Communication Systems Laboratory Manual

prepared by

Muhammad Tahir

Adeem Aslam

S. Irfan Shah

Sahar Idrees

Department of Electrical Engineering

University of Engineering and Technology Lahore

Copyright c© 2013 Department of Electrical Engineering, University of Engineering

and Technology Lahore, Pakistan.

Permission is granted to copy and distribute for educational purpose. However, any

commercial use of the material, in any form, is not allowed.

2

Contents

1 Exponential Fourier Series 4

2 Fourier Series using Matlab 8

3 Autocorrelation and Energy Spectral Density 13

4 Amplitude Modulation 18

5 Envelope Detection 20

6 Study the Basic Operation of Phase-Lock-Loop (PLL) 22

7 FM Modultion and Demodulation using PLL 28

8 Single Transistor FM Voice Transmitter 31

9 A Simple Sampler using 555 Timer 33

10 Pulse Width Modulation 37

11 Pulse Position Modulation 39

3

Experiment 1

Exponential Fourier Series

Objective

The objective of this experiment is to calculate and plot exponential Fourier series coefficients.

Background

In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum

of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or complex

exponentials). The study of Fourier series is a branch of Fourier analysis.

Using Eulers Equation, and a little trickery, we can convert the standard Rectangular Fourier

Series into an exponential form. Even though complex numbers are a little more complicated

to comprehend, we use this form for a number of reasons:

1. Only need to perform one integration

2. A single exponential can be manipulated more easily than a sum of sinusoids

3. It provides a logical transition into a further discussion of the Fourier Transform

Description

In this lab, you will perform the following tasks:

1. Evaluate the fourier series coefficients using

Dn =1

4e−jn

π4 sinc(n

π

4) (1.1)

Plot the magnitude | Dn | (in volts) and phase 6 Dn (in degrees) of the first twenty-one

coefficients n = −10,−9, ..., 10 versus frequency (in rad/sec).

2. Plot two periods of g(t) , directly i.e., by creating a vector of samples of g(t) and plotting

that vector.

3. Plot an approximation to g(t) using these first twenty-one terms of the exponential Fourier

series.

Make a function file sinc1.m using the following code listing.

Listing 1.1: Sinc function

1 f unc t i on y = s inc1 ( x ) % s i n c func t i on implementation

4

5

2 k = length ( x ) ;

3 f o r i = 1 : k

4 i f x ( i ) == 0

5 y ( i ) = 1 ;

6 e l s e

7 y ( i ) = s i n ( x ( i ) ) /x ( i ) ;

8 end

9 end

10 end

Magnitude and Phase of Fourier Series Coefficients

Write the following code in Matlab and run it. You will get the output shown in Figure 1.1(a)

& (b).

Listing 1.2: Magnitude and Phase Response

1 n = [ −10 : 10 ] ; % s e t s up the vec to r o f i n t e g e r i n d i c e s .

2 z = n∗( p i /4) ;

3 Dn = 0.25∗ exp(− i ∗z ) .∗ s i n c1 ( z ) ; % s inc1 ( ) i s de f i ned above .

4 magDn = abs (Dn) ; % magnitude o f Four i e r s e r i e s c o e f f i c i e n t s .

5 argDn = angle (Dn) ∗(180/ p i ) ; % phase o f Four i e r s e r i e s c o e f f i c i e n t s .

6 w = 0.5∗n ;

7 stem (w,magDn) , x l a b e l ( ’ Frequency in rad/ sec ( un i t s o f p i ) ’ )

8 g r id

9 t i t l e ( ’ Magnitude o f the Exponent ia l Four i e r S e r i e s C o e f f i c i e n t s ’ )

10 stem (w, argDn ) , x l a b e l ( ’ Frequency in rad/ sec ( un i t s o f p i ) ’ )

11 y l a b e l ( ’ degree s ’ )

12 g r id

13 t i t l e ( ’ Phase o f the Exponent ia l Four i e r S e r i e s C o e f f i c i e n t s ’ )

(a) (b)

Figure 1.1: Magnitude of the Exponential Fourier Series Coefficients

6 CHAPTER 1. EXPONENTIAL FOURIER SERIES

Sum of Fourier Series Coefficients:

The signal g(t) can be reconstructed by adding the Fourier coefficients. To verify this we find

the sum given by

g(t) ≈n=+10∑n=−10

Dnejnwt (1.2)

The following code in Listing 1.3 is used to find the sum in (1.2). The output is shown in

Figure 1.2.

Listing 1.3: Approximation of g(t)

1 n = [ −10 : 10 ] ;

2 z = n∗( p i /4) ;

3 Dn = 0.25∗ exp(− i ∗z ) .∗ s i n c1 ( z ) ; % symbol .∗ means element−by−element

m u l t i p l i c a t i o n

4 nwo = n∗( p i /2) ; % d e f i n e e l even f r e q u e n c i e s f o r sum

5 t = [ 0 : 0 . 0 1 : 8 ] ; % d e f i n e time sampling po in t s

6 BIG = nwo ’ ∗ t ; % c r e a t e b ig matrix to do matrix m u l t i p l i c a t i o n f o r sum

7 g = Dn ∗ exp ( i ∗BIG) ; % here ’ s where the sum i s done

8 p lo t ( t , r e a l ( g ) ) , gr id , x l a b e l ( ’ Seconds ’ )

9 t i t l e ( ’ Approximation to g ( t ) us ing the f i r s t ten components o f the Four i e r

s e r i e s ’ )

Figure 1.2: Approximation to g(t) using the first ten components of the Fourier Series

We can approximate g(t) using the first ten components of the Fourier series. The following

code is used to generate two periods of function g(t). It uses a custom made unit step function,

u(t), a copy of which is also provided below. The ability to use the unit step function to write

piecewise functions proves extremely effective. Below is code lisitng. You will get the output in

Figure 1.3.

