{
"metadata": {
"name": "",
"signature": "sha256:37cf075e7171812be5843be8bfa73abd6fa4ec1e75c4ee917f74396ed076786b"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter9 - Active filters"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.2 - page : 273"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi\n",
"fH=1 #kHz\n",
"Ap=2 #Pass band gain\n",
"print \"Various design parameters are :-\"\n",
"C=0.05 #micro F#Chosen for the design\n",
"print \"Capacitance is %0.2f micro F \" %C\n",
"R=1/(2*pi*fH*1000*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.1f kohm \" %R \n",
"#Ap=1+Rf/Ri\n",
"RfBYRi=Ap-1 #Rf=Ri here\n",
"#R=Rf||Ri\n",
"Ri=2*R #kohm\n",
"Rf=Ri #kohm\n",
"print \"Resistance Ri = %0.1f kohm \" %Ri\n",
"print \"Resistance Rf = %0.1f kohm \" %Rf"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance is 0.05 micro F \n",
"Resistance R = 3.2 kohm \n",
"Resistance Ri = 6.4 kohm \n",
"Resistance Rf = 6.4 kohm \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.3 - page : 273"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"f0=800 #Hz\n",
"#For Butterworth filter : f0=fH=f_3dB\n",
"fH=f0 #Hz\n",
"f_3dB=f0 #Hz\n",
"BW=fH #Hz\n",
"print \"Bandwidth = %0.2f Hz \" %BW "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Bandwidth = 800.00 Hz \n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.4 - page 274"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi\n",
"fH=2 #kHz(Cutoff frequency)\n",
"Ap=1 #Pass band gain\n",
"print \"Various design parameters are :-\"\n",
"C=0.05 #micro F#Chosen for the design between 0.01 & 1 micro F\n",
"print \"Capacitance = %0.2f micro F \" %C\n",
"R=1/(2*pi*fH*1000*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.1f kohm \" %R\n",
"Rdash=R #/kohm(To eliminate the effect of offset)\n",
"print \"Resistance R* = %0.1f kohm \" %Rdash "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance = 0.05 micro F \n",
"Resistance R = 1.6 kohm \n",
"Resistance R* = 1.6 kohm \n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.5 - page : 275"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi\n",
"f0=1 #kHz(Cutoff frequency)\n",
"f0dash=1.5 #kHz(Cutoff frequency)\n",
"print \"Various design parameters are :-\"\n",
"#For Butterworth filter\n",
"fH=f0 #kHz\n",
"fHdash=f0dash #kHz\n",
"K=f0/f0dash #ratio\n",
"R=3.2 #kohm\n",
"Rdash=K*R #kohm\n",
"print \"Resistance Rdash = %0.1f kohm \" %Rdash \n",
"C=0.05 #micro F#Chosen for the design\n",
"print \"Capacitance = %0.2f micro F \" %C\n",
"fHdash=1/(2*pi*Rdash*1000*C*10**-6)/1000 #kHz\n",
"print \"Cutoff frequency is %0.1f kHz \" %fHdash "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Resistance Rdash = 2.1 kohm \n",
"Capacitance = 0.05 micro F \n",
"Cutoff frequency is 1.5 kHz \n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.6 - page : 278"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi\n",
"fL=400 #Hz\n",
"Ap=2 #Pass band gain\n",
"print \"Various design parameters are :-\"\n",
"C=0.05 #micro F#Chosen for the design between 0.01 & 1 micro F\n",
"print \"Capacitance is %0.2f micro F \" %C\n",
"R=1/(2*pi*fL*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.2f kohm \" %R\n",
"#Ap=1+Rf/Ri\n",
"RfBYRi=Ap-1 #Rf=Ri here\n",
"#R=Rf||Ri\n",
"Ri=2*R #kohm\n",
"Rf=Ri #kohm\n",
"print \"Resistance Ri = %0.1f kohm \" %Ri\n",
"print \"Resistance Rf = %0.1f kohm \" %Rf\n",
