Answer Happy

Problem 3: 16 points Consider the double balanced diode ring mixer in the figure below: 1 EXE LO RF port 6 Local oscillator port W IF port w Load This mixer is used to multiply two signals Vin(t) = 10 cos(2nfct) and Vlo(t) = A, cos(21fot). Assume fe = 100Hz and fo = 500Hz The output signal v(t) = Kvin(t)s(t), where s(t) is a periodic square wave with frequency fo = as shown below. Assume K = 1. $() Uh- a) Compute the periods T, = and T, = of both Vin(t) and s(t). Sketch both signals over a time interval 0 St < 0.02. Sketch their corresponding product v, (t) = Kvin(t)s(t), assuming K = 1. b) Since s(t) is a periodic signal, it can be written as a Fourier Series such that: s(t) = 3 smejzan for 00 n=-00 n where Cn 70 for all odd integers n (i.e. for n = +1, +3, +5,...), and cn = 0 otherwise. Compute the spectrum S(f) = F{s(t)}.