{
"metadata": {
"name": "",
"signature": "sha256:4a9283ba6472e11de214bfc0c69a7f007685d94fb7b513179011a2e471e81b7b"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7:Operational Amplifiers"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1,Page number 361"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"V1=120 #negative terminal Vn(uV)\n",
"V2=80 #positive terminal Vp(uV)\n",
"Ad=10**3 #difference mode gain\n",
"\n",
"\n",
"#Calculations\n",
"Vd=V1-V2 #difference mode signal(uV) \n",
"Vc=(V1+V2)/2 #common mode signal(uV)\n",
"\n",
"#Part a\n",
"CMRR=100. #common mode rejection ratio\n",
"Vo=Ad*Vd*(1+(Vc/(CMRR*Vd))) #output voltage(mV)\n",
" \n",
"#Part b\n",
"CMRR=10**5. #common mode rejection ratio\n",
"Vo1=Ad*Vd*(1+(1/CMRR)*(Vc/Vd)) #output voltage(mV) \n",
"\n",
"#Results\n",
"print\"output voltage is\",round(Vo/1E+3),\"mV\"\n",
"print\"output voltage is\",round(Vo1/1E+3),\"mV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"output voltage is 41.0 mV\n",
"output voltage is 40.0 mV\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2,Page number 365"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"deltavi=0.5 #change in vi(V)\n",
"deltat=10 #change in time(us)\n",
"s=1 #slew rate(V/us)\n",
"\n",
"#Calculations\n",
"Kvf=(s*deltat)/deltavi #closed loop gain of amplifier\n",
"\n",
"#Results\n",
"print\"closed loop gain of amplifier is\",Kvf"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"closed loop gain of amplifier is 20.0\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3,Page number 365"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"f=50*10**3. #OPAMP freequency(Hz)\n",
"Vm=0.02 #maximum value of signal voltage(V)\n",
"S=.5*10**6 #slew rate(V/s)\n",
"\n",
"#Calculations\n",
"Kvf=S/(2*(math.pi)*f*Vm) #closed loop gain of amplifier\n",
"\n",
"#Results\n",
"print\"closed loop gain of amplifier is\",round(Kvf)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"closed loop gain of amplifier is 80.0\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.4,Page number 369"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Ic=100 #current at quinscent point(uA)\n",
"beta=2000. #current gain\n",
"Ad=250 #difference mode gain\n",
"CMRR=5000 #as 74 dB=5000,common mode rejection ratio(dB)\n",
"\n",
"#Calculations\n",
"rpi=(25*beta)/Ic #dynamic internal resistance(k ohms) \n",
"gm=beta/rpi #transconductance(mS)\n",
"Re=CMRR/gm #emitter resistance(k ohms)\n",
"Rc=(Ad*2)/gm #collector resistance(k ohms) from formula Ad=gmRc/2\n",
"Rin=2*rpi #input resistance(k ohms)\n",
"\n",
"#Results\n",
"print\"Re is\",Re,\"k ohms\"\n",
"print\"Rc is\",Rc,\"k ohms\"\n",
"print\"input resistance is\",Rin,\"k ohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Re is 1250.0 k ohms\n",
"Rc is 125.0 k ohms\n",
"input resistance is 1000.0 k ohms\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6,Page number 371"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Icq=.428 #current at quinscent point(uA)\n",
"beta=200. #current gain\n",
" #as 74 dB=5000,common mode rejection ratio(dB)\n",
"Rc=10. #collector resistance(k ohms) \n",
"Re=16. #emitter resistance(k ohms) \n",
"Vcc=15. #supply voltage(V)\n",
"\n",
"#Calculations\n",
"#Part b\n",
"Ibq=Icq/beta #Ib at Q(uA)\n",
"rpi=(25*beta)/Icq #dynamic resistance(k ohms)\n",
"gm=beta/rpi #transconductance\n",
"\n",
"#Part b\n",
"vo1=Vcc-(Icq*Rc) #terminal 1 voltage(V) \n",
"vo2=vo1 #terminal 2 voltage(V) \n",
"\n",
"#Part c \n",
"Ad=(gm*Rc)/2 #differential mode gain\n",
"Ac=Rc/(2*Re) #common mode gain\n",
"CMRR=Ad/Ac #common mode rejection ratio\n",
