Question

1. Given the following AM rectifier detector circuit and its input and output signals: a t m()] cos RIr) LA + m(o) ? m(1) Low-pass A + m()) cos m(t) a. [40 points] Find Va(t), the modulated input signal into the low-pass filter. b. [10 points] Show that (1/T)m(t) is the signal across the output resistor R.

Answer 1

a) * Am signal is applied to diode and resistor circuit, the Negative part of the AM wave will be supposed * The Output across the resistor is the half wave rectified Version of the AM signal means multiplying AM with W(+) * The diode acts like a pair of scissors by cutting off any Negative half - cycle of the modulated sinusoid At the rectifier output, the AM signal is multiplied by w (t) Then Half wave rectified output V_R (t) is V_R (t) = {(A + m (t) cos w_c + } W (t) \r\n V_R (t) = {[A + m (t)] Cos w_c t} w(t) where W (t) is the periodic square pulse train with Fourier series as W (t) = 1/2 + 2/pi [cos w_c t - 1/3 cos 3 w_c t + 1/5 cos 5 w_c t - Ellipsis] \r\n V_R (t) =