TABLE OF CONTENTS Now that we have discussed the four approximation methods and displayed third-order and fourth-order magnitude and phase plots, we are in a position to compare the results. First, we look at the magnitude plots of Figures 2.7, 2.13, 2.19, and 2.25. Table 2.1 shows the gains achieved at the stopband edge frequency of 2 rad/sec for each normalized filter type and order. (Each filter was designed with a passband gain of-1 dB.) Obviously, if attenuation characteristics in the stopband are the primary concern, an elliptic filter would have to be the choice.
| Filter Type | 3rd Order | 4th Order |
|---|---|---|
| Butterworth | -12.5 dB | -18.3 dB |
| Chebyshev | -22.5 dB | -33.8 dB |
| Inverse Chebyshev | -22.5 dB | -33.8 dB |
| Elliptic | -34.5 dB | -51.9 dB |
It provides 12 dB more attenuation than the Chebyshev types and 22 dB more attenuation than the Butterworth filter for the third-order case. In the fourth-order case, the differences increase to over 18 and 33 dB compared to the Chebyshev and Butterworth filters. The Chebyshev filter types themselves afford better stopband characteristics when compared to the Butterworth filter. They provide 10 and 15 dB more attenuation for the third-order and fourth-order cases. Although the table only lists the gains for third-order and fourth-order filters, the same trend continues for higher-order filters.
Although the Chebyshev and inverse Chebyshev filters provide the same gains at the passband and stopband edge frequencies, their responses are not identical. If we were...
