ring of rectangular waveguide - a bit like an annulus. The ports are then joined to the

annulus at the required points. Again, if signal enters one port, it does not appear at allt he others.

The hybrid ring is used primarily in high-power radar and communications systems where it acts

as a duplexer - allowing the same antenna to be used for transmit and receive functions.

During the transmit period, the hybrid ring waveguide junction couples microwave energy from

the transmitter to the antenna while blocking energy from the receiver input. Then as the receive

cycle starts, the hybrid ring waveguide junction couples energy from the antenna to the receiver.

During this period it prevents energy from reaching the transmitter.

Multicavity klystron: Gain of about 10-20 dB are typical with two cavity tubes. A higher overall gain can be achieved by connecting several two cavity tubes in cascade, feeding the output of each of the tubes to the input of the succeeding one. With four cavities, power gains of around 50 dB cab be easily achieved. The cavities are tuned the same frequency.

Reflex klystron:

In the reflex klystron (also known as a 'Sutton' klystron after its inventor), the electron beam passes through a single resonant cavity. The electrons are fired into one end of the tube by an electron gun. After passing through the resonant cavity they are reflected by a negatively charged reflector electrode for another pass through the cavity, where they are then collected. The electron beam is velocity modulated when it first passes through the cavity. The formation of electron bunches takes place in the drift space between the reflector and the cavity. Thevoltage on the reflector must be adjusted so that the bunching is at a maximum as the electron beam re-enters the resonant cavity, thus ensuring a maximum of energy is transferred from the electron beam to the RFoscillations in the cavity. The voltage should always be switched on before providing the input to the reflex klystron as the whole function of the reflex klystron would be destroyed if the supply is provided after the input. The reflector voltage may be varied slightly from the optimum value, which results in some loss of output power, but also in a variation in frequency. This effect is used to good advantage for automatic frequency control in receivers, and in frequency modulation for transmitters. The level of modulation applied for transmission is small enough that the power output essentially remains constant. At regions far from the optimum voltage, no oscillations are obtained at all. This tube is called a reflex klystron because it repels the input supply or performs the opposite function of a klystron.

33

Magnetron:

A cross-sectional diagram of a resonant cavity magnetron. Magnetic lines of force are parallel to

the geometric axis of this structure All cavity magnetrons consist of a hot cathode with a high (continuous or pulsed) negative potential by a high-voltage, direct-current power supply. The cathode is built into the center of an evacuated, lobed, circular chamber. A magnetic field parallel to the filament is imposed by a permanent magnet. The magnetic field causes the electrons, attracted to the (relatively) positive outer part of the chamber, to spiral outward in a circular path rather than moving directly to this a node. Spaced around the rim of the chamber are cylindrical cavities. The cavities are open along their length and connect the common cavity space. As electrons sweep past these openings, they induce a resonant, high-frequency radio field in the cavity, which in turn causes the electrons to bunch into groups. A portion of this field is extracted with a short antenna that is connected to a waveguide (a metal tube usually of rectangular cross section). The waveguide directs the extracted RF energy to the load, which may be a cooking chamber in a microwave oven or a high-gain antenna in the case of radar.

Travelling Wave Tube (TWT): A traveling-wave tube (TWT) is an electronic device used to amplify radio frequency signals to high power, usually in an electronic assembly known as a traveling-wave tube amplifier (TWTA).

Cutaway view of a TWT (1) Electron gun; (2) RF input; (3) Magnets; (4) Attenuator; (5) Helix coil;

(6) RF output; (7) Vacuum tube; (8) Collector.

Crossed Field Amplifier (CFA): A crossed-field amplifier (CFA) is a specialized vacuum tube, first introduced in the mid-1950s and frequently used as a microwave amplifier in very-high-power transmitters. A CFA has lower gain and bandwidth than other microwave amplifier tubes (such as klystrons or traveling-wave tubes); but it is more efficient and capable of much higher output power. Peak output powers of many megawatts and average power levels of tens of kilowatts can be achieved, with efficiency ratings in excess of 70 percent.

Backward oscillator: A backward wave oscillator (BWO), also called carcinotron (a trade name for tubes manufactured by CSF, now Thales) or backward wave tube, is a vacuum tubethat is used to generate microwaves up to the terahertz range. It belongs to the traveling-wave tube family. It is an oscillator with a wide electronic tuning range.

