In a 3-terminal linear RC network, sinusoidal input, what is the maximum
gain (out/inp) possible?
In response to your original question. If you do steady state sinusoidal analysis on the RC circuit you will find that that complex gain (assuming that vout is measured across the capacitor) takes the form:
vout = vin / (1 + RCwj)
It can be seen that the maximum gain you can get occurs when the angular frequency w is 0 (DC) and the gain is 1.
If you look at the voltage across the resistor the form is:
vout = vin / (1 - j/RCw)
This function has gain 1 when w is infinite.
Hope that answered your question. You can never get more than a gain of 1 for any simple passive RC or RL circuit.
My apologies!
In a passive network of ONLY capacitors and resistors or ONLY inductors and resistors, the gain will never be greater than unity... the maximum gain really depends on how the components are connected.
To work out the maximum gain, you derive a function for the gain in terms of w. Get the derivative of that function and set it to zero to get the value of w resulting in the maximum gain and then substitute that value into the original function to get your gain. This gets mighty complicated to slove for even a small network but thats what "mathematica" type tools are for.
Unfortunately, I can't give you a "simple" proof of why it doesn't exceed unity. I will suggest that if you do derive the function for the gain and it's derivative (as I suggested in my last post) that you'll never get a gain greater than 1.
The only time you can get voltage-gain in a passive network is when there are both capacitors and inductors present. That's just a known fact.
I'm not asking for a "simple" proof - even a complicated proof will do! You say it's a known fact. Known by whom? Can you give me references to that fact?
Later:
I don't need a proof, because it's NOT true! (But I'd SURE lile to see one!)
I want to thank you for teaching me how to analyze networks. I tried your method on some various ones, until I came across one with an open-circuit voltage gain of 1.078! It had 2 resistors and 2 capacitors. Now this is only
slightly greater than 1, but it does show that all your previous comments
are wrong!
Even later:
Now I've found a 2-resistor 2-capacitor network with a maximum gain of 1.15!
Sure. I'd love to, but I can't seem to.
5spice is a beautiful program whereby you can define networks and inputs and it will solve for the various outputs.
Well, I can't upload my 5spice files. I don't know why.
I have 5spice files for RC networks and their frequency response