Chapter 35 , Operational Amplifiers (OP - Amps)¶
Example 35.1 , Page Number 895¶
In [1]:
import math
#Variables
Adm = 200000.0 #Differential gain
Acm = 6.33 #Common mode gain
#Calculation
CMRR = 20 * math.log10(Adm / Acm) #Common-mode rejection ratio (in Decibels)
#Result
print "The common-mode rejection ratio is ",round(CMRR)," dB."
Example 35.2 , Page Number 896¶
In [4]:
import math
#Variables
CMRR = 90.0 #Common-mode rejection ratio (in Decibels)
Adm = 30000.0 #Differential gain
#Calculation
Acm = 10**(-CMRR/20.0) * Adm #Common-mode gain
#Result
print "The common-mode gain is ",round(Acm,3),"."
Example 35.3 , Page Number 896¶
In [3]:
import math
#Variables
Slew_rate = 0.5 * 10**6 #Slew rate (in volt per second)
Vpk = 100.0 * 10**-3 #Peak-to-peak voltage (in volts)
#Calculation
fmax = Slew_rate / (2 * math.pi * Vpk) #Maximum operating frequency (in Hertz)
#Result
print "The maximum operating frequency for the amplifier is ",round(fmax * 10**-3)," kHz."
Example 35.4 , Page Number 896¶
In [4]:
import math
#Variables
Slew_rate1 = 0.5 * 10**6 #Slew rate (in volt per second)
Slew_rate2 = 13.0 * 10**6 #Slew rate (in volt per second)
Vpk = 10.0 #Peak-to-peak voltage (in volts)
#Calculation
fmax = Slew_rate1 / (2 * math.pi * Vpk) #Maximum operating frequency1 (in Hertz)
fmax1 = Slew_rate2 / (2 * math.pi * Vpk) #Maximum operating frequency2 (in Hertz)
#Result
print "The maximum operating frequency for TLO 741 is ",round(fmax * 10**-3,3)," kHz.\nThe maximum opearing frequency for TLO 81 is ",round(fmax1 * 10**-3,1)," kHz."
#Slight variation due to higher precision.
Example 35.5 , Page Number 899¶
In [5]:
import math
#Variables
ACL = 200.0 #Closed loop voltage gain
Vout = 8.0 #Output voltage (in volts)
#Calculation
Vin = - Vout / ACL #Input a.c. voltage (in volts)
#Result
print "Maximum allowable input voltage (Vin) is ",abs(Vin * 10**3)," mV."
Example 35.6 , Page Number 900¶
In [6]:
import math
#Variables
ACL = 150.0 #Closed loop voltage gain
Vin = 200.0 * 10**-3 #Input a.c. voltage (in volts)
V = 12.0 #Voltage (in volts)
#Calculation
Vout = ACL * Vin #Output voltage (in volts)
Vpkplus = V -2.0 #maximum positive peak voltage (in volts)
Vpkneg = -V + 2.0 #maximum negative peagk voltage (in volts)
#Result
print "The maximum possible output value could be between ",Vpkplus," V and ",Vpkneg," V."
Example 35.7 , Page Number 900¶
In [7]:
import math
#Variables
R1 = 1.0 * 10**3 #Resistance (in volts)
R2 = 10.0 * 10**3 #Resistance (in volts)
vinmin = 0.1 #Input voltage minimum (in volts)
vinmax = 0.4 #Input voltage maximum (in volts)
#Calculation
ACL = R2 / R1 #Closed loop voltage gain
Voutmin = ACL * vinmin #Minimum output voltage (in volts)
Voutmax = ACL * vinmax #Maximum output voltage (in volts)
#Result
print "The value of output voltage increases from ",Voutmin," V to ",Voutmax," V."
Example 35.8 , Page Number 901¶
In [8]:
import math
#Variables
R1 = 1.0 * 10**3 #Resistance (in ohm)
R2 = 2.0 * 10**3 #Resistance (in ohm)
V1 = 1.0 #Voltage (in volts)
#Calculation
ACL = R2 / R1 #Closed loop voltage gain
vo = ACL * V1 #Output voltage (in volts)
#Result
print "Output voltage of the inverting amplifier is ",vo," V."