34

An electron gun generates an electron beam that is interacting with a slow-wave structure. It sustains the oscillations by propagating a traveling wave backwards against the beam. The generated electromagnetic wave power has its group velocity directed oppositely to the direction of motion of the electrons. The output power is coupled out near the electron gun. It has two main subtypes, the M-type, the most powerful, (M-BWO) and the O-type (O-BWO). The O-type delivers typically power in the range of 1 mW at 1000 GHz to 50 mW at 200 GHz. Carcinotrons are used as powerful and stable microwave sources. Due to the good quality wavefront they produce, they find use as illuminators in terahertz imaging.

Gunn Diode: A Gunn diode, also known as a transferred electron device (TED), is a form of diode used in high-frequency electronics. It is somewhat unusual in that it consists only of N-doped semiconductor material, whereas most diodes consist of both P and N-doped regions. In the Gunn diode, three regions exist: two of them are heavily N-doped on each terminal, with a thin layer of lightly doped material in between. When a voltage is applied to the device, the electrical gradient will be largest across the thin middle layer. Conduction will take place as in any conductive material with current being proportional to the applied voltage. Eventually, at higher field values, the conductive properties of the middle layer will be altered, increasing its resistivity and reducing the gradient across it, preventing further conduction and current actually starts to fall down. In practice, this means a Gunn diode has a region of negative differential resistance. The negative differential resistance, combined with the timing properties of the intermediate layer, allows construction of an RF relaxation oscillator simply by applying a suitable direct current through the device. In effect, the negative differential resistance created by the diode will negate the real and positive resistance of an actual load and thus create a "zero" resistance circuit which will sustain oscillations indefinitely. The oscillation frequency is determined partly by the properties of the thin middle layer, but can be tuned by external factors

IMPATT Diode : An IMPATT diode (IMPact ionization Avalanche Transit-Time) is a form of high power diode used in high-frequency electronics and microwave devices. They are typically made with silicon carbide owing to their high breakdown fields. They operate at frequencies between about 3 and 100 GHz or more. A main advantage is their high power capability. These diodes are used in a variety of applications from low power radar systems to alarms. A major drawback of using IMPATT diodes is the high level of phase noise they generate. This results from the statistical nature of the avalanche process. Nevertheless these diodes make excellent microwave generators for many applications.

Tunnel Diode: A tunnel diode or Esaki diode is a type of semiconductor diode which is capable of very fast operation, well into the microwave frequency region, by using quantum mechanical effects. It was invented in August 1957 by Leo Esaki when he was with Tokyo Tsushin Kogyo, now known as Sony. In 1973 he received the Nobel Prize in Physics, jointly with Brian Josephson, for discovering the electron tunneling effect used in these diodes. Robert Noyce independently came up with the idea of a tunnel diode while working for William Shockley, but was discouraged from pursuing it.

These diodes have a heavily doped p–n junction only some 10 nm (100 Å) wide. The heavy doping results in a broken bandgap, where conduction band electron states on the n-side are more or less aligned with valence band hole states on the p-side. Tunnel diodes were manufactured by Sony for the first time in 1957

followed by General

Electric and other companies from about 1960, and are still made in low volume today. Tunnel diodes are usually made from germanium, but can also be made in gallium arsenide and silicon materials. They can be used as oscillators, amplifiers, frequency

35

PIN Diode:

A PIN diode is a diode with a wide, lightly doped 'near' intrinsic semiconductor region between a p-type semiconductor and an n-type semiconductor region. The p-type and n-type regions are typically heavily doped because they are used for ohmic contacts. The wide intrinsic region is in contrast to an ordinary PN diode. The wide intrinsic region makes the PIN diode an inferior rectifier (the normal function of a diode), but it makes the PIN diode suitable for attenuators, fast switches, photodetectors, and high voltage power electronics applications.

