{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"CHAPTER 21 ACTIVE FILTERS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-1, Page 806"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"Rf=39.0 #feedback path resistance Rf (KOhm)\n",
"R1=1.0 #inverting input resistance R1(KOhm)\n",
"R2=12.0*10**3 #non-inverting input resistance R2(Ohm)\n",
"C=680*10**-12 #capacitance at non-inverting input(F)\n",
"\n",
"Av=(Rf/R1)+1 # voltage gain\n",
"fc=(2*math.pi*R2*C)**-1 #cutoff frequency(Hz)\n",
"\n",
"print 'voltage gain Av = ',Av\n",
"print 'cutoff frequency fc = ',round((fc/1000),2),'KHz'\n",
"print 'frequency response:'\n",
"print 'voltage gain is 32 dB in pass band. response breaks at 19.5 KHz.'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"voltage gain Av = 40.0\n",
"cutoff frequency fc = 19.5 KHz\n",
"frequency response:\n",
"voltage gain is 32 dB in pass band. response breaks at 19.5 KHz.\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-2, Page 807"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"Rf=43.0 #feedback path resistance Rf (KOhm)\n",
"R1=0.220 #non-inverting input resistance R1(KOhm)\n",
"C=100*10**-12 #capacitance (F)\n",
"\n",
"Av=(-Rf/R1) # voltage gain\n",
"fc=((2*math.pi*Rf*C)**-1)/10**6 #cutoff frequency(KHz)\n",
"\n",
"print 'voltage gain Av = ',round(Av,2)\n",
"print 'cutoff frequency fc = ',round(fc,2),'KHz'\n",
"print 'voltage gain is 45.8 dB in pass band. response breaks at 37 KHz.'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"voltage gain Av = -195.45\n",
"cutoff frequency fc = 37.01 KHz\n",
"voltage gain is 45.8 dB in pass band. response breaks at 37 KHz.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-3, Page 811"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"R1=30 #non-inverting input resistance R1(KOhm)\n",
"R2=30 #non-inverting input resistance R2(KOhm)\n",
"C2=1.64*10**-9 #feedback path capacitance (F)\n",
"C1=820*10**-12 #non-inverting input capacitance (F)\n",
"\n",
"Q=0.5*((C2/C1)**0.5) #Q\n",
"fp=((2*math.pi*R1*(C1*C2)**0.5)**-1)/10**6 #pole frequency(KHz)\n",
"fc=fp #cutoff frequency(KHz)\n",
"\n",
"print ' Q = ',round(Q,3)\n",
"print 'pole frequency fp = ',round(fp,2),'KHz'\n",
"print 'cutoff frequency fc = fp, ',round(fc,2),'KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Q = 0.707\n",
"pole frequency fp = 4.57 KHz\n",
"cutoff frequency fc = fp, 4.57 KHz\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-4, Page 811"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"R1=51 #non-inverting input resistance R1(KOhm)\n",
"R2=51 #non-inverting input resistance R2(KOhm)\n",
"C2=440*10**-12 #feedback path capacitance (F)\n",
"C1=330*10**-12 #non-inverting input capacitance (F)\n",
"kc=0.786 #constant for bessel response \n",
"\n",
"Q=0.5*((C2/C1)**0.5) #Q\n",
"fp=((2*math.pi*R1*(C1*C2)**0.5)**-1)/10**6 #pole frequency(KHz)\n",
"fc=kc*fp #cutoff frequency(KHz) \n",
"\n",
"print ' Q = ',round(Q,2)\n",
"print 'pole frequency fp = ',round(fp,2),'KHz'\n",
"print 'cutoff frequency fc = ',round(fc,2),'KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Q = 0.58\n",
"pole frequency fp = 8.19 KHz\n",
"cutoff frequency fc = 6.44 KHz\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-5, Page 812"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"R1=22 #non-inverting input resistance R1(KOhm)\n",
"R2=22 #non-inverting input resistance R2(KOhm)\n",
"C2=27*10**-9 #feedback path capacitance (F)\n",
"C1=390*10**-12 #non-inverting input capacitance (F)\n",
"kc=1.38 #constant for bessel response \n",
"k0=0.99 #constant for bessel response\n",
"k3=1.54 #constant for bessel response\n",
"\n",
"Q=0.5*((C2/C1)**0.5) #Q\n",
"fp=((2*math.pi*R1*(C1*C2)**0.5)**-1)/10**6 #pole frequency(KHz)\n",
"fc=kc*fp #cutoff frequency(KHz) \n",
"f3=k3*fp #3-dB frequency(KHz)\n",
"\n",
"print 'Q = ',round(Q,2)\n",
"print 'pole frequency fp = ',round(fp,2),'KHz'\n",
"print 'cutoff frequency fc = ',round(fc,2),'KHz'\n",
"print '3-dB frequency f(3dB) = ',round(f3,2),'KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Q = 4.16\n",