7

Listing 1.4: g(t) using unit step

1 gt = (u( t ) − u( t−1) ) + (u( t−4) − u( t−5) ) + u( t−8) ;

2 p lo t ( t , gt )

3 gr id , x l a b e l ( ’ seconds ’ )

4 t i t l e ( ’The r e a l g ( t ) ’ )

5 a x i s ( [ 0 8 −0.2 1 . 2 ] ) ;

Listing 1.5: u(t) Implementation

1 f unc t i on [ y ] = u( x )

2 y=0.5+0.5∗ s i gn ( x ) ;

3 end

Figure 1.3: The “real” g(t)

Experiment 2

Fourier Series using Matlab

Objective

The purpose of this lab experiment is to:

1. use Matlab functions FFT and FFTSHIFT to find Fourier series of a periodic signal.

2. compare the Matlab results with theoretical formula. In this lab we will take the following

example signal.

Dn =

j(−1)n(nπ) n 6= 0

0 n = 0.

Background

In mathematics, the discrete Fourier transform (DFT) is a specific kind of discrete transform,

used in Fourier analysis. It transforms one function into another, which is called the frequency

domain representation of the original function (which is often a function in the time domain).

The DFT requires an input function that is discrete. Such inputs are often created by

sampling a continuous function, such as a person’s voice. The discrete input function must

also have a limited (finite) duration, such as one period of a periodic sequence or a windowed

segment of a longer sequence.

Discrete Fourier Transform(DFT) decomposes a sequence of values into components of dif-

ferent frequencies. This operation is useful in many fields but computing it directly from the

definition is often too slow to be practical. An FFT is a way to compute the same result

more quickly, computing a DFT of N points using the definition, takes O(N2) arithmetical

operations, while an FFT can compute the same result in only O(N logN) operations.

The difference in speed can be substantial, especially for long data sets where N may be

in the thousands, the computation time can be reduced by several orders of magnitude in such

cases. This huge improvement made many DFT-based algorithms practical. FFTs are of great

importance to a wide variety of applications, from digital signal processing and solving partial

differential equations to algorithms for quick multiplication of large integers.

In particular, the DFT is widely employed in signal processing and related fields to analyze

the frequencies contained in a sampled signal, to solve partial differential equations, and to

perform other operations such as convolutions or multiplying large integers. A key enabling

factor for these applications is the fact that the DFT can be computed efficiently in practice

using a fast Fourier transform (FFT) algorithm.

8

9

Description

Plotting the Signal

This is the code segment for ploting the signal g(t). Vector g contains samples of function

g(t), which is formed by concatenating three individual vectors g1, g2 and g3. The result in

Figure 2.1 shows the plot of g(t) signal.

Listing 2.1: Plotting signal g(t)

1 g1 = [0 :1/32 :1 − (1/32) ] ;

2 g2 = [−1:1/32:1−(1/32) ] ;

3 g3 = [−1:1/32:0−(1/32) ] ;

4 g = [ g1 , g2 , g3 ] ;

5 t = [−1:1/64:1−(1/64) ] ;

6 p lo t ( t , g ) ;

7 a x i s ( [−1.5 1 .5 −1.5 1 . 5 ] )

8 g r id

Figure 2.1: Plot for the signal g(t).

Discrete Fourier Series using FFT

Using the following code we get the Fourier series coefficients.

Listing 2.2: FFT of g(t)

1 z = f f t ( g ) ;

2 stem ( t , z ) ;

10 CHAPTER 2. FOURIER SERIES USING MATLAB

If we plot this calculated fft what we get is an arrangement of those total 128 coefficients one

by one i.e. they are not arranged as a normal Fourier series spectrum. FFTSHIFT command

helps us to reach there. We will get a plot using FFTSHIFT command such that DC component

is at the centre, and plot gets the shape of a normal Fourier series plot.

Listing 2.3: Shifted version of FFT of g(t)

1 z1 = f f t s h i f t ( z ) ;

2 n = [ 1 : 1 : 1 2 8 ] ;

3 a = n−65;

4 f = 0 .5∗ a ;

5 stem ( f , abs ( z1 ) )

Figure 2.2: Plot using the Matlab function ’FFTSHIFT’.

The above approach uses the Matlab commands FFT and FFTSHIFT. Now by directly

using the formula we can also obtain the plot with the help of following code segment.

Listing 2.4: Finding spectrum of g(t)

1 m = 128 ;

2 a = 1 ;

3 f o r n = −m/ 2 : 1 :m/2−1

4 i f n == 0

5 Dn( a ) = 0 ;

6 e l s e

7 $Dn=( i ∗((−1) . ˆ n) ) /(n∗ pi ) ; $

8 end

11

9 a = a+1;

10 end

11 n = −m/2 :m/2−1;

12 stem (n , abs (Dn) )

Magnitude and phase of Dn can also be obtained as follows.

Listing 2.5: Magnitude and Phase of g(t)

1 magDn = abs (Dn) ;

2 argDn = angle (Dn) ;

3 stem ( f ,magDn) ;

4 stem ( f , argDn ) ;

Comments

1. FFT function plot the fourier series but with the DC component.

2. FFTSHIFT shifts the DC component to the center of spectrum.

3. Magnitude of the fourier series is plotted against frequency to remove the complex part

from the fourier series.

Assignment

Given the signal in Figure 2.3:

1. Plot the signal in MATLAB for two time periods.

2. Find its Fourier series and plot it. The plot should have DC component at the centre.

12 CHAPTER 2. FOURIER SERIES USING MATLAB

Figure 2.3: Example plot for the assignment.

