{
"metadata": {
"name": "",
"signature": "sha256:2a4ca46418f96503536124ea941a5521b6b652077fc912eba380767a1297ae00"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter04 : Basic Application of an Op-amp"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.2 : page 119"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"# given data\n",
"# KCL at node (b) (6-V)/30+(8-V)/40+(0-V)/30=0 \n",
"V=48/11 #in volts\n",
"print \"Voltage V = %0.2f Volt\"%V\n",
"# KCL at node (a) (3-V)/10+(4-V)/20=(V-Vo)/40\n",
"Vo=-(20-7*V) #in Volts\n",
"print \"Output Voltage of the circuit Vo = %0.2f Volt\"%Vo"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Voltage V = 4.36 Volt\n",
"Output Voltage of the circuit Vo = 10.55 Volt\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.3 : page 120"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import symbols, N\n",
"V1, V2 = symbols('V1 V2')\n",
"R1 = 11 # Kohm\n",
"R2 = 10 # Kohm\n",
"Ra = 99 # kohm\n",
"Ro = 100 # kohm\n",
"Va = Ra/(Ra+R1)*V1\n",
"Vo1 = (1+Ro/R2)*Va\n",
"A = Vo1/V1\n",
"Vo2 = -Ro/R2*V2\n",
"B = Vo2/V2\n",
"print \"Value of A : \",N(A,2)\n",
"print \"Value of B : \",N(B,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of A : 9.9\n",
"Value of B : -10.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.4 : page 120"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from sympy import symbols, N, solve\n",
"Va, R1, R3, Vb = symbols('Va R1 R3 Vb')\n",
"Ro = 100 # kohm\n",
"Voa = -2*Va\n",
"# Vo = Voa+Vob\n",
"eqn = Voa+Ro/R1*Va\n",
"R1 = solve(eqn, R1)[0] # kohm\n",
"print \"value of R1 = %0.2f kohm\"%R1\n",
"R2=R1 # kohm\n",
"V1 = R3*Vb/(R2+R3)\n",
"Vob = (1+Ro/R1)*V1\n",
"R3 = solve(Vob-Vb,R3)[0]\n",
"print \"value of R2 = %0.2f kohm\"%R2\n",
"\n",
"print \"value of R3 = %0.2f kohm\"%R3"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"value of R1 = 50.00 kohm\n",
"value of R2 = 50.00 kohm"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"value of R3 = 25.00 kohm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.5 : page 121"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sympy import symbols, solve, N\n",
"Vo = symbols('Vo')\n",
"R1 = 10 # kohm\n",
"R2 = 20 # kohm\n",
"Ro = 100 # kohm\n",
"V1 = -2 # V\n",
"V2 = +3 # V\n",
"I1 = V1/R1 # A\n",
"I2 = V2/R2 # A\n",
"If = (0-Vo)/Ro\n",
"eqn = I1+I2-If\n",
"Vo = solve(eqn, Vo)[0]\n",
"print \"Output voltage, Vo =\",N(Vo,2),\"Volt\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Output voltage, Vo = 5.0 Volt\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.7 : page 123"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"from sympy import symbols\n",
"Vo, Vx, Vy = symbols('Vo Vx Vy')\n",
"R1 = 2 # kohm\n",
"R2 = 2 # kohm\n",
"R3 = 2 # kohm\n",
"R4 = 8 # kohm\n",
"R5 = 1 # kohm\n",
"R6 = 7 # kohm\n",
"V1 = 1 # V\n",
"# Node X\n",
"Vz=1 # V\n",
"# KCL at node Y\n",
"eqn1 = 3*Vy-2*Vx-1\n",
"# KCL at node X\n",
"eqn2 = Vy-2*Vx+1\n",
"A=np.array([[-2,3],[-2,1]])\n",
"B=np.array([[1,-1]])\n",
"X=np.linalg.solve(A,B)\n",
