I am having trouble writing down a mathematical expression to explain AC coupling as a function of the input capacitor and the effective resistance. Does anyone have a suggestion on where I can find the formula, or know the formula? What I want to simulate is what the signal will look like on a scope when it is AC coupled. A complex signal is involved and I need to write a program to simulate the resulting signal.

Thanks,

 

I am having trouble writing down a mathematical expression to explain AC coupling as a function of the input capacitor and the effective resistance. Does anyone have a suggestion on where I can find the formula, or know the formula? What I want to simulate is what the signal will look like on a scope when it is AC coupled. A complex signal is involved and I need to write a program to simulate the resulting signal.

Thanks,

When you AC couple an output signal you are actually removing any DC that the signal has, however you said that you have a complex signal so the lower frequency components may suffer by using AC coupling. The higher the capacitance the less that the low freq. will be afected. If your signal is a video signal, capactive coupling will distort the signal. Usually AC coupling is used for protection and isolation in case someone shorted to ground or a supply voltage the output.
When you are dealing with complex signals I thinks the best is to try inserting diferent values of capacitors and see the output signal on the scope, then you can make some wild guess of what will happen to the signal at diferent coupling capacitances. There may be a formula to aproximate that but you are going to have to develop it if your signal is not a standard one. I think Matlab may help you.

 

The Impedance of the input capacitor forms a potential divider with the input resistance (impedance) of the circuit.

The trick is to arrange for the input capacitor impedance to be much lower than the input resistance at the signal frequency so that most of the signal voltage appears across the input (resistance) of the circuit.

Hope this helps.