Experiment 3

Autocorrelation and Energy Spectral

Density

Objective

The objective of this experiment is to verify that Energy Spectral Density(ESD) of a periodic

signal is equal to the Fourier Transform of Autocorrelation of the signal using Matlab.

Background

The correlation of a signal with itself is called the Autocorrelation. The Autocorrelation Ψ(τ)

of a real signal g(t) is defined as

Ψg(τ) =

∫ ∞−∞

(g(t)g(t+ τ)) dτ) (3.1)

It measures the similarity of a signal with itself. The Autocorrealtion provides valuable spectral

information which is helpful in analyzing the spectral energy density. The Energy Spectral

Density (ESD) is result of energies contributed by all the spectral components of the signal g(t)

i.e.

Ψg(f) = |G(f)2| (3.2)

An important relationship between the Autocorrelation of a signal g(t) and Energy Spectral

Density Ψg(τ) exist that is the Energy Spectral Density(ESD) of a periodic signal is equal to

the Fourier Transform of Autocorrelation of the signal i.e.

Ψg(f) = Ψg(τ) (3.3)

Description

Consider the following Figure 3.1 of signal x(n) which shows a discrete time rectangular signal

with length N=5.

The magnitude of the Fourier Transform of this signal is given below

X(w) =sin wN

2

sin w2

(3.4)

Plot the discrete time domain signal x(n) in Matlab using the following piece of code.

13

14 CHAPTER 3. AUTOCORRELATION AND ENERGY SPECTRAL DENSITY

Listing 3.1: Plot of the Signal x(n)

1 n=[−2:2 ] ;

2 x=[1 1 1 1 1 ] ;

3 stem (n , x ) ;

4 a x i s ([−5 5 0 2 ] )

5 t i t l e ( ’ D i s c r e t e Time Domain S igna l ’ )

The output graph produced should be similar to one in Figure 3.1. Using the signal x[n],

−5 −4 −3 −2 −1 0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2Discrete Time Domain Signal

Figure 3.1: Signal x(n)

find out the Autocorrelation y[n] of the signal by using the Matlab function xcorr(x,x). An im-

portant point to observe here is that the first sampling instant of Autocorrelation function y[n]

should be twice the first sampling instant of the signal x[n] itself. Same is true for the all the

points of the Autocorrelation function y[n] . Therefore, for writing the code for Autocorrelation

function y[n] we need to genrate the a timing vector twice that of the signal x[n] itself.

Listing 3.2: Plot of the Autocorrelation Function y(n)

1 n =[ −2 :1 : 2 ] ;

2 x = [ 1 , 1 , 1 , 1 , 1 ] ;

3 y=xcorr (x , x ) ;

4 ny =[ −4 :1 :4 ] ;

5 stem (ny , y )

6 a x i s ([−5 5 0 6 ] )

7 t i t l e ( ’ Autoco r r e l a t i on Function y [ n ] ’ )

The Autocorrelation function y[n] should be similar to the Figure 3.2. In order to plot the

Fourier Transform F [n] of the Autocorrelation function y[n] the following piece of code is used.

15

−5 −4 −3 −2 −1 0 1 2 3 4 50

1

2

3

4

5

6Autocorrelation Function y[n]

Figure 3.2: Autocorrelation y(n) of signal x(n)

Listing 3.3: Plot for the Fourier Transform F(n) of the Autocorrelation Function y(n)

1 M=20;

2 k=−M/2:M/2 ;

3 w=(2∗ pi /M) ∗k ;

4 Y=y∗( exp(−2∗ i ∗ pi /M) ) . ˆ ( ny ’∗ k ) ;

5 stem (w,Y)

6 a x i s ([−4 4 0 3 0 ] )

After plotting the Fourier Transform F [n] of the Autocorrelation Function y[n], find out

the Energy Spectral Density E[n] of the signal x[n] using its Fourier Transform. The Energy

Spectral Density E[n] of a signal is the magnitude square of its Fourier Transform. The following

piece of code finds out the Energy Spectral Density E[n].

Listing 3.4: Plot for Energy Spectral Density E(n) of the signal x(n)

1 N=5;

2 M=20;

3 i =1;

4 f o r k=−M/2:M/2

5 w=(2∗ pi /M) ∗k ;

6 i f k==0

7 $ X( i )=N; $8 e l s e

9 $X( i )=s i n (w∗N/2) / s i n (w/2) ; $10 end

11 i=i +1;

12 end

13 ESD=(abs (X) ) . ˆ 2 ;

14 w=(2∗ pi /M) ∗[−M/2:M/ 2 ] ;

15 stem (w,ESD)

16 CHAPTER 3. AUTOCORRELATION AND ENERGY SPECTRAL DENSITY

−4 −3 −2 −1 0 1 2 3 40

5

10

15

20

25

30

Figure 3.3: Fourier Transform F [n] of the Autocorrelation Function y[n]

16 a x i s ([−4 4 0 3 0 ] )

17 t i t l e ( ’ESD o f Actual S i gna l ’ )

Figure 3.3 representing the Fourier Transform F [n] of the Autocorrelation Function y[n]

and Energy Spectral Density E[n] of the signal x[n] represented by Figure 3.4 are similar to

each other thus showing that the Energy Spectral Density(ESD) of a periodic signal is equal

to the Fourier Transform of Autocorrelation of the signal. Plot all the figures on the same

window using the subplot command for the ease of comparison. Vary the period and range of

the sampling points separately to observe their effects in Matlab.

