A non-linear device with a transfer characteristic given

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A non-linear device with a transfer characteristic given by i = (0 + 2V_i + 0·2V_i²) mA is supplied with a carrier of 1V amplitude and a sinusoidal signal of 0.5V amplitude in series. If at the output the frequency component of AM signal is considered, the depth of modulation is—

1. 18%
2. 10%
3. 20%
4. 33.33%

Correct Option: B

Given transfer characteristic
i = (10 + 2V_i + 0·2 V_i²) mA …(A)
Since, according to question both carrier and sinusoidal signals are in series. Let assume V_i is represented as
V_i = A_m cos ω_mt + A_c cos ω_ct
or
V_i = 0·5 cos ω_mt + cos ω_ct (˙.˙ A_m = 0·5V, A_c = 1V)
Now, on putting the value of V_i in equation (A) we get amplitude modulated AM signal i.e.,
i = 10 + 2 (cos ω_ct + 0·5 cos ω_mt) + 0·2 (cos ω_ct + 0·5 cos ω_mt)²
or
i = 2 cos ω_c t + 0·2 cos ω_ct + cos ω_mt
(˙.˙ At the output only lower frequency terms are considered and neglecting the higher frequency terms)

i = 2		1 +	0.2	cos ω_mt			cos ω_ct
			2

...(B)
which is equal to standard AM equation.
i = A_c (1 + μ cos ω_mt) cos ω_ct …(C)
So, on comparing equation (B) and (C) we get

μ =	0.2	= 0.1
	2

and% modulation index = 0.1 x 100 = 10%.
Hence alternative (B) is the correct choice.