# Chapter 8: Differential, Instrumentation and Bridge amplifiers¶

### Example 8.1 Page No 218¶

In [1]:
#Given
m = 100.0              #Differential Gain
E1 = 10*10**-3
E2 = 10*10**-3         #input voltages
E3 = 0*10**-3
E4 = -20*10**-3        #input voltages

#Calculation
Vout1 = (m*E1)-(m*E2)
Vout2 = (m*E1)-(m*E3)
Vout3 = (m*E1)-(m*E4)

#Result
print" Output Voltages are   ", Vout1,"V, ",Vout2,"V ,",Vout3,"V"

 Output Voltages are    0.0 V,  1.0 V , 3.0 V


### Example 8.2 Page no. 220¶

In [5]:
#Given
V=5      #V
d=2       #mV
E1=V+d*10**-3
E2=V-d*10**-3

#Calculation
Eds=E1-E2
Ecm=(E1+E2)/2.0

#Result
print"Input signal voltage is",Eds*1000,"mV"
print"Common mode voltage is",Ecm,"V"

Input signal voltage is 4.0 mV
Common mode voltage is 5.0 V


### Example 8.2 Page No 225¶

In [2]:
#Given
a = 2/9.0       #Differential Gain
E1 = 10*10**-3
E2 = 5*10**-3   #Input Voltages

#Calculation
Vout = (E1 - E2)*(1+(2/a))

#Result
print" output voltage = ", Vout*1000,"mV"

 output voltage =  50.0 mV


### Example 8.3 Page No 227¶

In [6]:
#Given
R = 25*10**3
aR = 50.0

#Calculation
a = aR / R
Gain = 1 + (2/a)

#Result
print"Voltage Gain = " , Gain

Voltage Gain =  1001.0


### Example 8.4 Page No 227¶

In [1]:
#Given
import numpy
a=numpy.inf

#Calculation
Gain = 1+(2/a)

#Result
print" Voltage Gain =  ", Gain

 Voltage Gain =   1.0


### Example 8.5 Page No 227¶

In [9]:
#Given
m = 1001.0     #Gain
E1 = 5.001
E2 = 5.002
E3 = 5.001
E4 = 5.000
E5 = -1.001
E6 = -1.002

#Calculation
Vout1 = m*(E1-E2)
Vout2 = m*(E3-E4)
Vout3 = m*(E5-E6)

#result
print" Output Voltages are   ", Vout1,"V ",Vout2,"V ",Vout3,"V"

 Output Voltages are    -1.001 V  1.001 V  1.001 V


### Example 8.6 Page No 231¶

In [10]:
#Given
Vout = 5.0    #Output Voltage

#Calculation
Vce = Vout

#Result
print" Vce=",Vce,"V"

 Vce= 5.0 V


### Example 8.7 Page No 231¶

In [11]:
#Given
Vre = 1.2
Re = 1*10**3
Vce = 5
Vcc = 15         #Voltages in the circuit

#Calculation
Ie = Vre / Re
Vcol = Vce + Vre
Vrl = Vcc - Vcol

#Result
print" Collector Voltage =  ", Vcol,"V"
print" Voltage across Rl  =", Vrl,"V"

 Collector Voltage =   6.2 V
Voltage across Rl  = 8.8 V


### Example 8.8 Page No 232¶

In [6]:
#Given
Rs = 1*10**3
E1 = 100*10**-3
E2 = 0
Rl = 5*10**3
Gain = 10

#Calculation
Il = 10*((E1-E2)/Rs)
Vr = Il * Rs
Vref = Il * Rl
V9 = Vref + Gain*(E1 - E2)

#Result
print" Current across Load Resistor = ", Il*1000 ,"mA"
print" Voltage across R  =  ", Vr,"V"
print" Reference Voltage  =  ", Vref,"V"
print" Voltage at terminal 9 =", V9,"V"

 Current across Load Resistor =  1.0 mA
Voltage across R  =   1.0 V
Reference Voltage  =   5.0 V
Voltage at terminal 9 = 6.0 V


### Example 8.9 Page No 234¶

In [9]:
#Given
GF = 2.0     #Gage factor
DR = 0.001
R = 120.0

#calculation
L = DR /(R*GF)

#result
print" Change in length is ",round(L*10**6,1),"microinches per inch"

 Change in length is  4.2 microinches per inch


### Example 8.10 Page No 236¶

In [10]:
#Given
E = 1.0
DR = 0.001
R = 120.0    #Resistance in Ohm

#Calculation
Vout = (E*DR)/(4*R)

#Result
print" Output of the Bridge = ", round(Vout*10**6,1),"micro voltage"

 Output of the Bridge =  2.1 micro voltage


### Example 8.11 Page No 241¶

In [12]:
#Given
Vout = 100*10**-3
E = 5.0
R = 120.0
Gain = 1000.0
E1 = 30 *10**6
Gf = 2.0          #Gage factor

#calculation
Vbridge = Vout / Gain
DL = 20*10**-6
DR = (R * Vbridge)/E
Rratio = DR / R   #Change in Resistance
Strain = DL / Gf  #Change in Length
Stress = E1 * Strain

#Result
print " Change in Resistance =  ", DR*1000 ,"mohm"
print " Ratio of Resistance =  ", Rratio,"micro ohm/ohm"
print " Strain value =  ", Strain ,"micro inch/inch"
print " Stress value = ", Stress ,"psi"

 Change in Resistance =   2.4 mohm
Ratio of Resistance =   2e-05 micro ohm/ohm
Strain value =   1e-05 micro inch/inch
Stress value =  300.0 psi


### Example 8.12 Page No 245¶

In [2]:
#Given
T1=25    #C Temprature
T2=50
Tref=25   #C Reference temprature
Rref=10000
Rtrans=3603    #ohm, at 50 C

#Calculation
dR=Rtrans-Rref
R1=10     #Kohm say
E=1    #V trial choice
I=E/(R1+Rref/1000.0)
Vo=-I*dR

#result
print"The value of dR for each temprature is",dR,"ohm"
print"The current is",I,"mA"
print"Vo for each value of R",Vo,"mV"
#NOTE: In the book the value of Vo is calculated wrong

The value of dR for each temprature is -6397 ohm
The current is 0.05 mA
Vo for each value of R 319.85 mV