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

**If an AM signal is represented by **

v = ( 15 + 3 Sin( 2Π * 5 * 10^{3} t) ) * Sin( 2Π * 0.5 * 10^{6} 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.

a.) 1.6MHz and 8KHz, 0.6, 16 MHz

b.) 1.9MHz and 18KHz, 0.2, 16 KHz

c.) 2.4 MHz and 18KHz, 0.2, 16 KHz

d.) 1.6MHz and 8KHz, 0.2, 16 KHz

Correct Answer: d) 1.6MHz and 8KHz, 0.2, 16 KHz

**Explanation: **

The amplitude modulated wave equation is

v = ( 10 + 2 Sin( 2Π * 8 * 10^{3} t) ) * Sin( 2Π * 1.6 * 10^{6} t) volts

Instantaneous value of AM signal is represented by the equation

v = {V_{c} + V_{m} Sin ( ω_{m} t )} * Sin ( ω_{c} t )

comparing it with the given equation,

V_{c} = 10 V

V_{m} = 2V

ω_{c} (= 2Π f_{c}) = 2Π * 1.6 * 10^{6}

ω_{m} (= 2Π f_{m}) = 2Π * 8 * 10^{3}

(i) The carrier frequency f_{c} is = 1.6 * 10^{6} = 1.6 MHz

The modulating frequency f_{m} is = 8* 10^{3} = 8 kHz

(ii) The modulation index m = V_{m}/V_{c} = 2/10 = 0.2

(iii) The bandwidth BW = 2 f_{m} = 16 kHz