Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

Multiple-Amplifier Biquads 13-19withandN 3 (s) ¼ s 2 C 1 C 2 G 1 G 9 þ sC 2 ðG 7 G 8 G 3 þ G 8 G 2 G 3 G 8 G 1 G 4 Þþ ðG 9 G 7 G 10 G 5 þ G 9 G 10 G 2 G 5 G 9 G 10 G 4 G 6 Þ (13:60)D(s) ¼ s 2 C 1 C 2 ðG 1 G 9 þ G 2 G 9 ÞþsC 2 ðG 7 G 8 G 3 þ G 7 G 8 G 4 Þþ ðG 9 G 7 G 10 G 5 þ G 9 G 10 G 7 G 6 Þ (13:61)The two other output nodes lead to similar transfer expressions.The second biquad, which is based on the resonator in Figure 13.22, was proposed by Padukone et al.[7] and is depicted in Figure 13.24. Assuming ideal op-amps and choosing V 3 as output voltage, weobtain the following transfer function:H 3 (s) ¼ V 3V i¼ N 3(s)D(s)(13:62)withN 3 (s) ¼ s 2 ½C 2 C 3 ðG 2 G 6 G 1 G 3 ÞþC 1 C 2 G 1 G 8 Šþ sC ½ 1 G 2 G 5 G 9 C 3 G 2 G 5 G 7 þ C 2 G 1 G 4 G 8 ŠþðG 2 G 4 G 5 G 9 Þ (13:63)andD(s) ¼ s 2 ðC 1 þ C 3 ÞC 2 G 2 G 6 þ sC 2 G 1 G 4 ðG 3 þ G 8 Þþ G 2 G 4 G 5 ðG 7 þ G 9 Þ (13:64)It has been shown [7] that the pole sensitivities to all passive components are not greater than unity. Thefilter section has the main advantage of being particularly insensitive to gain-bandwidth variations evenwhen the op-amps are mismatched.V iR 1R 6 R 5+––– V 1 +V 2 +V 3R 2 R 4 C 2R 8 R 3 C 1 C 3 R 7 R 9FIGURE 13.24Padukone–Mulawka–Ghausi biquad.