Huang-Jen Chiu

Dept. of Electronic Engineering

National Taiwan University of
Science and Technology
Office: EE502-1
Tel: 02-2737-6419
E-mail: hjchiu@mail.ntust.edu.tw

Textbook
Power Electronics
--Converters, Applications, and Design
Third Edition
Mohan / Undeland / Robbins
02-23657999 02-3651662
Midterm: 50%

Final: 50%

Outlines
Power Electronic Systems
Overview of Power Semiconductor Switches
Switch-Mode DC/DC Converters
Switch-Mode DC/AC Inverters
Resonant Converters
Switching DC Power Supplies
Power Conditioners and Uninterruptible Power Supplies
Practical Converter Design Considerations

Chapter 1
Power Electronic Systems

Power Electronic Systems

Linear Power Supply

Series transistor as an adjustable resistor

Low Efficiency
Heavy and bulky

Switch-Mode Power Supply

Transistor as a switch
High Efficiency
High-Frequency Transformer

Basic Principle of
Switch-Mode Synthesis

Constant switching frequency

Pulse width controls the average

L-C filters the ripple

Application
in Adjustable Speed Drives

Conventional drive wastes energy across the

throttling valve to adjust flow rate
Using power electronics, motor-pump speed is
adjusted efficiently to deliver the required flow rate

Scope and Applications

Scope and Applications

Classification of Power Converters

ac-dc converters (controlled rectifiers)

dc-dc converters (dc choppers)
dc-ac converters (inverters)
ac-ac converters (ac voltage controllers)

Power Processor as a
Combination of Converters

Most practical topologies require an energy

storage element, which also decouples the input
and the output side converters

Power Flow through Converters

Converter is a general term

An ac/dc converter is shown here
Rectifier Mode of operation when power from ac to dc
Inverter Mode of operation when power from ac to dc

AC Motor Drive

Converter 1 rectifies line-frequency ac into dc

Capacitor acts as a filter; stores energy; decouples
Converter 2 synthesizes low-frequency ac to motor
Polarity of dc-bus voltage remains unchanged
ideally suited for transistors of converter 2

Matrix Converter

Very general structure

Would benefit from bi-directional and bi-polarity switches
Being considered for use in specific applications

Interdisciplinary Nature of
Power Electronics

Chapter 2 Overview of
Power Semiconductor Devices

Diodes

On and off states controlled by the power circuit

Diode Turn-Off

Fast-recovery diodes have a small reverse-recovery time

Thyristors

Semi-controlled device
Latches ON by a gate-current pulse if forward biased
Turns-off if current tries to reverse

Thyristor in a Simple Circuit

For successful turn-off, reverse voltage required for

an interval greater than the turn-off interval

Generic Switch Symbol

Idealized switch symbol

When on, current can flow only in the direction of the arrow
Instantaneous switching from one state to the other
Zero voltage drop in on-state
Infinite voltage and current handling capabilities

Switching Characteristics
(linearized)

Switching Power Loss is proportional to:

switching frequency
1
Ps = Vd I o f s (t c(on) + t c(off) )
turn-on and turn-off times
2

Bipolar Junction Transistors (BJT)

Used commonly in the past

Now used in specific applications

Replaced by MOSFETs and IGBTs

Various Configurations of BJTs

MOSFETs

Easy to control by the gate

Optimal for low-voltage operation at high switching frequencies
On-state resistance a concern at higher voltage ratings

Gate-Turn-Off Thyristors (GTO)

Slow switching speeds

Used at very high power levels
Require elaborate gate control circuitry

GTO Turn-Off

Need a turn-off snubber

Insulated Gate Bipolar Transistor

(IGBT)

MOS-Controlled Thyristor
(MCT)

Simpler Drive and faster switching speed than those of GTOs.

Current ratings are significantly less than those of GTOs.

Comparison of Controllable Switches

Summary of Device Capabilities

Rating of Power Devices

Chapter 3
Review of Basic Electrical and
Magnetic Circuit Concepts

Sinusoidal Steady State

P
PF = = cos
S

Three-Phase Circuit

Steady State in Power Electronics

Fourier Analysis

1
f(t) = F0 + f h (t) = a0 + {a h cos(h t) + bh sin(h t)}
2
h =1
h =1

Distortion in the Input Current

I s1
P I s1
PF = =
cos 1 =
DPF =
S
Is
Is
Voltage

1
1 + THD i2

DPF

is assumed to be sinusoidal

Subscript 1 refers to the fundamental

The angle is between the voltage and the current fundamental

Phasor Representation

Response of L and C

di L
vL = L
dt

dv c
ic = C
dt

Inductor Voltage and Current

in Steady State

Volt-seconds over T equal zero.

Capacitor Voltage and Current

in Steady State

Amp-seconds over T equal zero.