Microwave instruments: Power Dividers/Combiners, Isolators/Circulators, Attenuators, Couplers, Terminations, Power Amplifiers, Hybrids, Oscillators, Switches,

Power Dividers/Combiners: Strip line Power Dividers and Combiners

Lumped Element Power Dividers and Combiners

Strip line Power Dividers and Combiners:

2-Way Power Divider and Combiner (SMA) (PS2 Series)

2-Way Power Divider and Combiner (Type-N) (PS2-

NF Series)

3-Way Power Divider and Combiner (SMA) (PS3 Series)

3-Way Power Divider and Combiner (Type-N) (PS3-

NF Series)

4 Way Power Divider and Combiner (SMA) (PS4 Series)

4-Way Power Divider and Combiner (Type-N) (PS4-

NF Series)

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5-Way Power Divider and Combiner (PS5 Series)

6-Way Power Divider and Combiner (PS6 Series)

8-Way Power Divider and Combiner (SMA) (PS8 Series)

8-Way Power Divider and Combiner (Type-N) (PS8-

NF Series)

9,11,12-Way Power Divider and Combiner (PS9, PS11, and

PS12 Series)

10-Way Power Divider and Combiner (PS10 Series)

16-Way Power Divider and Combiner (PS16 Series)

32-Way Power Divider and Combiner (PS32 Series)

37

Lumped Element Power Dividers and Combiners:

2-Way Lumped Element Power Divider and

Combiner (PL2 Series)

3-Way Lumped Element Power Divider and Combiner (PL3

Series)

4-Way Lumped Element Power Divider and

Combiner (PL4 Series)

5,6-Way Lumped Element Power Divider and Combiner (PL5

and PL6 Series)

8-Way Lumped Element Power Divider and

Combiner (PL8 and PM8 Series)

10,11,12,16-Way Lumped Element Power Divider and

Combiner (PL10, PL11, PL12, and PL16 Series)

Connectorized-Broadband - 2-port Isolator and 3-port

Circulator

Connectorized-Broadband Double Junction Isolator and

Circulator

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Connectorized-Narrow Band Isolators and Circulators

Attenuators:

Drop-In Isolator and Circulator (DI Series)

Continuously Variable Attenuator

Fixed Coaxial Attenuator

Pin-Diode Attenuator (Linearized Voltage Controlled)

Power Coaxial Attenuators

Directional Couplers:

Directional Coupler Broadband Model, SMA (CB Series)

Directional Coupler Octave Model-NF (C-NF Series)

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Directional Coupler Octave Model-SMA (C Series)

Dual Directional Coupler - Stripline (DC Series)

High Power Directional Coupler (HC Series)

High Power Dual Directional Coupler (HD Series)

High Power Dual Directional Coupler (HDL-Series)

Lumped Element Directional Coupler (CL Series)

Terminations:

Coaxial Terminations

Power Coaxial Terminations

40

Amplifiers:

Amplifiers

Hybrids:

180 Degree- 4 Port Hybrid - Lumped Element

180 Degree Hybrid Coupler - SMA

90 Degree Hybrid - 10 Bandwidth - Lumped Element

90 Degree Hybrid - Stripline

41

Oscillators:

Dielectric Resonator Oscillator (PLDR Series)

Free Run Dielectric Resonator Oscillator

Pin Diode Switches:

SP1T Octave and Broadband Pin Diode Switches

SP2T Octave and Broadband Pin Diode Switches

SP3T Octave and Broadband Pin Diode Switches

SP4T Octave and Broadband Pin Diode Switches

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SP5T Octave and Broadband Pin Diode Switches

SP6T Octave and Broadband Pin Diode Switches

Connectors and Adapters:

Connectors (MC Series)

Adapters (ADS- ADN-ADT-ADB-ADX-ADZ-ADC- and ADD Series)

Directional Detectors:

Directional Detectors (DD Series)

Filters:

Combline Bandpass Filter

Interdigital Bandpass Filter

43

PRACTICAL NO 8 OBJECT Measurement of klystron characteristics and Measurement of VSWR .

THEORY Measurement of klystron characteristics: Klystron: A Klystron is a vacuum tube that can be used either as a generator or as an amplifier of power at microwave frequencies.

Two Cavity Klystron:

Two Cavity Klystron Amplifier : A two cavity klystron amplifier is basically a velocity modulated tube. The electron beam, accelerated by a positive potential, is constrained to travel through a cylindrical drift tube in a straight path. While passing through the first cavity, the electron beam is velocity modulated by the weak RF signal. In the moving frame of the electron beam, the velocity modulation is equivalent to a plasma oscillation. Plasma oscillations are rapid oscillations of the electron density in conducting media such as plasmas or metals. So in a quarter of one period of the plasma frequency, the velocity modulation is converted to density modulation, i.e. bunches of electrons. As the bunched electrons enter the second chamber they induce standing waves at the same frequency as the input signal. The signal induced in the second chamber is much stronger than that in the first.