Listing 3.5: Plot for both the figures on the same window

1 n =[ −2 :1 : 2 ] ;

2 x = [ 1 , 1 , 1 , 1 , 1 ] ;

3 f i g u r e (1 ) ;

4 stem (n , x )

5 a x i s ([−3 3 0 1 . 5 ] ) ;

6 t i t l e ( ’ Gate Function ’ ) ;

7 y=xcorr (x , x ) ;

8 ny =[ −4 :1 :4 ] ;

9 f i g u r e (2 ) ;

10 stem (ny , y )

11 a x i s ([−5 5 0 6 ] ) ;

12 t i t l e ( ’ Auto Cor r e l a t i on ’ ) ;

13 M=20;

14 k=−M/2:M/2 ;

15 w=(2∗ pi /M) ∗k ;

16 Y=y∗( exp(−2∗ j ∗ pi /M) ) . ˆ ( ny ’∗ k ) ;

17 f i g u r e (3 ) ;

17

−4 −3 −2 −1 0 1 2 3 40

5

10

15

20

25

30ESD of Actual Signal

Figure 3.4: Energy Spectral Density E[n] of the signal x[n]

18 stem (w,Y)

19 t i t l e ( ’ Energy Spec t r a l Density ’ ) ;

Assignment

Experiment 4

Amplitude Modulation

Objective

The objective of this experiment is to build a simple unbalanced Amplitude Modulator.

Background

Read Sections 4.2 and 4.3 of the text [Lathi(1998)] for theory background of the experiment.

Description

Before you build the circuit you need to make an inductor of approximately 22uH. The Appendix

at the end of this handout can be used as a guide to design your inductor. Build the circuit

in Figure 4.1 to implement an unbalanced Amplitude Modulator. In the circuit shown, V1 and

V2 are two sinusoidal sources for generating the message and carrier signals respectively. The

R1-V1-V2 network adds the carrier and message signal. The diode D1 is the nonlinear device

used to achieve modulation, while the network C1-L1-R4 is the band-pass (BP) filter. The

inductor developed will not have exactly the same inductance for which it is designed and hence

the resonant frequency of the BP filter will be different. Change the frequency of V2 source

and find out at what frequency the signal is maximum across the BP filter. This will be the

resonant frequency of the BP filter.

Note that the resistor R4 is not required in the actual hardware implementation. It was

used in the simulation to control the resistance of the inductor. You should be able to realize

that changing R4 affects the Q-factor of the band-pass filter.

Appendix: Designing an Inductor

The classic equation for calculating the inductance of a given single layer coil is [Murray(1967)]:

L =r2n2

9r + 10l(4.1)

In (4.1),

L is inductance in micro-Henry,

r is coil radius in inches (center of coil to center of conductor),

n is number of turns,

l is coil length in inches (center of starting turn to center of ending turn).

18

19

C1

.03µL122µ

R120k

R2

10k

R3

10k

D1

1N4148

R4.001k

V1

SINE(0 .7 1K)

V2

SINE(0 3 200K)

.tran 0 1s 0

--- D:\Tahir\UET\Teaching\BSc_Courses\EE354_Communication Systems\Labs_EE354\Lab4\AM_Mod.asc --- Figure 4.1: The unbalanced AM modulator.

This equation is generally accurate to around one percent for inductors of common dimen-

sions. It is more convenient to work with coil diameter and (4.1) can be written as:

L =d2n2

18r + 40l(4.2)

Experiment 5

Envelope Detection

Objective

To demonstrate envelope detection of AM signals.

Background

In an envelope detector, the output of the detector follows the envelope of the modulated signal.

The simple circuit shown in figure functions as an envelope detector. On the positive cycle of

the input signal, the input grows and may exceed the charged voltage on the capacity, turning

on the diode and the capacitor C to charge up the peak voltage of the input signal cycle. As

the input falls below this peak value, it falls quickly below the capacitor voltage(which is nearly

the peak voltage),thus causing the diode to open. The capacitor now discharges through the

resistor R at a slow rate(with a time constant RC ). During the next positive cycle,the same

drama repeats. As the input signal rises above the capacitor voltage,the diode conducts again.

The capacitor again charges to the peak value of this (new)cycle. The capacitor discharges

slowly during the cutoff period.

During each positive cycle,the capacitor charges up to the peak voltage of the input signal and

then decays slowly until the next positive cycle. Thus,the output voltage closely follows the

(rising)envelope of the input AM signal. Further knowledge about envelope detectors can be

found from topic 4.3 of the text book.

Figure 5.1: AM demodulation circuit.

20

21

Figure 5.2: Envelop detection of AM signal.

Description

1. Generate AM signal (D1,R1,R2,C1,L1) with modulation index less than 1 i.e. µ < 1.

2. Build the envelope detector (D2,C2,R3) as shown in figure 1 below.

3. Display the demodulated output of the envelope detector on the oscilloscope.

4. Compare the message signal to the demodulated signal on the oscilloscope.

5. Draw the message, modulated and the demodulated signal on the next page.

6. Investigate the effect of variation of varying the message frequency and modulation index.

Assignment

Suppose that we have a Single Side Band Signal with a Carrier (SSB+C) of the form

φ = Acoswt+ [m(t)coswt+mh(t)sinwt]

Show that the envelope of such a signal is given by e(t)=A+m(t).

Experiment 6

Study the Basic Operation of Phase-

Lock-Loop (PLL)

Objective

The ojective of this experiment is to understand the basic working principle of PLL.1

Description

1. Set the values of C1=0.03uF,R1=R2=18K Ω.

2. Find out the fmin and fmax of the VCO. To find fmin simply connect the VCO input (pin

9) to ground and to find fmax connect pin 9 to VDD.

3. Find out the free-running frequency fo of the VCO.This is the frequency of the output

signal when input is not applied to phase detector.

4. Apply an incoming signal Vi from the signal generator. Adjust its frequency to approx-

imately match the free-running frequency f0 of the VCO. When Vi is applied, the PLL

should operate in the locked condition,with fo exactly equal to fi.The locked condition

can be easily verified by observing Vi and Vosc simultaneously on a dual-trace oscillo-

scope.If fi=fosc,stable waveforms of both Vi and Vosc can be observed.Otherwise, one of

the waveforms on the scope screen is blurred or is moving with respect to the other.

5. By changing the frequency of the incoming signal,determine the actual lock range of the

PLL,i,e., determine the maximum and the minimum frequency fi such that starting from

the locked condition the PLL remains in the locked condition.The lock range should be

equal to fmax-fmin.

6. Record the readings for the lock range and the capture range below. fmin = ............

fmax = ............

fcap1=fo-fc = ............

fcap2=f0+fc = ............

Lock range=fmax-fmin = ..............

Capture range=fcap2-fcap1 = ............

1Refer to Appendix to understand the theory and the working principle of PLL

22

23

Appendix: Phase-Locked Loop

Phase-Locked Loop is a device which is used to track the phase and frequency of an incoming

signal.it uses a voltage-controlled oscillator(VCO),the output of which can be automaically syn-

chronized (”locked”) to a periodic input signal.The locking property of the PLL has numerous

applications in communication systems(such as frequency,amplitude,or phase modulation/de-

modulation,analog or digital),clock and data recovery ,self-tunable filters,frequency synthesis

etc.

Following figure represents the block diagram of PLL showing its basic function connected

together in a feedback loop.

Figure 6.1: Block diagram of a Phase-Locked(PLL)

• Voltage-Controlled oscillator(VCO)

• Phase detector(PD)

• Low-pass loop filter(LPF)

VCO is an oscillator of the frequency of which fosc is proportional to input voltage Vo .The

input voltage to VCO determines the frequency fosc of the periodic signal Vosc at the output of

the VCO. //Phase comparator is device that compares the phase of the output signal of VCO

and the incoming signal and produces a signal proportional to the phase diference between

the incoming signal and the VCO output signal.The output of the phase detector is filtered

by a low-pass loop filter.The loop is closed by connecting the filter output to the input of the

VCO.When the loop is locked on the incoming signal Vi,the frequency of the VCO output foscis

exactly equal to the frequency fi of the periodic signal Vi

fosc = fi

The basic function of PLL is to maintain the frequency lock(fosc=fi) between the input and the

output signals even if the frequency fi of the incoming signal varies with time.Assuming that

the PLL is in the locked condition and then if the frequency fi of the incoming signal increases

slightly , the phase difference between the VCO signal and the incoming signal will begin to

increase in time.As a result,the filter output voltage Vo increases, and the VCO output frequency

fosc increases until it matches fi,thus keeping the PLL in the locked condition. //The range

of frequencies from fi=fmin to fi=fmax where the locked PLL remains in the locked condition

24 CHAPTER 6. STUDY THE BASIC OPERATION OF PHASE-LOCK-LOOP (PLL)

is called the lock range the PLL.If the PLL is intially locked,and fi becomes smaller than

the fmin,or if fi exceeds fmax,the PLL fails to keep fosc equal to fi,and the PLL becomes

unlocked ,i.e. fosc !=fi.When the PLL is unlocked ,the VCO oscillates at the frequency fo

called the subtitle center frequency ,or the free-running frequency of the VCO .The lock can

be established again if the incoming singal frequency fi gets closed enough to fo.The range of

frequencies fi=fo-fc to fi=fo+fc such that the initially unlocked PLL becomes locked is called

the capture range of the PLL. The lock range is wider than the capture range.So,if the VCO

output frequency fosc is plotted against the incoming frequency fi,we obtain the PLL steady-

state characteristics shown in Fig 2. The characteristics simply shows that fosc=fi in the locked

condition,and that fosc=fo=constant when the PLL is unlocked. A hysteresis can be observed

in the fosc(fi) characteristic because the capture range is smaller than the lock range.

Figure 6.2: steady-state characteristics of the basic PLL

The 4046 Phase-Locked Loop IC

A diagram of the 4046 PLL is shown in Fig 3. A single positive supply voltage is needed for

the chip .The positive supply voltage VDD is connected to pin 16 and the ground is connected

to pin 8.In the lab we will use +VDD=+15V.The incoming signal Vi goes to the input of an

internal amplifier at the pin 14 of the chip.The internal amplifier has the input biased at about

+VDD/2.Therefore ,the incoming signal can be capacitively coupled to the input

as shown in Fig 3.The incoming ac signal Vi of about one volt peak-to-peak is sufficient for

proper operation.The output Vi2 of the amplifier is internally connected to one of the inputs of

the phase detector on the chip.

Phase Detector

The phase detector on the 4046 is simply an XOR logic gate,with logic low output (Vφ=0V)

when the two inputs are both high or low,and the logic high output Vφ=VDD)otherwise.Following

figure shows the operation of the XOR phase detector when the PLL is in the locked condition.

Vi2 and Vosc are two phase-shifted periodic square-wave signals at the same frequency

fosc = fi and with 50 percent duty cycle .The output of the phase detector is a periodic square-

25

Figure 6.3: Cmos 4046 PLL

Figure 6.4: Operation of the phase detector with XOR gate

wave signal Vφ(t) at the frequency 2fi,and with the duty ratio Dφ that depends on the phase

difference between Vi and Vosc.

VDD =φ

π(6.1)

The periodic signal Vφ(t) at the output of the XOR phase detector can be written as the Fourier

series:

Vφ(t) = Vo +∑k=1

Vksin((4kπfi)t− θk) (6.2)

where Vo is the dc component of Vφ(t),and Vk is the amplitude of the kth harmonic at the

frequency 2kfi.The dc component of the phase detector output can be found easily as the

average of Vφ(t)over a period TI=2

Vo =VDDΦ

π(6.3)

26 CHAPTER 6. STUDY THE BASIC OPERATION OF PHASE-LOCK-LOOP (PLL)

Loop filter

The output Vφ(t) of the phase detector is filtered by an external low-pass filter.In Fig3,the

loop filter is a simple passive RC filter.The purpose of the low-pass filter is to pass the dc and

low-frequency portions of Vφ(t) and to attenuate high-frequency ac component at frequencies

2kfi.The simple RC filter has the cut-off frequency:

fp =1

2πRC(6.4)

The cut-off frequency should be smaller than the input frequency for the output of the filter to

be approximately equal to Vo.Vo is proportional to the phase difference between the incoming

signal Vi and the signal Vosc from the VCO and the constant of proportionality ,

KD =VDDpi

(6.5)

is called the gain or the sensivity of the phase detector .This expression is valid for 0≤ φ ≤ π

.The filter output VO as a function of the phase differenceφ is shown in Fig 5.Note that Vo if

Vi and Vosc are in phase (φ=0),and that it reaches the maximum value Vo=VDD when the two

signals are exactly out of phase(φ=π).From fig4 it is easy to see that for φ <0,V0 increases and

for φ > π,V0 decreases.Of course ,the characteristic is periodic in φ with period 2π.The range

0 ≤ φ ≤ π is the range where the PLL can operate in the locked condition.

Figure 6.5: Characteristics of the phase detector

Voltage Controlled Oscillator

The voltage VO controls the charging and discharging currents through an external capacitor

C1,and therefore determines the time needed to charge (discharge) the capacitor to a pre-

determined threshold level.As a result ,the frequency fosc of the VCO output is determined by

VO.The VCO output Vosc is a square wave with 50percent duty cycle and frequency fosc.As

shown in Fig 3,the VCO characteristics are user-adjustable by three external components:R1,R2

and C1.When Vo is zero ,VCO operates at the minimum frequency fmin and when V0=VDD,the

27

VCO operates at the maximum frequency fmax.

The actual operating frequencies can differ significantly from the values predicted by the above

equations.So,one may need to tune the component values by experiment.

For fosc between the minimum fmin and the maximum fmax,the VCO output frequency fosc is

ideally a linear function of the control voltage Vo.The slope

Ko =4fosc4VO

(6.6)

is called the gain or the frequency sensitivity of the VCO,in HZV .

Lock Range and Capture Range

Once the PLL is in the locked condition ,it remains locked as long as the VCO output frequency

fosc can be adjusted to match the incoming signal frequency fi,i.e., as long as fmin ≤ fi ≤ fmax.

When the lock is lost,the VCO operates at the free-running frequency fo,which is between the

fmin and fmax.To establish the lock gain , i.e. to capture the incoming signal again,the incoming

signal frequency fi must be close enough to fo.Here ”close enough” means that fi must be in

the range from fo-fc to fo+fc,where 2fc is called the capture range.The capture range 2fc is

smaller than the lock range fmax-fmin as shown in Fig.2 .The capture range 2f − c depends on

the characteristics of the loop filter .For the simple RC filter,a very crude,approximate implicit

expression for the capture range can be found as:

fc ≈VDD

2

Ko√1 + ( fcfp )2

(6.7)

where fp is the cut-off frequency of the filter,VDD is the supply voltage and KO is the VCO

gain.Given ko and fp this relation can be solved for fc numerically which yields an approximate

theoretical prediction for the capture range 2fc.

If the capture range is much larger than the cut-off frequency of the filter, fcfp 1,then the

expression for the capture range is simplified.

2fc ≈√

2KOfpVDD (6.8)

Note that the capture range 2fc is smaller if the cut-off frequency fp of the filter is lower.It is

usually desirable to have a wider capture range,which can be accomplished by increasing the

cut-off frequency of the filter.On the other hand a lower cut-off fp is desirable in order to better

attenuate high frequency components of vφ at the phase detector output and improve noise

rejection in general.

Experiment 7

FM Modultion and Demodulation us-

ing PLL

Objective

In this Laboratory exercise you will generate a single-tone modulated FM signal using the

Voltage-controlled Oscillator (VCO) in a Phase-locked loop (PLL)

Task

Build the circuit shown next. This uses the VCO portion of the 4046 PLL.

Figure 7.1:

First, investigate it using the ”test input” circuit that is shown in Figure 2. Find the

frequency and sketch the waveform for the three VCO input voltages shown in the table below.

From that information, deterine the FM constant , Kf, for your modulator. See the data analysis

section below for guidence in this calculation.

Second, instead of the ”test input” circuit, use, as the input, the function generator with

the sinusoidal output listed as follows:

Frequency = 5 kHz (fm = modulating frequency)

Amplitude = 2 volts (p-p)

D.C.Offset = 5V

28

29

Figure 7.2:

Examine the time-domain signal at the VCO output. It should look similar to the plot of Figure

3. Essentially, this is a rectangular waveform with a varying frequency , i.e., a frequency that is

modulated. The maximum and minimum frequencies, fmax and fmin, can be determined using

the following formulas:

fmin = 1T1

fmax = 1T2

Write an expression for the time domain output, assuming that the output waveform is sinusoidal

like. What is the β for your signal? Examine the spectra using the spectrum analyzer. (Make

the Connection to the spectrum analyzer using a high impedence scope probe). Sketch the

spectra and measure the power in signicant sidebands (powers greater than one percent of the

total transmitted power). Record this data in the table shown in the ”report” section.

