5150174.ppt

Fundamentals of Power Electronics 1 Chapter 19: Resonant Conversion
19.3.1 Operation of the full bridge below resonance:
Zero-current switching
Series resonant converter example
Current bi-directional switches
ZCS vs. ZVS depends on tank current zero crossings with respect to
transistor switching times = tank voltage zero crossings
Operation below resonance: input tank current leads voltage
Zero-current switching (ZCS) occurs

Tank input impedance
Re
|| Zi ||
f0
L
R0
Qe
= R0
/Re
Operation below
resonance: tank input
impedance Zi is
dominated by tank
capacitor.
Zi is negative, and
tank input current
leads tank input
voltage.
Zero crossing of the
tank input current
waveform is(t) occurs
before the zero
crossing of the voltage
vs(t) – before switch
transitions

Switch network waveforms, below resonance
Zero-current switching
t
vs(t)
Vg
– Vg
vs1(t)
t
is(t)
t
Q1
Q4
D1
D4
Q2
Q3
D2
D3
Conducting
devices:
“Hard”
turn-on of
Q1
, Q4
“Soft”
turn-off of
Q1
, Q4
“Hard”
turn-on of
Q2
, Q3
“Soft”
turn-off of
Q2
, Q3
Conduction sequence: Q1–D1–Q2–D2
Tank current is negative at the end of
each half interval – antiparallel diodes
conduct after their respective switches
Q1 is turned off during D1 conduction
interval, without loss

Classical but misleading example: Transistor switching
with clamped inductive load (4.3.1)
Buck converter example
transistor turn-off
transition
Loss:

ZCS turn-on transition: hard switching
Q1 turns on while D2 is conducting. Stored
charge of D2 and of semiconductor output
capacitances must be removed. Transistor
turn-on transition is identical to hard-
switched PWM, and switching loss occurs.
t
ids(t)
t
Q1
Q4
D1
D4
Q2
Q3
D2
D3
Conducting
devices:
“Hard”
turn-on of
Q1, Q4
“Soft”
turn-off of
Q1, Q4
t
Vg
vds1(t)

19.3.2 Operation of the full bridge above resonance:
Zero-voltage switching
Series resonant converter example
Operation above resonance: input tank current lags voltage
Zero-voltage switching (ZVS) occurs

Tank input impedance
Re
|| Zi ||
f0
L
R0
Qe
= R0
/Re
Operation above
resonance: tank input
impedance Zi is
dominated by tank
inductor.
Zi is positive, and
tank input current lags
tank input voltage.
Zero crossing of the
tank input current
waveform is(t) occurs
after the zero crossing
of the voltage vs(t) –
after switch transitions

Switch network waveforms, above resonance
Zero-voltage switching
Conduction sequence: D1–Q1–D2–Q2
Tank current is negative at the
beginning of each half-interval –
antiparallel diodes conduct before
their respective switches
Q1 is turned on during D1 conduction
interval, without loss – D2 already off!
t
vs(t)
Vg
– Vg
vs1(t)
t
is(t)
t
Q1
Q4
D1
D4
Q2
Q3
D2
D3
Conducting
devices:
“Soft”
turn-on of
Q1
, Q4
“Hard”
turn-off of
Q1
, Q4
“Soft”
turn-on of
Q2
, Q3
“Hard”
turn-off of
Q2
, Q3

ZVS turn-off transition: hard switching?
When Q1 turns off, D2 must begin
conducting. Voltage across Q1 must
increase to Vg. Transistor turn-off transition
is identical to hard-switched PWM.
Switching loss may occur… but….
t
ids(t)
Conducting
devices:
t
Vg
vds1(t)
t
Q1
Q4
D1
D4
Q2
Q3
D2
D3
“Soft”
turn-on of
Q1, Q4
“Hard”
turn-off of
Q1, Q4

Classical but misleading example: Transistor switching
with clamped inductive load (4.3.1)
Buck converter example
transistor turn-off
transition
Loss:

Soft switching at the ZVS turn-off transition
Conducting
devices:
t
Vg
vds1(t)
Q1
Q4
D2
D3
Turn off
Q1
, Q4
Commutation
interval
X
• Introduce small
capacitors Cleg across
each device (or use
device output
capacitances).
• Introduce delay
between turn-off of Q1
and turn-on of Q2.
Tank current is(t) charges and discharges
Cleg. Turn-off transition becomes lossless.
During commutation interval, no devices
conduct.
So zero-voltage switching exhibits low
switching loss: losses due to diode stored
charge and device output capacitances are
eliminated.
Also get reduction in EMI.

