AN-6094
© 2012 Fairchild Semiconductor Corporation
www.fairchildsemi.com
Rev. 1.0.0 • 9/27/12
13
(Design Example)
The original resonance period is
measured as t
R
=25 ns.
Using a 1 nF test capacitor, the resonance period is
measure as t
RT
=25 ns.
Then, the resonant parameters are obtained as:
2
/[(
)
1] 395
RT
D
TST
R
t
C
C
pF
t
=
− =
2
1
(
)
40
2
R
LKS
D
t
L
nH
C
π
=
=
The snubber circuit parameters are calculated as:
10
,
2.5
1
LKS
SNB
SNB
D
D
L
R
C
C
nF
C
=
= Ω
=
=
[STEP-10] Design the Feedback Loop
Since the FAN302 operates a flyback converter in DCM
with a peak-current mode control, the control to output
transfer function of the power stage is given as:
ˆ
1
ˆ
1
o
Z
V
FB
P
v
s
G
v
s
ω
ω
+
=
⋅
+
(49)
where
2
p
L
OUT
R C
ω
=
;
1
Z
ES
OUT
R C
ω
=
; C
OUT
is
effective output capacitance; and R
ES
is the effective
series resistance of the output capacitor.
The gain G
V
of Equation (49) is defined as:
1
3
N
O
V
a
CS DS
V
m
G
m
m
R
I
= ⋅
⋅
+
(50)
where 1/3 is the attenuation factor of feedback voltage;
I
DS
is the peak drain current at given operating
condition; m
a
is the slope of slope compensation signal;
and m is the slope of current sensing signal, given as:
DL
CS
m
V
R
m
L
⋅
=
(51)
Note that the effect of slope compensation is weaker at
high line, which increases the gain of control-to-output
transfer function. Thus, the high line is the worst case for
feedback loop design.
Since the control to output transfer function is first order,
the feedback control loop can be implemented with a one-
pole and one-zero compensation circuit, as shown in
Figure 20. The transfer function of the compensation
network is given as:
1
1
ˆ
(
1)
ˆ
(
1)
CZ
EA
I
o
CP
s
v
v
s
s
ω
ω
ω
+
=
⋅
+
(52)
where
1
FB
I
F
bias
FR
R
R R
C
ω
=
;
1
1
1
(
)
CZ
FR
F
FR
R
R
C
ω
=
+
;
and
1
1
CP
FB
FB
R C
ω
=
.
Note that the opto-coupler introduces a mid-frequency
pole due to the collector-emitter junction capacitance.
Since the collector-base junction in a photo-transistor is
used as a light detector; its area is relatively large, which
introduces a large effective collector-emitter junction
capacitance. The typical collector-emitter junction
capacitance is about 3-10
nF for the opto-coupler
FOD817A, which brings a pole at around 1 kHz with a
bias resistor of 42 k
Ω
, as shown in Figure 20. This pole
can occur around the desired crossover frequency, making
the system unstable. Therefore, this additional pole should
be considered when designing the compensation network.
Figure 20. Feedback Loop Circuit
Figure 21. Frequency Response of Opto-Coupler