Amperes Law

H dl = i

Direction of magnetic field due to currents

Amperes Law: Magnetic field along a path

Direction of Magnetic Field

B = H

B-H Relationship; Saturation

Definition of permeability

Continuity of Flux Lines

1 + 2 + 3 = 0

Concept of Magnetic Reluctance

Flux is related to ampere-turns by reluctance

Analogy between Electrical and

Magnetic Variables

Analogy between Equations in

Electrical and Magnetic Circuits

Faradays Law and Lenzs Law

d
di
e= N
= L
dt
dt

Inductance L

Inductance relates flux-linkage to current

Analysis of a Transformer

Transformer Equivalent Circuit

Including the Core Losses

N1 2
Ll2' = (
) Ll2
N2
N1 2
R2' = (
) R2
N2

Chapter 4
Computer Simulation

System to be Simulated

Challenges in modeling power electronic systems

Large-Signal System Simulation

Simplest component models

Small-Signal Linearized Model

for Controller Design

System linearized around the steady-state point

Closed-Loop Operation:
Large Disturbances

Simplest component models

Nonlinearities, Limits, etc. are included

Modeling of Switching Operation

Detailed device models

Just a few switching cycles are studied

Modeling of a Simple Converter

di L
+ v c = v oi
dt
dv c v c
iL - C
=0
dt
R
rL i L + L

di L
dt
dv c
dt

rL

- L
= 1

1
L
1
CR
-

1
iL
+ L v oi

0
vc

Modeling using PSpice

Schematic approach is far superior

PSpice-based Simulation

Simulation results

Simulation using MATLAB

Chapter 5
Diode Rectifiers

Diode Rectifier Block Diagram

Uncontrolled utility interface (ac to dc)

A Simple Circuit

Resistive load

A Simple Circuit (R-L Load)

Current continues to flows for a while even

after the input voltage has gone negative

A Simple Circuit
(Load has a dc back-emf)

Current begins to flow when the input voltage exceeds the dc back-emf
Current continues to flows for a while even after the input voltage has
gone below the dc back-emf

Single-Phase Diode Rectifier Bridge

Large capacitor at the dc output for filtering and energy storage

Diode-Rectifier Bridge Analysis

Diode-Rectifier Bridge Input Current

Current Commutation

Assuming inductance in this circuit to be zero

Current Commutation

Current Commutation
in Full-Bridge Rectifier

Current Commutation

Rectifier with a dc-side voltage

Diode-Rectifier with a Capacitor Filter

Power electronics load is represented by

an equivalent load resistance

Diode Rectifier Bridge

Equivalent circuit for analysis on one-half cycle basis

Diode-Bridge Rectifier: Waveforms

Analysis using PSpice

Input Line-Current Distortion

Analysis using PSpice

Line-Voltage Distortion

PCC is the point of common coupling

Line-Voltage Distortion

Distortion in voltage supplied to other loads

Voltage Doubler Rectifier

In 115-V position, one capacitor at-a-time is

charged from the input.

A Three-Phase, Four-Wire System

A common neutral wire is assumed

Three-Phase, Full-Bridge Rectifier

Commonly used

Three-Phase, Full-Bridge Rectifier

Output current is assumed to be dc

Three-Phase, Full-Bridge Rectifier:

Input Line-Current

Assuming output current to be purely dc and

zero ac-side inductance

Rectifier with a Large Filter Capacitor

Output voltage is assumed to be purely dc

Chapter 6
Thyristor Converters

Controlled conversion of ac into dc

Chapter 6
Thyristor Converters

Controlled conversion of ac into dc

Thyristor Converters

Two-quadrant conversion

Primitive circuits with thyristors

Thyristor Triggering

Full-Bridge Thyristor Converters

Single-phase and three-phase

Single-Phase Thyristor Converters

Average DC Output Voltage

is ( t) = 2 I s1 sin( t - ) + 2 I s3 I s1 sin[3( t - )] + ...
I s1 =

2 I d = 0.9I d P = 0.9cos

Assuming zero ac-side inductance

Input Line-Current Waveforms

Harmonics, power and reactive power

1-Phase Thyristor Converter

Thyristor Converter

DC Voltage versus Load Current

Various values of delay angle

Thyristor Converters:
Inverter Mode

Assuming the ac-side inductance to be zero

Thyristor Converters:
Inverter Mode

Family of curves at various values of delay angle

Thyristor Converters:
Inverter Mode

Thyristor Converters:
Inverter Mode

3-Phase Thyristor Converters

Chapter 7
DC-DC Switch-Mode Converters

dc-dc converters for switch-mode dc power supplies and

dc-motor drives

Block Diagram of DC-DC Converters

Functional block diagram

Stepping Down a DC Voltage

A simple approach that shows the evolution

Pulse-Width Modulation in
DC-DC Converters

Step-Down DC-DC Converter

(Vd Vo )Ton = VoToff

Vo Ton
=
= D <1
Vd
T

Waveforms at the boundary of

Cont./ Discont. Conduction

ton
TsVd
1
I LB = I L, peak =
(Vd - Vo ) =
D(1 - D) = 4I LB,max D(1 - D)
2
2L
2L
Critical current below which inductor current becomes
discontinuous

Step-Down DC-DC Converter:

Discontinuous Conduction Mode

Vo
D2
=
Io
1
Vd
D2 + (
)
4 I LB, max

Steady state; inductor current discontinuous

Limits of Cont./ Discont.

Conduction
Vo
= D : CCM
Vd
Vo
D2
: DCM
=
Io
1
Vd
2
D + (
)
4 I LB, max

Output Voltage Ripple

Vo =

Q
C

I LTs
8C

Step-Up DC-DC Converter

Vd Ton = ( Vo Vd )Toff

Vo
1
=
>1
Vd
1 D

Output voltage must be greater than the input

Limits of Cont./ Discont.

Conduction

ton
TsVo
1
I LB = I L,peak = Vd =
D(1- D) = 4ILB,maxD(1- D)
2
2L
2L
TsVo
2 27
I oB = (1 - D)I LB =
D(1 - D) =
D(1 - D)2 I oB,max
2L
4

Discont. Conduction

Io
4 Vo Vo
D=
( - 1)
27 Vd Vd
IoB,max

Limits of Cont./ Discont.