Performance Characteristics: – Frequency:250Mhz to 100GHz – Power: 10kw-500kw (CW), 30 MW (Pulsed) – Power gain: 15 dB to 70 dB (60 dB nominal ) – Bandwidth: 10 – 60 MHz-generally used in fixed frequency applications. – Noise Figure: 15-20dB – Theoretical efficiency: 58% (30-40 %)

Multicavity Klystron: Gain of about 10-20 dB are typical with two cavity tubes. A higher overall gain can be achieved by connecting several two cavity tubes in cascade, feeding the output of each of the tubes to the input of the succeeding one. With four cavities, power gains of around 50 dB cab be easily achieved. The cavities are tuned the same frequency.

44

Two Cavity Klystron Oscillator: A klystron amplifier can be converted into an oscillator be feeding back a part of the catcher output in to the buncher in proper phase.

Measurement of VSWR (voltage standing wave ratio): In telecommunications, standing wave ratio (SWR) is the ratio of the amplitude of a partial standing wave at an antinode (maximum) to the amplitude at an adjacentnode (minimum), in an electrical transmission line. The SWR is usually defined as a voltage ratio called the VSWR, for voltage standing wave ratio. For example, the VSWR value 1.2:1 denotes a maximum standing wave amplitude that is 1.2 times greater than the minimum standing wave value. It is also possible to define the SWR in terms of current, resulting in the ISWR, which has the same numerical value. The power standing wave ratio (PSWR) is defined as the square of the VSWR. SWR is used as a efficiency measure for transmission lines, electrical cables that conduct radio frequency signals, used for purposes such as connecting radio transmitters and receivers with their antennas, and distributing cable television signals. A problem with transmission lines is that impedance mismatches in the cable tend to reflect the radio waves back toward the source end of the cable, preventing all the power from reaching the destination end. SWR measures the relative size of these reflections. An ideal transmission line would have an SWR of 1:1, with all the power reaching the destination and no reflected power. An infinite SWR represents complete reflection, with all the power reflected back down the cable. SWR meters are available which can measure the SWR of a transmission line, and checking the SWR is a standard part of installing and maintaining transmission lines. The voltage component of a standing wave in a uniform transmission line consists of the forward

wave (with amplitude Vf) superimposed on the reflected wave (with amplitude Vr).

Reflections occur as a result of discontinuities, such as an imperfection in an otherwise uniform transmission line, or when a transmission line is terminated with other than its characteristic

impedance. The reflection coefficient Γ is defined thus:

Γ is a complex number that describes both the magnitude and the phase shift of the

reflection. The simplest cases, when the imaginary part of Γ is zero, are:

Γ = − 1: maximum negative reflection, when the line is short-circuited,

Γ = 0: no reflection, when the line is perfectly matched,

Γ = + 1: maximum positive reflection, when the line is open-circuited.

For the calculation of VSWR, only the magnitude of Γ, denoted by ρ, is of interest.

Therefore, we define

ρ = | Γ | . At some points along the line the two waves interfere constructively, and the resulting

amplitude Vmax is the sum of their amplitudes:

At other points, the waves interfere destructively, and the resulting

amplitude Vmin is the difference between their amplitudes:

The voltage standing wave ratio is then equal to:

As ρ, the magnitude of Γ, always falls in the range [0,1], the VSWR is

always ≥ +1. The SWR can also be defined as the ratio of the maximum amplitude

of the electric field strength to its minimum amplitude, i.e. Emax / Emin

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PRACTICAL NO 9 OBJECT Measurement of Directivity and coupling coefficient of a directional coupler

THEORY Directional coupler: One specific class of power divider is the directional coupler. This is a four port device that samples the power flowing into port 1 coupled in to port 3 (the coupled port) with the remainder of the power delivered to port 2 (the through port) and no power delivered to the isolated port.

Usually the isolated port is terminated within the coupler casing. In such case, the coupler appears to be a three port device. In ideal case no power is delivered to port 4 (the isolated port). Directional couplers are described by three specifications:

• Coupling (C) - The ratio of input power to the couple power. • Directivity (D)- The ratio of coupled power to the power at the isolated port. • Isolation (I) – The ratio of input power to power out of the isolated port.

