Calculating v-out for high and low pass filters...

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Resistanceisfutile

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I'm trying to do some stuff with filters and have been using the equation for corner frequency. However, I haven't been able to find any way of calculating the voltage output when a particular frequency is applied to a particular filter. Does anyone know if there is any equation for this?
 

If you have the transfer function of the filter (Vout/Vin) you are able, of course, to calculate the output voltage for any input voltage and for any frequency.
For this purpose, replace the complex variable "s" by "jw".
To circumvent the calculation it is wise to use a simulation program for displaying the magnitude and the phase of the transfer function.
 
A simple RC filter is 1st-order and has a slope that is -3dB (0.707 times the voltage) at the cutoff frequency and is at 6dB (2 times or 1/2 the voltage) per octave (10 times or 1/10th the frequency).
A Butterworth 2nd-order filter is also -3dB at cutoff and its slope is 12dB (4 times or 1/4) per octave.
A Butterworth 3rd-order filter is also -3dB at cutoff and its slope is 18dB (8 times or 1/8th) per octave.
A Butterworth 4th-order filter is also -3dB at cutoff and its slope is quess what.
 

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