"\n",
"#Part d\n",
"Rid=2*rpi #differential input resistance(k ohms)\n",
"rpi=11.7 #dynamic resistance(k ohms)\n",
"Ric=rpi+(2*(beta+1)*Re) #common mode input resistance(k ohms)\n",
"\n",
"#Results\n",
"print\"Icq is\",Icq,\"mA,and Ibq is \",round((Ibq/1E-3),2),\"uA\"\n",
"print\"vo1 and vo2 have same value as\",vo1,\"V\"\n",
"print\"\",\n",
"print\"Ad:\",round(Ad/1E-3),\",Ac:\",round(Ac,3),\"and CMRR is\",round(CMRR/1E-3)\n",
"print\"Rid is\",round((Rid/1E+3),1),\"K ohms and Ric is\",round((Ric/1E+3),2),\" Mohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Icq is 0.428 mA,and Ibq is 2.14 uA\n",
"vo1 and vo2 have same value as 10.72 V\n",
" Ad: 86.0 ,Ac: 0.313 and CMRR is 274.0\n",
"Rid is 23.4 K ohms and Ric is 6.44 Mohms\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7,Page number 373"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R1=10. #series resistance(K ohms)\n",
"Rf=10**3. #feedback resistance(k ohms) \n",
"vo=-5. #output voltage(V)\n",
"Ri=1000 #input resistance(k ohms)\n",
"Av=2.5*10**5 #gain\n",
"\n",
"#Calculations\n",
"v1=-vo*(R1/Rf) #input signal voltage(V)\n",
"vi=-vo/Av #inverting voltage(V) \n",
"i1=((v1*10**-3)-vi)/R1 #current through R1(uA)\n",
"ii=vi/Ri #inverting current(uA)\n",
"iF=-ii #forward current(uA)\n",
"\n",
"#Results\n",
"print\"value of vi is\",vi,\"mV\"\n",
"print\"value of ii:\",ii,\"uA i1:,\",i1,\"uA and iF is\",iF,\"uA\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"value of vi is 2e-05 mV\n",
"value of ii: 2e-08 uA i1:, 3e-06 uA and iF is -2e-08 uA\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.8,Page number 374"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Vs=4 #source voltage(V)\n",
"R1=10. #resistance(k ohms)\n",
"Vb=Va=2 #voltage at point A and point B\n",
"Rf=30 #forward resistance(k ohms)\n",
"\n",
"#Calculations\n",
"I=(Vs-Vb)/R1 #current(mA)\n",
"Vo=(-I*Rf)+Vb #output voltage(V) \n",
"\n",
"#Result\n",
"print\"output voltage\",Vo,\"V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"output voltage -4.0 V\n"
]
}
],
"prompt_number": 45
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.9,Page number 375"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Rf=2 #as vs=2sinwt and vo=(1+Rf/Rs)*vb and vB=vA=vs\n",
"Rs=1\n",
"\n",
"\n",
"#Calculations\n",
"vo=(1+(Rf/Rs))*2 #output voltage(V)\n",
"\n",
"#Result\n",
"print\"output voltage\",vo,\"sinwt\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"output voltage 6 sinwt\n"
]
}
],
"prompt_number": 50
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.10,Page number 377"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Ro=100. #output resistance(ohms)\n",
"vo=10. #output voltage(V)\n",
"A=10**5. #gain \n",
"Ri=100*10**3 #input resistance(ohms) \n",
"Rs=1*10**3. #resistance(ohms)\n",
"Rl=10*10**3 #load resistance(ohms)\n",
"\n",
"#Calculations\n",
"#Part i\n",
"iL=vo/Rl #load current(mA)\n",
"Avi=vo+(iL*Ro) #voltage gain without feedback\n",
"vi=Avi/A #voltage(V)\n",
"ii=vi/Ri #current(A) \n",
"vs=vo+ii*(Rs+Ri) #source voltage(V)\n",
"\n",
"#Part ii\n",
"Avf=vo/vs #voltage gain with feedback \n",
"\n",
"\n",
"#Part iii\n",
"Rif=vs/ii #input resistance(ohms) \n",
"Rof=Ro/A #output resistance(ohms)\n",
"\n",
"#Results\n",
"print\"vs is\",round(vs,4),\"V\"\n",
"print\"vo/vs that is Avf is\",Avf\n",
"print\"input and output resistances are\",Rif,Rof,\"ohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"vs is 10.0001 V\n",
"vo/vs that is Avf is 0.999989799104\n",
