1. Information and carrier signals are given by vM(t) = 8 cos (2? x 103t) and vC

Question

1. Information and carrier signals are given by vM(t) = 8 cos (2? x 103t) and vC(t) = 12 cos (2? x 105 t), respectively. The modulation constant is given by kFM = 1000 Hz/V. a) Calculate the maximum frequency deviation, and the maximum and minimum values of the modulated frequency. b) What is the amplitude of the FM signal? c) Calculate modulation index. d) Using the table of Bessel Function coefficients given below, determine the number of side frequencies of the frequency spectrum of the FM signal. e) Calculate the bandwidth of this signal. 2. How does a varactor modulator produce an FM signal? Only explain the main idea. 3. How does a slope detector demodulator recover the modulating signal from the FM signal? Only explain the main idea.

1. Information and carrier signals are given by vM(t) = 8 cos (2pi x 10^3t) and vC(t) = 12 cos (2pi x 10^5 t), respectively. The modulation constant is given by kFM = 1000 Hz/V. a) Calculate the maximum frequency deviation, and the maximum and minimum values of the modulated frequency. b) What is the amplitude of the FM signal? c) Calculate modulation index. d) Using the table of Bessel Function coefficients given below, determine the number of side frequencies of the frequency spectrum of the FM signal. e) Calculate the bandwidth of this signal. 2. How does a varactor modulator produce an FM signal? Only explain the main idea. 3. How does a slope detector demodulator recover the modulating signal from the FM signal? Only explain the main idea.

Explanation / Answer

1.)
1.) fre deviation=wc+kf*am*cos(wmt)

=310+1000*12*cos(206t)

2.)amplitude of fm signal=12

3.)modulation index=w/wm

w=kfam

=kf*am/wm

=1000*8/206=12

4.)for = 12 bessel fnction =16

so total side band frequenct=16

5.)B=2*n*fm

=2*16*103/2

=1648

2.)Another fm modulator which is widely used in transistorized circuitryuses a voltage-variable capacitor (VARACTOR). The varactor is simply a diode, or pn junction, that isdesigned to have a certain amount of capacitance between junctions. The capacitance of a varactor, as withregular capacitors, is determined by the area of the capacitor plates and the distance between the plates.The depletion region in the varactor is the dielectric and is located between the p and n elements, whichserve as the plates. Capacitance is varied in the varactor by varying the reverse bias which controls thethickness of the depletion region. The varactor is so designed that the change in capacitance is linear withthe change in the applied voltage. This is a special design characteristic of the varactor diode. Thevaractor must not be forward biased because it cannot tolerate much current flow.

3.)

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