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Design >> Analog Design >> linear periodic time-varying system
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Message started by aaron_do on Jun 10^th, 2008, 6:44am

Title: linear periodic time-varying system
Post by aaron_do on Jun 10^th, 2008, 6:44am

Hi all,

i have a mixer where i'm treating it as a LPTV system and trying to calculate the transfer function. For the first sideband, i've arrived at the solution:

Beta1*Vout(jw-jwLO) = IRF(jw)

that's just a simplification where Beta1 is the first harmonic of the fourier series expansion of a conductance, and IRF(jw) is the input current. wLO is the LO frequency. So my problem is, in order to maximize Vout(jw-jwLO) i need to minimize Beta1. However, if Beta1 = 0, then there would be no sideband. So where have i gone wrong?

thanks,
Aaron

BTW, to get that equation, i simply put IRF into a time varying conductance. Therefore, IRF(t) = Vout(t).G(t) . So when you take the fourier transform, Vout(t).G(t) becomes 1/2pi Vout(jw)*G(jw) where * is convolution.