Chapter5-Rectifier and DC Power Supplies

Ex1-pg173

In [1]:
##Ex5_1
import math
Vm = 24.
RL = 1.8*10**3
Im = Vm/RL
Irms = Im/2.
Idc = Im/(math.pi)
r = ((Irms/Idc)**2. - 1.)**.5
print'%s %.2f %s'%("Vm = ",(Vm),"V")##applied voltage to half wave rectifier
print'%s %.2f %s'%("RL = ",(RL),"ohm")##load resistance
print'%s %.2f %s'%("Im = Vm/RL = ",(Im),"A")##peak current
print'%s %.2f %s'%("Irms = Im/2 = ",(Irms),"A")##rms current
print'%s %.2e %s'%("Idc = Im/pi = ",(Idc),"A")##D.C. current
print'%s %.2f %s'%("r= ",(r),"")##ripple factor

Vm =  24.00 V
RL =  1800.00 ohm
Im = Vm/RL =  0.01 A
Irms = Im/2 =  0.01 A
Idc = Im/pi =  4.24e-03 A
r=  1.21

Ex2-pg173

In [2]:
##Ex5_2
import math 
Vm = 18.

##in half wave circuit
Vdc = Vm/math.pi
PIV = Vm
print'%s %.2f %s'%("Vm = ",(Vm),"V")##peak voltage to rectifier
print'%s %.2f %s'%("Vdc = Vm/pi = ",(Vdc),"V")##D.C. voltage
print'%s %.2f %s'%("PIV = Vm = ",(PIV),"V")##peak inverse voltage

##in full wave circuit
Vdc = (2.*Vm/math.pi)
PIV = 2.*Vm
print'%s %.2f %s'%("Vdc = 2*Vm/pi = ",(Vdc),"V")##D.C. voltage
print'%s %.2f %s'%("PIV = 2*Vm = ",(PIV),"V")##peak inverse voltage for center trapped

##in full wave Bridge rectifier
print'%s %.2f %s'%("PIV = Vm = ",(Vm),"V")##peak inverse voltage

Vm =  18.00 V
Vdc = Vm/pi =  5.73 V
PIV = Vm =  18.00 V
Vdc = 2*Vm/pi =  11.46 V
PIV = 2*Vm =  36.00 V
PIV = Vm =  18.00 V

Ex3-pg174

In [3]:
##Ex5_3
import math
Vm = 12.
RL = 1.5*10**3
Im = Vm/RL
Irms = Im/(2**.5)
Idc = (2.*Im/math.pi)
r =(((Irms/Idc)**2)-1.)**.5
print'%s %.2f %s'%("Vm = ",(Vm),"V")##peak voltage to full rectifier
print'%s %.2f %s'%("Im = Vm/RL = ",(Im),"A")##peak current
print'%s %.2f %s'%("Irms = Im/(2^0.5) = ",(Irms),"A")##rms current
print'%s %.2f %s'%("Idc = (2*Im/pi) = ",(Idc),"A")##D.C. current
print'%s %.2f %s'%("r= ",(r),"")##ripple factor

Vm =  12.00 V
Im = Vm/RL =  0.01 A
Irms = Im/(2^0.5) =  0.01 A
Idc = (2*Im/pi) =  0.01 A
r=  0.48

Ex4-pg174

In [4]:
##Ex5_4
import math
Idc = 10*10**-3
Irms = 14*10**-3
RL = 1*10**3
Pdc = (Idc**2)*RL
Pac = (Irms**2)*RL
print'%s %.2f %s'%("Idc = ",(Idc),"A")##D.C. current
print'%s %.2f %s'%("Irms = ",(Irms),"A")##rms current
print'%s %.2f %s'%("RL = ",(RL),"ohm")##load resistance
print'%s %.2f %s'%("Pdc = (Idc^2)*RL = ",(Pdc),"W")##D.C. power 
print'%s %.2f %s'%("Pac = (Irms^2)*RL = ",(Pac),"W")##A.C. power
print'%s %.2f %s'%("eta_r = Pdc/Pac = ",(Pdc/Pac*100),"%")##Rectification efficiency

