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Consider the frequency demodulation scheme shown in Fig. below in which the incoming FM signal is passed through a delay line that produces adelay of T such that 2π fcT= π/2. The delay-line output is subtracted from the incoming FM signal and the resulting output is envelope detected. This demodulator finds wide application in demodulating microwave FM waves. Assuming that s(t) = Ac cos(2π fct βsin(2π fmt)) compute a(t) when β<1 and="" the="" delay="" t="" is="" such="" that2π=""><1. .?="">
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Consider the frequency demodulation scheme shown in Fig. below in whic...
Frequency Demodulation Scheme


The frequency demodulation scheme shown in the given figure is used to demodulate FM waves.

Delay Line


The incoming FM signal is passed through a delay line that produces a delay of T such that 2π fcT= π/2.

Subtraction


The delay-line output is subtracted from the incoming FM signal.

Envelope Detection


The resulting output is envelope detected.

Calculation of a(t)


Given, s(t) = Ac cos(2π fct βsin(2π fmt))

Let x(t) be the output of the delay line.

x(t) = s(t - T) = Ac cos[2π fc(t-T) + βsin(2π fm(t-T))]

On simplification, we get

x(t) = Ac cos[2π fcT + 2π fc(t/T - 1) + βsin(2π fm(t-T))]

x(t) = Ac cos[2π fcT + 2π f(t/T - 1) + βsin(2π fm(t-T))]

On subtracting x(t) from s(t), we get

y(t) = s(t) - x(t)

y(t) = Ac cos(2π fct βsin(2π fmt)) - Ac cos[2π fcT + 2π f(t/T - 1) + βsin(2π fm(t-T))]

y(t) = Ac [cos(2π fct βsin(2π fmt)) - cos(2π fcT + 2π f(t/T - 1) + βsin(2π fm(t-T)))]

Using trigonometric identity, we get

y(t) = -2Ac sin[2π f((t/T) - 1/2) + πβcos(2π fmt)/(2π fm)]

On envelope detection, we get

a(t) = |-2Ac sin[2π f((t/T) - 1/2) + πβcos(2π fmt)/(2π fm)]|

a(t) = 2Ac |sin[2π f((t/T) - 1/2) + πβcos(2π fmt)/(2π fm)]|

Explanation of the Result


The given frequency demodulation scheme uses a delay line to introduce a phase shift of π/2. This phase shift is used to convert the frequency modulation into amplitude modulation. By subtracting the output of the delay line from the incoming FM signal, we get a signal that is proportional to the frequency deviation. This signal is then envelope detected to obtain the baseband signal. The resulting a(t) is proportional to the frequency deviation and can be used to recover the modulating signal.
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Consider the frequency demodulation scheme shown in Fig. below in which the incoming FM signal is passed through a delay line that produces adelay of T such that 2π fcT= π/2. The delay-line output is subtracted from the incoming FM signal and the resulting output is envelope detected. This demodulator finds wide application in demodulating microwave FM waves. Assuming that s(t) = Ac cos(2π fct βsin(2π fmt)) compute a(t) when β
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Consider the frequency demodulation scheme shown in Fig. below in which the incoming FM signal is passed through a delay line that produces adelay of T such that 2π fcT= π/2. The delay-line output is subtracted from the incoming FM signal and the resulting output is envelope detected. This demodulator finds wide application in demodulating microwave FM waves. Assuming that s(t) = Ac cos(2π fct βsin(2π fmt)) compute a(t) when β for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Consider the frequency demodulation scheme shown in Fig. below in which the incoming FM signal is passed through a delay line that produces adelay of T such that 2π fcT= π/2. The delay-line output is subtracted from the incoming FM signal and the resulting output is envelope detected. This demodulator finds wide application in demodulating microwave FM waves. Assuming that s(t) = Ac cos(2π fct βsin(2π fmt)) compute a(t) when β covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the frequency demodulation scheme shown in Fig. below in which the incoming FM signal is passed through a delay line that produces adelay of T such that 2π fcT= π/2. The delay-line output is subtracted from the incoming FM signal and the resulting output is envelope detected. This demodulator finds wide application in demodulating microwave FM waves. Assuming that s(t) = Ac cos(2π fct βsin(2π fmt)) compute a(t) when β.
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