"# Answer in the textbook are inaccurate."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance is 0.05 micro F \n",
"Resistance R = 7.96 kohm \n",
"Resistance Ri = 15.9 kohm \n",
"Resistance Rf = 15.9 kohm \n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.7 - page : 279"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi\n",
"fL=400 #Hz\n",
"fLdash=800 #Hz\n",
"K=fL/fLdash #ratio\n",
"print \"Various parameters for retuning are :-\"\n",
"R=8.2 #kohm\n",
"Rdash=K*R #kohm\n",
"print \"Resistance Rdash = %0.2f kohm \" %Rdash\n",
"Rf=2*Rdash #kohm\n",
"Ri=2*Rdash #kohm\n",
"print \"Resistance Ri = %0.1f kohm \" %Ri\n",
"print \"Resistance Rf = %0.1f kohm \" %Rf "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various parameters for retuning are :-\n",
"Resistance Rdash = 4.10 kohm \n",
"Resistance Ri = 8.2 kohm \n",
"Resistance Rf = 8.2 kohm \n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.8 - page : 285"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"f0=3 #kHz(Critical frequency)\n",
"Ap=4 #Pass band gain\n",
"#For Butterworth filter using sallen key\n",
"alfa=1.414; klp=1 #constant\n",
"fH=f0 #kHz\n",
"f_3dB=f0 #kHz\n",
"print \"Various design parameters are :-\"\n",
"C1=0.01 #micro F#Chosen for the design\n",
"print \"Capacitance C1 = %0.2f micro F \" %C1 \n",
"C2=alfa**2*C1/4 #micro F\n",
"print \"Capacitance C2 = %0.3f micro F \" %C2 \n",
"C2=0.004 # micro F\n",
"R=1/(2*pi*fH*10**3*sqrt(C1*10**-6*C2*10**-6))/1000 #kohm\n",
"print \"Resistance R = %0.1f kohm \" %R\n",
"R=8.2 #kohm\n",
"#For offset minimization\n",
"Rdash=2*R #kohm\n",
"print \"Resistance R* = %0.2f kohm \" %Rdash \n",
"RfBYRi=Ap-1 #Rf=Ri here\n",
"#Ri=10 kohm chosen for design\n",
"Ri=10 #kohm\n",
"Rf=RfBYRi*Ri #kohm\n",
"print \"Resistance Ri = %0.1f kohm \" %Ri\n",
"print \"Resistance Rf = %0.1f kohm \" %Rf "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance C1 = 0.01 micro F \n",
"Capacitance C2 = 0.005 micro F \n",
"Resistance R = 8.4 kohm \n",
"Resistance R* = 16.40 kohm \n",
"Resistance Ri = 10.0 kohm \n",
"Resistance Rf = 30.0 kohm \n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.9 - page : 288"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"f0=2 #kHz(Critical frequency)\n",
"Ap=5 #dc gain\n",
"#For Butterworth filter using sallen key\n",
"alfa=1.414; klp=1 #constant\n",
"fH=f0 #kHz\n",
"f_3dB=f0 #kHz\n",
"Ap1=3-alfa #gain\n",
"RfBYRi=Ap1-1 #ratio\n",
"print \"Various design parameters are :-\" \n",
"C=0.05 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.2f micro F \" %C \n",
"R=klp/(2*pi*fH*10**3*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.1f kohm \" %R \n",
"#For offset minimization\n",
"#2*R=Rf||Ri=Rf/(RfBYRi+1)\n",
"Rf=2*R*(RfBYRi+1) #kohm\n",
"print \"Resistance Rf = %0.1f kohm \" %Rf \n",
"Ri=Rf/RfBYRi #kohm\n",
"print \"Resistance Ri = %0.1f kohm \" %Ri \n",
"#Ap=4 #dc gain in this case\n",
"Ap=4 #dc gain\n",
"Ap2=Ap/Ap1 #remainimg gain after 2nd order butterworth filter\n",
"RfdashBYRidash=Ap2-1 #ratio\n",
"#Ridash=10 #kohm chosen for design\n",
"Ridash=10 #kohm\n",
"print \"Resistance Ridash = %0.2f kohm \" %Ridash \n",
"Rfdash=RfdashBYRidash*Ridash #kohm\n",
"print \"Resistance Rfdash = %0.f kohm \" %Rfdash"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance C = 0.05 micro F \n",
"Resistance R = 1.6 kohm \n",
"Resistance Rf = 5.0 kohm \n",
