# How to solve transfer function of a bandpass filter with Butterworth approximation?

How can I calculate the transfer function of this bandpass filter characteristic with Butterworth approximation?

• $A_{max}$ = 0,9 dB
• $A_{min}$ = 6,5 dB
• $\omega$3 = 100
• $\omega$1 = 300
• $\omega$2 = 1100
• $\omega$4 = 3300

Which steps do I have to take and what are some good resources for learning these kinds of filter design problems?

Volki, be aware that the design will be rather involved. Here is a short summary of the main steps (active filter design):

1. Based on the given values (center frequency, bandwidth, midband gain, attenuation values) you must use existing formulas for the bandpass-lowpass transformation. As a result, you have corresponding lowpass requirements and you can calculate the corresponding lowpass order (n=2,3,..).

2. Applying again corresponding equations you can transform the lowpss poles back to the bandpass poles.

3. Now you have two alternatives for pole allocation (depending on the required filter order):

• Series connection of active lowpass and highpass sections
• Active bandpass stage (or series connection of several stages).

For passive topologies, you must rely on filter catalogues. In any case - I strongly recommend to make use from filter design programs which are available. For example: