lmece 303and ece353 latest_new 1-1

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LABORATORY MANUAL

ECE 303 and ECE353

Unified Electronics Lab-III

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Sr

No.

Name of the Experiment Page

No.

MATLAB (DSP)

1. To develop program for linear convolution and correlation using MATLAB. 3

2. To develop a program for computing circular convolution Using MATLAB. 6

3. To develop a program for computing DFT and IDFT using MATLAB. 9

4. To develop a program for computing inverse Z-transform using MATLAB. 12

5. To develop a program for designing FIR Filter in MATLAB. 14

6. To develop a program for designing IIR Filters in MATLAB. 18

AFTER MTE (Communications)

7. To generate a FM Signal and measure Depth of modulation. 21

8. To obtain Amplitude modulated envelope and determine depth of modulation 24

9. To study envelope detector for demodulation of AM signal and observe diagonal peak clipping effect. 27

10. Design Hartley oscillator and determine lowest and highest frequency it can generate. 29

11. Design and observe waveforms of colpitts oscillator, compare its characteristics with Hartleyoscillator.

32

12. Design RC phase shift oscillator and determine lowest and highest frequency it can generate. 35

1. LINEAR CONVOLUTION AND CORRELATION

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AIM: To verify Linear Convolution.

EQUIPMENTS: Software -- MATLAB 7.5

Learning Objectives: To make the students familiar with concept of discrete convolution

and correlation with the use of MATLAB.

THEORY: Convolution is a formal mathematical operation, just as multiplication, addition, and

integration. Addition takes two numbers and produces a third number, while convolution takestwo signals and produces a third signal. Convolution is used in the mathematics of many fields,

such as probability and statistics. In linear systems, convolution is used to describe the

relationship between three signals of interest: the input signal, the impulse response, and theoutput signal.

In this equation, x1(k), x2(n-k) and y(n) represent the input to and output from the system

at time n. Here we could see that one of the input is shifted in time by a value every time it ismultiplied with the other input signal. Linear Convolution is quite often used as a method of

implementing filters of various types.

ALGORITHM:

1. Enter the input Sequence ,x having length=4

2. Enter the Impulse Sequence, h having length=43. Performing the Convolution, store the value in y

4. Plotting the Input Sequence.5. Plotting the Impulse Sequence.6. Plotting the Output Sequence.

PROGRAM:

%linear convolution program:clc;clear all;close all;

disp('linear convolution program');x=input('enter i/p x(n):');

m=length(x);

disp(m);h=input('enter i/p h(n):');n=length(h);

disp(n);x=[x,zeros(1,n)];

subplot(2,2,1), stem(x);title('i/p sequence x(n)is:');

xlabel('---->n');ylabel('---->x(n)');grid;

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h=[h,zeros(1,m)];subplot(2,2,2), stem(h);

title('i/p sequence h(n)is:');xlabel('---->n');ylabel('---->h(n)');grid;

disp('convolution of x(n) & h(n) is y(n):');y=zeros(1,m+n-1);

for i=1:m+n-1y(i)=0;

for j=1:m+n-1 if(j


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stem(z);

subplot(2,2,1),stem(x)

title(input sequence 1)subplot(2,2,2),stem(y)

title(input sequence 2)

subplot(2,2,3),stem(z)title(output sequence)

ALGORITHM:

1 Enter the input Sequence ,x having length=4

2 Enter the Impulse Sequence, y having length=4

3 Performing the Correlation, store the value in y4 Plotting the Output Sequence ,store in z.

RESULT:

1 2 3 40

1

2

3

4input sequence 1

1 2 3 40

2

4

6input sequence 2

0 2 4 6 80

10

20

30

40output sequence

2. CIRCULAR CONVOLUTION

AIM: To verify Circular Convolution.

EQUIPMENTS:

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Software - MATLAB 7.5

Learning Objectives: To make the students familiar with concept of circular convolutionwith the help of MATLAB.

