SC4524C
Applications Information (Cont.)
Loop Compensation
The goal of compensation is to shape the frequency
response of the converter so as to achieve high DC
accuracy and fast transient response while maintaining
loop stability (see Figure 7).
It has an ESR zero FZ at
ωZ
=
R ESRCO
CONTROLLER AND SCHOTTKY DIODE
Io
CA
Rs
REF
+
EA
FB
-
Vc
Vramp
PWM
MODULATOR
COMP
C5
C8
R7
SW
L1
Co
Resr
Vo
R4
R6
It has a dominant low-frequency pole FP at
ωp
≈
RCO
and double poles at half the switching frequency.
Including the voltage divider (R4 and R6), the control to
feedback transfer function is found and plotted in Figure
8 as the converter gain.
Figure 7. Block diagram of control loops
The block diagram in Figure 7 shows the control loops of a
buck converter with the SC4524C. The inner loop (current
loop) consists of a current sensing resistor (Rs=5.5mW) and
a current amplifier (CA) with gain (GCA=18.5). The outer
loop (voltage loop) consists of an error amplifier (EA), a
PWM modulator, and a LC filter.
Since the current loop is internally closed, the remaining
task for the loop compensation is to design the voltage
compensator (C5, R7, and C8).
Since the converter gain has only one dominant pole at
low frequency, a simple Type-2 compensation network
is sufficient for voltage loop compensation. As shown in
Figure 8, the voltage compensator has a low frequency
integrator pole, a zero at FZ1, and a high frequency pole
at FP1. The integrator is used to boost the gain at low
frequency. The zero is introduced to compensate the
excessive phase lag at the loop gain crossover due to the
integrator pole (-90deg) and the dominant pole (-90deg).
The high frequency pole nulls the ESR zero and attenuates
high frequency noise.
60
For a converter with switching frequency FSW, output
inductance L1, output capacitance CO and loading R, the
control (VC) to output (VO) transfer function in Figure 7 is
given by:
Vo =
GPWM( + sRESR CO )
Vc ( + s / ωp )( + s / ωn Q + s2 / ωn2 )
This transfer function has a finite DC gain
30
0
-30
-60
1K
Fz1
Fp1
Fp
COMPENSATOR GAIN
CONVERTER
Fc
GAIN
LOOP GAIN
Fz Fsw/2
10K
100K
1M
10M
FREQUENCY (Hz)
GPWM
≈
R
GCA x
RS
Figure 8 — Bode plots for voltage loop design
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