"Vx = X[0][1] # V\n",
"Vo = Vx/R5*(R5+R6)\n",
"print \"Output Voltage, Vo = %0.f V\"%Vo"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Output Voltage, Vo = 4 V\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.9 : page 130"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# given data\n",
"R1=10 #in Kohm\n",
"R4=8 #in Kohm\n",
"R5=3 #in Kohm\n",
"RF=45 #in Kohm\n",
"AD=(1+2*R4/R5)*(RF/R1) \n",
"print \"Gain for the instrumention amplifier is : \",AD"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Gain for the instrumention amplifier is : 28.5\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.10 : page 131"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# given data\n",
"VA=3 #in mV\n",
"VB=5 #in mV\n",
"R1=10 #in Kohm\n",
"R2=10 #in Kohm\n",
"R3=45 #in Kohm\n",
"R4=8 #in Kohm\n",
"R5=3 #in Kohm\n",
"RF=45 #in Kohm\n",
"I=(VA-VB)/R5 #in mA\n",
"VoA=VA+I*R4 #in mVs\n",
"VoB=VB-I*R4 #in mVs\n",
"print \"Output of op-amp A1 = %0.2f mV\" %VoA\n",
"print \"Output of op-amp A2 = %0.2f mV\" %VoB\n",
"Vo1=(1+RF/R1)*(R3/(R3+R2))*VoB \n",
"Vo2=-(RF/R1)*VoA \n",
"Vo=Vo1+Vo2 #in mV\n",
"print \"Combined output of the circuit = %0.2f mV\"%Vo\n",
"# Answer in the textbook is not accurate."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Output of op-amp A1 = -2.33 mV\n",
"Output of op-amp A2 = 10.33 mV\n",
"Combined output of the circuit = 57.00 mV\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.12 : page 135"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# given data\n",
"RF=10 #in Kohm\n",
"R1=10 #in Kohm\n",
"R2=R1 #in Kohm\n",
"R3=R1 #in Kohm\n",
"R5max=50 #in Kohm\n",
"ADmin=5 #unitless\n",
"ADmax=200 #unitless\n",
"#Formula : ADmin=1+2*R4/R5max\n",
"R4=(ADmin-1)*(R5max/2) #in Kohm\n",
"#Formula : ADmax=1+2*R4/R5min\n",
"R5min=(2*R4)/(ADmax-1) #in Kohm\n",
"print \"Thus design values of resistors in Kohm are :\" \n",
"print \"R1 = \",R1,\"kohm\" \n",
"print \"R2 = \",R2,\"kohm\" \n",
"print \"R3 = \",R3,\"kohm\" \n",
"print \"R4 = \",R4,\"kohm\" \n",
"print \"RF = \",RF,\"kohm\" \n",
"print \"R5min = %0.f kohm\"%R5min\n",
"print \"R5max = \",R5max,\"kohm\" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Thus design values of resistors in Kohm are :\n",
"R1 = 10 kohm\n",
"R2 = 10 kohm\n",
"R3 = 10 kohm\n",
"R4 = 100.0 kohm\n",
"RF = 10 kohm\n",
"R5min = 1 kohm\n",
"R5max = 50 kohm\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.13 : page 136"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# given data\n",
"Vdc=10 #in Volt\n",
"R1=10 #in Kohm\n",
"R2=10 #in Kohm\n",
"R3=100 #in Kohm\n",
"RF=100 #in Kohm\n",
"# Part(i) Balance Bridge : RA=RB=RC=RT=150ohm and VAB=0\n",
"Vo = 0 # V\n",
"print \"(i) Balance bridge have output voltage Vo = %0.f volt\" %Vo\n",
"RA=150 #in ohm\n",
"RB=150 #in ohm\n",
"RC=150 #in ohm\n",
"RT=150 #in ohm\n",
"VAB=0 #in Volt\n",
"Vo=(-RF/R1)*VAB \n",
"# Part(ii) Unbalance Bridge : RT=200ohm\n",
"RT=200 #in ohm\n",
"VA=(RA/(RA+RT))*Vdc \n",
"VB=(RB/(RB+RC))*Vdc \n",
"VAB=VA-VB #in Volt\n",