Conduction
Vo
1
: CCM
=
Vd 1 D

D=

I
4 Vo Vo
( - 1) o : DCM
27 Vd Vd
IoB,max

Output Ripple

I o ton Vo DTs
Vo =
=
C
R C

Step-Down/Up DC-DC Converter

V d T on = V o T off

Vo
D
=
Vd
1 D

The output voltage can be higher or lower than

the input voltage

Limits of Cont./ Discont.

Conduction

ton
TsVo
1
I LB = I L, peak =
Vd =
(1 - D) = I LB,max (1 - D)
2
2L
2L
TsVo
I oB = (1 - D)I LB =
(1 - D)2 = I oB,max (1 - D)2
2L

Discontinuous Conduction Mode

Vo
Io
D=
Vd IoB,max

This occurs at light loads

Limits of Cont./ Discont.

Conduction
Vo
D
=
: CCM
1 D
Vd

V
Io
D= o
: DCM
Vd IoB,max

Output Voltage Ripple

I o ton Vo DTs
Vo =
=
C
R C

ESR is assumed to be zero

Cuk DC-DC Converter

The output voltage can

be higher or lower than
the input voltage

Converter for DC-Motor Drives

Converter Waveforms

Output Ripple in Converters for

DC-Motor Drives

Switch Utilization
in DC-DC Converters

It varies significantly in various converters

Reversing the Power Flow

in DC-DC Converters

Chapter 8
Switch-Mode DC-AC Inverters

Converters for ac motor drives and

uninterruptible power supplies

Switch-Mode DC-AC Inverter

Switch-Mode DC-AC Inverter

Synthesis of a Sinusoidal Output

by PWM
^

ma =

V control
^

V tri

fs
mf =
f1

Details of a Switching Time Period

Small mf (mf21): Synchronous PWM

Large mf (mf>21): Asynchronous PWM

Harmonics in the DC-AC Inverter

Output Voltage

Harmonics appear around the carrier frequency and its multiples

Harmonics due to Over-modulation

These are harmonics of the fundamental frequency

Square-Wave Mode of Operation

Harmonics are of the fundamental frequency

Less switching losses in high power applications
The DC input voltage must be adjusted

Half-Bridge Inverter

Capacitors provide the mid-point

Single-Phase Full-Bridge DC-AC Inverter

Consists of two inverter legs

PWM to Synthesize Sinusoidal Output

Analysis assuming Fictitious Filters

Small fictitious filters eliminate the switching-frequency

related ripple

DC-Side Current

Uni-polar Voltage Switching

DC-Side Current
in a Single-Phase Inverter

Sinusoidal Synthesis by Voltage Shift

Phase shift allows voltage cancellation to synthesize a

1-Phase sinusoidal output

Square-Wave and PWM Operation

PWM results in much smaller ripple current

Push-Pull Inverter

Only one switch conducts at any instant of time

High efficiency for low-voltage source applications

Three-Phase Inverter

Three inverter legs; capacitor mid-point is fictitious

Three-Phase PWM Waveforms

Three-Phase Inverter Harmonics

Three-Phase Inverter Output

Square-Wave and PWM Operation

PWM results in much smaller ripple current

DC-Side Current
in a Three-Phase Inverter

The current consists of a dc component and the

switching-frequency related harmonics

Effect of Blanking Time

Results in nonlinearity

Effect of Blanking Time

2t
T Vd , io > 0
Vo = s
2t
- Vd , io < 0
Ts

Voltage jump when the current reverses direction

Effect of Blanking Time

Effect on the output voltage

Programmed Harmonic Elimination

Angles based on the desired output

Tolerance-Band Current Control

Results in a variable frequency operation

Fixed-Frequency Operation

Better control is possible using dq analysis

Chapter 9
Zero-Voltage or Zero-Current Switchings

converters for soft switching

Hard Switching Waveforms

The output current can be positive or negative

Turn-on and Turn-off Snubbers

Switching Trajectories

Comparison of Hard versus soft switching

Undamped Series-Resonant Circuit

Vd

di L
+ vc = V d
dt
dv c
Cr
= iL
dt
Lr

i L (t) = I Lo cos o (t - t o ) +

V d - V co
sin o ( t t o )
Zo

v c (t) = V d - (V d - V co )cos o (t - t o ) + Z o I Lo sin o ( t t o )

Series-Resonant Circuit
with Capacitor-Parallel Load

di L
+ vc = Vd
dt
dv c
ic = C r
= iL - I o
dt
Lr

i L (t) = I o + (I Lo - I o )cos o (t - t o ) +

V d - V co
sin o ( t t o )
Zo

v c (t) = V d - (V d - V co )cos o (t - t o ) + Z o (I Lo - I o ) sin o ( t t o )

Impedance of a Series-Resonant Circuit

Q =

o Lr
R

Z
1
= o
oC r R
R

The impedance is capacitive below the resonance frequency

Undamped Parallel-Resonant Circuit

dv c
= Id
dt
di L
vc = Lr
dt

iL + C r

V co
sin o ( t t o )
i L (t) = I d + (I Lo - I d )cos o (t - t o ) +
Zo
v c (t) = Z o (I d - I Lo )sin o (t - t o ) + V c o cos o ( t t o )

