DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

A Signal Processing Perspective 369
filter that has no transmission zeros on the axis, other than at the origin, such as
required with Butterworth, Chebyshev Type I, Bessel, etc. highpass filters. The
transfer function for the circuit shown in Figure 11.8 is as follows:
where K, the high-frequency gain, is equal to As before, assuming a
complex-conjugate pair of poles, it is easy to show that the magnitude of those poles
is Therefore let where is defined as the
magnitude of the poles. Let the transfer function Q be defined as
where is the angle between the pole and the negative real axis
of the s plane. It is noted that and Q completely specify the pole locations. An
alternate expression of Q is as follows: Therefore,
(11.26) may be expressed as follows:
where
Section 11.2
Second-Order Stages