8.3.1 Lowpass Prototype Function and its Order

As described in the Section 8.2.3 (Bilinear Transformation Design Procedure), BLT design requires obtaining the analog filter with prewarped frequency specifications. These analog filter design requirements include the ripple specification at the passband frequency edge, the attenuation specification at the stopband frequency edge, and the type of lowpass prototype (which we shall discuss) and its order.

Table 8.3 lists the Butterworth prototype functions with 3 dB passband ripple specification. Tables 8.4 and 8.5 contain the Chebyshev prototype functions (type I) with 1 dB and 0.5 dB passband ripple specifications, respectively. Other lowpass prototypes with different ripple specifications and order can be computed using the methods described in Appendix C.

Table 8.3: 3 dB Butterworth lowpass prototype transfer functions ( ? = 1)

n	H P( s)
1
2
3
4
5
6

Table 8.4: Chebyshev lowpass prototype transfer functions with 0.5 dB ripple ( ? = 0.3493)

n	H P( s)
1
2
3
4
5
6

Table 8.5: Chebyshev lowpass prototype transfer functions with 1 dB ripple ( ? = 0.5088)

n	H P( s)
1
2
3
4
5
6

In this section, we will focus on the Chebyshev type I filter. The Chebyshev type II filter design can be found in...