BLOCK DIAGRAM VERIFICATION OF SAMPLING THEOREM

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BLOCK DIAGRAM

VERIFICATION OF SAMPLING THEOREM

A SIGNAL GENERATOR

CARRIER

MESSAGE

SIGNAL SAMPLE O/P SAMPLE AND HOLD O/P

DEMODULATOR DEMODULATED OUTPUT

BINARY COUNTER

MULTIPLI

ER

STAGE CONVERTOR

-10 + -

BCD COUNTER

4 BIT

COMPARATOR

LATCH

2ND ORDER LOW PASS FILTER(+/~)

4TH ORDER LOW PASS FILTER(+/~)

OSC

8 1

5 7



EXP.No:

DATE :

SAMPLING THEOREM

AIM

To obtain the sampling and sample & hold output for the given input

waveform .

APPARATUS REQUIRED

1. Sampling and reconstruction trainer kit ST2101.

2. CRO

3. Connecting wires

THEORY

Sampling is the process of conversion of analog signal to discrete signal.

Sampling Theorem shows that a continuous-time band-limited signal may be

represented perfectly by its samples at uniform intervals of T seconds, if T is small

enough. In other words, the continuous-time signal may be reconstructed perfectly

from its samples; sampling at a high enough rate is information-lossless.

Sampling theorem states that

1.The band limited signal of finite energy, which has no frequency

component higher than w hertz, is completely described by specify the value of

signal at instant of time separated by 1/2w second .

2.The band limited signal of finite energy, which has no frequency

component higher than w hertz, must be completely recovered from knowledge of

its samples taken at rate of 2w per second.

Fs >= 2 fm

If the sampling frequency is less than Nyquist rate, then a distortion is called

aliasing.

( ) ( ) ( ) s s

n

g t g nT t nT

( ) denote the ideal sampled signal g t

1 :sampling rates sf T

: sampling periodsT



MODEL GRAPH

SAMPLING THEOREM MESSAGE SIGNAL

Time in ms CARRIER SIGNAL Time in ms SAMPLE OUTPUT Time in ms SAMPLE AND HOLD O/P

Time in ms

DEMODULATED OUTPUT

Time in ms

Am

plit

ud

e in

vo

lts(

V)



PROCEDURE

1. Connections are given as per the block diagram.

2. Take the sine wave as input of 1KHZ from signal generator block.

3. Observe the carrier waveform and note down the amplitude and time period of the

signal.

4. Observe the sampled signal and note down the amplitude and time period of the

signal.

5. Observe the sampled and hold signal and note down the amplitude and time period

of the signal.

6. Then the sampled signal is given as an input to low pass filter and then reconstructed

waveform is obtained in output of low pass filter.

7. Plot the graph for the Sampled signal and Sample and Hold Signal.



TABULATION

Name of the

Signal

AMPLITUDE in

Volts

TIME PERIOD

in secs





TIME DIVISION MULTIPLEXING Carrier Signal DEMODULATED O/P Message Signal 1

C1 Message Signal 2

C2 TDM O/P

C3

C4

FUNCTION GENERATOR

OSCILLATOR DECODER TRANSMITTER TIMING LOGIC

SELECTOR PHASE LOCK LOOP TIMING LOGIC

RECEIVER TIMING LOGIC

DECODER

+/~

+/~

+

/~

+/~

COMPARATOR

LPF VOC



EXP.NO:

DATE :

TIME DIVISION MULTIPLEXING

AIM

To perform the Time Division Multiplexing using the given waveforms.

APPARATUS REQUIRED

1. TDM/PAM Modulation and Demodulation trainer kit.

2. CRO

3. Connecting wires

THEORY

TDM can be implemented in two ways. Synchronous TDM and

asynchronous TDM. In synchronous, the multiplexer allocates exactly the same

time slot to each device at all times whether or not a device has anything to

transmit. In asynchronous, the multiplexer allocates time slot depends on

requirement by the channel.

In TDM, by interleaving samples of several source waveforms in time, it is

possible to transmit enough information to a receiver, via only one channel to

recover all message waveforms.

The four channels CH0, CH1, CH2, and CH3 are multiplexed on a single

line Transmitter and send through the same channel. In demodulated circuit each

signal can be recovered separately.

PROCEDURE

1. Connections are made as per the block diagram.

2. The message signal1 is connected to the channel 0 and note down the amplitude

and time period of the signal.

3. The message signal 2 is connected to the channel 1 and note down the amplitude

and time period of the signal.

4. Observe the TDM waveform in the CRO.

5. Plot the TDM waveform for the obtained readings



MODEL GRAPH

TIME DIVISION MULTIPLEXING

MESSAGE SIGNAL 1 Time in ms MESSAGE SIGNAL 2 Time in ms TDM OUTPUT SIGNAL

Time in ms

Am

plit

ud

e in

Vo

lts

(V)



TABULATION

Name of the

Signal

AMPLITUDE in

Volts

TIME PERIOD

in secs





CIRCUIT DIAGRAM AM MODULATION CIRCUIT

AM DEMODULATION CIRCUIT

R2 1.2 kΩ

2.2kΩ

R4 1.2 kΩ

R5 1.2kΩ

C1 0.1 µF

-

+

VG2

Vcc 1 5 V

C2 0.01 µF

-

+

VG1

10 kΩ

BC107

C3 0.01 µF

VM1

V VM2

AM OUTPUT SIGNAL

MSG

C1 0.01µF

R1 10k R2 100k

D1 1N4007

C2 0.01µF

C2 22 µF

VM

VM VM

VM

AM AM INPUT DE MODULATED OUTPUT

Carrier signal



EXP.NO:

DATE :

AMPLITUDE MODULATION AND DEMODULATION

AIM

To perform the amplitude modulation and demodulation of the given signal.