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

19.4 Load-dependent properties
of resonant converters
Resonant inverter design objectives:
1. Operate with a specified load characteristic and range of operating
points
• With a nonlinear load, must properly match inverter output
characteristic to load characteristic
2. Obtain zero-voltage switching or zero-current switching
• Preferably, obtain these properties at all loads
• Could allow ZVS property to be lost at light load, if necessary
3. Minimize transistor currents and conduction losses
• To obtain good efficiency at light load, the transistor current should
scale proportionally to load current (in resonant converters, it often
doesn’t!)

Topics of Discussion
Section 19.4
Inverter output i-v characteristics
Two theorems
• Dependence of transistor current on load current
• Dependence of zero-voltage/zero-current switching on load
resistance
• Simple, intuitive frequency-domain approach to design of resonant
converter
Example
Analysis valid for resonant inverters with resistive loads as well as
resonant converters operating in CCM

CCM PWM vs. resonant inverter output characteristics
CCM PWM
• Low output impedance – neglecting
losses, output voltage function of
duty cycle only, not of load
• Steady-state IV curve looks like
voltage source
Resonant inverter (or converter
operating in CCM)
• Higher output impedance – output
voltage strong function of both
control input and load current (load
resistance)
• What does steady-state IV curve
look like? (i.e. how does || v ||
depend on || i ||?)

Analysis of inverter output characteristics –
simplifying assumptions
• Load is resistive
– Load does not change resonant frequency
– Can include any reactive components in tank
• Resonant network is purely reactive (neglect losses)

Thevenin equivalent of tank network output port
Voltage divider
Sinusoidal steady-state

Output magnitude

Inverter output characteristics

Let H be the open-circuit (R→)
transfer function:
and let Zo0 be the output impedance
(with vi →short-circuit). Then,
The output voltage magnitude is:
with
This result can be rearranged to obtain
Hence, at a given frequency, the
output characteristic (i.e., the relation
between ||vo|| and ||io||) of any
resonant inverter of this class is
elliptical.

General resonant inverter
output characteristics are
elliptical, of the form
This result is valid provided that (i) the resonant network is purely reactive,
and (ii) the load is purely resistive.
with

Matching ellipse
to application requirements
Electronic ballast Electrosurgical generator

Example of gas discharge lamp ignition and steady-state
operation from CoPEC research
LCC resonant inverter
Vg = 300 V
Iref = 5 A

Example of repeated lamp ignition attempts with overvoltage
protection
LCC resonant inverter
Vg = 300 V
Iref = 5 A
Overvoltage protection
at 3500 V

19.4 Load-dependent properties
of resonant converters
Resonant inverter design objectives:
1. Operate with a specified load characteristic and range of operating
points
• With a nonlinear load, must properly match inverter output
characteristic to load characteristic
2. Obtain zero-voltage switching or zero-current switching
• Preferably, obtain these properties at all loads
• Could allow ZVS property to be lost at light load, if necessary
3. Minimize transistor currents and conduction losses
• To obtain good efficiency at light load, the transistor current should
scale proportionally to load current (in resonant converters, it often
doesn’t!)

Input impedance of the resonant tank network
vs1(t)
Effective
resistive
load
R
is(t) i(t)
v(t)
+
–
Zi Zo
Transfer function
H(s)
+
–
Effective
sinusoidal
source
Resonant
network
Purely reactive
where

ZN and ZD
ZD is equal to the tank output
impedance under the
condition that the tank input
source vs1 is open-circuited.
ZD = Zo
ZN is equal to the tank
output impedance under
the condition that the
tank input source vs1 is
short-circuited. ZN = Zo0

Magnitude of the tank input impedance
If the tank network is purely reactive, then each of its impedances and
transfer functions have zero real parts, and the tank input and output
impedances are imaginary quantities. Hence, we can express the input
impedance magnitude as follows:

A Theorem relating transistor current variations to
load resistance R
Theorem 1: If the tank network is purely reactive, then its input impedance
|| Zi || is a monotonic function of the load resistance R.
 So as the load resistance R varies from 0 to , the resonant network
input impedance || Zi || varies monotonically from the short-circuit value
|| Zi0 || to the open-circuit value || Zi ||.
 The impedances || Zi || and || Zi0 || are easy to construct.
 If you want to minimize the circulating tank currents at light load,
maximize || Zi ||.
 Note: for many inverters, || Zi || < || Zi0 || ! The no-load transistor current
is therefore greater than the short-circuit transistor current.

Proof of Theorem 1
 Derivative has roots at:
Previously shown:  Differentiate:
So the resonant network input
impedance is a monotonic function
of R, over the range 0 < R < .
In the special case || Zi0 || = || Zi||,
|| Zi || is independent of R.

Zi0 and Zi for 3 common inverters

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