Impedance of a Parallel-Resonant Circuit

Q = o RC r =

R
R
=
o Lr
Zo

The impedance is inductive at below the resonant frequency

Series-Loaded Resonant (SLR) Converter

2s<o

Turn off with ZVS and ZCS

Turn on with ZCS

Thyristors

used

Large peak current, high conduction losses

ZVS, ZCS
ZCS

SLR Converter Waveforms

1/2o<s<o

Turn off with ZVS and ZCS

Thyristors

used

Large turn - on switching losses

ZVS, ZCS

SLR Converter Waveforms

s>o

Turn on with ZVS and ZCS

Large turn - off switching losses
Controllable switches used

ZVS, ZCS

Lossless Snubbers in SLR Converters

The operating frequency is above the resonance frequency

SLR Converter Characteristics

The operating frequency is varied to regulate the output voltage

SLR Converter Control

The operating frequency is varied to regulate the output voltage

Parallel-Loaded Resonant (PLR) Converter

No turn - on and turn - off losses

ZVS, ZCS

ZCS

1
o
2

PLR Converter Waveforms

No turn - off losses

ZVS, ZCS

1
o < s < o
2

PLR Converter Waveforms

No turn - on losses

ZVS

PLR Converter Characteristics

Output voltage as a function of operating frequency

for various values of the output current

Hybrid-Resonant DC-DC Converter

Combination of series- and parallel-loaded resonances

A SLR offers an inherent current limiting under short-circuit conditions and
a PLR regulating its voltage at no load with a high-Q resonant tank is not a
problem

Parallel-Resonant
Current-Source Converter
Resistive

Induction Coil

Capacitive

Basic circuit to illustrate the operating principle at the

fundamental frequency

Parallel-Resonant
Current-Source Converter

Using thyristors; for induction heating

Class-E Converters
Used for high - frequency
electronic ballasts
Sin-wave Current

Single-switch

ZCS Turn-on

No switching losses

ZVS Turn-off

High peak volatge and current

Class-E Converters

Resonant Switch Converters

ZCS Resonant-Switch Converter

Voltage is regulated by varying

the switching frequency
ZCS Turn-off
ZCS Turn-on

ZCS Resonant-Switch Converter

Accelerating diode
ZCS Turn-off

ZCS Turn-on

Discharge slowly at light load

ZVS Resonant-Switch Converter

ZVS Turn-off
ZVS Turn-on

MOSFET Internal Capacitances

ZVS is preferable over ZCS at

high switching frequencies

These capacitances affect the MOSFET switching

ZVS-CV DC-DC Converter

ZVS Turn-on

The inductor current must reverse direction

during each switching cycle

ZVS-CV DC-DC Converter

ZVS-CV Principle Applied to

DC-AC Inverters

Three-Phase ZVS-CV DC-AC Inverter

Very large ripple in the output current

Output Regulation by Voltage Control

Each pole operates at nearly 50% duty-ratio

ZVS-CV with Voltage Cancellation

Commonly used

Resonant DC-Link Inverter

ZVS Turn-on

The dc-link voltage is made to oscillate

Three-Phase Resonant DC-Link Inverter

Modifications have been proposed

High-Frequency-Link Inverter

Basic principle for selecting integral half-cycles of

the high-frequency ac input

High-Frequency-Link Inverter

Low-frequency ac output is synthesized by selecting

integral half-cycles of the high-frequency ac input

High-Frequency-Link Inverter

Shows how to implement such an inverter

Chapter 10
Switching DC Power Supplies

One of the most important applications of power electronics

Linear Power Supplies

Very poor efficiency and large weight and size

Switching DC Power Supply

High efficiency and small weight and size

Switching DC Power Supply:

Multiple Outputs

In most applications, several dc voltages are required,

possibly electrically isolated from each other

Transformer Analysis

Needed to discuss high-frequency isolated supplies

PWM to Regulate Output

Flyback Converter

Derived from buck-boost; very power at small power

(> 50 W ) power levels

Flyback Converter

Switch on and off states (assuming incomplete

core demagnetization)

Flyback Converter

Switching waveforms (assuming incomplete

core demagnetization)

Other Flyback Converter Topologies

Forward Converter

Derived from Buck; idealized to assume that the

transformer is ideal (not possible in practice)

Forward Converter: in Practice

Switching waveforms (assuming incomplete

core demagnetization)

Forward Converter:
Other Possible Topologies

Two-switch Forward converter is very commonly used

Push-Pull Inverter

Leakage inductances become a problem

Half-Bridge Converter

Derived from Buck

Full-Bridge Converter

Used at higher power levels (> 0.5 kW )

Current-Source Converter

More rugged (no shoot-through) but both switches must

not be open simultaneously

Ferrite Core Material

Several materials to choose from based on applications

Core Utilization in Various

Converter Topologies

At high switching frequencies, core losses limit excursion

of flux density

Control to Regulate Voltage Output

Linearized representation of the feedback control system

Linearization of the Power Stage

x = A1x + B1vd , dTs

x = A2 x + B2vd , (1 d)Ts

vo = C1x , dTs

vo = C2 x , (1 d)Ts

x = [ A1d + A2 (1 d)]x +[B1d + B2 (1 d)]vd
vo = [C1d + C2 (1 d)]x

X + x = {A1 (D + d ) + A2[1 (D + d )]}(X + x) + [B1 (D + d ) + B2[1 (D + d )]Vd

~

= [ A1D + A1 d + A2 (1 D) A2 d](X + x) +[B1D + B1 d + B2 (1 D) B2 d]Vd

~

= [ A1D + A2 (1 D)]X +[B1D + B2 (1 D)]Vd +[(A1 A2 ) X + (B1 B2 )Vd ] d

~

~ ~

+[ A1D + A2 (1 D)]x+ ( A1 A2 ) d x

Linearization of the Power Stage

X + x AX + BVd + A x+[(A1 A2 ) X + (B1 B2 )Vd ] d

X = 0 = AX + BVd
~

x = A x+[(A1 A2 ) X + (B1 B2 )Vd ] d

~

Vo + vo = {C1(D + d ) + C2[1 (D + d )][X + x]

