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SLUS846 – SEPTEMBER 2008
In this equivalent circuit, the V
ge
and V
oe
are the fundamental harmonics of the voltage generated by the half
bridge and the voltage on the transformer primary side, respectively. These voltages can be calculated through
Fourier analysis. The load resistor R
e
is the equivalent resistor of the load, and it can be calculated as:
R
e
=
8
2
n R
p
2
(1)
Based on this equivalent circuit, the converter gain at different switching frequencies can be calculated as:
j
w
L
m
R
e
V
o
j
w
L
m
+
R
e
=
j
w
L
m
R
e
1
V
DC
/
2
+
+
j
w
L
r
j
w
L
m
+
R
e
j
w
C
r
In this equation V
DC
/2 is the equivalent input voltage due to the half bridge structure.
Table 1. Circuit Definition Calculations
NORMALIZED GAIN
RESONANT
FREQUENCY
QUALITY FACTOR
NORMALIZED
FREQUENCY
INDUCTOR RATIO
(2)
M
=
V
o
V
DC
/
2
f
0
=
1
2
p
L
r
C
r
Q
e
=
L
r
/ C
r
R
e
f
n
=
f
f
0
L
n
=
L
m
L
r
Following the definitions in
the converter gain at different switching frequencies can be written as:
L
n
f
n
2
M
=
L
n
f
n
2
+
(
f
n
-
1
)(
f
n
+
1
+
jf
n
L
n
Q
e
)
(3)
Because of the FHA, this gain equation is an approximation. When the switching frequency moves away from the
resonant frequency, the error becomes larger. However, this equation can be used as the design tool. The final
results need to be verified by the time based simulation or hardware test.
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