11.6 Other Low-Pass Filter Approximations

We will briefly discuss two other filter types, the Inverted Chebyshev, and the Cauer or Elliptic.

The Inverted Chebyshev, also known as Type II Chebyshev, is characterized by the following amplitude-square approximation.

and has the ripple in the stop-band as opposed to Type I which has the ripple in the pass-band. In (11.64), the frequency ? _C defines the beginning of the stop band.

The characteristics of a typical Type II Chebyshev low-pass filter are shown in Figure 11.22.

Figure 11.22: Type II Chebyshev low-pass filter

We can design Type II Chebyshev low-pass filters with the MATLAB cheb2ap function. Thus, the statement [z,p,k] = cheb2ap(N,Rs) where N denotes the order of the filter, returns the zeros, poles, and gain of an N ? th order normalized prototype Type II Chebyshev analog lowpass filter with ripple Rs decibels in the stop band.

Solution:

We use the code

<span class="serif">w=0:0.01:1000; [z,p,k]=cheb2ap(3,3); [b,a]=zp2tf(z,p,k); Gs=freqs(b,a,w);...semilogx(w,abs(Gs)); xlabel('Frequency in rad/sec'); ylabel('Magnitude of G(s)');title('Type 2 Chebyshev Low-Pass Filter, k=3, 3 dB ripple in stop band'); grid</span>

The plot for this filter is shown in Figure 11.23.

Figure 11.23: Plot for the filter of Example 11.13

The elliptic (Cauer) filters are characterized by the low-pass amplitude-squared function

where R _k( x) represents a rational elliptic...