Idc =  0.01 A
Irms =  0.01 A
RL =  1000.00 ohm
Pdc = (Idc^2)*RL =  0.10 W
Pac = (Irms^2)*RL =  0.20 W
eta_r = Pdc/Pac =  51.02 %

Ex5-pg175

In [5]:
##Ex5_5
import math
print("v = 12 sin(wt)")
Vm = 12.
RL = 1*10**3
Rf = 10.
Im = Vm/(RL+Rf)
Idc =Im/math.pi
Vdc = Idc*RL
Irms = Im/2.
Pi = (Irms**2)*(RL+Rf)
VNL = Vm/math.pi
VL = Idc*RL
Regulation = (VNL - VL)/VL
print'%s %.2f %s'%("Vm = ",(Vm),"V")##amplitude of applied signal
print'%s %.2f %s'%("RL = ",(RL),"ohm")##load resistance
print'%s %.2f %s'%("Rf = ",(Rf),"ohm")##forward resistance
print'%s %.2f %s'%("Im = Vm/(RL+Rf) = ",(Im),"A")##peak current
print'%s %.2f %s'%("Idc = Im/pi = ",(Idc),"A")##D.C. current
print'%s %.2f %s'%("Vdc = Idc*RL = ",(Vdc),"V")##D.C, voltage
print("Pi = (Irms^2)*(RL+Rf)")
print'%s %.2f %s'%("Irms = Im/2 = ",(Irms),"A")##rms current
print'%s %.2f %s'%("Pi = ",(Pi),"W")##input power
print("%Regulation = (VNL - VL)/VL")
print'%s %.2f %s'%("VNL = Vm/pi = ",(VNL),"V")##non load voltage
print'%s %.2f %s'%("VL = Idc*RL = ",(VL),"")##load voltage
print'%s %.2f %s'%("%Regulation = ",(Regulation*100),"%")##percentage regulation


##   NOTE : THE POWER CALCULATED IN THE TEXTBOOK IS WRONG.

v = 12 sin(wt)
Vm =  12.00 V
RL =  1000.00 ohm
Rf =  10.00 ohm
Im = Vm/(RL+Rf) =  0.01 A
Idc = Im/pi =  0.00 A
Vdc = Idc*RL =  3.78 V
Pi = (Irms^2)*(RL+Rf)
Irms = Im/2 =  0.01 A
Pi =  0.04 W
%Regulation = (VNL - VL)/VL
VNL = Vm/pi =  3.82 V
VL = Idc*RL =  3.78 
%Regulation =  1.00 %

Ex6-pg176

In [6]:
##Ex5_6
import math
Vdc = 15.
print'%s %.2f %s'%("Vdc = ",(Vdc),"V")##applied D.C. voltage
##Half Wave Rectifier
Vm = math.pi*Vdc
PIV = Vm
print'%s %.2f %s'%("Vm = Vdc*pi = ",(Vm),"V")##D.C. voltage for half wave rectifier
print'%s %.2f %s'%("PIV = Vm = ",(PIV),"V")##peak inverse voltage for half wave rectifier
##Full Wave Rectifier
Vm = math.pi*Vdc/2.
PIV = 2.*Vm
print'%s %.2f %s'%("Vm = Vdc*pi/2 = ",(Vm),"V")##D.C. voltage for full wave rectifier
print'%s %.2f %s'%("PIV = 2*Vm = ",(PIV),"V")##peak inverse voltage for full wave rectifier
##Bridge Rectifier
Vm = math.pi*Vdc/2.
PIV = Vm
print'%s %.2f %s'%("Vm = Vdc*pi/2 = ",(Vm),"V")##D.C. voltage for bridge rectifier
print'%s %.2f %s'%("PIV = Vm = ",(PIV),"V")##peak inverse voltage for bridge rectifier