"pole frequency fp = 2.23 KHz\n",
"cutoff frequency fc = 3.08 KHz\n",
"3-dB frequency f(3dB) = 3.43 KHz\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-6, Page 817"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"R1=47 #non-inverting input resistance R1(KOhm)\n",
"R2=47 #non-inverting input resistance R2(KOhm)\n",
"C2=330*10**-12 #feedback path capacitance (F)\n",
"C1=330*10**-12 #non-inverting input capacitance (F)\n",
"R3=51 #inverting input resistance R3(KOhm)\n",
"Rf=30.0 #feedback path resistance Rf (KOhm)\n",
"\n",
"Av=(Rf/R3)+1 #voltage gain \n",
"Q=(3-Av)**-1 #Q\n",
"fp=((2*math.pi*R1*(C1*C2)**0.5)**-1)/10**6 #pole frequency(KHz)\n",
"fc=fp #cutoff frequency(KHz) \n",
"\n",
"print ' Q = ',round(Q,2)\n",
"print 'pole frequency fp = ',round(fp,2),'KHz'\n",
"print 'cutoff frequency fc = ',round(fc,2),'KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Q = 0.71\n",
"pole frequency fp = 10.26 KHz\n",
"cutoff frequency fc = 10.26 KHz\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-7, Page 817"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"R1=82 #non-inverting input resistance R1(KOhm)\n",
"R2=82 #non-inverting input resistance R2(KOhm)\n",
"C2=100*10**-12 #feedback path capacitance (F)\n",
"C1=100*10**-12 #non-inverting input capacitance (F)\n",
"R3=56 #inverting input resistance R3(KOhm)\n",
"Rf=15.0 #feedback path resistance Rf (KOhm)\n",
"kc=0.786 #constant for bessel response \n",
"\n",
"Av=(Rf/R3)+1 #voltage gain \n",
"Q=(3-Av)**-1 #Q\n",
"fp=((2*math.pi*R1*(C1*C2)**0.5)**-1)/10**6 #pole frequency(KHz)\n",
"fc=kc*fp #cutoff frequency(KHz) \n",
"\n",
"print 'Q = ',round(Q,2)\n",
"print 'pole frequency fp = ',round(fp,2),'KHz'\n",
"print 'cutoff frequency fc = ',round(fc,2),'KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Q = 0.58\n",
"pole frequency fp = 19.41 KHz\n",
"cutoff frequency fc = 15.26 KHz\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-8, Page 818"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"R1=56 #non-inverting input resistance R1(KOhm)\n",
"R2=56 #non-inverting input resistance R2(KOhm)\n",
"C2=220*10**-12 #feedback path capacitance (F)\n",
"C1=220*10**-12 #non-inverting input capacitance (F)\n",
"R3=20.0 #inverting input resistance R3(KOhm)\n",
"Rf=39.0 #feedback path resistance Rf (KOhm)\n",
"kc=1.414 #constant for bessel response \n",
"k0=1.0 #constant for bessel response\n",
"k3=1.55 #constant for bessel response\n",
"\n",
"Av=(Rf/R3)+1 #voltage gain \n",
"Q=(3-Av)**-1 #Q\n",
"fp=((2*math.pi*R1*(C1*C2)**0.5)**-1)/10**6 #pole frequency(KHz)\n",
"fc=kc*fp #cutoff frequency(KHz) \n",
"f0=k0*fp #resosnant frequency(KHz)\n",
"f3=k3*fp #3-dB frequency (KHz)\n",
"Av1=((1.01*Rf)/(0.99*R3))+1 #voltage gain considering 1% tolerance \n",
"Q1=(3-Av1)**-1 #Q\n",
"\n",
"print 'Q = ',Q\n",
"print 'pole frequency fp = ',round(fp,2),'KHz'\n",
"print 'cutoff frequency fc = ',round(fc,2),'KHz'\n",
"print 'resonant frequency f0 = ',round(f0,2),'KHz'\n",
"print '3-dB frequency f(3-dB) = ',round(f3,2),'KHz'\n",
"print 'circuit produces 26-dB peak in response at 12.9 KHz, rolls off to 0 dB at cutoff and 3 dB down at 20 KHz'\n",
"print 'after considering tolerance in resistance, Q changed to',Q1,'approximately'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Q = 20.0\n",
"pole frequency fp = 12.92 KHz\n",
"cutoff frequency fc = 18.27 KHz\n",
"resonant frequency f0 = 12.92 KHz\n",
"3-dB frequency f(3-dB) = 20.02 KHz\n",
"circuit produces 26-dB peak in response at 12.9 KHz, rolls off to 0 dB at cutoff and 3 dB down at 20 KHz\n",
"after considering tolerance in resistance, Q changed to 94.2857142857 approximately\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-9, Page 820"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"R1=24 #non-inverting input resistance R1(KOhm)\n",
"R2=12 #feedback path resistance R2(KOhm)\n",
"C=4.7*10**-9 #non-inverting input capacitance (F)\n",
"\n",
"Q=0.5*((R1/R2)**0.5) #Q\n",
"fp=((2*math.pi*C*(R1*R2)**0.5)**-1)/10**6 #pole frequency(KHz)\n",
"fc=fp #cutoff frequency(KHz) \n",
