Page 84 - Analog and Digital Filter Design

Time and Frequency Response 81

The third column gives the order of a Cauer filter that will meet the specifica-
tion. In some cases the specification will be exceeded.

The Cutoff Frequency

There are two schools of thought concerning the cutoff frequency. The purists
would say that it depends upon the filter design. The Butterworth response has
a natural cutoff frequency at the point where signal loss through the filter is
3dB. However, Chebyshev and Cauer filters have a natural cutoff at the point
where the attenuation is equal to the passband ripple. Bessel filters are designed
from their group delay characteristics, so their natural cutoff point depends on
the filter order. Inverse Chebyshev filters have a natural frequency at the edge
of the stopband, because their response is derived from inverting Chebyshev
pole positions.

My view is that a 3dB cutoff point should be used for all filter responses. All
filters can be normalized to have a 3dB cutoff frequency by suitable scaling.
This gives some consistency and allows a direct comparison of performance
to be made. It also makes sense from an engineering perspective because the
transmitted power is halved at this point. An example where this is used is in a
diplexer. A diplexer comprises two filters that are connected together, and each
one is required to have a 3 dB cutoff frequency in order for the overall response
to be correct. Diplexers are described further in Chapter 8 and are used for
frequency band separation of signals.

References

1. Weinberg, L. “Additional Tables for Design of Optimum Ladder
Networks.” Journal of the Franklin Institute, August 1957: 127-1 38.
2. Huelsman, L. P. Active und Passive Analog Filter Design. New York:
McGraw-Hill, 1993.
3. Zverev, A. I. Handbook of Filter Synthesis. New York: John Wiley &
Sons, 1967.

4. Amstutz, P. “Elliptic Approximation and Elliptic Filter Design on
Small Computers.” IEEE Circuits and Systems, vol. CAS-25, no. 12.
December 1978: 1001-101 1.
5. Cuthbert, Thomas R. Circuit Design Using Personal Computers. New
York: John Wiley & Sons, 1983.
6. Baez-Lopez, David. “Synthesis and Sensitivity Analysis of Elliptical
Networks.” Ph.D. dissertation, University of Arizona, 1979.