Ideally Directivity should be infinite but is mostly between 30-35 dB If all ports matched (S11=S22=S33= S44=0), symmetry and S14=S23=0 to be satisfied

The equations reduce to 6 equations:

0*

3413

*

2412 SSSS

12412 SS

13413 SS 0*

3424

*

1312 SSSS

13424 SS By comparing these equations yield 2413 SS

By comparing these equations yield 3412 SS

00

0

00

00

0

3424

34

24

13

12

1312

SS

S

S

S

S

SS

S

Results:

S/N P1 P2 P3 P4 C D I

3

1log10P

PC

4

3log10P

PD

4

1log10P

PI dBCDI

11312 SS

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PRACTICAL NO 10 OBJECT To determination of the phase-shift of a phase shifter

THEORY Phase shifter: A phase shifter is a microwave network which provides a controllable phase shift of the RF signal. Phase shifters are used in phased arrays. Phase shifters are devices in which the phase of an electromagnetic wave of a given frequency propagating through a transmission line can be shifted. A phase shift circuit is designed to shift the phase of an input signal on the basis of the phase shift characteristics of the circuit and output the resultant signal.

A microwave (6 to 18 GHz) Phase Shifter and Frequency Translator

The theory of operation is to divide the input signal into two equal signals 90 degrees apart, I (in-phase) and Q (Quadrature). This allows the magnitude of each signal to be re-located along its vectors' axis. The two signals are then combined. Using The Pythagorean Theorem, the sum of the vectors produces the resultant output signal.

Digital phase shifter: The circuit for this digital phase shifter consists of a 3 dB, 90 degree Quadrature Hybrid, two Variable Attenuators capable of a 180 degree phase shift, an In-Phase Power Combiner and drive circuits to control the variable attenuators. The key component is a 3 dB, 90 degree, Quadrature Hybrid. The hybrid is used nine times. The input signal is processed by the first hybrid. It equally divides the amplitude with a 90 degree phase shift to the Quadrature path and the two signals are isolated. This places the I & Q Vectors on their respective axis. The balances of the hybrids are divided in the I & Q channels for the Variable Attenuators. Each attenuator controls the magnitude with 180 phase shift allowing four quadrant operations. The final stage is the In-Phase Power Combiner which combines the signals in vector addition to the output. In the RF design of a digital phase shifter the preferred media is microstrip. Traditional hybrids are designed in stripline. Whether incorporating the hybrid as part of the circuit or as a discrete component like hybrids for microstrip configurations, the result is, the microwave fields of propagation are excited. This creates a discontinuity within the transmission line of the device. Techniques can be employed to minimize the discontinuity; but with nine 4 port hybrids, this event occurs directly or in-directly 36 times. To this end, changing media alters fringing fields, thus creating adverse effects and degrading performance.

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Active versus passive: Active phase shifters provide gain, while passive phase shifters are lossy

Active:

– Applications: active electronically scanned array

– Gain: The phase shifter amplifies while phase shifting

– Noise figure (NF)

– Reciprocity: not reciprocal

Passive:

– Applications: passive electronically scanned array

– Loss: the phase shifter attenuates while phase shifting

– NF: NF = loss

– Reciprocity: reciprocal

Analog versus digital: Analog phase shifters provide a continuously variable phase shift or time delay

Digital phase shifters provide a discrete set of phase shifts or time delays. Discretization

leads to quantization errors. Digital phase shifters require parallel bus control.

Observation: Results:

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PRACTICAL NO 11 OBJECT Implementation of frequency shift keying modulator and demodulator using matlab/simulink.

THEORY FSK (frequency shift keying) modulator: Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave. The simplest FSK is binary FSK (BFSK). BFSK literally implies using a pair of discrete frequencies to transmit binary (0s and 1s) information.

