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POWER ELECTRONICS Devices, Circuits, and Applications FOURTH EDITION
CHAPTER CHAPTER
13
Power Supplies
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Learning Outcomes
After completing this chapter, students should be able to do the following: List the types of power supplies. List the circuit topologies of power supplies. Explain the operation of power supplies. Design and analyze power supplies. List the parameters of magnetic circuits. Design and analyze transformers and inductors.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Symbols and Their Meanings
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.1 Flyback converter. (a) Circuit, (b) Transistor Q1 voltage, (c) Secondary voltage, (d) Primary current, (e) Secondary current, and (f) Output voltage.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.5 and 13.6
Flyback Converter
• Because energy is transferred from the
source to the output during the time interval 0 to kT only, the input power is given by
• For an efficiency of η, the output power Po
can be found from
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.7 and 13.8
Flyback Converter
• The output power Po can be equated to Po
= Vo2/RL so that we can find the output voltage Vo as
• The allowable kmax for the discontinuous
mode can be found from Eq. (13.7) as
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.10
Flyback Converter
• Because the collector voltage VQ1 of Q1 is
maximum when Vs is maximum, the maximum collector voltage VQ1(max), as shown in Figure 13.1b, is given by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.11
Flyback Converter
• The peak primary current Ip(pk), which is
the same as the maximum collector current IC(max) of the power switch Q1, is given by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.2
Double-ended flyback converter.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.3 Forward converter. (a) Circuit, (b) Primary voltage, (c) Transistor voltage, (d) Primary current, (e) Current of diode D3, (f) Current of inductor L1, and (g) Output voltage.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.4
Current components in the primary winding.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.20 and 13.21
Current Components in the Primary Winding
• The output voltage Vo, which is the time
integral of the secondary winding voltage, is given by
• The maximum collector current IC(max) during
turn-on is equal to I'p(pk) as given by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.22 and 13.24
Current Components in the Primary Winding
• The maximum collector voltage VQ1(max) at turn-
off, which is equal to the maximum input voltage Vi(max) plus the maximum voltage Vr(max) across the tertiary, is given by
• which, after replacing Vr/Vs by Nr/Np, gives the
maximum duty cycle kmax as
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.5
Double-ended forward converter.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.6
Push-pull converter configuration.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.25
Push–Pull Converter
• The average output voltage is
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.7 Half-bridge converter. (a) Circuit, (b) Primary voltage, (c) Transistor Q2 voltage, (d) Transistor Q1 voltage, (e) Primary current, (f) Inductor L1 current, and (g) Rectifier output voltage.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.30
Half-Bridge Converter
• The output voltage Vo can be found from
the time integral of the inductor voltage νL1 over the switching period T.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.31
Half-Bridge Converter
• The output power Po is given by
where Ip(avg) is the average primary current.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.32 and 13.33
Half-Bridge Converter
• Assuming that the secondary load current
reflected to the primary side is much greater than the magnetizing current, the maximum collector currents for Q1 and Q2 are given by
• The maximum collector voltages for Q1
and Q2 during turn-off are given by Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.8 Full-bridge converter. (a) Circuit, (b) Primary voltage, (c) Transistor Q1 voltage, (d) Transistor Q2 voltage, (e) Rectifier output voltage, (f) Primary current, and (g) Inductor L1 current.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.39
Full-Bridge Converter
• The output voltage Vo can be found from
the time integral of the inductor voltage νL1 over the switching period T.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.40
Full-Bridge Converter
• The output power Po is given by
where Ip(avg) has the average primary current.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.41 and 13.42
Full-Bridge Converter
• Neglecting the magnetizing current, the
maximum collector currents for Q1, Q2, Q3, and Q4 are given by
• The maximum collector voltage for Q1, Q2,
Q3, and Q4 during turn-off is given by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.9
Configurations for resonant dc power supplies.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.10
Bidirectional dc power supply.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.43 and 13.44
Bidirectional Power Supplies
• For power flow from the source to the
load, the inverter operates in the inversion mode if
• For power flow from the output to the
input, the inverter operates as a rectifier if
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.11
UPS configurations.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.12
Arrangement of UPS systems.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.13
Switched-mode ac power supplies.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.14
Resonant ac power supply.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.15
Bidirectional ac power supplies.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.16
Multistage conversions.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.17
Cycloconverters with bilateral switches.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.18
Voltage-mode control of forward converter.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.46 and 13.47
Voltage-mode control
• The dc operating point is given by
• The small-signal term can be separated
from the dc operating point as
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.49
Voltage-mode control
• The small-signal duty cycle is related to
the small-signal error voltage by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.19 A current-mode controlled flyback regulator. (a) Circuit, (b) Switching current, (c) R-latch input, (d) Clock signal, and (e) Gate drive signal.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.20
Transformer apparent power for various converter circuits.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.21
Core area for various core types.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.53 and 13.55
Core Area for Various Core Types
• For N1 = N2 = N and I1 = I2 = I, the
primary or secondary volt–amperes are given by
• Substituting NI from Eq. (13.54) into Eq.
(13.53) gives the area product as
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.56
Core Area for Various Core Types
• The current density J is related to Ap by [1]
where Kj and x are constants that depend on the magnetic core, as given in Table 13.1.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.57
Core Area for Various Core Types
• Substituting J from Eq. (13.56) into Eq.
