Chapter 1 - Electronic Voltmeters

Example 1 - pg 1_17

In [1]:
#Chapter-1,Example1_1,pg 1_17
#calculate the required multiplier resistance
import math
#given
Erms=10.
Rm=200
#calculations
Ep=math.sqrt(2)*Erms
Eav=0.6*Ep
E=Eav/2.
Edc=0.45*Erms
Idc=1*10**-3
Rs=(Edc/Idc)-Rm
#results
print"required multiplier resistance (kohm) = ",Rs/1000.
required multiplier resistance (kohm) =  4.3

Example 2 - pg 1_18

In [2]:
#Chapter-1,Example1_2,pg 1_18
#calculate the required multiplier resistance
#given
Eav=9.
Erms=10.
Rm=500.
Idc=2*10**-3
#calculations
Edc=0.9*Erms
Rs=(Edc/Idc)-Rm
#results
print "required multiplier resistance(kohm) = ",Rs/1000.
required multiplier resistance(kohm) =  4.0

Example 3 - pg 1_20

In [3]:
#Chapter-1,Example1_3,pg 1_20
#calculate the percentage error
#given
Kf=1#Erms=Em for 1 time period
Kf1=1.11#Kf(sine)/Kf(square)
#calculations
pere=(Kf-Kf1)/Kf*100.#percentage error
#results
print"percentage error = ",pere
percentage error =  -11.0

Example 4 - pg 1_20

In [4]:
#Chapter-1,Example1_4,pg 1_20
#calculate the percentage error
import math
import scipy
from scipy import integrate
#given
A=50.
T=2.
Kf2=1.11
#calculations
def f(t):
	E=(50*t)**2#e=At(ramp function)
	return E


I=scipy.integrate.quad(f,0,T)

Erms=math.sqrt((1./T)*I[0])
def f1(t):
	e=50*t#e=At(ramp function)
	return e


I1=scipy.integrate.quad(f1,0,T)
Eav=(1./T)*I1[0]
Kf=Erms/Eav
kfr=Kf2/Kf #Kf(sine)/Kf(sawtooth)
pere=(1-kfr)/1*100#percentage error
#results
print"percentage error (percent) = ",round(pere,2)
percentage error (percent) =  3.87

Example 5 - pg 1_27

In [5]:
#Chapter-1,Example1_5,pg 1_27
#calculate the total meter resistance
#given
Idc=25*10**-3
Erms=200.
Rm=100.
Rf=500.
#calculations
Rd=2*Rf
Rm1=Rm+Rd#total meter resistance
Rs=(0.9*Erms)/Idc-Rm1
#results
print "total meter resistance (ohm) = ",Rs
total meter resistance (ohm) =  6100.0

Example 6 - pg 1_38

In [6]:
#Chapter-1,Example1_6,pg 1_38
#calculate the meter current
#given
V1=2.
Rm=50.
Rd=15.*10**3
gm=0.006
rd=100*10**3
#calculations
Im=(gm*rd*Rd/(rd+Rd)*V1)/((2*(rd*Rd/(rd+Rd))+Rm))
#results
print "meter current (mA) = ",round(Im*1000.,2)
meter current (mA) =  5.99

Example 7 - pg 1_38

In [7]:
#Chapter-1,Example1_7,pg 1_38
#calculate the meter current
#given
V1=1
Rm=50
Rd=15*10**3
gm=0.006
rd=100*10**3
#calculations
Im=(gm*rd*Rd/(rd+Rd)*V1)/((2*(rd*Rd/(rd+Rd))+Rm))
#results
print "meter current (mA) = ",round(Im*1000.,1)
meter current (mA) =  3.0

Example 8 - pg 1_39

In [8]:
#Chapter-1,Example1_8,pg 1_39
#calculate the resistance values
#given
V1=1.
Vin=30.
Rin=9.*10**6
#calcuations
R4=Rin/100.#for Vin=100V
R3=(Rin-50*R4)/50#for Vin=50V
R2=(Rin-30*R3-30*R4)/30#for Vin=30V
R1=Rin-R2-R3-R4
#results
print "resistance values are"
print "R1 (Mohm) = ",round(R1/10**6,1)
print "R2 (kohm) = ",round(R2/10**3,1)
print "R3 (kohm) = ",round(R3/10**3,1)
print "R4 (kohm) = ",round(R4/10**3,1)
resistance values are
R1 (Mohm) =  8.7
R2 (kohm) =  120.0
R3 (kohm) =  90.0
R4 (kohm) =  90.0

Example 9 - pg 1_40

In [9]:
#Chapter-1,Example1_9,pg 1_40
#calculate the current, series resistance
#given
rd=10*10**3
gm=0.003
Rs=15*10**3
V1=1#input voltage
Rm=1800.
Img=0.1*10**-3#meter current given
#calculations
rdf=rd/(1+gm*rd)#actual rd
Vo=(gm*rdf*Rs)*V1/(rdf+Rs)
Rth=(2*Rs*rdf/(Rs+rdf))
Im=Vo/(Rth+Rm)
Rf=(Vo/Img)-Rth-Rm#series resistance
#results
print "current Im (mA) = ",round(Im*1000.,4)
print "series resistance (kohm) = ",round(Rf/10**3,3)
current Im (mA) =  0.3896
series resistance (kohm) =  7.042

Example 10 - pg 1_41

In [10]:
#Chapter-1,Example1_10,pg 1_41
#calculate the calibration resistance
#given
rd=200.*10**3
gm=0.004
Rs=40.*10**3
Rm=1000.
V1=1
#calculations
rdf=rd/(1+gm*rd)#actual rd
Rth=(2*Rs*rdf/(Rs+rdf))
Vo=(gm*rdf*Rs)*V1/(rdf+Rs)
Im=50*10**-6
Rcal=(Vo/Im)-Rth-Rm#calibration resistance
#results
print "calibration resistance (kohm) = ",round(Rcal/1000.,1)
calibration resistance (kohm) =  18.4

Example 11 - pg 1_42

In [11]:
#Chapter-1,Example1_11,pg 1_42
#calculate the resistances
#given
Vin=3.
V1=1.
Rin=1.*10**6#input resistance of FET
#calculations
R4=Rin/100.#for Vin=100V
R3=(Rin-30*R4)/30.#for Vin=30V
R2=(Rin-3*R3-3*R4)/3.#for Vin=3V
R1=Rin-R2-R3-R4
#results
print "Resistances are "
print "R1(kohm) = ",round(R1/1000.,2)
print "R2(kohm) = ",round(R2/1000.,0)
print "R3(kohm) = ",round(R3/1000.,2)
print "R4(kohm) = ",round(R4/1000.,0)
Resistances are 
R1(kohm) =  666.67
R2(kohm) =  300.0
R3(kohm) =  23.33
R4(kohm) =  10.0