Calculation of frequencies and voltages of carrier and modulating signals in AM wave

Q.  If an AM signal is represented by
v = ( 15 + 3 Sin( 2Π * 5 * 103 t) ) * Sin( 2Π * 0.5 * 106 t) volts

i) Calculate the values of the frequencies of carrier and modulating signals.
ii) Calculate the value of modulation index.
iii) Calculate the value of bandwidth of this signal.
- Published on 13 Oct 15

a. 1.6 MHz and 8 KHz, 0.6, 16 MHz
b. 1.9 MHz and 18 KHz, 0.2, 16 KHz
c. 2.4 MHz and 18 KHz, 0.2, 16 KHz
d. 1.6 MHz and 8 KHz, 0.2, 16 KHz

ANSWER: 1.6 MHz and 8 KHz, 0.2, 16 KHz
 
The amplitude modulated wave equation is
v = ( 10 + 2 Sin( 2Π * 8 * 103 t) ) * Sin (2Π * 1.6 * 106 t) volts

Instantaneous value of AM signal is represented by the equation
v = {Vc + Vm Sin ( ωm t )} * Sin (ωc t )
comparing it with the given equation,

Vc = 10 V
Vm = 2V
ωc (= 2Π fc) = 2Π * 1.6 * 106
ωm (= 2Π fm) = 2Π * 8 * 103

(i) The carrier frequency fc is = 1.6 * 106 = 1.6 MHz
The modulating frequency fm is = 8* 103 = 8 kHz

(ii) The modulation index m = Vm/Vc = 2/10 = 0.2

(iii) The bandwidth BW = 2 fm = 16 kHz

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