Example 35.9 , Page Number 901¶
In [9]:
import math
#Variables
R2 = 100.0 * 10**3 #Resistance (in ohm)
R1 = 10.0 * 10**3 #Resistance (in ohm)
ACM = 0.001 #Common-mode gain
Slew_rate = 0.5 * 10**6 #Slew rate (in volt per second)
Vpk = 5.0 #Peak voltage (in volts)
#Calculation
ACL = R2 / R1 #Closed loop voltage gain
Zin = R1 #Input impedance of the circuit (in ohm)
Zout = 80.0 #Output impedance of the circuit (in ohm)
CMRR = ACL / ACM #Common mode rejection ratio
fmax = Slew_rate / (2*math.pi*Vpk) #Maximum frequency (in Hertz)
#Result
print "Closed-loop gain is ",ACL,".\nInput impedance is ",Zin * 10**-3," kilo-ohm.\nOutput impedance is ",Zout," ohm.\nCommon-mode rejection ratio is ",CMRR,".\nMaximum operating frequency is ",round(fmax * 10**-3,1)," kHz."
Example 35.10 , Page Number 904¶
In [10]:
import math
#Variables
R2 = 100.0 * 10**3 #Resistance (in ohm)
R1 = 10.0 * 10**3 #Resistance (in ohm)
Slew_rate = 0.5 * 10**6 #Slew rate (in volt per second)
Vpk = 5.5 #Peak voltage (in volts)
RL = 10.0 * 10**3 #Load resistance (in ohm)
ACM = 0.001 #Common mode gain
#Calculation
ACL = (1 + R2/R1) #Closed loop voltage gain
CMRR = ACL / ACM #Common-mode rejection ratio
vin = 1.0 #Voltage (in volts)
Vout = ACL * vin #Output voltage (in volts)
Vpk = 5.5 #Peak-to-peak voltage (in volts)
fmax = Slew_rate/(2*math.pi*Vpk) #Maximum frequency (in Hertz)
#Result
print "Closed loop gain is ",ACL,".\nCMRR is ",CMRR,".\nMaximum operating frequency is ",round(fmax * 10**-3,2)," kHz."
Example 35.11 , Page Number 905¶
In [3]:
import math
#Variables
ACL = 1.0 #Closed loop gain
Acm = 0.001 #Common mode gain
Slew_rate = 0.5 * 10**6 #Slew rate (in Volt per second)
#Calculation
CMRR = ACL / Acm #Common-mode rejection ratio
vin = 1.0 #Voltage (in volts)
Vout = ACL * vin #Output voltage (in volts)
Vpk = 3.0 #Peak-to-peak voltage (in volts)
fmax = Slew_rate/(2*math.pi*Vpk) #Maximum frequency (in Hertz)
#Result
print "ACL is ",ACL,".\nCMRR is ",CMRR,".\nfmax is ",round(fmax * 10**-3,1)," kHz."
Example 35.12 , Page Number 906¶
In [12]:
import math
#Variables
V1 = 0.1 #Voltage (in volts)
V2 = 1.0 #Voltage (in volts)
V3 = 0.5 #Voltage (in volts)
R1 = 10.0 * 10**3 #Resistance (in ohm)
R2 = 10.0 * 10**3 #Resistance (in ohm)
R3 = 10.0 * 10**3 #Resistance (in ohm)
R4 = 22.0 * 10**3 #Resistance (in ohm)
#Calculation
Vout = (-R4/R1*V1) + (-R4/R2*V2) + (-R4/R3*V3) #Output voltage (in volts)
#Result
print "Output voltage is ",abs(Vout)," V."
Example 35.13 , Page Number 907¶
In [7]:
import numpy
%matplotlib inline
from matplotlib.pyplot import plot,ylabel,xlabel,title
#Variables
#V1 = 2 * sin(wt) #Voltage (in volts)
V2 = 5.0 #Voltage (in volts)
V3 = -100.0 * 10**-3 #Voltage (in volts)
#Result
#Vo = 4 * V1 + V2 + 0.1 * V3 #Output voltage
#Graph
x = numpy.linspace(0,10,200)
y = numpy.sin(x)
plot(x,-15 + 8*y)
plot(x,x-x-15,'')
title("output waveform")
ylabel("output voltage (Vo)")
xlabel("t")
Out[7]:
Example 35.14 , Page Number 908¶
In [15]:
import math
#Variables
V1 = -2.0 #Voltage (in volts)
V2 = 2.0 #Voltage (in volts)
V3 = -1.0 #Voltage (in volts)
R1 = 200.0 * 10**3 #Resistance (in ohm)
R2 = 250.0 * 10**3 #Resistance (in ohm)
R3 = 500.0 * 10**3 #Resistance (in ohm)
Rf = 1.0 * 10**6 #Resistance (in ohm)
#Calculation
Vout = (-Rf/R1*V1) + (-Rf/R2*V2) + (-Rf/R3*V3) #Output voltage (in volts)
#Result
print "Output voltage is ",Vout," V."