Analog Lowpass Filter Prototype Design ELEC 423 Prof. Siripong Potisuk

Linear Design Specifications Passband: F p = the passband cutoff frequency  p = the passband ripple (  p > 0) Stopband: F T = the stopband cutoff frequency  S = the stopband attenuation (  S > 0) Transition band: the band of frequencies between F p and F T.

Logarithmic Design Specifications

Analog Lowpass Butterworth Filter Maximally flat passband filter magnitude response decreases monotonically starting from 1 at DC (F = 0) As n, the order of the filter, increases, the transition band decreases (steeper roll-off)

Design Parameters n, the order of the filter

Design Parameters F C, the 3-dB cutoff frequency

Example. Design a Butterworth lowpass filter to meet the following linear design specifications: F p = 1000 Hz, F T = 2000 Hz, and  p =  s = 0.05.

Transfer Function na0a0 a1a1 a2a2 a3a3 a4a

Analog Frequency Transformations Convert toReplace s with Lowpass with cutoff  0 Highpass with cutoff  0 Bandpass with cutoffs  1 and  2 Bandstop with cutoffs  1 and  2

Example. Determine the transfer function of the following filters: (a)1 st order highpass Butterworth filter, (b) 2 nd order analog bandpass filter.