Signal Processing and Linear Systems-B.P.Lathi copy

# Wt t he output is t he desired signal m t multiplied

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Unformatted text preview: he viability of demodulation of AM by an envelope detector. When A &lt; m p , Eq. (4.76) shows t hat J1 &gt; 1 (overmodulation). In this case, the option of envelope detection is no longer viable. We t hen need t o use synchronous demodulation. Note t hat synchronous demodulation can be used for any value of J1 (see P rob. 4.7-4). T he envelope detector, which is considerably simpler a nd less expensive t han t he synchronous detector, can be used only for J1 :::; 1. • E xample 4.19 Sketch 'PAM(t) for modulation indices of J1 = 0.5 (50% modulation) and J1 = 1 (1~0% modulation), when m (t) = B cos wmt. This case is referred to as t one m odulatIOn because the modulating signal is a pure sinusoid (or tone). In this case, m p = B and the modulation index according to Eq. (4.76) is Hence, B = J1A and m (t) = B cos wmt = c A M signal R Envelope detector output R C too large 'PAM(t) = [A I +0.5 cos (Om t &quot;/ + m(t)] cos wet = ~ &quot; &gt;. ~&quot; + J1cos wmt] cos wet 2A (4.78) .., .... ( b) .... F ig. 4 .36 .. ' ... ,.. K, . i ' 1'&quot; .... ;;&quot;, 0 ~~f'-&quot; J1Acos wmt A[1 \ ..... , '1&quot; ,&lt; ~~nvelOpe 1 &quot;, .,., Therefore ( a) .... &quot; ..... &quot;' . Envelope detector. l +cosoom t 3A/2 Demodulation of A M: T he Envelope Detector We shall consider here one of t he noncoherent methods of AM demodulation, the e nvelope d etection. t I n a n envelope detector, t he o utput of t he d etector follows t he envelope of t he ( modulated) i nput signal. T he c ircuit illustrated in Fig. 4.36a functions as a n envelope detector. During the positive cycle of t he i nput signal, t he diode conducts and t he c apacitor C charges up t o t he p eak voltage of t he i nput signal (Fig. 4.36b). As t he i nput signal falls below this peak value, t he diode is c ut off, because t he c apacitor voltage (which is very nearly t he p eak voltage) is g reater t han t he i nput signal voltage, a circumstance causing t he diode t o open. T he c apacitor now discharges through t he resistor R a t a slow r ate ( with a time constant R C). D uring the n ext positive cycle, the same d rama r epeats. When t he i nput signal becomes greater t han t he c apacitor voltage, t he d iode conducts again. T he c apacitor again charges to t he p eak value of this (new) cycle. As t he i nput voltage falls below t he new peak value, t he diode cuts off again a nd t he c apacitor discharges slowly during the cutoff period, a process t hat changes t he c apacitor voltage very slightly. T he A M signal can be demodulated coherently by a locally generated carrier (see P rob. 4.7-4). However, coherent, or synchronous, demodulation of AM (with J1 :::; 1) will defeat t he very purpose o f AM and, hence, is r arely used in practice. tThere are also other methods of noncoherent detection. The rectifier detector consists of a rectifier followed by a lowpass filter. This method is also simple and almost as inexpensive as the envelope detector4 . The nonlinear detector, although simple and inexpensive, results in a distorted output. A A...
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