Figure 7.3:

30 CHAPTER 7. FM MODULTION AND DEMODULATION USING PLL

Data Analysis

The FM constant, Kf , can be determined by plotting the VCO’s output frequency v/s the

VCO’s input voltage. This should give (approximately) a straight line, its slope is Kf in hert-

per-volt. You will want to conver it to radians/second-per-volt in order to write the expression

for the FM signal you generate. To find β , use

β = [peakmodulatingtoneamplitude/modulatingtonefrequency(inHz)]kf .

An alternative method is given by

β =fmax − fmin

fm

Use the following circuit for FM demodulation. It is not necessary to use the buffer and

output low pass filter.

4

Use the following circuit for FM demodulation. It is not necessary to use the buffer and output low pass filter..

C=1000pF

Vin

CD4046

10k

VCO

CD4046

VCO

+10v

10k

10k

100pF

5kVout

digital link

V1

Rx=8kCx=100pF

6711

58

4

3

1416

2

9

Rx=8kCx=100pF

6711

58

49

16

10uF

0.1uF

Figure 4. A frequency modulation and demodulation circuit.

Figure 7.4:

Experiment 8

Single Transistor FM Voice Transmit-

ter

Objective

The objective of this experiment is to build a simple FM voice transmitter, transmit the fre-

quency modulated voice signal and then receive it by an ordinary FM receiver.

Background

Read Sections 5.3 and 5.4 of the text and working of Colpitts oscillator for theory background

of the experiment.

Description

1. Implement the circuit as shown in Figure 8.1.

2. Between Port A and Port B Mic will be placed.

3. Leave wire hanging at the output.This will act as an antenna.

4. Place a FM receiver at some distance from the antenna and hear the signal sent from the

Mic.

5. Capacitor C1 is for providing AC ground for carrier frequencies and providing high

impedance at audio frequencies so that whole signal is delivered at the base of BJT .

6. C2, C3, base-emitter capacitance BEC and collector-base capacitance CBC provide the

Tank circuit capacitances.

7. C2,C3 and BEC are fix capacitances while CBC is variable.This is because base-collector

junction is reverse biased and any change in base voltage at low frequency will change

junction capacitance and thus the oscillation frequency of the tank circuit.

8. The tank circuit oscillating frequency is found by performing AC analysis. C3 is in series

with BEC giving us an equivalent capacitance CE of their series combination. This

CE,CBC and C2 are in parallel and their sum is the equivalent capacitance CEQ of the

tank circuit.

9. From the data sheet of 2N2222, BEC and CBC are 25pF and 8pF (mean value) respec-

tively.Thus CEQ comes out to be equal to 25pF .

31

32 CHAPTER 8. SINGLE TRANSISTOR FM VOICE TRANSMITTER

10. Substituting CEQ in the formula of the oscillatiob frequency of the tank circuit we can

find the required inductance L1 for any oscillation frequency.

11. For oscillation frequency of FM100 channel i.e. 100MHz the inductance is 0.1µH. Note

that the capacitor C1 is not required in the actual hardware implementation.

Results

Using a receiving antenna connected directly to spectrum analyzer try to locate the FM trans-

mitter frequency of oscillation. If that frequency is in the commercial FM band of 88 MHz to 108

MHz, then the transmission of message signal from the Mic can be listened on the commercial

FM receiver.

Figure 8.1: Circuit diagram for the single transistor FM transmitter.

Experiment 9

A Simple Sampler using 555 Timer

Objective

The objective of this lab session is to sample a baseband signal m(t) using transistor as a switch.

The switching sequence is generated by 555 timer in ASTABLE mode.

Background

Go through section 6.1 of your textbook for complete theoretical background of Sampling. A

brief overview is given below.

In signal processing, sampling is the reduction of a continuous signal to a discrete signal.

A common example is the conversion of a sound wave (a continuous signal) to a sequence of

samples (a discrete-time signal). A sample refers to a value or set of values at a point in time

and/or space. A sampler is a subsystem or operation that extracts samples from a continuous

signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of

the continuous signal at the desired points. Nyquist Sampling theorem is of great importance

in sampling the signals.

It states that:-

A signal can be completely determined from its samples if they are taken at uniform intervals

each of length (less than or equal to) 1/2B where B is the bandwidth of the signal.

Description

The circuit used for this lab session uses 555 timer. 555 timer is an IC used in variety of

applications like pulse generators and oscillators. It is called 555 because it has three resistances

of 5k. It has 3 modes of operation:-

1. Bistable Multivibator Stable in both states

2. Monostable Multivibator Stable in only one state

3. Astable Multivibator Unstable in both states

The two states are Triggered and Non-Triggered

Internal circuit of 555 is shown in Figure 1.1. The trigger pin (#2) is bised at 13V cc and the

control pin (#5) is biased at 23V cc. Vcc for 555 timer can vary from 6-18 volts depending on the

operation.In Astable mode, two resistors are used as shown in the Fig 11.2. The capacitor C1 is

charged through the series combination of R1 and R2 and it discharges through R2. Capacitor

C2 is used for noise elimination. When the capacitor charges up to (or slightly above) 23V cc,

33

34 CHAPTER 9. A SIMPLE SAMPLER USING 555 TIMER

Figure 9.1: Internal circuit of 555.

the voltage at pin #6 becomes larger than the voltage at pin #5, the reset input of SR Latch

is activated and the state triggers at that point. When reset is high, the active low output of

SR Latch is high and it turns on the transistor. Now, the capacitor starts to discharge through

this transistor and R2 resistance. When the voltage of capacitor falls below 13V cc, the state

triggers again. The active low output of SR Latch is disabled and transistor switches off again

thus providing path for the capacitor to charge again through R1 and R2. In this way, it creates

a pulse waveform. The duty cycle of this waveform can be controlled by properly selecting the

values of R1, R2 and C1.

