NX9415
Compensator Design
APPLICATION INFORMATION
Symbol Used In Application Information:
Due to the double pole generated by LC filter of the
power stage, the power system has 180o phase shift ,
and therefore, is unstable by itself. In order to achieve
accurate output voltage and fast transient response,
compensator is employed to provide highest possible
bandwidth and enough phase margin.Ideally,the Bode
plot of the closed loop system has crossover frequency
between1/10 and 1/5 of the switching frequency, phase
margin greater than 50o and the gain crossing 0dB with -
20dB/decade. Power stage output capacitors usually
decide the compensator type. If electrolytic capacitors
are chosen as output capacitors, type II compensator
can be used to compensate the system, because the
zero caused by output capacitor ESR is lower than cross-
over frequency. Otherwise type III compensator should
be chosen.
VIN
- Input voltage
- Output voltage
- Output current
VOUT
IOUT
∆VRIPPLE - Output voltage ripple
- Working frequency
FS
∆IRIPPLE - Inductor current ripple
Output Inductor Selection
The selection of inductor value is based on induc-
tor ripple current, power rating, working frequency and
efficiency. Larger inductor value normally means smaller
ripple current. However if the inductance is chosen too
large, it brings slow response and lower efficiency. Usu-
ally the ripple current ranges from 20% to 40% of the
output current. This is a design freedom which can be
decided by design engineer according to various appli-
cation requirements. The inductor value can be calcu-
lated by using the following equations:
A. Type III compensator design
For low ESR output capacitors, typically such as
Sanyo oscap and poscap, the frequency of ESR zero
caused by output capacitors is higher than the cross-
over frequency. In this case, it is necessary to compen-
sate the system with type III compensator. The follow-
ing figures and equations show how to realize the type III
compensator by transconductance amplifier.
V -VOUT VOUT
1
IN
LOUT
=
´
´
DIRIPPLE
V
F
S
IN
...(1)
IRIPPLE =k ´ IOUTPUT
where k is between 0.2 to 0.4.
Output Capacitor Selection
1
Output capacitor is basically decided by the
amount of the output voltage ripple allowed during steady
state(DC) load condition as well as specification for the
load transient. The optimum design may require a couple
of iterations to satisfy both condition.
FZ1
FZ2
=
=
=
=
...(3)
...(4)
...(5)
...(6)
2´ p ´ R4 ´ C2
1
2´ p ´ (R2 + R3 )´ C3
1
F
P1
2´ p ´ R3 ´ C3
The amount of voltage ripple during the DC load
condition is determined by equation(2).
1
F
P2
C1 ´ C2
2´ p ´ R4 ´
DIRIPPLE
C1 + C2
DVRIPPLE = ESR´ DIRIPPLE
+
...(2)
8´ F ´ COUT
S
Where ESR is the output capacitors' equivalent
series resistance,COUT is the value of output capacitors.
Typically when ceramic capacitors are selected as
output capacitors, DC ripple spec is easy to be met, but
mutiple ceramic capacitors are required at the output to
meet transient requirement.
where FZ1,FZ2,FP1 and FP2 are poles and zeros in
the compensator. Their locations are shown in figure 10.
The transfer function of type III compensator for
transconductance amplifier is given by:
Ve
1- gm ´ Zf
=
VOUT
1+ gm ´ Zin + Zin /R1
Rev.1.2
12/28/09
9
