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

Single-Amplifier Multiple-Feedback Filters 12-7Example 12.2Design the MFB bandpass filter characterized in Example 12.1 as a high-pass=low-pass cascade ofsecond-order sections. Use the design equations of Table 12.2 and, where possible, set capacitorsequal to 5600 pF. It is suggested that you use the same impedance denormalization factor in eachstage. Select the nearest preferred 1% resistor values.SolutionSince the peak gain of the overall cascade is to be 10, let this also be the gain of stage 1 (this solutionyields the best noise performance). The peak gain of the low-pass section is given byH 1 Qpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi¼ 7:16H 1 ¼ 10 \ H 1 ¼ 1:3971 1=2Q 2The overall transfer function (from Example 12.1) isV o0:4s 2¼V i s 4 þ 0:2824s 3 þ 2:04s 2 þ 0:2824s þ 1\ H 1 H 2 ¼ 0:4 so that H 2 ¼ 0:286Thus, assuming a low-pass=high-pass cascade, we haveV o 1:397¼V i s 2 þ 0:15145 þ 1:1522 0:286s 2s 2 þ 0:1314s þ 0:8679section 1 section 2Design the low-pass section (section 1) using Table 12.2 to yieldH 1G 1 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi¼ 1:301, so that R 1 ¼ 0:7684 V1:15218 2v 2 p þ H 1C 2 ¼Q p ¼ 22:77 Fv 2 pG 3 ¼ v p ¼ 1:0733, so that R 3 ¼ 0:9316 V ¼ R 4C 5 ¼ 1=C 2 ¼ 0:0439 FNow, design the high-pass section (section 2) to yieldC 0 1 ¼ 0:286 FG 0 2 ¼ v pð2 þ H 2 ÞQ ¼ 15:099, so that R 0 2 ¼ 0:0662 VC3 0 ¼ C0 4 ¼ 1FG 0 5 ¼ v pQ p (2 þ H) ¼ 0:0574,so that R0 5 ¼ 17:397 VTo obtain as many 5600 pF capacitors as possible, the two sections should be denormalized separately.However, in this example, a single impedance denormalization will be used. Setting C3 0 ¼ C0 4¼ 5600 pFyields z n ¼ 18,947.