Filter stages can be cascaded to make higher-order filters. Cascading two low-pass filters makes a 2nd order low-pass filter that attenuates high-frequency signals at twice the rate in terms of dB/decade. Connect a high-pass and a low-pass filter in series, and a bandpass filter is created. Connect a low-pass and a high-pass filter in parallel and a notch filter is created.
Transfer Functions of 2nd Order Filters
Second order filters have transfer functions with second order denominator polynomials. Here is the standard form for a 2nd order filter transfer function. N(s) is a polynomial of s of degree less than or equal to 2.
, constant, the filter is lowpass with low-frequency gain of k
, the filter is bandpass with max gain of k
, the filter is highpass with high frequency gain of k
, the filter is a notch filter with gain of k