THEORY:

Circular convolution is another way of finding the convolution sum of two input signals.It resembles the linear convolution, except that the sample values of one of the input signals isfolded and right shifted before the convolution sum is found. Also note that circular convolution

could also be found by taking the DFT of the two input signals and finding the product of the

two frequency domain signals. The Inverse DFT of the product would give the output of the

signal in the time domain which is the circular convolution output. The two input signals couldhave been of varying sample lengths. But we take the DFT of higher point, which ever signals

levels to. For eg. If one of the signal is of length 256 and the other spans 51 samples, then we

could only take 256 point DFT. So the output of IDFT would be containing 256 samples insteadof 306 samples, which follows N1+N2 1 where N1 & N2 are the lengths 256 and 51

respectively of the two inputs. Thus the output which should have been 306 samples long is

fitted into 256 samples. The 256 points end up being a distorted version of the correct signal.This process is called circular convolution.

PROGRAM:

%circular convolution program:clc;clear all;close all;

disp('circular convolution program');x=input('enter i/p sequence x(n):');a=length(x);

disp(a);h=input('enter i/p sequence h(n):');b=length(h);

disp(b);subplot(2,2,1), stem(x);

title('i/p sequence x(n)is:');xlabel('---->n');ylabel('---->x(n)');grid;

subplot(2,2,2), stem(h);title('i/p sequence h(n)is:');

xlabel('---->n');ylabel('---->h(n)');gridminor;

disp('circular convolution of x(n) & h(n) is y(n):');

if(a>b)n=a;

elsen=b;

end if(a-b~=0) if(a>b)

h=[h,zeros(1,a-b)];else

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x=[x,zeros(1,b-a)];end

enddisp(x);disp(h);

y=zeros(1,n); for i=1:n

y(i)=0;k=i;

for j=1:ny(i)=y(i)+(x(j)*h(k));if k==1

k=n+1; end

k=k-1; end end

subplot(2,2,[3,4]),stem(y);

title('circular convolution of x(n) & h(n) is:');xlabel('---->n');ylabel('---->y(n)');grid;

disp(y);

RESULT:

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3. DFT AND IDFT

AIM: To develop a program for Computing DFT and IDFT in MATLAB

REQUIREMENTS: MATLAB 7.5

Learning Objectives: To make the students familiar with concept of DFT and IDFT withthe use of MATLAB.

THEORY: The discrete Fourier transform (DFT) X[k] of a finite-length sequence x[n] can beeasily computed in MATLAB using the function fft. There are two versions of this function.

fft(x) computes the DFTX[k] of the sequencex[n] where the length ofX[k] is the same as that of

x[n]. fft(x,L) computes the L-point DFT of a sequence x[n] of length NwhereL N. IfL > N,x[n] is zero-padded with LN trailing zero-valued samples before the DFT is computed. The

inverse discrete Fourier transform (IDFT)x[n] of a DFT sequenceX[k] can likewise be computed

using the function ifft, which also has two versions.

ALGORITHM (For DFT):

1 Enter the input Sequence ,x having length=4

2 Set the range of k according to the length of x.3 Computing DFT, store the value in X(k).

4 Plotting the DFT of given Sequence,store in X(k).

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PROGRAM CODE:

% Program to perform Discrete Fourier Transform:clc;clear all;

close allhidden;x=input('The given i/p sequence is x(n): ');

subplot(2,2,[1,2]), stem(x);title('i/p sequencce x(n)is:');

xlabel('---->n');ylabel('---->x(n)');grid;

N=length(x);for k=1:N

X(k)=0; for n=1:N

X(k)=X(k)+x(n).*exp(-j.*2.*pi.*(n-1).*(k-1)./N);end

enddisp('The DFT of the i/p sequence x(n) is X(n):')

p=0:(N-1);subplot(2,2,[3,4]), stem(p,abs(X));

title('The DFT of the i/p sequence x(n) is X(n):');xlabel('---->n');ylabel('---->X(n)');grid;

disp(X);

Input Sequence:-

RESULT:

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0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

14

16

18

20

Fig shows DFT of input sequence

ALGORITHM (For IDFT):

1 Enter the input Sequence, x having length=4

2 Set the range of k according to the length of x.

3 Computing IDFT, store the value in X(k).4 Plotting the IDFT of given Sequence, store in X(k).

% Program to perform Inverse Discrete Fourier Transform:clc;clear all;close allhidden;