"Resistance Ri = 8.6 kohm \n",
"Resistance Ridash = 10.00 kohm \n",
"Resistance Rfdash = 15 kohm \n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.10 - page : 289"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"f0=2 #kHz(Critical frequency)\n",
"fH=f0 #kHz\n",
"f_3dB=f0 #kHz\n",
"#For Butterworth filter using sallen key\n",
"alfa=1.414; klp=1 #constant\n",
"Ap=3-alfa # band pass gain\n",
"RfBYRi=Ap-1 #ratio\n",
"print \"Various design parameters are :-\"\n",
"C=0.05 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.2f micro F \" %C\n",
"R=1/(2*pi*fH*10**3*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.1f kohm \" %R \n",
"#For offset minimization\n",
"#2*R=Rf||Ri=Rf/(RfBYRi+1)\n",
"Rf=2*R*(RfBYRi+1) #kohm\n",
"print \"Resistance Rf = %0.1f kohm \" %Rf \n",
"Ri=Rf/RfBYRi #kohm\n",
"print \"Resistance Ri = %0.1f kohm \" %Ri \n",
"#Answer in the book is not accurate. Some calculation mistake is there while working for offset minimization."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance C = 0.05 micro F \n",
"Resistance R = 1.6 kohm \n",
"Resistance Rf = 5.0 kohm \n",
"Resistance Ri = 8.6 kohm \n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.11 - page : 290"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"f0=2 #kHz(Critical frequency)\n",
"fH=f0 #kHz\n",
"f_3dB=f0 #kHz\n",
"#For Bessel filter of 2nd order\n",
"alfa=1.73; klp=0.785 #constant\n",
"Ap=3-alfa # band pass gain\n",
"RfBYRi=Ap-1 #ratio\n",
"print \"Various design parameters are :-\" \n",
"C=0.05 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.2f micro F \" %C \n",
"R=klp/(2*pi*fH*10**3*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.2f kohm \" %R\n",
"#For offset minimization\n",
"#2*R=Rf||Ri=Rf/(RfBYRi+1)\n",
"Rf=2*R*(RfBYRi+1) #kohm\n",
"print \"Resistance Rf = %0.2f kohm \" %Rf \n",
"Ri=Rf/RfBYRi #kohm\n",
"print \"Resistance Ri = %0.2f kohm \" %Ri\n",
"# Answer in the textbook are inaccurate."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance C = 0.05 micro F \n",
"Resistance R = 1.25 kohm \n",
"Resistance Rf = 3.17 kohm \n",
"Resistance Ri = 11.75 kohm \n"
]
}
],
"prompt_number": 31
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.12 - page : 291"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"f0=.12 #kHz(Cutoff frequency)\n",
"fH=f0 #kHz\n",
"#For Butterworth filter of 2nd order\n",
"alfa=1.414; klp=1 #constant\n",
"Ap=3-alfa # band pass gain\n",
"RfBYRi=Ap-1 #ratio\n",
"print \"Various design parameters are :-\"\n",
"C=0.33 #micro F#Chosen for the design choosing between 0.01 & 1 micro F\n",
"print \"Capacitance C = %0.2f micro F \" %C \n",
"R=klp/(2*pi*fH*10**3*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.f kohm \" %R \n",
"#For offset minimization\n",
"#2*R=Rf||Ri=Rf/(RfBYRi+1)\n",
"Rf=2*R*(RfBYRi+1) #kohm\n",
"print \"Resistance Rf = %0.2f kohm \" %Rf\n",
"Ri=Rf/RfBYRi #kohm\n",
"print \"Resistance Ri = %0.f kohm \" %Ri \n",
"# Answer in the textbook are inaccurate."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance C = 0.33 micro F \n",
"Resistance R = 4 kohm \n",
"Resistance Rf = 12.75 kohm \n",
"Resistance Ri = 22 kohm \n"
]
}
],
"prompt_number": 36
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.13 - page : 295"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt, floor\n",
"fL=20 #Hz(Cutoff frequency)\n",
"#For Butterworth filter of 2nd order\n",
"alfa=1.414; klp=1 #constant\n",
"Ap=3-alfa # band pass gain\n",
"RfBYRi=Ap-1 #ratio\n",
"print \"Various design parameters are :-\"\n",
"C=0.22 #micro F#Chosen for the design choosing between 0.01 & 1 micro F\n",
"print \"Capacitance C = %0.2f micro F \" %C\n",
"R=klp/(2*pi*fL*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.2f kohm \" %R \n",
"#For offset minimization\n",
"#R=Rf||Ri=Rf/(RfBYRi+1)\n",
"Rf=R*(RfBYRi+1) #kohm\n",
"print \"Resistance Rf = %0.f kohm \" %Rf \n",
"Ri=Rf/RfBYRi #kohm\n",
"Ri=floor(Ri) #kohm\n",
"print \"Resistance Ri = %0.f kohm \" %Ri "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance C = 0.22 micro F \n",
"Resistance R = 36.17 kohm \n",
"Resistance Rf = 57 kohm \n",
"Resistance Ri = 97 kohm \n"
]
}
],
"prompt_number": 40
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.14 - page : 297"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"fH=2 #kHz(Cutoff frequency)\n",
"Ap=4 #Pass band gain\n",
"print \"Butterworth filter = cascading of 1st and 2nd order high pass filter.\"\n",
"#Butterworth polynomial is (s+1)*(s**2+s+1)\n",
"alfa=1 #for sallen key\n",
"Ap2=3-alfa #gain for 2nd order filter\n",
"Ap1=Ap/Ap2 #gain for 1st order filter\n",
"#Design parameters for 1st order filter : \n",
"print \"Various design parameters for 1st order filter are :-\"\n",
"C=0.01 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.2f micro F \" %C \n",
"R=1/(2*pi*fH*10**3*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.2f kohm \" %R\n",
"R=8.2 #kohm\n",
"#Ap1=Rf/Ri+1 with Ap1=2 we have Rf=Ri\n",
"Rf=2*R #kohm\n",
"Ri=2*R #kohm\n",
"print \"Resistance Rf = %0.2f kohm & Ri = %0.2f kohm \" %(Rf,Ri) \n",
"#Design parameters for 2nd order filter : \n",
"kLp=1/alfa #unitless\n",
"#Ap2=Rfdash/Ridash+1 with Ap2=2 we have Rfdash=Ridash\n",
"print \"Various design parameters for 2nd order filter are :-\" \n",
"C=0.033 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.3f micro F \" %C \n",
"R=kLp/(2*pi*fH*10**3*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.2f kohm \" %R\n",
"Rf=2*R #kohm\n",
"Ri=2*R #kohm\n",
"print \"Resistance Rfdash =%0.1f kohm & Ridash = %0.1f kohm \" %(Rf,Ri) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Butterworth filter = cascading of 1st and 2nd order high pass filter.\n",
"Various design parameters for 1st order filter are :-\n",
"Capacitance C = 0.01 micro F \n",
"Resistance R = 7.96 kohm \n",
"Resistance Rf = 16.40 kohm & Ri = 16.40 kohm \n",
"Various design parameters for 2nd order filter are :-\n",
"Capacitance C = 0.033 micro F \n",
"Resistance R = 2.41 kohm \n",
"Resistance Rfdash =4.8 kohm & Ridash = 4.8 kohm \n"
]
}
],
"prompt_number": 43
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.15 - page : 301"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"fL=200 #Hz\n",
"fH=1 #kHz\n",
"Ap=4 #Pass band gain\n",
"fc=sqrt(fH*1000*fL) #Hz(Cutoff frequency)\n",
"BW=fH*1000-fL #Hz\n",
"Q=fc/BW #Quality Factor\n",
"print \"Quality factor is %0.2f \" %Q\n",
"print \"As Q<12, it is a wide band filter.\"\n",
"Ap1=2 #Pass band gain for high pass section\n",
"print \"Various design parameters for high pass section are :-\"\n",
"C=0.033 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.3f micro F \" %C\n",
"R=1/(2*pi*fL*C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.1f kohm \" %R \n",
