I'm working on time-varying circuit analysis (i'm an electrical engineer), and i'm trying to come up with a frequency domain equation for a simple time-varying circuit. Basically i've come up with something similar to equation (1).
where Vout is the output, iw is the complex frequency, Iin is the input and iwX is another input frequency. However, I know that in this special case, i can combine R and α to form β(using circuit analysis techniques). Which leads to equation (2). The way to interpret equation (2) is that the output at frequency jw is equal to the input at frequencies iw-njwX multiplied by some coefficient. I used the Fourier transform to get these equations.
So my question is, "knowing that (1) can be rewritten as (2), is there a simple way to interpret (1)?" My problem is, if i want to find Vout(jw) in terms of Iin(jw-njwX) using equation (1), i have an extra term Vout(jw-njwX) which i don't know how to interpret...
This is kinda difficult to explain cos i don't know how familiar anybody else is with circuit theory, but i know there are some pretty good mathematicians here so...
any help is most welcome and thanks in advance,
ok assume i only want the n=1 term of Iin and n=0 term of Vout. Is it true that
Vout(jw) + Beta0.Vout(jw)/R = Beta1.Iin(jw - jwX) ???
therefore, Vout(jw)/Iin(jw - jwX) = Beta1.R/(Beta0 + R)