AN-9738 Datasheet, PDF (13/25 Pages) Fairchild Semiconductor – Design Guideline on 150W Power Supply for LED Street Lighting Design Using FL7930B and FAN7621S

AN-9738
(Design Example) Maximum inductor current is 4.889A
and sensing resistor is calculated as:
R_CS
= ^{VCS ,LIM}
I_ipnkd ⋅1.1
=
0.8
7.392 ⋅1.1
= 0.098 [ Ω]
Choosing 0.1Ω as R_CS, power loss is calculated as:
P_RCS,LOSS = I_Q²_,RMS ⋅ R_CS = 2.436² ⋅0.098 =0.58[W ]
Recommended power rating of sensing resistor is 1.19W.
[STEP-8] Design Compensation Network
The boost PFC power stage can be modeled as shown in
Figure 26 MOSFET and diode can be changed to loss-free
resistor model and then modeled as a voltage-controlled
current source supplying RC network.
APPLICATION NOTE
( ) ^∧
v OUT
∧
v COMP
= K_SAW ⋅
V_LINE ² R_L
4V_OUT ⋅ L
⋅
1
1
+
2
s
π
f
p
(36)
where
f_p
=
2
2 π ⋅ R_LC_OUT
and R_L is the output load resistance in a
given load condition.
Figure 27 and Figure 28 show the variation of the control-
to-output transfer function for different input voltages and
different loads. Since DC gain and crossover frequency
increase as input voltage increases, and DC gain increases
as load decreases, high input voltage and light load is the
worst condition for feedback loop design.
Figure 27. Control-to-Output Transfer Function for
Different Input Voltages
Figure 26. Small Signal Modeling of the Power Stage
By averaging the diode current during the half line cycle,
the low-frequency behavior of the voltage controlled current
source of Figure 26 is obtained as:
I _DOUT,AVE = K_SAW ⋅
2V_{LINE â‹}
4V_OUT
2V_{LINE [ A]}
L
(35)
where:
L is the boost inductance;
V_OUT is the output voltage; and
K_SAW is the internal gain of sawtooth generator (that of
FL7930B is 8.496×10^-6).
Then the low-frequency, small-signal, control-to-output
transfer function is obtained as:
Figure 28. Control-to-Output Transfer Function for
Different Loads
Proportional and integration (PI) control with high-
frequency pole is typically used for compensation, as shown
in Figure 29. The compensation zero (f_CZ) introduces phase
boost, while the high-frequency compensation pole (f_CP)
attenuates the switching ripple.
The transfer function of the compensation network is
obtained as:
∧
vCOMP
∧
vOUT
=
2π f_I
s
1
⋅
1
+
2
s
π f_CZ
+
2
s
π f_CP
(37)
© 2011 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 4/20/11
13
www.fairchildsemi.com