(13.55), we can find Ap as given by
where Bm is in flux density/cm2.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.22
Cores with two permeability regions.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
CHAPTER CHAPTER
13
Power Supplies
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Learning Outcomes
After completing this chapter, students should be able to do the following: List the types of power supplies. List the circuit topologies of power supplies. Explain the operation of power supplies. Design and analyze power supplies. List the parameters of magnetic circuits. Design and analyze transformers and inductors.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Symbols and Their Meanings
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.1 Flyback converter. (a) Circuit, (b) Transistor Q1 voltage, (c) Secondary voltage, (d) Primary current, (e) Secondary current, and (f) Output voltage.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.5 and 13.6
Flyback Converter
• Because energy is transferred from the
source to the output during the time interval 0 to kT only, the input power is given by
• For an efficiency of η, the output power Po
can be found from
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.7 and 13.8
Flyback Converter
• The output power Po can be equated to Po
= Vo2/RL so that we can find the output voltage Vo as
• The allowable kmax for the discontinuous
mode can be found from Eq. (13.7) as
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.10
Flyback Converter
• Because the collector voltage VQ1 of Q1 is
maximum when Vs is maximum, the maximum collector voltage VQ1(max), as shown in Figure 13.1b, is given by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.11
Flyback Converter
• The peak primary current Ip(pk), which is
the same as the maximum collector current IC(max) of the power switch Q1, is given by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.2
Double-ended flyback converter.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.3 Forward converter. (a) Circuit, (b) Primary voltage, (c) Transistor voltage, (d) Primary current, (e) Current of diode D3, (f) Current of inductor L1, and (g) Output voltage.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.4
Current components in the primary winding.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.20 and 13.21
Current Components in the Primary Winding
• The output voltage Vo, which is the time
integral of the secondary winding voltage, is given by
• The maximum collector current IC(max) during
turn-on is equal to I'p(pk) as given by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.22 and 13.24
Current Components in the Primary Winding
• The maximum collector voltage VQ1(max) at turn-
off, which is equal to the maximum input voltage Vi(max) plus the maximum voltage Vr(max) across the tertiary, is given by
• which, after replacing Vr/Vs by Nr/Np, gives the
maximum duty cycle kmax as
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.5
Double-ended forward converter.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.6
Push-pull converter configuration.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.25
Push–Pull Converter
• The average output voltage is
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.7 Half-bridge converter. (a) Circuit, (b) Primary voltage, (c) Transistor Q2 voltage, (d) Transistor Q1 voltage, (e) Primary current, (f) Inductor L1 current, and (g) Rectifier output voltage.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.30
Half-Bridge Converter
• The output voltage Vo can be found from
the time integral of the inductor voltage νL1 over the switching period T.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.31
Half-Bridge Converter
• The output power Po is given by
where Ip(avg) is the average primary current.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.32 and 13.33
Half-Bridge Converter
• Assuming that the secondary load current
reflected to the primary side is much greater than the magnetizing current, the maximum collector currents for Q1 and Q2 are given by
• The maximum collector voltages for Q1
and Q2 during turn-off are given by Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.8 Full-bridge converter. (a) Circuit, (b) Primary voltage, (c) Transistor Q1 voltage, (d) Transistor Q2 voltage, (e) Rectifier output voltage, (f) Primary current, and (g) Inductor L1 current.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.39
Full-Bridge Converter
• The output voltage Vo can be found from
the time integral of the inductor voltage νL1 over the switching period T.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.40
Full-Bridge Converter
• The output power Po is given by
where Ip(avg) has the average primary current.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.41 and 13.42
Full-Bridge Converter
• Neglecting the magnetizing current, the
maximum collector currents for Q1, Q2, Q3, and Q4 are given by
• The maximum collector voltage for Q1, Q2,
Q3, and Q4 during turn-off is given by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.9
Configurations for resonant dc power supplies.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.10
Bidirectional dc power supply.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.43 and 13.44
Bidirectional Power Supplies
• For power flow from the source to the
load, the inverter operates in the inversion mode if
• For power flow from the output to the
input, the inverter operates as a rectifier if
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.11
UPS configurations.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.12
Arrangement of UPS systems.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.13
Switched-mode ac power supplies.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.14
Resonant ac power supply.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.15
Bidirectional ac power supplies.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.16
Multistage conversions.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.17
Cycloconverters with bilateral switches.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.18
Voltage-mode control of forward converter.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.46 and 13.47
Voltage-mode control
• The dc operating point is given by
• The small-signal term can be separated
from the dc operating point as
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.49
Voltage-mode control
• The small-signal duty cycle is related to
the small-signal error voltage by
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.19 A current-mode controlled flyback regulator. (a) Circuit, (b) Switching current, (c) R-latch input, (d) Clock signal, and (e) Gate drive signal.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.20
Transformer apparent power for various converter circuits.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.21
Core area for various core types.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equations 13.53 and 13.55
Core Area for Various Core Types
• For N1 = N2 = N and I1 = I2 = I, the
primary or secondary volt–amperes are given by
• Substituting NI from Eq. (13.54) into Eq.
(13.53) gives the area product as
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.56
Core Area for Various Core Types
• The current density J is related to Ap by [1]
where Kj and x are constants that depend on the magnetic core, as given in Table 13.1.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Equation 13.57
Core Area for Various Core Types
• Substituting J from Eq. (13.56) into Eq.
(13.55), we can find Ap as given by
where Bm is in flux density/cm2.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
Figure 13.22
Cores with two permeability regions.
Power Electronics: Devices, Circuits, and Applications, 4e Muhammad H. Rashid
Copyright ©2014 by Pearson Education, Inc. All rights reserved.
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