X=input('The given i/p sequence is X(n): ');

subplot(2,2,[1,2]), stem(X);title('i/p sequencce X(n)is:');

xlabel('---->n');ylabel('---->X(n)');grid;

N=length(X);for n=1:N

x(n)=0; for k=1:N

x(n)=x(n)+X(k).*exp(j.*2.*pi.*(n-1).*(k-1)./N);x(n)=x(n)./N;

end enddisp('The IDFT of the i/p sequence X(n) is x(n):')

p=0:(N-1);subplot(2,2,[3,4]), stem(p,abs(x));

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title('The IDFT of the i/p sequence X(n) is x(n):');xlabel('---->n');ylabel('---->x(n)');grid;

disp(x);

RESULT:

0 0.5 1 1.5 2 2.5 30

1

2

3

4

5

6

7

8

9

10

Fig shows IDFT of input sequence

4. INVERSE Z TRANSFORM

AIM: To develop a program for Computing Inverse Z-Transform

EQUIPMENTS: MATLAB 7.5

Learning Objectives: To make the students familiar with concept of inverse Z-transformwith the use of MATLAB.

THEORY:

Description: In mathematics and signal processing, the Z-transform converts a discretetime-domain signal, which is a sequence of real or complex numbers, into a complex frequency-

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domain representation. The Z-transform, like many other integral transforms, can be defined as

either a one-sided or two-sided transform.

The bilateral or two-sided Z-transform of a discrete-time signal x[n] is the function X(z)defined as

.

Alternatively, in cases where x[n] is defined only for n 0, the single-sided or unilateralZ-transform is defined as

In signal processing, this definition is used when the signal is causal.

Rational Z-transform to partial fraction form:

Consider the transfer function in the rational form i-e;18z3

G(z)= ------------------18z3+3z2-4z-1

We can evaluate the partial fraction form of the above system using matlab command. Thepartial fraction form be,

G(z)= 0.36__ + __0.24__ + _0.4____

1 0.5z-1 1+0.33 z-1 (1+0.33 z-1)Matlab command that converts rational z-transform in to partial fraction form is

residuez.

If you want to see the poles and zeros in a zplane. This function displays the poles and zerosof discrete-time systems. Use the under given matlab command

zplane(b,a)

ALGORITHM:

1. Write the poles and zeros of the input sequence.

2. Returned vector R contains the residues, Column vector contains P contains the pole

locations. And row vector contains the direct terms.Input Sequence:

PROGRAM CODE:

%program to perform Inverse Z-Transform

b=[1,0.4*sqrt(2)];

a=[1,-0.8*sqrt(2),0.64];

[R,P,C]=residuez(b,a);

R

P

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http://en.wikipedia.org/wiki/Signal_processinghttp://en.wikipedia.org/wiki/Causal_systemhttp://en.wikipedia.org/wiki/Causal_systemhttp://en.wikipedia.org/wiki/Causal_systemhttp://en.wikipedia.org/wiki/Signal_processing


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C

Zplane(b,a);

RESULT:

5. FIR FILTER.

AIM: To verify FIR filters.

EQUIPMENTS:Constructor MATLAB Software

Learning Objectives: To make the students familiar with designing concepts of FIR filterwith the use of MATLAB.

THEORY:A Finite Impulse Response (FIR) filter is a discrete linear time-invariant system whose

output is based on the weighted summation of a finite number of past inputs. An FIR transversal

filter structure can be obtained directly from the equation for discrete-time convolution.

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In this equation, x(k) and y(n) represent the input to and output from the filter at time n.

h(n-k) is the transversal filter coefficients at time n. These coefficients are generated by using

FDS (Filter Design Software or Digital filter design package).FIR filter is a finite impulse response filter. Order of the filter should be specified.

Infinite response is truncated to get finite impulse response. placing a window of finite lengthdoes this. Types of windows available are Rectangular, Barlett, Hamming, Hanning, Blackmann

window etc. This FIR filter is an all zero filter.

