Transfer Functions

[Stiganator]

I have a homework question that asks for you to derive the operational and sinusoidal transfer functions for a RC highpass filter.

All I can come up with is Vo/Vi= R/((1/jwC)+R)=wRC/(sqrt(1+(wCR)^2))

I haven't had much in circuits and such I didn't know there were multiple kinds of transfer functions. Which one am I deriving above? How is the other different?

It then asks for the step response and the complete phase and magnitude response.

Can I do those in excel or how would you go about doing it?

 

[Qacer]

To tell you the truth, I've never heard of a sinusoidal transfer function before. I assumed that the operational transfer function is just your traditional output vs input function. I did some searching on Google and found this explanation for sinusoidal transfer functions:
http://books.google.com/books?...awI3IfI25h4zQ#PPA16,M1

The idea behind a sinusoidal transfer function applies if you have a sinusoidal input. For this type of input, the output is also assumed to be a sinusoid of the same frequency with a different amplitude and phase shift. This is probably assuming that your signal is just going thru an amplifier and not necessarily a mixer. With this assumption, the input-output relationship can be describe by amplitude and phase shift ratios.

From you equation, it looks like your high pass filter is just a simple capacitor-resistor series. Is that correct?

Anyway, this might help, too:
http://www.play-hookey.com/ac_...y/hi_pass_filters.html

 

[TuxDave]

Originally posted by: Stiganator
I have a homework question that asks for you to derive the operational and sinusoidal transfer functions for a RC highpass filter.

All I can come up with is Vo/Vi= R/((1/jwC)+R)=wRC/(sqrt(1+(wCR)^2))

I haven't had much in circuits and such I didn't know there were multiple kinds of transfer functions. Which one am I deriving above? How is the other different?

It then asks for the step response and the complete phase and magnitude response.

Can I do those in excel or how would you go about doing it?

I never used those terms but I would guess:

Sinusoidal Transfer Function = With respect to frequency (omega) which is what you derived.

Operational = With respect to time so you just use your Kirchoff equations.

 

[cirthix]

For linear circuits, all you need is the transfer function (not sure what you'e talking about when you say sinusodial transfer function). Basic method:

write down the impedance of each element
write the node equations
solve for output in terms of input
write H(iw)=your transfer function

for any input in(t), out(t)=ilaplace(h(iw)*laplace(in(t))

This is the simple way, there are others. I don't think excel can do this properly, but it's easy to do in matlab (ilaplace above=matlab command for inverse laplace transferm, laplace=matlab command for laplace transform).

If you want the step response, think about what the laplace transform of the unit step is (heaviside in matlab) and apply the above principle. For this kind of stuff, if you ahve to do it by hand, do yourself a favor and print out a sheet of basic laplace transforms and properties.

For magnitude, take the real part of the transfer function. for phase, look at the phase of the transfer function