NX2124/2124A
It should be considered that the proposed equa-
tion is based on ideal case, in reality, the droop or over-
shoot is typically more than the calculation. The equa-
tion gives a good start. For more margin, more capaci-
tors have to be chosen after the test. Typically, for high
frequency capacitor such as high quality POSCAP es-
pecially ceramic capacitor, 20% to 100% (for ceramic)
more capacitors have to be chosen since the ESR of
capacitors is so low that the PCB parasitic can affect
the results tremendously. More capacitors have to be
selected to compensate these parasitic parameters.
F
Z1
=
F
Z2
=
F
P1
=
F
P2
=
1
2
× π ×
R
4
×
C
2
1
2
× π ×
(R
2
+
R
3
)
×
C
3
1
2
× π ×
R
3
×
C
3
1
C
×
C
2
2
× π ×
R
4
×
1
C
1
+
C
2
...(11)
...(12)
...(13)
...(14)
where F
Z1
,F
Z2
,F
P1
and F
P2
are poles and zeros in
the compensator. Their locations are shown in figure 4.
The transfer function of type III compensator for
transconductance amplifier is given by:
V
e
1
−
g
m
×
Z
f
=
V
OUT
1
+
g
m
×
Z
in
+
Z
in
/ R
1
Compensator Design
Due to the double pole generated by LC filter of the
power stage, the power system has 180
o
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 fre-
quency between1/10 and 1/5 of the switching frequency,
phase margin greater than 50
o
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 com-
pensator can be used to compensate the system, be-
cause the zero caused by output capacitor ESR is lower
than crossover frequency. Otherwise type III compensa-
tor should be chosen.
For the voltage amplifier, the transfer function of
compensator is
V
e
−
Z
f
=
V
OUT
Z
in
To achieve the same effect as voltage amplifier,
the compensator of transconductance amplifier must
satisfy this condition: R
4
>>2/gm. And it would be desir-
able if R
1
||R
2
||R
3
>>1/gm can be met at the same time.
Zin
R3
Vout
Zf
C1
C2
Fb
gm
Ve
R4
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.
R2
C3
R1
Vref
Figure 3 - Type III compensator using
transconductance amplifier
Rev.1.8
02/28/08
8
MICROSEMI [ MICROSEMI CORPORATION ]