~

~ ~

= [C1D + C2 (1 D)]X +[(C1 C2 ) X ] d +[C1D + C2 (1 D)] x+ (C1 C2 ) x d

~

Vo + vo CX +[(C1 C2 ) X ] d + C x
Vo = CX

vo = C x+[(C1 C2 ) X ] d

Linearization of the Power Stage

X = 0 = AX + BVd
and Vo = CX

Steady-state
Vo
1
= CA B
Vd
DC voltage transfer ratio
~

x = A x+[(A1 A2 ) X + (B1 B2 )Vd ] d

~

s x(s) = A x(s) +[(A1 A2 ) X + (B1 B2 )Vd ] d (s)

~

x(s) = [sI A] [(A1 A2 ) X + (B1 B2 )Vd ] d (s)

vo = C x+[(C1 C2 ) X ] d

Tp (s) =

vo (s)
~

d (s)

= C[sI A]1[(A1 A2 ) X + (B1 B2 )Vd ] + (C1 C2 ) X

Forward Converter: An Example

Vd + L x1 + rL x1 + R(x1 C x2 ) = 0

x2 + Crc x2 + R(x1 C x2 ) = 0

A1 =A2

Rrc + RrL + rcrL

R

L(R + rc )
L(R + rc ) 1
x1 =
+ L Vd
1 x2
R
x
0

2
C(R + rc )
C(R + rc )

B1
B2=0

C1=C2

Rrc
vo = R(x1 C x2 ) =
R + rc

A = A1

, B = B1D

R x1

R + rc x2

, C = C1

1 C = C1 = C2 [rc 1]
rc + rL

L
L
R >> (rC + rL ) A = A1 = A2
1
1 B = B D = 1/ LD
1

0


CR
C

1
1

Vo
R + rc

LC
1
CR
L
=D
D
A =
1

Vd
R + (rc + rL )
rc + rL
1+ (rc + rL ) / R

L
C
~

Tp (s) =

vo (s)
~

= C[sI A]1[(A1 A2 ) X + (B1 B2 )Vd ] + (C1 C2 ) X

d (s)
1+ srcC
o2
s + z
Vd
= Vd
2
z s2 + 2os + o2
LC{s + s[1/ CR+ (rc + rL ) / L] +1/ LC}

Forward Converter:
Transfer Function Plots
o2
s + z
Tp (s) = Vd
z s2 + 2os + o2

Flyback Converter:
Transfer Function Plots
(1+ s / z1)(1 s / z 2 )
Tp (s) = Vd f (D)
as2 + bos + c

Linearizing the PWM Block

Tm (s) =

d (s)
~

1
^

vc (s) Vr

vo (s) vo (s) d (s)

Tl (s) = ~ = ~
= Tp (s)Tm (s)
~
vc (s) d (s) vc (s)

Typical Gain and Phase Plots of the

Open-Loop Transfer Function

Definitions of the crossover frequency, phase and gain margins

A General Amplifier for

Error Compensation

Can be implemented using a single op-amp

Type-2 Error Amplifier

Shows phase boost at the crossover frequency

Feedback-Loop Stabilization

Feedback-Loop Stabilization
Fp
Fco
K =
=
Fz
Fco

Feedback-Loop Stabilization
K =

total

lag

= 270 tan 1 K + tan 1

1
K

Fp
Fco
=
Fz
Fco

Compensator Design Example

Vo
5V
Io(nom)
10A
Io(min)
1A
Switching frequency
100kHz
Minimum output ripple 50mVP-P

3V o T 3 5 10 10 6
Lo =
=
= 15 H
I on
10
Co = 65 10 6
Fo =

dI
2
= 65 10 6
= 2600 F
Vor
0.05

1
= 806 Hz
2 L o C o

Fesr =

1
1
=
= 2 . 5 kHz
6
2 R esr C o 2 65 10

Compensator Design Example

Gm =

0 .5 (V sp 1)
3

0 . 5 (11 1)
= + 4 . 5 dB
3

G m + G s = 4 . 5 + 20 log(

2 .5
) = 4 .5 6 = 1 .5 dB
5

R2 = R1 100 ( 40 dB ) = 1k 100 = 100 k

Compensator Design Example

Fco =

1
Fs = 20 kHz
5

Fco
20 k
=
= 8 lag = 97
Fesr
2 .5 k

EA lag = 360 45 97 = 218 K = 4

Fco 20
1
=
= 5 kHz C 1 =
= 318 pF
Fz =
K
4
2 (100 k )( 5 k )
1
= 20 pF
F p = K Fco = 4 20 = 80 kHz C 2 =
2 (100 k )( 80 k )

Voltage Feed-Forward

Makes converter immune from input voltage variations

Voltage versus Current Mode Control

Various Types of Current Mode Control

Peak Current Mode Control

Slope compensation is needed

A Typical PWM Control IC

Current Limiting

Implementing Electrical Isolation

in the Feedback Loop

Implementing Electrical Isolation

in the Feedback Loop

Input Filter

Needed to comply with the EMI and harmonic limits

ESR of the Output Capacitor

ESR often dictates the peak-peak voltage ripple

Chapter 11
Power Conditioners and
Uninterruptible Power Supplies

Becoming more of a concern as utility de-regulation proceeds

Distortion in the Input Voltage

The voltage supplied by the utility may not be sinusoidal

Typical Voltage Tolerance

Envelope for Computer Systems

This has been superceded by a more recent standard

Typical Range of Input Power Quality

Electronic Tap Changers

Controls voltage magnitude by connecting the output to

the appropriate transformer tap

Uninterruptible Power Supplies

(UPS)

