Lowpass Filters (above)
Highpass Filters (above)
Bandpass and Bandstop Filters (above)
This entire page has been reworked to make the denormalization of prototype lowpass
filter component values much easier to understand. I have received numerous questions
about the process over the years, particularly regarding the swapping of capacitor and
inductor values for highpass transformations. Bandpass and bandstop transformations can
be equally confusing. The original page pretty much regurgitated the type of presentation
made by many textbooks, but this new format should make amply clear the transformation
from normalized lowpass component values (1 rad/sec cutoff, 1 Ω source & load impedance)
to denormalized values for any frequency and source/load impedance. My reference is "Filter Design," by Steve Winder.
Texas Instruments' TINA circuit
simulator (free download) was used with calculated component values to assure correctness.
See schematics and plots to the right. Note that attenuators were used in 1 dB increments
to make plots for individual circuits distinguishable.
My graphic is specifically for when the source and load impedance are equal and purely
resistive (R ± j0), which is by far the most typical case. You will
need to find another source for unequal and/or reactive source/load impedances.
Butterworth prototype values are used in the example,
but you can also get them for Chebyshev and
Bessel.
Posted March 31, 2018
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