Frequency Spectrum for PWM Wave , Pulse Width Modulation (PWM) :-
PULSE TIME MODULATION
In pulse time modulation, the signal to be transmitted is sampled as in pulse amplitude modulation (PAM). In pulse time modulation, amplitude of pulse is held constant, whereas position of pulse or width of pulse is made proportional to the amplitude of signal at the sampling instant. There are two types of pulse time modulation, viz. Pulse Width Modulation (PWM) and Pulse Position Modulation (PPM). Because in both PWM and PPM, amplitude is held constant and does not carry any information, therefore amplitude limiters can be used. The amplitude limiters, similar to those used in FM, will clip off the portion of the signal corrupted by noise and hence provide a good degree of noise immunity.
3.14.1. Pulse Width Modulation (PWM)
Let us first discuss Pulse Width Modulation (PWM). This is also known as Pulse Duration Modulation (PDM). Three variations of pulse width modulation are possible. In one variation, the leading edge of the pulse is held constant and change in pulse width with signal is measured with respect to the leading edge. In other variation, the tail edge is held constant and with respect to it, pulse width is measured. In the third variation, centre of the pulse is held constant and pulse width changes on either side of the centre of the pulse. This has been illustrated in figure 3.28.
The modulating signal is at its positive peak at point (A) and at its negative peak at (B). In figure 3.28 (a), the leading edge of pulse is kept constant and pulse width is measured from the lead edge. As shown, pulse width is maximum corresponding to point (A), while it is minimum at point (B).
In figure 3.28 (b), the tail edge of the pulse is kept constant and pulse width is measured from the tail end of the pulse. As before, pulse width is maximum corresponding to positive peak of the modulating signal and minimum at the negative peak.
As shown in figure 3.28 (c), the center of the pulse is kept constant and pulse extends on either side of the center of the pulse, depending upon the modulating signal.
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FIGURE 3.28 PWM waveforms
3.14.2. Frequency Spectrum for PWM Wave
With a sinusoidal modulating signal at frequency fm, the spectrum of PWM signal consists the modulating signal frequency fm along with several harmonics. This is shown in figure 3.29.
To have a better separation with respect to frequency, between highest frequency of baseband signal [in Fig. 3.29, fm] and lower sidebands of fs (sampling frequency), a higher sampling frequency which is more than Nyquist rate is used; and pulse width deviation is kept small.
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FIGURE 3.29 Spectrum of PWM signal
3.14.3. Modulation of PWM Signal or PWM Generation
Figure 3.30 shows pulse width modulator. It is basically a monostable multivibrator with a modulating input signal applied at the control voltage input. Internally, the control voltage is adjusted to the 2/3 VCC. Externally applied modulating signal changes the control voltage, and hence the threshold voltage level. As a result, the time period required to charge the capacitor up to threshold voltage level changes, giving pulse modulated signal at the output, as shown in the figure 3.30 (b).
FIGURE 3.30
Figure 3.31 illustrates another monostable multivibrator circuit to generate pulse width modulation (PWM).
The stable state for above circuit is achieved when T1 is OFF and T2 is ON. The positive going trigger pulse at B1 switches T1 ON. Because of this, the voltage at C1 falls as T1 now begins to draw the collector current. As a result, voltage at B2, also falls and T2 is switched OFF, C begins to charge up to the collector supply voltage (VCC) through resistor R. After a time Input determined by the supply voltage and signal the RC time constant of the charging network, the base of the T2 becomes sufficiently positive to switch T2 ON. The transistor T1 is simultaneously switched OFF by regenerative action and stays OFF until the arrival of the next trigger pulse. To make T2 ON, the base of the T2 must be slightly more positive than the voltage across resistor RE. This voltage depends on the emitter curent IE which is controlled by the signal voltage applied at the base of transistor T1. Therefore, the changing voltage necessary to turn OFF transistor T2 is decided by the signal voltage. If
signal voltage is maximum, the voltage that capacitor should charge to turn ON T2 is also maximum. Therefore, at maximum signal voltage, capacitor has to charge to maximum voltage requiring maximum time to charge. This gives us maximum pulse width at maximum input signal voltage. At minimum signal voltage, capacitor has to charge for minimum voltage and we get minimum pulse width at the output. With this discussion, it can be noted that pulse width is controlled by the input signal voltage, and we get pulse width modulated waveform at the output.