Block diagram; energy storage is shown to be in

batteries but other means are being investigated

UPS: Possible Rectifier Arrangements

The input normally supplies power to the load as well

as charges the battery bank

UPS: Another Possible Rectifier

Arrangement

Consists of a high-frequency isolation transformer

UPS: Another Possible Input

Arrangement

A separate small battery charger circuit

Battery Charging Waveforms as

Function of Time

Initially, a discharged battery is charged with a constant current

UPS: Various Inverter Arrangements

Depends on applications, power ratings

UPS: Control

Typically the load is highly nonlinear and the voltage output

of the UPS must be as close to the desired sinusoidal
reference as possible

UPS Supplying Several Loads

With higher power UPS supplying several loads,

malfunction within one load should not disturb the other
loads

Another Possible UPS Arrangement

Functions of battery charging and the inverter are combined

UPS: Using the Line Voltage as Backup

Needs static transfer switches

Chapter 16
Residential and Industrial Applications

Significant in energy conservation; productivity

Inductive Ballast of Fluorescent Lamps

Inductor is needed to limit current

Rapid-Start Fluorescent Lamps

Starting capacitor is needed

Electronic Ballast for Fluorescent Lamps

Lamps operated at ~40 kHz

Induction Cooking

Pan is heated directly by circulating currents increases

efficiency

Industrial Induction Heating

Needs sinusoidal current at the desired frequency: two options

Welding Application

Switch-Mode Welders

Can be made much lighter weight

Chapter 17
Electric Utility Applications

These applications are growing rapidly

HVDC Transmission

There are many such systems all over the world

Control of HVDC Transmission System

Inverter is operated at the minimum extinction angle

and the rectifier in the current-control mode

HVDC Transmission: AC-Side Filters

Tuned for the lowest (11th and the 13th harmonic)

frequencies

Effect of Reactive Power on

Voltage Magnitude

Thyristor-Controlled Inductor (TCI)

Increasing the delay angle reduces the reactive power

drawn by the TCI

Thyristor-Switched Capacitors (TSCs)

Transient current at switching must be minimized

Instantaneous VAR Controller (SATCOM)

Can be considered as a reactive current source

Characteristics of Solar Cells

The maximum power point is at the knee of the characteristics

Photovoltaic Interface

This scheme uses a thyristor inverter

Harnessing of Wing Energy

A switch-mode inverter may be needed on

the wind generator side also

Active Filters for Harmonic Elimination

Active filters inject a nullifying current so that the current

drawn from the utility is nearly sinusoidal

Chapter 18
Utility Interface

Power quality has become an important issue

Various Loads Supplied by

the Utility Source

PCC is the point of common coupling

Diode-Rectifier Bridge

Typical Harmonics in the Input Current

Single-phase diode-rectifier bridge

Harmonic Guidelines: IEEE 519

Commonly used for specifying limits on the input current

distortion

Harmonic Guidelines: IEEE 519

Limits on distortion in the input voltage supplied by the utility

Reducing the Input Current Distortion

use of passive filters

Power-Factor-Correction (PFC) Circuit

For meeting the harmonic guidelines

Power-Factor-Correction (PFC)
Circuit Control

generating the switch on/off signals

Power-Factor-Correction (PFC) Circuit

Operation during each half-cycle

Switch-Mode Converter Interface

Bi-directional power flow; unity PF is possible

Switch-Mode Converter Control

DC bus voltage is maintained at the reference value

Switch-Mode Converter Interface

EMI: Conducted Interefence

Common and differential modes

Switching Waveforms

Typical rise and fall times

Conducted EMI

Various Standards

Conducted EMI Filter

Turn-off Snubber

D
D F

Io

R s
C s

Iotfi
Cs=2V ,
d

Io

Df
V

D s
S

Turn-off
snubber

Io -i
i

C s

ton>2.3RsCs, Vd/Rs<0.2Io

sw

Cs

sw

Turn-on Snubber
isw

+
D

R
Snubber
circuit

Ls

Ls
D

Io

+
Ls
D
V

Ls

Io

Without
With
snubber snubber

Ls

di
Ls sw
dt

Ls

Sw

LsIo
vsw= t
ri

toff>2.3Ls/Rs

v
sw

Sw

V
d

Pr=1/2LsIo^2fs

Aspects of EMC (EMIEMS)

EMC is concerned with the generation,
transmission, and reception of
electromagnetic energy
EMI occurs if the received energy
causes the receptor to behave in an
undesired manner

EMI Sources and Sensors

Three Ways to Prevent Interference

y

Suppress the emission at its source

Make the coupling path as inefficient as

possible

Make the receptor less susceptible to

the emission

Four Basic EMC Problems

Other Aspects of EMC

EMC Requirements
Those required by governmental agencies
Those imposed by the product manufacturer

Frequency Range of
EMC Requirements

National Regulations Summary

Federal Communications
Commission (FCC)
Class A for use in a commercial, industrial
or business environment

Class B for use in a residential

environment

FCC Emission for Class B

FCC Emission for Class A

Comparison of the FCC Class A and

Class B Radiated Emission Limits

Open Area Test Site

Chamber for Measurement of

Radiated Emissions

Radiated EMI Test Setup

Antennas

Conducted EMI Test Setup

Line Impedance Stabilization Network

(LISN)

Conducted Emissions Test Layout

Conducted Emissions Test Layout

CISPR Bandwidth Requirements

Three Detection Modes

Envelope
Detector

Quasi-Peak
Detector

Average
Detector

Design Constraints for Products

y Product Cost
y Product Marketability
y Product Manufacturability
y Product Development Schedule

