Rainbow Electronics MAX15041 - Manual (Page 12)

MAX15041
Having defined the power modulator’s transfer function
gain, the total system loop gain can be written as fol-
lows (see Figure 1):
where R OUT is the quotient of the error amplifier’s DC
gain, A VEA , divided by the error amplifier’s transcon-
ductance, g MV ; R OUT is much larger than R C and C C is
much larger than C CC .
Rewriting:
The dominate poles and zeros of the transfer loop gain
is shown below:
The order of pole-zero occurrence is:
Note under heavy load, f P2 , may approach f Z1 .
A graphical representation of the asymptotic system
closed-loop response, including the dominant pole and
zero locations is shown in Figure 2.
f f f f f
P P Z Z P 1 2 1 2 3
< < < ≤
f
g
C
f
C ESR
P
MV
AVEA dB
C
P
OUT
1
20
2
2 10
1
2
=
Ч Ч
=
Ч + π π _ / R R
f
C R
f
C R
f
LOAD
P
CC C
Z
C C
Z
( )
=
Ч
=
Ч
=
3 1
2
1
2
1
2
1
2
π π
ππ × C ESR
OUT
Gain
V
V
A
sC R
sC
A
g
FB
OUT
VEA
C C
C
VEA
MV
= Ч
+
( )
⎛
⎝⎜ ⎞
⎠⎟
+
1
1 1 1
1
⎡
⎣
⎢
⎤
⎦
⎥ Ч +
( )
Ч Ч
+
( )
sC R
G R
sC ESR
CC C
MOD LOAD
OUT
s sC ESR R
OUT LOAD
+
( )
+ ⎡⎣ ⎤⎦
1
α =
Ч +
( )
+
( )
+
( )
+ ⎡⎣ ⎤⎦ Ч
R sC R
s C C R R s C
OUT C C
C CC C OUT
1
1
C C CC C OUT
MOD LOAD
O
C R R
G R
sC
|| ||
( )( )
+ ⎡⎣ ⎤⎦
= Ч Ч
1
β U UT
OUT LOAD
ESR
sC ESR R
Gain
R
R
+
( )
+
( )
+ ⎡⎣ ⎤⎦
=
1
1
2
1
++
Ч Ч Ч
R
A
R
VEA
OUT 2
α β
Low-Cost, 3A, 4.5V to 28V Input, 350kHz, PWM
Step-Down DC-DC Regulator with Internal Switches
12 ______________________________________________________________________________________
L0
Q HS
CONTROL
LOGIC
V COMP V OUT
PWM
COMPARATOR
COMP
R
C R OUT g MV
V IN
POWER MODULATOR
OUTPUT FILTER
AND LOAD
NOTE: THE G MOD STAGE SHOWN ABOVE MODELS THE AVERAGE CURRENT OF
THE INDUCTOR INJECTED INTO THE OUTPUT LOAD. THIS REPRESENTS A
SIMPLIFICATION FOR THE POWER MODULATOR STAGE DRAWN ABOVE.
ERROR AMPLIFIER FEEDBACK
DIVIDER
COMPENSATION
RAMP
g MC
DCR
I
L Q LS
V
OUT
V OUT
I L
ESR
C OUT
R LOAD
C C
REF
*C
CC
IS OPTIONAL.
R OUT = A VEA /g MV
*C CC
FB
R 1
R 2
G MOD
Σ
Figure 1. Peak Current-Mode Regulator Transfer Model