"\n",
"print 'Q = ',round(Q,2)\n",
"print 'pole frequency fp = ',math.ceil(fp),'KHz'\n",
"print 'cutoff frequency fc = ',math.ceil(fc),'KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Q = 0.71\n",
"pole frequency fp = 2.0 KHz\n",
"cutoff frequency fc = 2.0 KHz\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-10, Page 821"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"R1=30 #non-inverting input resistance R1(KOhm)\n",
"R2=30 #feedback path resistance R2(KOhm)\n",
"C=1*10**-9 #non-inverting input capacitance (F)\n",
"R3=10.0 #inverting input resistance R3(KOhm)\n",
"Rf=15.0 #feedback path resistance Rf (KOhm)\n",
"kc=1.32 #constant for bessel response \n",
"k0=0.94 #constant for bessel response\n",
"k3=1.48 #constant for bessel response\n",
"\n",
"Av=(Rf/R3)+1 #voltage gain \n",
"Q=(3-Av)**-1 #Q\n",
"fp=((2*math.pi*R1*C)**-1)/10**6 #pole frequency(KHz)\n",
"fc=fp/kc #cutoff frequency(KHz) \n",
"f0=fp/k0 #resosnant frequency(KHz)\n",
"f3=fp/k3 #3-dB frequency (KHz)\n",
"\n",
"print 'Q = ',Q\n",
"print 'pole frequency fp = ',round(fp,2),'KHz'\n",
"print 'cutoff frequency fc = ',round(fc,2),'KHz'\n",
"print 'resonant frequency f0 = ',round(f0,2),'KHz'\n",
"print '3-dB frequency f(3-dB) = ',round(f3,2),'KHz'\n",
"print 'circuit produces 6.3-dB peak in response at 5.65 KHz, rolls off to 0 dB at cutoff at 4.02 KHz and 3 dB down at 3.59 KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Q = 2.0\n",
"pole frequency fp = 5.31 KHz\n",
"cutoff frequency fc = 4.02 KHz\n",
"resonant frequency f0 = 5.64 KHz\n",
"3-dB frequency f(3-dB) = 3.58 KHz\n",
"circuit produces 6.3-dB peak in response at 5.65 KHz, rolls off to 0 dB at cutoff at 4.02 KHz and 3 dB down at 3.59 KHz\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-11, Page 825"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"R1=18 #non-inverting input resistance R1(KOhm)\n",
"R2=30 #feedback path resistance R2(KOhm)\n",
"C=8.2*10**-9 #non-inverting input capacitance (F)\n",
"R31=0.080 #inverting max input resistance R3(KOhm)\n",
"R32=0.015 #inverting min input resistance R3(KOhm)\n",
"\n",
"BW=((2*math.pi*R1*C)**-1)/10**6 #bandwidth(KHz)\n",
"f0=((2*math.pi*C*((2*R1*((R1**-1+R31**-1)**-1))**0.5))**-1)/10**6 #minimum center frequency(KHz)\n",
"f01=((2*math.pi*C*((2*R1*((R1**-1+R32**-1)**-1))**0.5))**-1)/10**6 #minimum center frequency(KHz)\n",
"\n",
"print 'bandwidth BW = ',round(BW,2),'KHz'\n",
"print 'minimum center frequency f0 = ',round(f0,2),'KHz'\n",
"print 'maximum center frequency f0 = ',round(f01,2),'KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"bandwidth BW = 1.08 KHz\n",
"minimum center frequency f0 = 11.46 KHz\n",
"maximum center frequency f0 = 26.42 KHz\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-12, Page 827"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"R=22.0 #non-inverting input resistance(KOhm)\n",
"C=120*10**-9 #non-inverting input capacitance (F)\n",
"R1=13.0 #inverting input resistance(KOhm)\n",
"R2=10.0 #feedback path resistance(KOhm)\n",
"\n",
"Av=(R2/R1)+1 #voltage gain \n",
"Q=0.5/(2-Av) #Q\n",
"f0=((2*math.pi*R*C)**-1)/10**3 #center frequency(KHz)\n",
"\n",
"print 'voltage gain Av = ',round(Av,2)\n",
"print 'Q = ',round(Q,2)\n",
"print 'center frequency f0 = ',round(f0,2),'KHz'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"voltage gain Av = 1.77\n",
"Q = 2.17\n",
"center frequency f0 = 60.29 KHz\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21-13, Page 833"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"R=1.0 #non-inverting input resistance(KOhm)\n",
"C=100*10**-9 #non-inverting input capacitance (F)\n",
"f=1.0 #frequency given(KHz)\n",
"\n",
"f0=((2*math.pi*R*C)**-1)/10**6 #center frequency(KHz)\n",
"phi=(2*math.atan(f0/f))*180/math.pi #phase shift(deg)\n",
"\n",
"print 'center frequency f0 = ',round(f0,2),'KHz'\n",
"print 'phase shift = ',math.ceil(phi),'degrees'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"center frequency f0 = 1.59 KHz\n",
"phase shift = 116.0 degrees\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}