無線增益多路負反饋帶通濾波器的研究

原創

2020-06-26 02:18

濾波器的參數是：中心頻率f0，中心頻率所對應的放大倍數爲H(jf0)，品質因數Q，帶寬爲B

設計方法，有式（6）可推出R1,R2,R3

現在上式（6.5）中，只要C1，C2未知，可通過編寫程序來解決，python程序如下：

import numpy as np
import scipy
import os

os.system('clear')

pi = 3.14159265358

f0 = 30/60
H = 10
B = 0.31

#f0 = 200/60
#H = 17
#B = 2

Q = f0/B
Re_neg3 = [1, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.2, 8.2, 9.1,
           10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 72, 82, 91,
           100, 110, 120, 130, 150, 160, 180, 200, 220, 240, 270, 300]
#, 330, 360, 390, 430, 470, 510, 560, 620, 680, 720, 820, 910
a = lambda x:x*1000
R = [a(x) for x in Re_neg3]

E24 = [1, 1.1, 1.2, 1.3, 1.5, 1.6, 1.8, 2.0, 2.2, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, 4.3, 4.7, 5.1, 5.6, 6.2, 6.8, 7.5, 8.2, 9.1,
       10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91,
       100, 110, 120, 130, 150, 160, 180, 200, 220, 240, 270, 300, 330, 360, 390, 430, 470, 510, 560, 620, 680, 750, 820, 910]

E12 = [1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2,
       10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82,
       100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820]

E6 = [0.01, 0.015, 0.022, 0.033, 0.047, 0.068,
      0.1, 0.15, 0.22, 0.33, 0.47, 0.68,
      1.0, 1.5, 2.2, 3.3, 4.7, 6.8,
      10, 15, 22, 33, 47, 68,
      100, 150, 220, 330, 470, 680]

a = lambda x,y: abs(x-y)/y
cr12 = []
offset = 0.05
for i in E6:
    for j in E6:
        C1 = i*1e-6
        C2 = j*1e-6
        R3 = Q*(C1+C2)/(2*pi*f0*C1*C2)
        R1 = R3/((1+C1/C2)*H)
        try:
            R2 = R1/(((2*pi*f0)**2)*C1*C2*R1*R3-1)
        except Exception as e:
            R2 = -1
        else:
            if  min([a(R1,y) for y in R]) < offset and  min([a(R2,y) for y in R]) < offset and  min([a(R3,y) for y in R]) < offset:
                cr12.append([C1*1e6,C2*1e6,R1*1e-3,R2*1e-3,R3*1e-3])

程序解出來的，頻率響應爲