PROGRAM:

%fir filt design window techniques

clc;clearall;

close all;rp=input('enter passband ripple');

rs=input('enter the stopband ripple');

fp=input('enter passband freq');fs=input('enter stopband freq');

f=input('enter sampling freq ');

wp=2*fp/f;ws=2*fs/f;

num=-20*log10(sqrt(rp*rs))-13;

dem=14.6*(fs-fp)/f;

n=ceil(num/dem);n1=n+1;

if(rem(n,2)~=0)

n1=n;n=n-1;

end

c=input('enter your choice of window function 1. rectangular 2. triangular 3.kaiser: \n ' );if(c==1)

y=rectwin(n1);

disp('Rectangular window filter response');

end

if(c==2)y=triang(n1);

disp('Triangular window filter response');end

if(c==3)

y=kaiser(n1);disp('kaiser window filter response');

end

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%LPF

b=fir1(n,wp,y);

[h,o]=freqz(b,1,256);m=20*log10(abs(h));

subplot(2,2,1);plot(o/pi,m);

title('LPF');ylabel('Gain in dB-->');

xlabel('(a) Normalized frequency-->');

%HPFb=fir1(n,wp,'high',y);

[h,o]=freqz(b,1,256);

m=20*log10(abs(h));

subplot(2,2,2);plot(o/pi,m);title('HPF');

ylabel('Gain in dB-->');

xlabel('(b) Normalized frequency-->');

%BPFwn=[wp ws];

b=fir1(n,wn,y);[h,o]=freqz(b,1,256);

m=20*log10(abs(h));

subplot(2,2,3);plot(o/pi,m);

title('BPF');ylabel('Gain in dB-->');

xlabel('(c) Normalized frequency-->');

%BSFb=fir1(n,wn,'stop',y);

[h,o]=freqz(b,1,256);

m=20*log10(abs(h));subplot(2,2,4);plot(o/pi,m);

title('BSF');

ylabel('Gain in dB-->');xlabel('(d) Normalized frequency-->')

RESULTS:

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6. IIR FILTER.

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AIM: To design and implement IIR (LPF/HPF) filters.

EQUIPMENTS:

Software - MATLAB

Learning Objectives: To make the students familiar with designing concepts of FIR filterwith the use of MATLAB.

THEORY:

The IIR filter can realize both the poles and zeroes of a system because it has a rational

transfer function, described by polynomials in z in both the numerator and the denominator:

The difference equation for such a system is described by the following:

M and N are order of the two polynomials.

bk and ak are the filter coefficients. These filter coefficients are generated using FDS (FilterDesign software or Digital Filter design package).

IIR filters can be expanded as infinite impulse response filters. In designing IIR

filters, cutoff frequencies of the filters should be mentioned. The order of the filter

can be estimated using butter worth polynomial. Thats why the filters are named asbutter worth filters. Filter coefficients can be found and the response can be plotted.

PROGRAM:

% IIR filters LPF & HPF

clc;clearall;close all;disp('enter the IIR filter design specifications');

rp=input('enter the passband ripple');

rs=input('enter the stopband ripple');wp=input('enter the passband freq');

ws=input('enter the stopband freq');

fs=input('enter the sampling freq');

w1=2*wp/fs;w2=2*ws/fs;[n,wn]=buttord(w1,w2,rp,rs,'s');

c=input('enter choice of filter 1. LPF 2. HPF \n ');

if(c==1)disp('Frequency response of IIR LPF is:');

[b,a]=butter(n,wn,'low','s');

end

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if(c==2)

disp('Frequency response of IIR HPF is:');

[b,a]=butter(n,wn,'high','s');end

w=0:.01:pi;

[h,om]=freqs(b,a,w);m=20*log10(abs(h));

an=angle(h);

figure,subplot(2,1,1);plot(om/pi,m);title('magnitude response of IIR filter is:');

xlabel('(a) Normalized freq. -->');

ylabel('Gain in dB-->');

subplot(2,1,2);plot(om/pi,an);title('phase response of IIR filter is:');

xlabel('(b) Normalized freq. -->');

ylabel('Phase in radians-->');

RESULTS:

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Experiment -720 | P a g e


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1. AIM : To generate a FM Signal and measure Depth of modulation2. APPARATUS: IC LM 2206,10k, two 100k, three 4.7k, 220ohm resistor values,22F,1F, 10F, 0.01F capacitor values, CRO(20 Mhz), Function generator (1Mhz),connecting wires and probes.3. Learning Objectives: To implement the concept of Frequency modulation (already

taught).4. CIRCUIT DIAGRAM:

