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

14-16 Passive, Active, and Digital FiltersTABLE 14.4Design Values and Tuning ProceduresTuning SequenceCircuitTransferNumberDesign Values Function Realized v n v p Q p Q z1 R 2 ¼ R, R 4 ¼ RQ 1=2p ,v 2 p— RTR 5 ¼ 2R = (aH LP ),3 ¼ H 5 R 4 —LPD(s)R 6 ¼ R = [a(1 H LP = 2)], H LP < 2 s 2= HHP ,T 1 ¼ H HP — R 6 R 4 —2 R 1 ¼ R 1 þ Q 1=2pR 2 ¼ R 1 þ Q 1=2 hp 1 þ Q 1=2pR 4 ¼ RQ 1=2p , R 6 ¼ R=a,H HP < 1 þ Q 1=2p3 R 2 ¼ R, R 3 ¼ 2RQ 1=2Qpp H BP ,T 3 ¼ H BPR 4 ¼ RQ 1=2D(s)p = 1 H BP = 2,R 6 ¼ R=a, H BP < 24 R 1 ¼ R 1 þ Q 1=2 s 2 þ v 2 np = HN ,T 1 ¼ H ND(s)R 2 ¼ 1(G = G 1 ),R 4 ¼ RQ 1=2p , R 6 ¼ 1(aG = G 5 ),R 5 ¼ Rv 2 p 1 þ Q 1=2 p aHN v 2 n ,H N < 1 þ Q 1=2 p ,H N ¼< v 2 p 1 þ Q 1=2 p v2n for v n > v ps 2 vz5 For all-pass: R 1 ¼ R,T 1 ¼ H s þ v2 Qz zAPR 4 ¼ RQ 1=2D(s)p R 5 ¼ R=a, R 1 ¼ R 7 ,R 2 ¼1, H AP ¼ 1Notes: D(s) ¼ s 2 þ (v p =Q p )s þ v 2 p , a ¼ 2Q1=2 p = 1 þ Q 1=2 p .C 1 ¼ C 2 ¼ C ¼ 1=(v p R), R 10 ¼ aR, R 8 ¼ RQ 1=2p , R 7 ¼ R 8 ¼ R.H HPi,D(s)svp— R 6 R 3 —R 5 R 6 R 4 —R 5 R 4OA finite gain and bandwidth, and low element-spread design, in circuits 1–5 in Table 14.3. Using theseconstraints, a possible design for LP, HP, BP, AP, and N sections is obtained, as indicated in Table 14.4.It is seen that Q p , v p , v n , Q z , and v z , can be independently adjusted by trimming at most three resistors.A trimming sequence is also given in Table 14.4.14.11 Practical Sixth-Order Elliptic BP Filter DesignUsing the 3-OA CGIC BiquadThe sixth-order elliptic bandpass filter specified in Section 14.7 was designed using the 3-OA CGICbiquad and similar components to those in Section 14.7.The realization shown in Figure 14.13a uses cascaded sections of the types 3 and 4 in Table 14.4.The element design values are also given in Figure 14.13a. The measured frequency response is shownin Figure 14.13b and c; it is in agreement with the theoretical response. Figure 14.13d shows the frequencyresponse for supply voltages of 7.5 V (lower curve), and 15 V (upper curve); the input voltage is 0.3 V.The passband ripple remains less than 0.34 dB and the deviation in the stopband is negligible. Figure14.13e and f illustrate the effect of temperature variations. The passband ripple remains less than 0.5 dB inthe temperature range from 108C (right-hand curve) to 708C (left-hand curve). A center frequencydisplacement of 9 Hz has been measured, which corresponds to a change of 75 ppm=8C.These results illustrate the additional performance improvements compared with the results in Section14.7 using the 2-OA CGIC biquad.