Transcript 19.4 Load-dependent properties of 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!)
Fundamentals of Power Electronics
1
Chapter 19: Resonant Conversion
Input impedance of the resonant tank network
Appendix C: Section C.4.4
Expressing the tank input impedance as a function of the load resistance R:
where
Fundamentals of Power Electronics
2
Chapter 19: Resonant Conversion
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:
Fundamentals of Power Electronics
3
Chapter 19: Resonant Conversion
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.
Fundamentals of Power Electronics
4
Chapter 19: Resonant Conversion
Series resonant tank
Fundamentals of Power Electronics
5
Chapter 19: Resonant Conversion
Parallel resonant tank
Fundamentals of Power Electronics
6
Chapter 19: Resonant Conversion
fm of parallel resonant tank
Fundamentals of Power Electronics
7
Chapter 19: Resonant Conversion
LCC tank
Fundamentals of Power Electronics
8
Chapter 19: Resonant Conversion
Zi0 and Zi for 3 common inverters
Fundamentals of Power Electronics
9
Chapter 19: Resonant Conversion
Example: || Zi || of LCC
• for f < f m, || Zi ||
increases with
increasing R .
• for f > f m, || Zi ||
decreases with
increasing R .
• for f = fm, || Zi || constant
for all R .
• at a given frequency f,
|| Zi || is a monotonic
function of R.
• It’s not necessary to
draw the entire plot: just
construct || Zi0 || and
|| Zi ||.
Fundamentals of Power Electronics
10
Chapter 19: Resonant Conversion
Discussion wrt transistor current scaling –
LCC
LCC example
|| Zi0 || and || Zi || both represent
series resonant impedances,
whose Bode diagrams are easily
constructed.
|| Zi0 || and || Zi || intersect at
frequency fm.
For f < fm
then || Zi0 || < || Zi || ; hence
transistor current decreases as
load current decreases
For f > fm
then || Zi0 || > || Zi || ; hence
transistor current increases as
load current decreases, and
transistor current is greater
than or equal to short-circuit
current for all R
Fundamentals of Power Electronics
11
Chapter 19: Resonant Conversion
Discussion wrt ZVS and transistor current scaling
Series and parallel tanks
•
•
•
•
•
Fundamentals of Power Electronics
12
fs above resonance:
•
No-load transistor current = 0
•
ZVS
fs below resonance:
•
No-load transistor current = 0
•
ZCS
fs above resonance:
•
No-load transistor current greater than short circuit current
•
ZVS
fs below resonance but > fm :
•
No-load transistor current greater than short circuit current
•
ZCS for no-load; ZVS for short-circuit
fs < fm:
•
No-load transistor current less than short circuit current
•
ZCS for no-load; ZVS for short-circuit
Chapter 19: Resonant Conversion
Discussion wrt ZVS and transistor current scaling
LCC tank
•
•
•
•
Fundamentals of Power Electronics
13
fs > finf
•
No-load transistor current greater than short circuit current
•
ZVS
fm < fs < finf
•
No-load transistor current greater than short circuit current
•
ZCS for no-load; ZVS for short-circuit
f0 < fs < f m
•
No-load transistor current less than short circuit current
•
ZCS for no-load; ZVS for short-circuit
fs < f0
•
No-load transistor current less than short circuit current
•
ZCS
Chapter 19: Resonant Conversion
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!)
Fundamentals of Power Electronics
14
Chapter 19: Resonant Conversion
A Theorem relating the ZVS/ZCS boundary to load
resistance R
Theorem 2: If the tank network is purely reactive, then the boundary between
zero-current switching and zero-voltage switching occurs when the load
resistance R is equal to the critical value Rcrit, given by
It is assumed that zero-current switching (ZCS) occurs when the tank input
impedance is capacitive in nature, while zero-voltage switching (ZVS) occurs when
the tank is inductive in nature. This assumption gives a necessary but not sufficient
condition for ZVS when significant semiconductor output capacitance is present.
Fundamentals of Power Electronics
15
Chapter 19: Resonant Conversion
Zi phasor
Fundamentals of Power Electronics
16
Chapter 19: Resonant Conversion
Proof of Theorem 2
Previously shown:
Note that Zi, Zo0, and Zo have zero
real parts. Hence,
If ZCS occurs when Zi is capacitive,
while ZVS occurs when Zi is
inductive, then the boundary is
determined by Zi = 0. Hence, the
critical load Rcrit is the resistance
which causes the imaginary part of Zi
to be zero:
Solution for Rcrit yields
Fundamentals of Power Electronics
17
Chapter 19: Resonant Conversion
Algebra
Fundamentals of Power Electronics
18
Chapter 19: Resonant Conversion
Algebra
Fundamentals of Power Electronics
19
Chapter 19: Resonant Conversion
Discussion —Theorem 2





Again, Zi, Zi0, and Zo0 are pure imaginary quantities.
If Zi and Zi0 have the same phase (both inductive or both capacitive),
then there is no real solution for Rcrit.
Hence, if at a given frequency Zi and Zi0 are both capacitive, then ZCS
occurs for all loads. If Zi and Zi0 are both inductive, then ZVS occurs for
all loads.
If Zi and Zi0 have opposite phase (one is capacitive and the other is
inductive), then there is a real solution for Rcrit. The boundary between
ZVS and ZCS operation is then given by R = Rcrit.
Note that R = || Zo0 || corresponds to operation at matched load with
maximum output power. The boundary is expressed in terms of this
matched load impedance, and the ratio Zi / Zi0.
Fundamentals of Power Electronics
20
Chapter 19: Resonant Conversion
LCC example




f > f: ZVS occurs for all R
f < f0: ZCS occurs for all R
f0 < f < f, ZVS occurs for
R< Rcrit, and ZCS occurs for
R> Rcrit.
Note that R = || Zo0 ||
corresponds to operation at
matched load with maximum
output power. The boundary
is expressed in terms of this
matched load impedance,
and the ratio Zi / Zi0.
Fundamentals of Power Electronics
21
Chapter 19: Resonant Conversion
LCC example, continued
Typical dependence of Rcrit and matched-load
impedance || Zo0 || on frequency f, LCC example.
Fundamentals of Power Electronics
Typical dependence of tank input impedance phase
vs. load R and frequency, LCC example.
22
Chapter 19: Resonant Conversion
Switch network waveforms, above resonance
Zero-voltage switching
vs1 (t)
Vg
vs(t)
t
– Vg
is(t)
Conduction sequence: D1–Q1–D2–Q2
t
Conducting D 1
devices: D
4
“Soft”
turn-on of
Q 1, Q 4
t
Q1
Q4
D2
D3
Tank current is negative at the
beginning of each half-interval –
antiparallel diodes conduct before
their respective switches
Q2
Q3
Q1 is turned on during D1 conduction
interval, without loss – D2 already off!
“Hard”
“Soft”
“Hard”
turn-off of turn-on of turn-off of
Q 1, Q 4
Q 2, Q 3
Q2, Q3
Fundamentals of Power Electronics
23
Chapter 19: Resonant Conversion
19.4.4 Design Example
Select resonant tank elements to design a resonant inverter that meets the
following requirements:
• Switching frequency fs = 100 kHz
• Input voltage Vg = 160 V
• Inverter is capable of producing a peak open circuit output voltage
of 400 V
• Inverter can produce a nominal output of 150 Vrms at 25 W
Fundamentals of Power Electronics
24
Chapter 19: Resonant Conversion