Advantages of EMC Design

y Minimizing the additional cost required

by suppression elements or redesign

y Maintaining the development and product

announcement schedule
y Insuring that the product will satisfy

the regulatory requirements

Effects of Component Leads

Resistors

1000, Carbon Resistor

having 1/4 Inch Lead Lengths

Capacitors

470 pF Ceramic Capacitor with

Short Lead Lengths

470 pF Ceramic Capacitor with

1/2 Inch Lead Lengths

0.15 F Tantalum Capacitor with

Short Lead Lengths

0.15 F Tantalum Capacitor with

1/2 Inch Lead Lengths

Inductors

1.2H Inductor

Common-Mode Choke

Common-Mode Choke

Frequency Response of the

Relative Permeabilities of Ferrite

Ferrite Beads

Multi-Turn Ferrite Beads

Driver Circuit of the DC Motor

The Periodic, Trapezoidal Pulse

Train Representing Clock and
Data Signals

The key parameters that contribute to the highfrequency spectral content of the waveform are the
rise-time and fall-time of the pulse.

The Spectra of 1V, 10MHz,

50% Duty Cycle Trapezoidal Pulse Trains
for Rise-/Fall-time of 20ns/5ns

Spectrum Analyzer

The Effect of Bandwidth on Spectrum

The Effects of Differential-Mode

Current and Common-Mode Currents

Common-mode current often produce larger radiated

emissions than the differential-mode currents

Differential-Mode Current Emission

E D , max
|
| = Kf
ID

Radiated Emission due to

the Differential-Mode Currents

Common Mistakes that Lead to

Unnecessarily Large DM Emissions

Common-Mode Current Emission

E C , max
|
|= Kf L
IC

Radiated Emission due to

the Common-Mode Currents

Susceptibility Models

10V/m, 100MHz Incident

Uniform Plane Wave

Measurement of Conducted Emissions

Line Impedance Stabilization Network

(LISN)

Differential-Mode and Common-Mode

Current Components

Methods of Reducing the Common-Mode

Conducted Emissions

Definition of the Insertion Loss

of a Filter

Four Simple Filters

V L , wo
L
IL = 20 log 10 (
) = 20 log 10 (
)
RS + RL
V L ,w

Insertion Loss Tests

Conducted EMI Filter

Common-Mode Choke

The Equivalent Circuit of the Filter

for Common-Mode Currents

The Equivalent Circuit of the Filter

for Differential-Mode Currents

The Dominant Component of

Conducted Emission

I Total = I C I

A Device to Separate the CM

and DM Conducted Emissions

Measured Conducted Emissions

without Power Supply Filter

Measured Conducted Emissions

with 3300pF Line-to-Ground Cap.

Measured Conducted Emissions

with a 0.1F Line-to-Line Cap.

Measured Conducted Emissions

with a Green Wire Inductor

Measured Conducted Emissions

with a Common-Mode Choke

Nonideal Effects in Diodes

Construction of Transformers

The Effect of Primary-to-Secondary

Capacitance of a Transformer

The Proper Filter Placement in the

Reduction of Conducted Emissions

Crosstalk
The unintended EM coupling between wires and
PCB lands that are in close proximity.

Crosstalk between wires in cables or between lands

on PCBs concerns the intrasystem interference
performance of the product.

Three-Conductor Transmission
Line illustrating Crosstalk

Wire-type Line illustrating Crosstalk

PCB Transmission Lines

illustrating Crosstalk

The Equivalent Circuit of TEM Wave

on Three-Conductor Transmission Line

The Simple Inductive-Capacitive

Coupling Model

Frequency Response of the Crosstalk

Transfer Functions

NE
^
VS

= j(

R NE
Lm
R NE R FE
RLC m
+
)
R NE + R FE R S + R L R NE + R FE R S + R L

IND
CAP
= j ( M NE
+ M NE
)
^

FE

VS

= j(

R FE
Lm
R NE R FE
RLC m
+
)
R NE + R FE R S + R L R NE + R FE R S + R L

IND
CAP
= j ( M FE
+ M FE
)

Effect of Load Impedance

Common-impedance Coupling

V NE
^

IND
CAP
CI
= j ( M NE
+ M NE
) + M NE

VS
^

V FE
^

VS

IND
CAP
CI
= j ( M FE
+ M FE
) + M FE

Time-Domain Crosstalk for R=50

Time-Domain Crosstalk for R=1K

The Capacitance Equivalent for

the Shielded Receptor Wire

The Lumped Equivalent Circuit for

Capacitive Coupling

^ CAP

NE

^ CAP

= V FE

R NE R FE
C RS C GS
VG DC
R NE + R FE C RS + C GS

Illustration of Placing a Shield

on Inductive Coupling

The Lumped Equivalent Circuit

for Inductive Coupling

^ IND

NE

^
R NE
R SH
=
j LGR I G
R NE + R FE
R SH + j L SH

SF =

R SH

R SH
+ j LSH

Explanation of the Effect

of Shield Grounding

Twisted Wires

The Inductive-Capacitive
Coupling Model

Terminating a Twisted Pair

A Model for the Unbalanced

Twisted Receptor Wire Pair

Explanation of the Effect

of an Unbalanced Twisted Pair

The Three Levels of

Reducing Inductive Crosstalk

A Coupling Model
for the Balanced Termination

The Effect of Balanced

and Unbalanced Terminations

Purposes of a Shield
To prevent the emissions of the electronics
of the product from radiating outside the
boundaries of the product
To prevent radiated emissions external to
the product from coupling to the products
electronics