5. Procedure:I. Connect the circuit as per the given circuit diagram.II. Apply the modulating signal of 100HZ with 3Vp-p.III. Trace the modulated wave on the C.R.O & plot the same on graph.IV. Find the modulation index by measuring minimum and maximum frequency

deviations from the carrier frequency using the CRO.V. M = S/f = maximum Frequency deviation /modulating signal frequency

VI. Repeat the steps 3& 4 by changing the amplitude and /or frequency of themodulating Signal.

6. EXPECTED WAVEFORMS

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7. OBSERVATION TABLE

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Formula used: m f = / f mwhere = k Vm fcK is the proportionality constant

Experiment -8

AIM : To design and implement on a breadboard a circuit to perform Amplitude modulation.

APPARATUS: Two IC BC 107BP, 10k, 20kohm resistor, three 0.01F capacitor, CRO(20Mhz), Function generator(1Mhz), connecting wires and probes.

Circuit diagram:

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PROCEDURE:-1. Connect the circuit as per the given circuit diagram.2. Apply fixed frequency carrier signal to carrier input terminals.

3. Apply modulating signal from function generator of 0.8VP-P of 1KHz.

4. Note down and trace the modulated signal envelop on the CRO screen. 5. Find the modulation

index by measuring Vmax and Vmin from the modulated (detected/ traced) envelope.M=(Vmax Vmin)/(Vmax+Vmin)

6. Repeat the steps 3,4 & 5 by changing the frequency or/& amplitude of the modulating signalso as to observe over modulation, under modulating and perfect modulation.7. For demodulation, apply the modulated signal (A.M) as an input to the demodulator and verify

the demodulated output with respect to the applied modulating signals and their respective

outputs.

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Observed m= (Vmax + V min) / (V max V min )

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ERROR ANALYSIS: Calculate Modulation index using mathematical formula mc = Vm/Vc.

%AGE ERROR = ((m mc)/ mc)x100% RESULT:

Experiment -9

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1. AIM : To study envelop detector for demodulation of AM signal and observediagonal peak clipping effect.2. APPARATUS: diode (0A79), 100 K-ohm resistance, capacitor 2uF, CRO (20Mhz),Function generator(1Mhz),connecting wires and probes.3. Learning Objectives: Practically implement the concept of Amplitude demodulation

(already learnt).4. CIRCUIT DIAGRAM:

5. Procedure:I. Connect the circuit diagram as shown above.II. Feed the AM wave to the demodulator circuit and observe the output

III. Note down frequency and amplitude of the demodulated output waveform.IV. Draw the demodulated wave form .,m=1

6. Waveforms:

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Observation table:

Precautions:1. Check the connections before giving the power supply2. Observations should be done carefully.

Experiment-10

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1. Aim: Design Hartley oscillator and determine lowest and highest frequency it cangenerate.2. Apparatus: BF594, 56k,5.6k, 1k, 100ohm-resistors,330pf variablecapacitor(ganged), inductor coil,22uF, 0.1uFcapacitor, CRO(20 Mhz), connecting wiresand probes.

3. Learning Objectives: to implement the concept of oscillator designing in laboratory.

4. Theory: In the Hartley Oscillator the tuned LC circuit is connected between thecollector and the base of the transistor amplifier. As far as the oscillatory voltage isconcerned, the emitter is connected to a tapping point on the tuned circuit coil. Thefeedback of the tuned tank circuit is taken from the centre tap of the inductor coil oreven two separate coils in series which are in parallel with a variable capacitor, C asshown.

The Hartley circuit is often referred to as a split-inductance oscillator because coil L iscentre-tapped. In effect, inductance L acts like two separate coils in very close proximitywith the current flowing through coil section XY induces a signal into coil section YZbelow. An Hartley Oscillator circuit can be made from any configuration that uses either

a single tapped coil (similar to an autotransformer) or a pair of series connected coils inparallel with a single capacitor. In Hartley Oscillator circuit, the frequency of oscillation isgiven as.

Note: LT is the total cumulatively coupled inductance if two separate coils are usedincluding their mutual inductance, M.

