Datasheet

ADP1829 Data Sheet
Rev. C | Page 20 of 28
The rest of the system gain is needed to reach 0 dB at crossover.
The total gain of the system, therefore, is given by
A
T
= A
MOD
+ A
FILTER
+ A
COMP
(26)
where:
A
MOD
is the gain of the PWM modulator.
A
FILTER
is the gain of the LC filter including the effects of
the ESR zero.
A
COMP
is the gain of the compensated error amplifier.
Additionally, the phase of the system must be brought back up
to guarantee stability. Note from the bode plot of the filter that
the LC contributes −180° of phase shi. Additionally, because
the error amplifier is an integrator at low frequency, it contrib-
utes an initial −90°. erefore, before adding compensation or
accounting for the ESR zero, the system is already down −270°.
To avoid loop inversion at crossover, or −180° phase shift, a
good initial practical design is to require a phase margin of 60°,
which is therefore an overall phase loss of −120° from the initial
low frequency dc phase. The goal of the compensation is to
boost the phase back up from −270° to −120° at crossover.
The two common compensation schemes used are sometimes
referred to as Type II or Type III compensation, depending on
whether the compensation design includes two or three poles.
(Dominant-pole compensations, or single-pole compensation,
is referred to as Type I compensation, but unfortunately, it is not
very useful for dealing successfully with switching regulators.)
If the zero produced by the ESR of the output capacitor provides
sufficient phase boost at crossover, Type II compensation is
adequate. If the phase boost produced by the ESR of the output
capacitor is not sufficient, another zero is added to the
compensation network, and thus, Type III is used.
In Figure 27, the location of the ESR zero corner frequency
gives significantly different net phase at the crossover frequency.
Use the following guidelines for selecting between Type II and
Type III compensators:
If
2
CO
ESRZ
f
f 
, use Type II compensation.
If
2
CO
ESRZ
f
f 
, use Type III compensation.
GAIN
FREQUENCY
PHASE
LC FILTER BODE PLOT
PHASE CONTRIBUTION AT CROSSOVER
OF VARIOUS ESR ZERO CORNERS
f
SW
f
CO
f
ESR3
f
ESR2
f
ESR1
0dB
f
LC
–40dB/dec
–20dB/dec
0°
–90°
–180°
Φ
1
Φ
2
Φ
3
06784-026
Figure 27. LC Filter Bode Plot
The following equations were used for the calculation of the
compensation components as shown in Figure 28 and Figure 29:
I
Z
Z1
CR
f


2
1
(27)
)(2
1
FF
TOP
FF
Z2
RRC
f

 (28)
HFI
HFI
Z
P1
CC
CC
R
f



2
1
(29)
FFFF
P2
CR
f


2
1
(30)
where:
f
Z1
is the zero produced in the Type II compensation.
f
Z2
is the zero produced in the Type III compensation.
f
P1
is the pole produced in the Type II compensation.
f
P2
in the pole produced in the Type III compensation.