Degradation of Shielding
Effectiveness

Termination of a Cable Shield

to a Noisy Point
y

The cable shield may become a monopole antenna, if

the ground potential is varying

Peripheral cables such as printer cables for PC tend

to have lengths of order 1.5m, which is a quarterwavelength at 50MHz

Resonances in the radiated emissions of a product due

to common-mode currents on these types of
peripheral cables are frequently observed in the
frequency range of 50-100MHz

Shielding Effectiveness
y

R represents
the reflection loss

A represents
the absorption loss

M represents
the additional effects
of multiple reflections

SE dB = R dB + AdB + M dB

/ transmissions

Reflection Loss
R dB
y

)
r o

By referring to
copper,

R dB
y

1
o
20 log 10 ( ) 20 log 10 (
4
4

r
= 168 + 10 log 10 (
)
r f

The reflection loss is larger at lower

frequencies and high-conductivity metals

Absorption Loss
AdB = 20 log 10 e

t/

= 131 .4 t

f r r

The absorption loss increases with increasing

frequencies as

Shielding Effectiveness

Shielding Effectiveness
y Reflection loss is the primary contributor to

the shielding effectiveness at low frequencies

y At the higher frequencies, ferrous materials

increase the absorption loss and the total

shielding effectiveness

Shielding Effectiveness of Metals

The Methods of Shielding against

Low-Frequency Magnetic Fields

The permeability of ferromagnetic materials decreases

with increasing frequency

The permeability of ferromagnetic materials decrease

with increasing magnetic field strength

The Frequency Dependence

of Various Ferromagnetic Materials

The Phenomenon of Saturation of

Ferromagnetic Materials

The Bands to Reduced the

Magnetic Field of Transformer
Leakage Flux

Effects of Apertures

Since it is not feasible to determine the direction of the

induced current and place the slot direction appropriately,
a large number of small holes are used instead

ESD Events
y

Typical rise times are of order 200ps-70ns, with a

total duration of around 100ns-2s

The peak levels may approach tens of amps for a

voltage difference of 10kV

The spectral content of the arc may have large

amplitudes, and can extend well into the GHz
frequency range

Effects of the ESD Events

y The intense electrostatic field created by

the charge separation prior to the ESD arc

y The intense arc discharge current

Three Techniques for Preventing

Problems Caused by an ESD Event
y

Prevent occurrence of the ESD event

Prevent or reduce the coupling (conduction or radiation)

to the electronic circuitry of the product (hardware
immunity)

Create an inherent immunity to the ESD event in the

electronic circuitry through software (software
immunity)

Preventing the ESD Event

y

Electronic components such as ICs are placed in pink

polyethlene bags or have their pins inserted in antistatic
foam for transport

Some products can utilize charge generation prevention

techniques

For example, printers constantly roll paper around a

rubber platen. This causes charge to be stripped off the
paper, resulting in a building of static charge on the rubber
platen.

Wires brushes contacting the paper or passive ionizers

prevent this charge building

Hardware Immunity
y Secondary arc discharges
y Direct conduction
y Electric field (Capacitive) coupling
y Magnetic field (Inductive) coupling

Preventing the Secondary

Arc Discharges

Single-point Ground

Use of Shielded Cables to

Exclude ESD Coupling

The Methods of Preventing

ESD-induced Currents

Reduction of Loop Area in

Power Distribution Circuits

Reduction of Loop Areas to Reduce

the Pickup of Signal Lines

Software Immunity
y Watchdog routines that periodically check
whether program flow is correct
y The use of parity bits, checksums and errorcorrecting codes can prevent the recording of
ESD-corrupted data
y Unused module inputs should be tied to ground
or +5V to prevent false triggering by an ESD
event

Packaging Consideration

A critical aspect of incorporating good EMC design is

an awareness of these nonideal effects throughout
the functional design process

Another critical aspect in successful EMC design of a

system is to not place reliance on brute force fixes
such as shielding and grounding

Common-impedance Coupling

The Effect of Conductor

Inductance on Ground Voltage

Segregation of Grounds

Ground Problems between

Analog and Digital Grounds

The Generation and Blocking of

CM Currents on Interconnect Cables

Methods for Decoupling

Subsystems

Interconnection and
Number of PCBs

z It is preferable to have only one system PCB rather

than several smaller PCBs interconnected by cables

z The PCBs can be interconnected by plugging their

edge connectors into the motherboard

Use of Interspersed Grounds

to Reduce Loop Areas

PCB and Subsystem Placement

Attention should be paid to the placement and

orientation of the PCBs in the system

Decoupling Subsystems
y

Common-mode currents flowing between subsystems can

be effectively blocked with ferrite, common-mode
chokes

Another method of decoupling subsystems is insert a

filter in the connection wires or lands between the
subsystems. This filter can be in the form of R-C packs,
ferrite beads, or a combination

High-frequency signals on the power distribution system

between subsystems can be reduced by the use of
decoupling capacitors

Splitting Crystal/ Oscillator Frequencies

The 16th harmonics (32MHz and 31.696MHz) are separated by

304kHz, so that they will not add in the bandwidth of the receiver

The 100th harmonic of the 2MHz signal (200MHz) and the 101st
harmonic of the 1.981MHz signal (200.081MHz) will be within
81kHz of each other and will add in the bandwidth of the receiver

Component Placement

Component Placement

A Good Layout for a

Typical Digital System

Creation of a Quiet Ground

where Connectors Enter a PCB

Unintentional Coupling of Signals

between Chip Bonding Wires

Placing a small inductor in series with that pin to block

the high-frequency signal

Ferrite beads could also be used, but their impedance is

typically limited to a few hundred ohms

Use of Decoupling Capacitors

Decoupling Capacitor Placement

Minimizing the Loop Area of

the Power Distribution Circuits