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5. Circuit diagram

Procedure:I. Connect the circuit as shown in figure.II. Connect CRO at the output terminal.III. Observe the output of the oscillator on a CRO,IV. Note down the repetition period (T) of observed signal. Compute fo== 1/TV. Calculate the theoretical frequency of the circuit using the formulae.

Observation Table:

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Precautions:1. Connections must be done very carefully.2. Readings should be taken without parallax error.Result:The frequency of Hartley oscillator is practically observed.

Expeiment-111. Aim: Design and observe waveforms of colpitts oscillator, compare its

characteristics with Hartley oscillator.2. Apparatus: BF494, capacitor-0.1uF, 330pF,inductance-variable, resistor-56kohm,supply voltage, CRO.3. Learning Objectives: to implement the concept of oscillator designing in laboratory.4. Theory:

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The Colpitts Oscillator, named after its inventor Edwin Colpitts is another type of LCoscillator design. In many ways, the Colpitts oscillator is the exact opposite of theHartley Oscillator we looked at in the previous tutorial. Just like the Hartley oscillator,the tuned tank circuit consists of an LC resonance sub-circuit connected between the

collector and the base of a single stage transistor amplifier producing a sinusoidaloutput waveform.The basic configuration of the Colpitts Oscillator resembles that of theHartley Oscillatorbut the difference this time is that the centre tapping of the tank sub-circuit is now made at the junction of a "capacitive voltage divider" network instead of atapped autotransformer type inductor as in the Hartley oscillator.

Colpitts Oscillator Circuit

The Colpitts oscillator uses a capacitor voltage divider as its feedback source. The twocapacitors, C1 and C2 are placed across a common inductor, L as shown so that C1,C2 and L forms the tuned tank circuit the same as for the Hartley oscillator circuit. Theadvantage of this type of tank circuit configuration is that with less self and mutual

inductance in the tank circuit, frequency stability is improved along with a more simpledesign.As with the Hartley oscillator, the Colpitts oscillator uses a single stage bipolartransistor amplifier as the gain element which produces a sinusoidal output.

The frequency of oscillations for a Colpitts oscillator is determined by the resonantfrequency of the LC tank circuit and is given as:

where CT is the capacitance of C1 and C2 connected in series and is given as:.

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Circuit Diagram:

Procedure:I. Connect the circuit as shown in figure.II. Connect CRO at the output terminal.III. Observe the output of the oscillator on a CRO,

IV. Note down the repetition period (T) of observed signal. Compute fo== 1/TV. Calculate the theoretical frequency of the circuit using the formulae.

Observation Table:

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Precautions:1. Connections must be done very carefully.

2. Readings should be taken without parallax error.Result:The frequency of colpitts is practically observed and compare with frequency of Hartley oscillator.

Expeiment-121. Aim: Design RC phase shift oscillator and determine lowest and highest frequencyit can generate2. Apparatus:

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3. Learning Objectives: to implement the concept of oscillator designing in laboratory.4. Theory: In the RC phase shift oscillator, the combination RC provides self-bias for the ampli fier. The phase of the signal at the input gets reverse biased whenit is amplified by the amplifier. The output of amplifier goes to a feedback networkconsists of three identical RC sections. Each RC section provides a phase shift of60o . T h u s a t o t a l o f 1 8 0 ophase shift is provided by the feedback network.The output of this circuit is in the same phase as the input to the amplifier. The frequencyof oscillations is given by F=1/2 RC (6+4K)1/2 where, R1=R2=R3=R andC1= C2= C3=C and K= Rc/R.

5. Circuit diagram

Procedure:

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I. Connect the circuit as shown.I I. S wi tc h o n t he p ow er s up pl y.I II . Connect the CRO at the output of the circuit .IV. Adjust the RE to get undistorted waveform.V. Measure the Ampli tude and Frequency.

VI. Compare the theoretical and practical values.VII. Plot the graph amplitude versus frequency

Theoretical Values and Observation table:f = 1 / 2 RC 6+4K=1 / 2 (10K) (0.01F) 6+4(0.01)= 647.59Hz

Result: The frequency of RC Phase Shift Oscillator is determined.

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