"input and output resistances are 9901091099.01 0.001 ohms\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.11,Page number 382"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"Vb=Va=3 #voltage at A and B \n",
"R1=40*10**3. #input resistance(ohms)\n",
"t=50*10**-3 #time after switch is open(mS)\n",
"V1=5 #input voltage(V)\n",
"\n",
"#Calculations\n",
"#Part a\n",
"vo=-3 #as Va=Vb=3\n",
"\n",
"#Part b\n",
"i1=(V1-Vb)/R1 #input current(A)\n",
"vo1=(-250*t)-Va #vo at 50 mS\n",
"\n",
"#Result\n",
"print\"output voltage\",vo1,\"V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"output voltage -15.5 V\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.14,Page number 388"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"BW=30*10**3 #specified bandwidth(k Hz)\n",
"fc=18*10**3 #centered frequency(Hz)\n",
"R1=20 #resistance(k ohms) \n",
"R2=180 #resistance(k ohms) \n",
"C=1.2*10**-9 #capacitance(F)\n",
"G=40 #pass band gain(dB)\n",
"g=20 #pass region gain(dB)\n",
"\n",
"#Calculationsv\n",
"fc1=fc-(BW/2) #high pass section frequency(Hz)\n",
"fc2=fc+(BW/2) #low pass section frequency(Hz)\n",
"Rfc1=1/(2*math.pi*fc1*C) #high pass section resistance(k ohms)\n",
"Rfc2=1/(2*math.pi*fc2*C) #low pass section resistance(k ohms)\n",
"Gfc1=G-g #gain at frequency 0.3KHz(dB)\n",
"Gfc2=G-2*6 #gain at frequency 132KHz(dB)\n",
"\n",
"#Results\n",
"print\"R1 and R2 are\",R1,\"K ohms and\",R2,\"K ohms\"\n",
"print\"Rfc1 is\",round(Rfc1/1E+3),\"k ohms and Rfc2 is\",round(Rfc2/1E+3),\"k ohms\"\n",
"print\"filter gain at frequencies 0.3 KHz is\",Gfc1,\"dB and 132 k Hz are\",Gfc2,\"dB\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"R1 and R2 are 20 K ohms and 180 K ohms\n",
"Rfc1 is 44.0 k ohms and Rfc2 is 4.0 k ohms\n",
"filter gain at frequencies 0.3 KHz is 20 dB and 132 k Hz are 28 dB\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.21,Page number 402"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R=250 #resistance(k ohms)\n",
"\n",
"#Calculations\n",
"#part a\n",
"R1=-R/(-5) #as vo=-5va+3vb(given),so when vb=0,vo/voa=-250/R1=-5\n",
"\n",
"#part b\n",
"R2=R1/(2-1) #as va=0\n",
" #vx=(R1/R1+R)*vob=(1/6)*vb\n",
" #vy=(R2/R1+R2)*vb\n",
" #vx=vy\n",
" #(1/6)*vob=(R2/R1+R2)*vb\n",
" #vob=3vb\n",
" #(1/6)*3=R2/(50+R2)\n",
" \n",
"#Result\n",
"print\"R1 and R2 are\",R1,\"K ohms and\",R2,\"K ohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"R1 and R2 are 50 K ohms and 50 K ohms\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.22,Page number 403"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R1=10*10**3 #resistance(k ohms)\n",
"C1=10**-6 #capacitance(uF) \n",
"C=0.1*10**-6 #capacitance(uF) \n",
"R=100*10**3 #resistance(k ohms) \n",
"\n",
"#Calculations\n",
"#part b \n",
"wc1=1/C1*R1 #angular frequency(rad/s)\n",
"wc2=1/C*R #angular frequency(rad/s)\n",
"wc=wc1=wc2 #angular frequency(rad/s)\n",
"\n",
"#Results\n",
"print\"wc1 is\",wc1/1E+10,\"rad/s\"\n",
"print\"wc2 is\",wc2/1e+10,\"rad/s\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"wc1 is 100.0 rad/s\n",
"wc2 is 100.0 rad/s\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.23,Page number 404"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"vo1=5 #say (V)\n",
"K=25 #proportionality constant \n",
"Q=250 #volume of fluid passed across metering point(cm^3) \n",
"R1=2.5 #output resistance(k ohms)\n",
"\n",
"#Calculations\n",
"C1=(K*Q)/(R1*vo1) #capacitor(nF)\n",
"\n",
"#Results\n",
"print\"C1 is\",round(C1/1E+1),\"uF\"\n",
"print\"vo1 is -5V when Q=250 cm^3\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"C1 is 50.0 uF\n",
"vo1 is -5V when Q=250 cm^3\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}