APPARATUS REQUIRED

S.NO. APPARATUS RANGE QUANTITY

1. Resistor 2.2kΩ , 1.2kΩ , 10kΩ , 100kΩ. 1,3,2,1

2. Capacitor 0.1µF , 0.01µF , 22µF. 1,4,1

3. Transistor BC107 1

4. Diode IN 4007 1

5. Function

generator

----- 2

6. CRO ----- 1

7. Power supply 10 V 1

THEORY

Amplitude Modulation is a process by which amplitude of the carrier signal

is varied in accordance with the instantaneous value of the modulating signal, but

frequency and phase of carrier wave remains constant.

The modulating and carrier signal are given by

Vm(t) = Vm sinmt

VC(t) = VC sinCt

The modulation index is given by, ma = Vm / VC.

Vm = Vmax – Vmin and VC = Vmax + Vmin

The amplitude of the modulated signal is given by,

VAM(t) = VC (1+ma sinmt) sinCt

Where

Vm = maximum amplitude of modulating signal

VC = maximum amplitude of carrier signal

Vmax = maximum variation of AM signal

Vmin = minimum variation of AM signal



MODEL GRAPH MESSAGE SIGNAL Time in ms CARRIER SIGNAL Time in ms AM MODULATED SIGNAL Time in ms AM DEMODULATED SIGNAL Time in ms

Am

plit

ud

e in

Vo

lts

(V)



PROCEDURE

1. Connections are given as per the circuit diagram.

2. The carrier and the message signal representation frequencies are set to 10kHz and

1kHz respectively.

3. Vcc is given as 15 V.

4. The Voltage and Time division knob of CRO is adjusted to obtain the AM modulated

wave.

5. The Amplitude and time period for message signal , Carrier signal and AM signal are

noted from the CRO.

6. The AM output is given as input to demodulated circuit

7. The Amplitude and time period for reconstructed message signal is noted from the

CRO.

8. The graph is plotted for the AM signal and reconstructed message signal.



TABULATION

Name of the

Signal

AMPLITUDE in

Volts

TIME PERIOD in

Secs





BLOCK DIAGRAM

FREQUENCY MODULATION & DEMODULATION DEMODULATOR CIRCUITS Message Signal MODULATOR CIRCUIT

FM OUTPUT

AUDIO OSCILLATOR

QUADRATURE DETECTOR

DETUNED RESONATOR

CIRCUIT

REACTANCE MODULATOR

VARACTOR MODULATOR

SUMMING AMPLIFIER

FOSTER AND SELLEY (RATIO DETECTOR)

PHASE LOCKED LOOP

AMPLITUDE LIMITER

LOW PASS FILTER

VOC MOD I/P MOD O/P

Demodulated

O/P



EXP.NO:

DATE :

FREQUENCY MODULATION AND DEMODULATION AIM

To obtain the frequency modulation and demodulation of the message signal

and to plot the waveform.

APPARATUS REQUIRED

S.NO. APPARATUS RANGE QUANTITY

1. ST2203 FM transmitter and

receiver trainer board.

----- 1

2. CRO (0-30)M Hz 1

3. Connecting wires ----- As required

THEORY

Frequency modulation and phase modulation are called as angle modulation. Frequency

modulation is defined as changing the frequency of the carrier with respect to the message signal

amplitude. Here the amplitude of the carrier remains fixed and timing parameter frequency is

varied. When the modulating signal has zero amplitude, then the carrier has frequency of fc as

amplitude of the modulating signal increases. The frequency of the carrier increases, similarly, as

the amplitude of the modulating signal decreases, the frequency of the carrier decreases.

In telecommunications and signal processing, Frequency Modulation (FM)

conveys information over a carrier wave by varying its instantaneous frequency.

If the baseband data signal (the message) to be transmitted is xm(t) and

the sinusoidal carrier is , where fc is the carrier's base frequency

and Ac is the carrier's amplitude, the modulator combines the carrier with the baseband data

signal to get the transmitted signal.

http://en.wikipedia.org/wiki/Information

http://en.wikipedia.org/wiki/Carrier_wave

http://en.wikipedia.org/wiki/Frequency

http://en.wikipedia.org/wiki/Sinusoid



MODEL GRAPH

FREQUENCY MODULATION MESSAGE SIGNAL

Time in ms CARRIER SIGNAL Time in ms FM OUTPUT Time in ms DEMODULATED OUTPUT Time in ms

A A

mp

litu

de

in V

olt

s (V

)



PROCEDURE

1. Connections are made as per the circuit diagram.

2. Turn the audio oscillator block amplitude pre set the clock fully clockwise and

measure the modulating signal output on the oscilloscope.

3. Monitor and measure the carrier signal output frequency (fc) and peak-to-peak

volts(Vc)frequency at the test point 34 without the input.

4. Next monitor and measure modulated output of reactance modulator and VCO and

mixer/amplifier block output at the test point 34 with input.

5. Finally monitor and measure the demodulated output waveform at the low pass

filter/amplifier block.

6. Draw the FM demodulated output on the graph



TABULATION

Name of the

Signal

AMPLITUDE in

Volts

TIME PERIOD in

Secs



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BLOCK DIAGRAM VERIFICATION OF SAMPLING THEOREM