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

16-24 Passive, Active, and Digital FiltersTABLE 16.2 Filter Parameters for Equation 16.45Pole Frequency(Normalized to 10 7 s 1 )Pole Quality Factor(Normalized to 10 7 s 1 )ZeroBiquad 1 v 1 ¼ 1.14762 Q 1 ¼ 0.68110 s z ¼ 0.95Biquad 2 v 2 ¼ 1.71796 Q 2 ¼ 1.11409Biquad 3 v 3 ¼ 2.31740 Q 3 ¼ 2.02290Section 4 s ¼ 0.86133 —magnetic disk storage system,* where the most critical specification is constant delay, i.e., linear phase.To this end, let us discuss the design of a seventh-order cascade low-pass with a constantdelay approximated in the Chebyshev (equiripple) sense. The specifications call for a delay variation ofmaximally 1 ns over the passband and a bandwidth f c ¼ 10 MHz. The transfer function to be implementedisH 7 (s) ¼K 0 s 2 s 2 z(s þ s) ðs 2 þ sv 1 =Q 1 þ v 2 1Þðs 2 þ sv 2 =Q 2 þ v 2 2Þðs 2 þ sv 3 =Q 3 þ v 2 3Þ(16:45)with the required parameters given in Table 16.2. The purpose of the symmetrical pair of zeros at s z ismagnitude equalization to effect a gain boost for pulse slimming. Note that these zeros do not affect thephase or the delay because the factor (v 2 þ s z 2 ) is real on the jv-axis. The fully differential second-ordercircuit chosen for the low-pass sections is shown in Figure 16.25a. Simple analysis shows that it realizesthe functionH LP (s) ¼ V LPV i¼g m1 g m2s 2 C 1 C 2 þ sC 1 g m2 þ g m1 g m2¼v 2 0s 2 þ sv 0 =Q 0 þ v 2 0(16:46)whererffiffiffiffiffiffiffiffiffiffiffiffiffig m1 g m2v 0 ¼C 1 C 2(16:47a)2C 1 2C 2+V ig ++m1 g ++g– + –+m2 m2 g m1 Vo– – – – –+–+2C 1 2C 22C 1 2C 2+g ++ +g m1 g + – +V m2m2 g–im1– – – – – +–+2C 1 2C 2V o(a)(b)+–K– +FIGURE 16.25(a) Second-order low-pass g m -C section; (b) an equalizer section.* A similar commercially successful design in bipolar technology is discussed in Ref. [12].