"#Ap1=Rf/Ri+1 with Ap1=2 we have Rf=Ri\n",
"Rf=2*R #kohm\n",
"Ri=2*R #kohm\n",
"print \"Resistance Rf = %0.f kohm & Ri = %0.f kohm \" %(Rf,Ri) \n",
"Ap2=2 #Pass band gain for low pass section\n",
"print \"Various design parameters for low pass section are :-\"\n",
"C=0.033 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.3f micro F \" %C \n",
"K=fL/(fH*1000) #unitless\n",
"Rdash=K*R #kohm\n",
"print \"Resistance Rdash = %0.1f kohm \" %Rdash \n",
"#Ap1=Rf/Ri+1 with Ap1=2 we have Rf=Ri\n",
"Rf=2*Rdash #kohm\n",
"Ri=2*Rdash #kohm\n",
"print \"Resistance Rf = %0.f kohm & Ri = %0.f kohm \" %(Rf,Ri) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Quality factor is 0.56 \n",
"As Q<12, it is a wide band filter.\n",
"Various design parameters for high pass section are :-\n",
"Capacitance C = 0.033 micro F \n",
"Resistance R = 24.1 kohm \n",
"Resistance Rf = 48 kohm & Ri = 48 kohm \n",
"Various design parameters for low pass section are :-\n",
"Capacitance C = 0.033 micro F \n",
"Resistance Rdash = 4.8 kohm \n",
"Resistance Rf = 10 kohm & Ri = 10 kohm \n"
]
}
],
"prompt_number": 48
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.16 - page : 306"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"print \"Part(a)\"\n",
"fc=1.2 #kHz\n",
"Q=4 #Quality Factor\n",
"Ap=10 #Pass band gain\n",
"print \"Here 2*Q**2=32>AP=10, hence it can be designed using single op-amp.\"\n",
"print \"Various design parameters are :-\"\n",
"C=0.05 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.2f micro F \" %C \n",
"#fc/Q=1/(pi*R2*C)\n",
"R2=Q/(fc*1000)/pi/(C*10**-6)/1000 #kohm\n",
"print \"Resistance R2 = %0.1f kohm \" %R2 \n",
"R1=R2/(2*Ap) #kohm\n",
"print \"Resistance R1 = %0.2f kohm \" %R1 \n",
"R3=R1*1000/(4*pi**2*R1*1000*R2*1000*(C*10**-6)**2*(fc*1000)**2-1) #ohm\n",
"print \"Resistance R3 = %0.2f ohm \" %R3 \n",
"print \"Part(b)\"\n",
"R3=460 #ohm\n",
"fc_new=1.5 #kHz\n",
"fc_old=1.2 #kHz\n",
"R3new=R3*(fc_old/fc_new)**2 #ohm\n",
"print \"Resistance R3 should be changed from %0.2f ohm to %0.2f ohm\" %(R3, R3new) \n",
"#Answer for R3 is wrong in the book"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Part(a)\n",
"Here 2*Q**2=32>AP=10, hence it can be designed using single op-amp.\n",
"Various design parameters are :-\n",
"Capacitance C = 0.05 micro F \n",
"Resistance R2 = 21.2 kohm \n",
"Resistance R1 = 1.06 kohm \n",
"Resistance R3 = 482.29 ohm \n",
"Part(b)\n",
"Resistance R3 should be changed from 460.00 ohm to 294.40 ohm\n"
]
}
],
"prompt_number": 52
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.17 - page : 308"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"fL=3 #kHz\n",
"fH=3.6 #kHz\n",
"Ap=-6 #Pass band gain\n",
"fc=sqrt(fH*fL)*1000 #Hz\n",
"BW=(fH-fL)*1000 #Hz\n",
"Q=fc/BW #Quality factor\n",
"print \"Quality factor is %0.2f\" %Q\n",
"print \"Here 1<=Q<=12 criteria fulfills, hence it can be designed using single op-amp.\"\n",
"print \"Various design parameters are :-\"\n",
"C=0.01 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.2f micro F \" %C \n",
"#fc/Q=1/(pi*R2*C)\n",
"R2=1/pi/(BW)/(C*10**-6)/1000 #kohm\n",
"print \"Resistance R2 = %0.f kohm \" %R2 \n",
"R1=-R2/(2*Ap) #kohm\n",
"print \"Resistance R1 = %0.2f kohm \" %R1 \n",
"R3=R1*1000/(4*pi**2*R1*1000*R2*1000*(C*10**-6)**2*(fc)**2-1) #ohm\n",
"print \"Resistance R3 = %0.f ohm \" %R3\n",