Vdc =  15.00 V
Vm = Vdc*pi =  47.12 V
PIV = Vm =  47.12 V
Vm = Vdc*pi/2 =  23.56 V
PIV = 2*Vm =  47.12 V
Vm = Vdc*pi/2 =  23.56 V
PIV = Vm =  23.56 V

Ex11-pg179

In [7]:
##Ex5_11
import math
Rf = 10.
RL = 150.
eta_r = 40.6/(1.+Rf/RL)
print'%s %.2f %s'%("Rf = ",(Rf),"ohm")##forward resistance
print'%s %.2f %s'%("RL = ",(RL),"ohm")##load resistance
print'%s %.2f %s'%("eta_r = 40.6/(1+Rf/RL) = ",(eta_r),"%")##rectification efficiency

Rf =  10.00 ohm
RL =  150.00 ohm
eta_r = 40.6/(1+Rf/RL) =  38.06 %

Ex12-pg180

In [8]:
##Ex5_12
import math
Rf = 12.5
RL = 100.
eta_r = 80.1/(1.+Rf/RL)
print'%s %.2f %s'%("Rf = ",(Rf),"ohm")##forward resistance
print'%s %.2f %s'%("RL = ",(RL),"ohm")##load resistance
print'%s %.2f %s'%("eta_r = 80.1/(1+Rf/RL) = ",(eta_r),"%")##rectification efficiency

Rf =  12.50 ohm
RL =  100.00 ohm
eta_r = 80.1/(1+Rf/RL) =  71.20 %

Ex13-pg180

In [9]:
##Ex5_13
import math
Vdc = 32.
Vm = math.pi*Vdc/2.
Vrms = Vm/(2**.5)
PIV = Vm
print'%s %.2f %s'%("Vdc = ",(Vdc),"V")##D.C. voltage
print'%s %.2f %s'%("Vm = pi*Vdc/2 = ",(Vm),"V")##peak voltage
print'%s %.2f %s'%("Vrms = Vm/(2^.5) = ",(Vrms),"V")##rms voltage
print'%s %.2f %s'%("PIV = ",(PIV),"V")##peak inverse voltage


## note : value calculated for Vrms in the textbook is wrong.

Vdc =  32.00 V
Vm = pi*Vdc/2 =  50.27 V
Vrms = Vm/(2^.5) =  35.54 V
PIV =  50.27 V

Ex14-pg180

In [10]:
##Ex5_14
import math
C = 10.*10**-3
f = 50.
Idc = 200.*10**-3
Vr = Idc/(2.*f*C)
print'%s %.2f %s'%("C = ",(C),"F")##circuit capacitance
print'%s %.2f %s'%("f = ",(f),"Hz")##operating frequency
print'%s %.2f %s'%("Idc = ",(Idc),"A")##D.C. current
print'%s %.2f %s'%("Vr = Idc/(2*f*C) = ",(Vr),"V")##ripple voltage

C =  0.01 F
f =  50.00 Hz
Idc =  0.20 A
Vr = Idc/(2*f*C) =  0.20 V

Ex15-pg180

In [12]:
##Ex5_15
import math
C = 600.*10**-6
T = 20.*10**-3
Vr = 1.2
Vdc = 9.
Vac =Vr/(2.*(3**.5))
r = Vac/Vdc
Idc = (Vr*C)/(T/2.)
RL = Vdc/Idc
print'%s %.2e %s'%("C = ",(C),"F")##rectifier capacitance
print'%s %.2f %s'%("T = ",(T),"s")##time
print'%s %.2f %s'%("Vr = ",(Vr),"V")##ripple voltage
print'%s %.2f %s'%("Vdc = ",(Vdc),"V")##D.C. voltage
print'%s %.2f %s'%("Vac = ",(Vac),"V")##A.C. voltage
print'%s %.2f %s'%("r = ",(r),"")##ripple factor
print'%s %.2f %s'%("Idc = ",(Idc),"A")##D.C. current
print'%s %.2f %s'%("RL = ",(RL),"ohm")##load resistance

C =  6.00e-04 F
T =  0.02 s
Vr =  1.20 V
Vdc =  9.00 V
Vac =  0.35 V
r =  0.04 
Idc =  0.07 A
RL =  125.00 ohm