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FIGURE 3.31 Monostable multivibrator generating pluse width modulation (PWM).
3.14.4. Demodulation of PWM Signal
Figure 3.32 (a) shows the block diagram of PWM detector. As shown in the figure 3.32 (a), the received PWM signal is applied to the Schmitt trigger circuit. This Schmitt trigger circuit removes the noise in the PWM waveform. The regenerated PWM is then applied to the ramp generator and the synchronization pulse detector. The ramp generator produces ramps for the duration of pulses such that height of ramps are proportional to the widths of PWM pulses. The maximum ramp voltage is retained till the next pulse. On the other hand, synchronous pulse detector produces reference pulses with constant amplitude and pulse width. These pulses are delayed by specific amount of delay as shown in the figure 3.32(b). The delayed reference pulses and the output of
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FIGURE 3.32 (a) PWM detector
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figure 3.32 I(b) Waveforms for PWM detection circuit.
ramp generator is added with the help of adder. The output of adder is given to the level shifter. Here, negative offset shifts the waveform as shown in the figure 3.32 (b)⑥. Then the negative part of the waveform is clipped by rectifier. Finally, the output of rectifier is passed through low-pass filter to recover the modulating signal, as shown in the figure 3.32 (b).
(i)         Unlike, PAM, noise is less, since in PWM, amplitude is held constant.
(ii)        Signal and noise separation is very easy, as shown in figure 3.32 (b)②.
(iii)       PWM communication does not require synchronization between transmitter and receiver.
(i)         In PWM, pulses are varying in width and therefore their power contents are variable. This requires that the transmitter must be able to handle the power contents of the pulse having maximum pulse width.
(ii)        Large bandwidth is required for the PWM communication as compared to PAM.
3.14.7. Pulse Position Modulation

 DO YOU KNOW? Pulse duration modulation represents a series of pulses. in which the duration of each pulse represents the amplitude of the information signal at a given time.

In this system, the amplitude and width of the pulses are kept constant, while the position of each pulse, with reference to the position of a reference pulse, is changed according to the instantaneous sampled value of the modulating signal. Thus, the transmitter has to send synchronizing pulses to keep the transmitter and receiver in synchronism. As the amplitude and width of the pulses are constant, the transmitter handles constant power output, a definite advantage over the PWM. But the disadvantage of the PPM system is the need for transmitter-receiver synchronization. Pulse position modulation is obtained from pulse width modulation, shown in the figure 3.33. Each trailing edge of the PWM pulse is a starting point of the pulse in the PPM. Therefore, position of the pulse is 1:1 proportional to the width of pulse in PWM and hence it is proportional to the instantaneous amplitude of the sampled modulating signal.
3.14.8. Generation of PPM Signal
Figure 3.34 (a) shows the PPM generator. It consists of differentiator and a monostable multivibrator. The input to the differentiator is a PWM waveform. The differentiator generates positive and negative spikes corresponding to leading and trailing edges of the PWM waveform. Diode D1 is used to bypass the positive spikes. The negative spikes are used to the trigger monostable multivibrator. The monostable multivibrator then generates the pulses of same width and amplitude with reference to trigger to give pulse position modulated waveform, as shown in figure 3.34 (b).
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FIGURE 3.34 (a) PPM generator
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FIGURE 3.34 (b) Waveforms of PPM generator
3.14.9. Demodulation of PPM
Incase of pulse-position modulation, it is customary to convert the received pulses that vary in position to pulses that vary in length. One way to achieve this is illustrated in figure 3.35.
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FIGURE 3.35 PPM demodulator
As shown in figure 3.35, flip-flop circuit is set or turned ‘ON’ (giving high output) when the reference pulse arrives. This reference pulse is generated by reference pulse generator of the receiver with the synchronization signal from the transmitter. The flip-flop circuit is reset or turned ‘OFF’ (giving low output) at the leading edge of the position modulated pulse. This repeats and we get PWM pulses at the output of the flip-flop.
The PWM pulses are then demodulated by PWM demodulator to get orginal modulating signal.
FIGURE 3.36 Demodulation waveform for PPM