Applications: Most early telephone-line modems used audio frequency-shift keying to send and receive data, up to rates of about 300 bits per second. Matlab Code: %*********FSK**************% clc; clear all; close all; s= [1 0 1 0]; f1=10; f2=50; a=length (s); for i=1:a if s(1,i)==1 freq=f1*s(1,i); for t= (i-1)*100+1:i*100 x(t)= sin(2*pi*freq*t/1000); end elseif s(1,i)==0 b=(2*s(1,i))+1; freq=f2*b; for t=(i-1)*100+1:i*100 x(t)= sin(2*pi*freq*t/1000); end end end plot(x); xlabel('title in secs'); ylabel('amplitude in volts') title ('FSK') grid on;

49

Results

0 50 100 150 200 250 300 350 400-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

title in secs

ampl

itude

in v

olts

FSK

50

PRACTICAL NO 12 OBJECT Implementation of phase shift keying modulator and demodulator using matlab/simulink

THEORY PSK (phase shift keying) modulator:

Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave).

Any digital modulation scheme uses a finite number of distinct signals to represent digital data. PSK uses a finite number of phases, each assigned a unique pattern of binary digits. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. This requires the receiver to be able to compare the phase of the received signal to a reference signal — such a system is termed coherent (and referred to as CPSK).

Alternatively, instead of using the bit patterns to set the phase of the wave, it can instead be used to change it by a specified amount. The demodulator then determines the changes in the phase of the received signal rather than the phase itself. Since this scheme depends on the difference between successive phases, it is termed differential phase-shift keying (DPSK). DPSK can be significantly simpler to implement than ordinary PSK since there is no need for the demodulator to have a copy of the reference signal to determine the exact phase of the received signal (it is a non-coherent scheme). In exchange, it produces more erroneous demodulations. The exact requirements of the particular scenario under consideration determine which scheme is used.

Matlab Code: Initializing Variables: The first step is to initialize variables for number of samples per symbol, number of symbols to simulate, alphabet size (M) and the signal to noise ratio. The last line seeds the random number generators. nSamp = 8; numSymb = 100; M = 4; SNR = 14; seed = [12345 54321]; rand('state', seed(1)); randn('state', seed(2));

51

Generating Random Information Symbols Next, use RANDSRC to generate random information symbols from 0 to M-1. Since the % simulation is of QPSK, the symbols are 0 through 3. The first 10 data points are plotted. numPlot = 10; rand('state', seed(1)); msg_orig = randsrc(numSymb, 1, 0:M-1); stem(0:numPlot-1, msg_orig(1:numPlot), 'bx'); xlabel('Time'); ylabel('Amplitude');

Phase Modulating the Data

Use MODEM.PSKMOD object to phase modulate the data and RECTPULSE to upsample to a sampling rate 8 times the carrier frequency. Use SCATTERPLOT to see the signal constellation.

grayencod = bitxor(0:M-1, floor((0:M-1)/2)); msg_gr_orig = grayencod(msg_orig+1); msg_tx = modulate(modem.pskmod(M), msg_gr_orig); msg_tx = rectpulse(msg_tx,nSamp); h1 = scatterplot(msg_tx);

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Creating the Noisy Signal Then use AWGN to add noise to the transmitted signal to create the noisy signal at the receiver. Use the 'measured' option to add noise that is 14 dB below the average signal power (SNR = 14 dB). Plot the constellation of the received signal. randn('state', seed(2)); msg_rx = awgn(msg_tx, SNR, 'measured', [], 'dB'); h2 = scatterplot(msg_rx);

Recovering Information from the Transmitted Signal Use INTDUMP to downsample to the original information rate. Then use MODEM.PSKDEMOD object to demodulate the signal, and detect the transmitted symbols. The detected symbols are

53

plotted in red stems with circles and the transmitted symbols are plotted in blue stems with x's. The blue stems of the transmitted signal are shadowed by the red stems of the received signal. Therefore, comparing the blue x's with the red circles indicates that the received signal is identical to the transmitted signal. close(h1(ishandle(h1)), h2(ishandle(h2))); msg_rx_down = intdump(msg_rx,nSamp); msg_gr_demod = demodulate(modem.pskdemod(M), msg_rx_down); [dummy graydecod] = sort(grayencod); graydecod = graydecod - 1; msg_demod = graydecod(msg_gr_demod+1)'; stem(0:numPlot-1, msg_orig(1:numPlot), 'bx'); hold on; stem(0:numPlot-1, msg_demod(1:numPlot), 'ro'); hold off; axis([ 0 numPlot -0.2 3.2]); xlabel('Time'); ylabel('Amplitude');