"Vo=(-RF/R1)*VAB \n",
"print \"(ii) Unbalance bridge have output voltage Vo = %0.1f Volt\" %Vo"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Balance bridge have output voltage Vo = 0 volt\n",
"(ii) Unbalance bridge have output voltage Vo = 7.1 Volt\n"
]
}
],
"prompt_number": 40
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.15 : page 146"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"# given data\n",
"Gain=10 #Unitless\n",
"fb=10 #in KHz\n",
"#Assuming fa=fb/10\n",
"fa=fb/10 #in KHz\n",
"# Formula : fa=1/(2*pi*RF*CF)\n",
"RFCF=1/(2*np.pi*fa) \n",
"#Assuming R1=1Kohm\n",
"R1=1 #in Kohm\n",
"RF=10*R1 #in Kohm\n",
"CF=RFCF/RF #in uF\n",
"Rcomp=(R1*RF)/(R1+RF) # in Kohm\n",
"print \"Value of RF = %0.2f kohm\"%RF\n",
"print \"Value of CF = %0.3f uF\"%CF\n",
"print \"Value of Rcomp = %0.f ohm\"%(Rcomp*1000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of RF = 10.00 kohm\n",
"Value of CF = 0.016 uF\n",
"Value of Rcomp = 909 ohm\n"
]
}
],
"prompt_number": 44
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.16 : page 146"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Using superposition theorem\n",
"CF=10 #in uF\n",
"R1=1/(3*CF*10**-6) #in KOhm\n",
"R2=1/(2*CF*10**-6) #in KOhm\n",
"print \"Value of R1 = %0.2f kohm \"%(R1/1000) \n",
"print \"Value of R2 = %0.2f kohm \"%(R2/1000) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of R1 = 33.33 kohm \n",
"Value of R2 = 50.00 kohm \n"
]
}
],
"prompt_number": 45
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.22 : page 156"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"# given data\n",
"fa=1.5 #in KHz\n",
"fmax=1.5 #in KHz\n",
"C1=0.1 #in uF\n",
"RF=1/(2*np.pi*fa*C1) #in Kohm\n",
"fb=10*fa #in Khz\n",
"R1=1/(2*np.pi*fb*C1) #in Kohm\n",
"CF=(R1*C1)/RF #in uF\n",
"Rcomp=RF #in Kohm\n",
"print \"Value of resistance RF = %0.2f kohm\"%(RF)\n",
"print \"Value of resistance R1 = %0.2f ohm\"%(R1*1000)\n",
"print \"Value of Capacitance CF = %0.2f uF\"%(CF)\n",
"print \"Value of resistance Rcomp = %0.2f kohm\"%(Rcomp)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of resistance RF = 1.06 kohm\n",
"Value of resistance R1 = 106.10 ohm\n",
"Value of Capacitance CF = 0.01 uF\n",
"Value of resistance Rcomp = 1.06 kohm\n"
]
}
],
"prompt_number": 46
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Exa 4.25 : page 159"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"# given data\n",
"C1=0.1 #in uF\n",
"f=100 #in Hz\n",
"T=1/f #in sec\n",
"# Given also R1C1=0.2*T \n",
"R1=(0.2*T)/(C1*10**-6) #in ohm\n",
"RF=0.05/(C1*10**-6) #in ohm\n",
"CF=(R1*C1)/RF #in uF\n",
"print \"Value of resistance R1 = %0.2f ohm\"%(R1/1000)\n",
"print \"Value of resistance RF = %0.2f kohm\"%(RF/1000)\n",
"print \"Value of Capacitance CF = %0.2e uF\"%(CF)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Value of resistance R1 = 20.00 ohm\n",
"Value of resistance RF = 500.00 kohm\n",
"Value of Capacitance CF = 4.00e-03 uF\n"
]
}
],
"prompt_number": 47
}
],
"metadata": {}
}
]
}