# lecture3 2008 postlec by ye58M2

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```									                                       ECEN 5817
Housekeeping update

•    For both on-campus and CAETE students: A DVD of recorded lectures
from Professor Erickson’s Spring ’06 class will be mailed to you
sometime next week. These will not be available on the CAETE
•    For on-campus students: You will not have access to this semesters
recorded lectures on the CAETE website
•    For CAETE students: By popular request, scanned and e-mailed
homework will be accepted provided the submissions meet the
following requirements:
• Black and white (no color, no grayscale)
• 200 – 300 dpi
• All problems scanned into ONE PDF file for the whole assignment
• PDF file is easy to read, easy to open, and easy to print

Fundamentals of Power Electronics          1               Chapter 19: Resonant Conversion
Chapter 19
Resonant Conversion

Introduction
19.1     Sinusoidal analysis of resonant converters
19.2     Examples
Series resonant converter
Parallel resonant converter
19.3     Soft switching
Zero current switching
Zero voltage switching

19.4     Load-dependent properties of resonant converters

19.5 Exact characteristics of the series and parallel resonant
converters

Fundamentals of Power Electronics            2              Chapter 19: Resonant Conversion
Equivalent circuit of rectifier

Rectifier input port:
Fundamental components of
current and voltage are
sinusoids that are in phase
Hence rectifier presents a
Effective resistance Re is
Rectifier equivalent circuit

With a resistive load R, this becomes

Loss free resistor

Fundamentals of Power Electronics            3                Chapter 19: Resonant Conversion
19.1.4 Solution of converter
voltage conversion ratio M = V/Vg

Eliminate Re:

Fundamentals of Power Electronics      4             Chapter 19: Resonant Conversion
Conversion ratio M

So we have shown that the conversion ratio of a resonant converter,
having switch and rectifier networks as in previous slides, is equal to
the magnitude of the tank network transfer function. This transfer
function is evaluated with the tank loaded by the effective rectifier
input resistance Re.

Fundamentals of Power Electronics          5                    Chapter 19: Resonant Conversion
19.2.2 Subharmonic modes of the SRC

Example: excitation of
tank by third harmonic of
switching frequency
Can now approximate vs(t)
by its third harmonic:

Result of analysis:

Fundamentals of Power Electronics   6           Chapter 19: Resonant Conversion
Subharmonic modes of SRC

• Not often used - reduced switch
utilization and decreased voltage
conversion ratio
• Still need to be aware their existence

Fundamentals of Power Electronics       7                     Chapter 19: Resonant Conversion
19.2 Examples
19.2.1 Series resonant converter

Fundamentals of Power Electronics      8             Chapter 19: Resonant Conversion
Model: series resonant converter

Fundamentals of Power Electronics      9             Chapter 19: Resonant Conversion
Construction of Zi – Resonant (high Q) case
C = 0.1 μF, L = 1 mH, Re = 10 Ω

Fundamentals of Power Electronics   10           Chapter 19: Resonant Conversion
Construction of H = V / Vg – Resonant (high Q) case
C = 0.1 μF, L = 1 mH, Re = 10 Ω

Buck characteristic

Fundamentals of Power Electronics   11      Chapter 19: Resonant Conversion
Construction of Zi

Fundamentals of Power Electronics         12             Chapter 19: Resonant Conversion
Construction of H

Qe  R0 / Re

Fundamentals of Power Electronics        13             Chapter 19: Resonant Conversion
Model: series resonant converter

Fundamentals of Power Electronics       14            Chapter 19: Resonant Conversion
Construction of Zi – Non-resonant (low Q) case
C = 0.1 μF, L = 1 mH, Re = 1 kΩ

Fundamentals of Power Electronics   15        Chapter 19: Resonant Conversion
Construction of H – Non-resonant (low Q) case
C = 0.1 μF, L = 1 mH, Re = 1 kΩ

Fundamentals of Power Electronics   16        Chapter 19: Resonant Conversion
19.2.3 Parallel resonant dc-dc converter

Differs from series resonant converter as follows:
Different tank network
Rectifier is driven by sinusoidal voltage, and is connected to
inductive-input low-pass filter
Need a new model for rectifier and filter networks

Fundamentals of Power Electronics          17                    Chapter 19: Resonant Conversion
Model of uncontrolled rectifier
with inductive filter network – input port

Fundamental component of iR(t):

Fundamentals of Power Electronics    18               Chapter 19: Resonant Conversion
Model of uncontrolled rectifier
with inductive filter network – output port

Output inductor volt second balance:
dc voltage is equal to average
rectified tank output voltage

Fundamentals of Power Electronics   19                Chapter 19: Resonant Conversion
Effective resistance Re

Again define

In steady state, the dc output voltage V is equal to the average value
of | vR |:

For a resistive load, V = IR. The effective resistance Re can then be
expressed

Fundamentals of Power Electronics           20                  Chapter 19: Resonant Conversion
Equivalent circuit model of uncontrolled rectifier
with inductive filter network

Dependent voltage source based on rectified tank voltage.
Vs. SRC, dependent current source based on rectified tank current.
Fundamentals of Power Electronics        21                  Chapter 19: Resonant Conversion
Equivalent circuit model
Parallel resonant dc-dc converter

Fundamentals of Power Electronics      22             Chapter 19: Resonant Conversion
2 different ways to construct transfer function H

Fundamentals of Power Electronics   23          Chapter 19: Resonant Conversion
Construction of Zi – Resonant (high Q) case
C = 0.1 μF, L = 1 mH, Re = 1 kΩ

Fundamentals of Power Electronics   24           Chapter 19: Resonant Conversion
Construction of H = V / Vg – Resonant (high Q) case
C = 0.1 μF, L = 1 mH, Re = 1 kΩ

Buck-boost characteristic

Fundamentals of Power Electronics      25   Chapter 19: Resonant Conversion
Construction of Zo

Fundamentals of Power Electronics         26             Chapter 19: Resonant Conversion
Construction of H

Fundamentals of Power Electronics        27             Chapter 19: Resonant Conversion
Dc conversion ratio of the PRC

At resonance, this becomes

• PRC can step up the voltage, provided R > R0
• PRC can produce M approaching infinity, provided output current is
limited to value less than Vg / R0

Fundamentals of Power Electronics       28                  Chapter 19: Resonant Conversion
Comparison of approximate and exact characteristics

1.0

Series resonant                                0.8

converter

M = V/Vg
exact M, Q=2
0.6                                                       approx M, Q=2
exact M, Q=10
approx M, Q=10
Below resonance:                            0.4
exact M, Q=0.5
approx M, Q=0.5

0.5 < F < 1                        0.2

0.0
0.5   0.6       0.7           0.8   0.9      1.0
F
1.0
Above resonance:
0.8
1<F
M=V/Vg

exact M, Q=0.5
0.6                                                      approx M, Q=0.5
exact M, Q=10
approx M, Q=10
0.4
exact M, Q=2
approx M, Q=2
0.2

0.0
1          2             3         4         5
F
Fundamentals of Power Electronics                         29                                     Chapter 19: Resonant Conversion
Comparison of approximate and exact characteristics

Exact equation:                    Parallel resonant converter
solid lines
Sinusoidal approximation: