the equation of an angle modulated voltage is v 10 sin l08t 3 sin 104 what form of angle modulat

1. The form of angle modulation for the equation v = 10 sin (108t + 3 sin 104t) is Frequency Mod

The equation of an angle modulated voltage is v 10 sin l08t...

The equation of an angle-modulated voltage is v = 10 sin (108t + 3 sin 104t). What form of angle modulation is this? Calculate the carrier and modulating frequencies, the modulation index and deviation, and the power dissipated in a 100-ohm resistor. Find the carrier and the modulating frequencies, the modulation index and the maximum deviation of an FM wave represented by v = 15 sin (6 x 10^8 t + 5 sin 1500t). (Note: the FM equation is v = A sin (Ï‰ct + m sin Ï‰mt). When the modulating frequency in an FM system is 500 Hz and the modulating voltage is 2.5V, the modulation index is 60. Calculate the maximum deviation. What is the modulation index when the modulating frequency is reduced to 250 Hz and the modulating voltage is simultaneously raised to 3.4V.

Transcript

00:01 So here in this question we are given an angle modulated signal.

00:08 So angle modulated signal is given which is a frequency modulation.

00:12 So the standard equation of an fm is that we are considering about the party of the question is represented as s of t that is equals to vc multiplied by the sine of omega ct plus mf multiplied by the sine of omega mt.

00:30 In this question we are given the value of v that is equals to 10 sine of 108 t plus 3 sine of 104.

00:41 So here what we can say that that here we are having the value of omega c.

00:48 So omega c is representing 108.

00:50 So the value of omega c is 108.

00:52 So 2 pi f of c the value of the 2 pi f of c from here is equals to omega 108 because omega t is equals to 25 fc.

01:02 So the value of fc from here is equals to 108 divided by the 2 pi.

01:06 So we get from here we get the value of fc that is equals to 70 .189 hertz.

01:11 On comparing the given signal with the standard equation we get the value of omega m that is equals to 104.

01:18 So in the same way we get the value of fm that is equals to 16 .55 hertz.

01:23 So by comparison we get the value of mf that is equals to 3 and the value of delta f from here is mf multiplied by the fm.

01:32 So the value of delta of f from here is equals to 3 multiplied by the 16 .55.

01:37 So the value of delta f is equals to 49 .65 hertz.

01:41 So the power deficit created in the 100 ohm resistor is calculated as p which is equals to rms value of fm square of this term divided by the r that is equals to vc divided by the under root 2 raised to the power 2 which is divided by the r that is equals to 100.

02:01 So plugging into the value 10 divided by the under root 2 to the whole square of this term divided by the 100.

02:07 So the value of p from here is equals to 0 .5 watt.

02:11 So the required values for mf here is 3.

02:15 The value of fc is 17 .189 hertz.

02:18 The value of fm from here is 16 .55 hertz and that of delta f from here is 49 .65 hertz and that of p which is equals to 0 .5 watt.

02:32 So this is the answer to the part a of the question.

02:34 Now we are considering about the part b.

02:36 We are given the value of v which is equals to 15 sin of 6 multiplied by the 108 t plus 5 sin of 1500 t.

02:47 So here we have to find out the value of carrier frequency, modulating frequency, frequency dimension of delta f and modulating in fact index.

02:56 So fm for the fm we are having the value of v.

03:00 So phi of t from here is equals to omega c of t plus phi of t...

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