"print \"Design Verification : \"\n",
"print \"(i) Is 2*Q**2>|Ap| ?\\n\", 2*Q**2>abs(Ap) \n",
"print \"For op-amp 741, GBW=1 MHz\"\n",
"GBW=1 #MHz\n",
"print \"Is GBW*10**6>20*Q**2*fc ?\\n\",GBW*10**6>20*Q**2*fc\n",
"print \"2nd criteria failed. The op-amp should have higher GBW product. Use LF411\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Quality factor is 5.48\n",
"Here 1<=Q<=12 criteria fulfills, hence it can be designed using single op-amp.\n",
"Various design parameters are :-\n",
"Capacitance C = 0.01 micro F \n",
"Resistance R2 = 53 kohm \n",
"Resistance R1 = 4.42 kohm \n",
"Resistance R3 = 491 ohm \n",
"Design Verification : \n",
"(i) Is 2*Q**2>|Ap| ?\n",
"True\n",
"For op-amp 741, GBW=1 MHz\n",
"Is GBW*10**6>20*Q**2*fc ?\n",
"False\n",
"2nd criteria failed. The op-amp should have higher GBW product. Use LF411\n"
]
}
],
"prompt_number": 56
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.18 - page : 310"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"Ap=-10 #Pass band gain\n",
"Q=22 #Quality factor\n",
"fc=50 #Hz\n",
"R=60 #dB/decade(Roll off rate)\n",
"print \"\"\"Roll off rate of single op-amp=20 dB/decade.\n",
"No. of stages will be 3.\n",
"Desired design can be obtained by cascading three stages.\"\"\"\n",
"n=3 #no. of op-amps(as single op-amp has 20 dB/decade)\n",
"fc1=fc #Hz\n",
"fc2=fc #Hz\n",
"fc3=fc #Hz\n",
"Q1=Q*sqrt(2**(1/n)-1) #Quality factor of each stage\n",
"Q2=Q1 #Quality factor\n",
"Q3=Q1 #Quality factor\n",
"Ap1=-(-Ap)**(1/n) #Band pass gain of each stage\n",
"Ap2=Ap1 #Band pass gain\n",
"Ap3=Ap1 #Band pass gain\n",
"#Design of a single op-amp\n",
"C=0.1 #micro F#Chosen for the design\n",
"print \"Various design parameters for a single stages are :\"\n",
"print \"Capacitance C = %0.2f micro F \" %C \n",
"R2=Q1/pi/(fc)/(C*10**-6)/1000 #kohm\n",
"print \"Resistance R2 = %0.f kohm \" %R2 \n",
"R1=-R2/(2*Ap1) #kohm\n",
"print \"Resistance R1 = %.f kohm \" %R1 \n",
"R3=R1/(4*pi**2*R1*1000*R2*1000*(C*10**-6)**2*(fc)**2-1) #kohm\n",
"print \"Resistance R3 = %0.1f ohm \" %R3 \n",
"#Answer for R2 is wrong in the book."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Roll off rate of single op-amp=20 dB/decade.\n",
"No. of stages will be 3.\n",
"Desired design can be obtained by cascading three stages.\n",
"Various design parameters for a single stages are :\n",
"Capacitance C = 0.10 micro F \n",
"Resistance R2 = 714 kohm \n",
"Resistance R1 = 166 kohm \n",
"Resistance R3 = 1.4 ohm \n"
]
}
],
"prompt_number": 60
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex 9.20 - page : 326"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import pi, sqrt\n",
"fNO=50 #Hz\n",
"Q=20 #Quality Factor\n",
"print \"Various design parameters are :-\"\n",
"C=1 #micro F#Chosen for the design\n",
"print \"Capacitance C = %0.2f micro F \" %C \n",
"R=1/(2*pi*fNO)/(C*10**-6)/1000 #kohm\n",
"print \"Resistance R = %0.2f kohm \" %R \n",
"#Q=(RA+RB)/4/RA\n",
"RA=1 #kohm(chosen for the design)\n",
"RB=Q*4*RA-RA #kohm\n",
"print \"Resistance RA = %0.f kohm \" %RA \n",
"print \"Resistance RB = %0.f kohm \" %RB"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Various design parameters are :-\n",
"Capacitance C = 1.00 micro F \n",
"Resistance R = 3.18 kohm \n",
"Resistance RA = 1 kohm \n",
"Resistance RB = 79 kohm \n"
]
}
],
"prompt_number": 62
}
],
"metadata": {}
}
]
}