Ex16-pg181

In [13]:
##Ex5_16
import math
L = 1.## assuming inductance
f = 50.##operating frequency
XL = 2.*math.pi*f*L##inductance
RL = 100.##assuming load resistance
r = .01##ripple factor

##let, capacitances C1 = C2 = C
##that implies XC1 = XC2 = XC
print'%s %.2f %s'%("XL = 2*math.pi*f*L = ",(XL),"ohm")
print'%s %.2f %s'%("r = ",(r),"")
XC = ((r*8.*XL*RL)/(2**.5))**.5##capacitive resistance
print'%s %.2f %s'%("XC = ((r*8*XL*RL)/(2^.5))^.5 = ",(XC),"ohm")
print'%s %.2f %s'%("XC = 1/wC = 1/(2*pi*f*C) = ",(XC),"")
C = 1./(2.*math.pi*f*XC)##capacitance
print'%s %.4f %s'%("C = 1/(2*pi*f*XC) = ",(C),"F")
## thus, design parameters are : 
print("design parameters:")
print'%s %.4f %s'%("C1 = C2 = ",(C),"F")
print'%s %.2f %s'%("RL = ",(RL),"ohm")
print'%s %.2f %s'%("L = ",(L),"H")


## Note : the calculations done in the textbook for the given problem is wrong.

XL = 2*math.pi*f*L =  314.16 ohm
r =  0.01 
XC = ((r*8*XL*RL)/(2^.5))^.5 =  42.16 ohm
XC = 1/wC = 1/(2*pi*f*C) =  42.16 
C = 1/(2*pi*f*XC) =  0.0001 F
design parameters:
C1 = C2 =  0.0001 F
RL =  100.00 ohm
L =  1.00 H

Ex17-pg182

In [14]:
##Ex5_17
import math
f =50.
print("vi = 16 sin(wt)")
Vdc = 16.
RL = 100.
C1 = 2.*10**-3
C2 = 2.*10**-3
L = 1.0
Idc = Vdc/RL
XC1 = 1./(2.*math.pi*f*C1)
XC2 = 1./(2.*math.pi*f*C2)
XL = 2.*math.pi*f*L
r = ((2**.5)*XC1*XC2)/(8.*XL*RL)
print'%s %.2f %s'%("L = ",(L),"H")##inductance
print'%s %.4f %s'%("C1 = ",(C1),"F")##capacitance 1
print'%s %.4f %s'%("C2 = ",(C2),"F")##capacitance 2
print'%s %.2f %s'%("RL = ",(RL),"ohm")##load resistance
print'%s %.2f %s'%("f = ",(f),"Hz")##operating frequency
print'%s %.2f %s'%("Vdc = ",(Vdc),"V")##d.c. voltage
print'%s %.2f %s'%("Idc = Vdc/RL = ",(Idc),"A")##d.c. current
print'%s %.2f %s'%("XL = 2*%pi*f*L = ",(XL),"ohm")##inductive resistance
print'%s %.2f %s'%("XC1 = 1/(2*%pi*f*C1) = ",(XC1),"ohm")##capacitive resistance due to capacitance 1
print'%s %.2f %s'%("XC2 = 1/(2*%pi*f*C2) = ",(XC2),"ohm")##capacitive resistance due to capacitance 2
print'%s %.2e %s'%("r = ((2^.5)*XC1*XC2)/(8*XL*RL) = ",(r),"")##ripple factor

vi = 16 sin(wt)
L =  1.00 H
C1 =  0.0020 F
C2 =  0.0020 F
RL =  100.00 ohm
f =  50.00 Hz
Vdc =  16.00 V
Idc = Vdc/RL =  0.16 A
XL = 2*%pi*f*L =  314.16 ohm
XC1 = 1/(2*%pi*f*C1) =  1.59 ohm
XC2 = 1/(2*%pi*f*C2) =  1.59 ohm
r = ((2^.5)*XC1*XC2)/(8*XL*RL) =  1.43e-05