Experimental Tasks

1. Connect the circuit as shown in Figure 1.2.

2. 555 timer is used to generate the switching sequence for the transistor which is operated in

its saturation region. 555 timer is used in its astable mode as described above. The duty

cycle of the output square wave is set to be much higher than 50% to generate the sampled

impulses at the output. This is in accordance with the Nyquist Sampling Theorem.

3. The input to the transistor is shown in Figure 1.3.

4. The time period of such an astable output is given by the sum of high time and low time

TH=0.7(R1 + R2) C1

TL=0.7*R2*C1

where THand TLare high and low times respectively.

35

Figure 9.2: Circuit

Figure 9.3: Input to the transistor

5. Design 555 timer in astable mode so that duty cycle of the output waveform is 95%. Use

C1=0.1uF.

6. The baseband signal m(t) is connected in series with the transistor. A dc component is

added to m(t) to ensure that it remains positive. Negative values of m(t) cannot keep

transistor in saturation mode. When transistor is OFF, m(t) appears at the output and

when it is ON output voltage is zero. In this way m(t) is sampled.

7. Keep the baseband signal amplitude to 2V and dc offset to 3V.

8. Observe the sampled output on oscilloscope.

9. The sampling period in this case will be

TS=TH+TL

The sampling period can be changed by changing the time period of the output waveform.

Change the sampling time by using different values of resistors keeping the duty cycle to

95%.

36 CHAPTER 9. A SIMPLE SAMPLER USING 555 TIMER

10. Finally, you can design a filter to obtain the signal m(t). The filter will be a simple first

order RC low pass as shown in Figure 1.4. Choose the cut off frequency of your filter less

than the sampling frequency to obtain m(t) at the filter output.

RC <1

2π ∗ fs

where fs = 1Ts

Figure 9.4: Low pass RC filter

Experiment 10

Pulse Width Modulation

Objective

To build a simple pulse width modulator.

Background

Pulse width modulation has numerous applications. It is widely used in motor speed con-

trol,light dimming control applications to name a few.

Description

Using the circuit diagram below construct an astable multivibrator. To check the circuit func-

tionality you can connect a capacitor at pin 5 of the chip. In this mode a constant width pulse

train will be produced.

EE 354 Communication Systems Lab #11

Pulse Width Modulation

Objective

The objective of this experiment is to build a simple Pulse Width Modulator (PWM).

Background

Pulse width modulation has numerous applications. It is widely used in motor speed control, light dimming control applications to name a few.

Description

Using the circuit diagram below, construct an astable multi-vibrator. To check the circuit functionality you can connect a capacitor at pin 5 (labelled CV) of the chip. In this mode a constant width pulse train will be produced.

Once the above mentioned step is validated experimentally, connect a sinusoidal source with 1V (rms), 200Hz and 3.0V DC offset added into it.

Figure 1: Pulse width modulation circuit diagram for sinusoidal modulation.

Figure 10.1:

Once the above mentioned step is validated experimentally, connect a sinusoidal source with

1V RMS, 200Hz and 3V dc offset added into it. The graph of Figure 10.2 shows the modulating

and the PWM signal simultaneously.

37

38 CHAPTER 10. PULSE WIDTH MODULATION

Results

The graph on the next page shows the modulating and the PWM signal simultaneously.

Figure 2: Modulating sinusoidal and PWM signals.

0.0ms 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms 4.5ms 5.0ms0.0V

0.6V

1.2V

1.8V

2.4V

3.0V

3.6V

4.2V

4.8V

5.4VV(n004) V(n006)

Figure 10.2:

Experiment 11

Pulse Position Modulation

Objective

The objective of this lab session is to build a simple pulse position modulator (PPM) using two

555 timer ICs.

Background

Pulse-position modulation (PPM) is widely used in optical communications including optical

fiber as well as IR remote controls. It is suitable for those applications, where efficiency is more

important and external interference is minimal.

Description

EE321 Communication Systems

Lab session # 12

Pulse Position Modulation

Objective

The objective of this lab session is to build a simple pulse position modulator (PPM) using two 555 timer ICs.

Figure 1: Pulse position modulator circuit Figure 11.1: The circuit for PPM generation.

39

40 CHAPTER 11. PULSE POSITION MODULATION

0.0ms 0.4ms 0.8ms 1.2ms 1.6ms 2.0ms 2.4ms 2.8ms 3.2ms 3.6ms 4.0ms0.0V

0.5V

1.0V

1.5V

2.0V

2.5V

3.0V

3.5V

4.0V

4.5V

5.0VV(n009) V(n006)

--- D:\UET\Teaching\BSc_Courses\EE354_Communication Systems\Labs_EE354\Lab12\PPM.raw ---

Figure 11.2: The modulating signal (sine wave) and the resulting PPM output.

The circuit diagram of the PPM is shown in Figure 11.1. The first 555 timer IC is used in

its astable multivibrator mode to produce a square wave of 50% duty cycle. The second 555

timer IC is used in its monostable mode. To verify the operation of the circuit, connect 0.1uF

capacitor at pin 5 of both ICs. Doing so should produce a constant width square wave with

equal high and low times. Once, the circuit has been verified, connect a sinusoidal signal of

0.5V peak and 2.5V DC offset at pin 5 of the astable multivibrator and verify that the output

is a pulse train with constant high time but varying low time (PPM) as shown in Figure 11.2.

Bibliography

[Lathi(1998)] B.P. Lathi. Modern Digital and Analog Communication Systems 3e Osece. Oxford

University Press, 1998.

[Murray(1967)] R. Murray. The Radio Amateur’s Handbook. The American Radio Relay

League, Newington, Conn., 44 edition, 1967.

41