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PULSE MODULATION. CONTENTS. SAMPLING T.D.M. PULSE MODULATION P.A.M. P.T.M. SAMPLING. Process of converting a continuous time signal to an equivalent discrete time signal. Continuous time signal x(t) is applied at input of multiplexer. Other input of multiplexer is train of impulse.
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CONTENTS SAMPLING T.D.M. PULSE MODULATION P.A.M. P.T.M.
SAMPLING • Process of converting a continuous time signal to an equivalent discrete time signal. • Continuous time signal x(t) is applied at input of multiplexer. • Other input of multiplexer is train of impulse. • At the output of multiplexer we get the sampled version of x(t)
SAMPLING cont. • One important property of sampling is that the signal can be fully represented by their sampled value at some discrete time instant. • If the sampled values are known the signal can be reconstructed or recovered as original signal. • The time interval can be used by other signals if a suitable transmission is produced. • The concept of use of time interval by several signal is known as T.D.M. (Time Division Multiplexing) • The sampling occurs at regular intervals of time Ts seconds apart. Thus sampling frequency fs may be represented as fs =1/Ts
SAMPLING cont. • Sampling theorem is defined for 2 signals • Low pass signal • A band limiting signal which has no frequency component above a frequency fmHz can be uniquely described by taking its sample at uniform intervals less than equals to 1/2fm sec apart. So that the sampling rate = 1/2fm seconds. • A band limiting signal which has no frequency component above a frequency fmHz can be uniquely recovered from the knowledge of the sample taken at a rate of 2fm per sec. so that the sampling frequency is greater than equal to 2fm . • Band pass signal • Band width is smaller compare with the highest frequency components and its possible to use sampling rate i.e. less than the twice the highest frequency component present in the signal. • Frequency interval fc-fm<=fc<=fc+fm • Minimum sampling frequency = 2(fc+fm)/m where m is integer
TIME DIVISION MULTIPLEXING • Sampling theorem makes it possible to transmit the complete information of the continuous signal by transmitting more samples of f(t) at regular intervals. • This is done on time sharing basis. • The transmission of sample engage the channel for only part of time. • All the signals to be transmitted are inter laced in transmitter. • It is switched from channel to channel I sequence to the sampling circuits by the pulse generated by the timing circuit. • At the receiver, the samples of each signal are separated. • Its sampling pulse is in synchronism. • The output of the sampling circuit is thus a signal which consist of samples of all signals interlaced
PAM Amplitude of pulse is proportional to amplitude of modulating signal. Band width of transmitting channel depends on width of pulse. Instantaneous power of transmitter varies. Noise interference is high. Complex system. Similar to A.M. DIFFERENCE PWM • Width of pulse is proportional to amplitude of modulating signal. • Band width of transmitting channel depends on rise time of the pulse. • Instantaneous power of transmitter varies. • Noise interference is minimum. • Simple to implement. • Similar to F.M. PPM • Relative position of pulse is proportional to amplitude of modulating signal. • Band width of transmitting channel depends on rise time of the pulse. • Instantaneous power remains constant. • Noise interference is minimum. • Simple to implement. • Similar to P.M.
PULSE AMPLITUDE MODULATION (PAM) • PAM can be defined as a process in which the amplitude of regular spaced rectangular pulse vary in direct proportion to the instantaneous sample values of continuous signal. • Its is quite similar to Amplitude Modulation. • The difference is that here a Pulse Train acts as carrier rather than high freq. sinusoidal wave • There are mainly 2 types of PAM signals • PAM with Natural Sampling • Pam with Flat Top
PAM with Natural Sampling • Width of pulse do not have flat top. • The top of pulse varies in accordance with the shape of modulating signal. • With the Natural Sampling, a signal sampled at NQUIST rate may be reconstructed exactly by passing through LOW PASS FILTER with cut off frequency fm . • where fm is the highest frequency component • If N signals are to be multiplied, the max sampled duration is T=Ts/N
Flat Top PAM • The top of pulses of this PAM is flat. • Noise interference at the top of transmitted pulse can be easily removed. • Due to this it is widely used. • Better than Natural PAM • Because in case of Natural PAM, the varying top signal is when received at receiver, it becomes quite difficult to determine shape of top of pulse due to noise (which is always present). • Thus errors are introduced in the receiving signals due to wich we prefer a flat top PAM.
Fig. shows sampled and hold circuit to Produce FLAT TOP sampled P.A.M. Sampled and hold circuit consist of 2 flat switches and a capacitor. The sampling switch is closed for a short duration by a short pulse applied to gate G1 of transistor. During this period the capacitor is charged up to a voltage equal to the instantaneous value of input signal x(t) When the sampling switch is opened the capacitor hold the charge. The discharge switch is then closed by a pulse applied to the gate G2 pf the other transistor. Due to this capacitor discharge to zero volts. Hence the output sampled and hold circuit consist of Flat Top Samples. Flat Top PAM cont.
PULSE TIMEMODULATION(PTM) • There are two types of Pulse Time Modulation • Pulse Width Modulation (PWM) • Pulse Phase Modulation (PPM) • In both PWM and PPM some time parameters of the pulse is modulated. • In PWM the width of pulse is varied. • In PPM position of the pulse is varied. • Amplitude of pulses remain constant for both PWM and PPM
DEMODULATION of P.W.M. • The transistor T1 acts as an inverter. • During the time interval when the signal is high, the input of transistor T2 is low. • Thus during this interval T2 is in cut-off stage. • Thus capacitor C is charged through RC combination. • During the time interval when the signal is low, the input of transistor is high. • Thus it get saturated during thus time. • The capacitor gets discharge very rapidly through transistor T2. • Hence the waveform at the collector transistor T2 is more or less a saw-tooth waveform whose envelop is modulating signal. • When this is passed through 2nd order Op-amp low pass filter, desired demodulated signal is obtained.
DEMODULATION of P.P.M. • This circuit makes use of the fact that the gaps between the pulses of PPM signal contains information regarding the Modulating signal. • During the gap between pulses • The transistor is in cut-off. • The capacitor gets charged through RC combination. • During the pulse duration • The transistor is in saturation. • Capacitor is discharged through transistor. • Thus the collector voltage becomes low. • Hence the waveform at the collector is approximately a saw-tooth waveform whose envelop is Modulating signal. • When this is passed through 2nd order low pass filter, the desired demodulated output is obtained.
