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PUNE INSTITUTE OF COMPUTER TECHNOLOGY, PUNE - 411043

Department of Electronics & Telecommunication

CLASS : T. E. (E &TC) SUBJECT : DC

EXPT. NO. : 1 DATE :

TITLE : To study pulse amplitude modulation & demodulation

PREREQUISITES FOR EXPT. : Amplitude modulation,

Need of modulation, Sampling Theorem, Natural & Flat Top sampling techniques, PAM Demodulation.

OBJECTIVE : (1) To generate natural sampled PAM signal & demodulate it. (2) To verify Nyquist sampling theorem. (3) To understand & observe the aliasing effect. (4) To generate Flat top sampled signal & demodulate it.

APPARATUS : Sr. No. Apparatus Range1. Sampling Theorem

Trainer model kit2. DSO Dual Channel, 60 MHz

THEORY : The process by which we can convert continuous time signal to discrete time signal is called sampling process. For the sampling process to be of practical utility it is necessary to choose the sampling rate properly.

Sampling Theorem: A continuous time signal x (t) can be completely represented in its sampled form and recovered back from the sampled form; if the sampling frequency fs ≥ 2fm where ‘fm’ is the maximum signal frequency of the continuous time signal x (t).

P:F-LTL_UG/03/R0 DC 1.1



a)Natural Sampling:- A much more reasonable and practically feasible manner of sampling is called as “Natural Sampling”, as shown in the figure below.

Looking at the waveforms in the figure we notice following important points:(i) Here the sampling waveform c (t) consists of a train of pulses each having duration and separated by the sampling time Ts.

(ii) The baseband or modulating signal x (t) and the sampled signal s(t) = c(t)x(t) as shown in the figure. The sampled signal is obtained by multiplication of x (t) and c (t).(iii) Observe that the sampled signal is a train of pulses of width τ, whose amplitudes are varying. These pulses do not have flat tops but their tops follow the waveform of the signal x (t).(iv) The sampling rate is greater than or equal to the Nyquist rate.




b) Flat Top Sampling:- In flat top sampling technique, the analog signal x(t) is sampled at the rate fs=1/Ts and the duration of each sample is lengthened to a duration ””, using sample & hold circuit.Flat Top sampling is shown in the figure below.

Thus the flat top sampled pulses are obtained by convolution of the ideally sampled signal xδ(t)and a pulse train of finite pulse width h(t). The width of each pulse is sec.




Aliasing: - The phenomenon of high frequency in the spectrum of the original signal x (t) taking on the identity of the lower frequency in the spectrum of the sampled signal xδ(t) is called aliasing or fold over error.Aliasing can be eliminated by using anti aliasing filter or prealias filter or by choosing sampling frequency fs>2fm so that guard band is created between the adjacent spectrums.

Demodulation: - Original signal x(t) can be recovered by passing the sampled signal through low pass filter whose cut off frequency is fm.

BLOCK DIAGRAM OF SAMPLING THEOREM:




PROCEDURE:




EXPT.(1) TO GENERATE NATURAL SAMPLED PAM SIGNAL AND DEMODULATE IT:- (See connection diagram CN1)

Connection Diagram CN1

1) Connect CRO channel-1 at Sine O/P terminal (T1). Connect ground of probe to ground terminal of Audio oscillator. Adjust amplitude of sine wave to 2 Vpp and audio frequency to 1 KHz. _____ Waveform (T1)

2) Connect CRO channel-2 at SAMP CLK terminal of Sampling Pulse generator. Connect ground of probe to ground terminal of Low pass filter.

Keep Frequency pot and Pulse width pot of Sampling pulse generator in mid positions, i.e. set pulse frequency approx. 16 KHz. __Waveform (T2)

3) Connect jumper link J1 in modulator section.

4) Connect CRO Channel-2 at PAM O/P terminal (T2) of Modulator. Trigger




CRO by channel 1. The Natural sampled PAM signal will be observed._______Waveform (T3)

5) Then connect CRO Channel-2 at demodulated output DEMOD O/P of Low

Pass filter. Observe sine wave signal. _______Waveform (T4) 6) Now vary amplitude of sine wave modulating signal and observe its effect on PAM output as well as on recovered signal.

7) Vary frequency of sine wave modulating signal and observe its effect on PAM output as well as on recovered signal.

EXPT. (2). TO VERIFY NYQUIST'S SAMPLING THEOREM

8) Keep modulating sine wave frequency to 2 KHz and amplitude 2Vpp. Vary sampling frequency slowly from 32KHz to 2 KHz by observing original signal and recovered demodulated signal. Measure the sampling frequency for which original signal and recovered demodulated signal are nearly same i.e. error is less. It will be more than 4 KHz, which proves Nyquist's Sampling Theorem.

EXPT. (3). TO UNDERSTAND AND OBSERVE THE ALIASING EFFECT

9) Keep modulating sine wave frequency to 2 KHz and amplitude 2Vpp. Now vary sampling frequency slowly from 2KHz. Observe the output at PAM O/P terminal. The slowly varying waveform will be seen. This is known as “Aliasing effect”




EXPT. (4). TO GENERATE SAMPLE/HOLD (S/H) PAM SIGNAL AND DEMODULATE IT:- (See connection diagram CN2)

Connection Diagram CN2

10) In above exp. remove Jumper link J1 and connect Jumper link J2. The Sampled/Hold PAM signal will be observed. _______Waveform (T5)

11) Vary amplitude of sine wave modulating signal and observe its effect on PAM output as well as on recovered signal.

12) Vary frequency of sine wave modulating signal and observe its effect on PAM output as well as on recovered signal.

EXPT. (5). TO GENERATE FLAT TOP SAMPLED PAM SIGNAL AND DEMODULATE IT:-




13) Now add jumper link J3 in above experiment. Vary pulse width pot of sampling pulse generator. The sample/hold PAM signal will be observed at one typical position. __________________ Waveform (T6)

GRAPHS:

1) Modulating signal, with scale stating frequency and amplitudes.

2) Sampling pulse signal stating frequency and amplitudes.

3) The naturally sampled PAM signal in synchronization with T1 and T2.

3) PAM demodulated o/p with scale and proper projections stating frequency and amplitude.

4) Repeat the above waveforms for flat top sampling on another graph sheet.

CONCLUSION:

RERFERENCES: 1. Modern Digital & Analog communication system-B.P.Lathi2. Sigma Trainer Manual3. “Communication Systems”- Carlson4. “Principles of Communication System”- Taub-schilling





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