Datasheet

1
f
ESR
=
2SC
OUT
R
ES
R
O
+ R
DCR
f
LC
=
1
2S
L
OUT
C
OUT
(R
O
+ R
ESR
)
G
PWM
=
V
in
ÂV
ramp
V
IN
L
OUT
C
OUT
R
FB1
R
FB2
C
C2
C
C1
R
C1
V
OUT
C
C3
R
C2
FB
+
-
R
DCR
COMP
DRIVER
EA
+
-
PWM
Error Amplifier and Compensation
R
O
PWM Modulator
SW
R
ESR
Power Train
0.6V
LM21215A
www.ti.com SNOSB87B –MARCH 2011–REVISED MARCH 2013
Figure 33. Loop Diagram
The power train consists of the output inductor (L) with DCR (DC resistance R
DCR
), output capacitor (C
0
) with
ESR (effective series resistance R
ESR
), and load resistance (R
o
). The error amplifier (EA) constantly forces FB to
0.6V. The passive compensation components around the error amplifier help maintain system stability. The
modulator creates the duty cycle by comparing the error amplifier signal with an internally generated ramp set at
the switching frequency.
There are three transfer functions that must be taken into consideration when obtaining the total open loop
transfer function; COMP to SW (Modulator) , SW to V
OUT
(Power Train), and V
OUT
to COMP (Error Amplifier).
The COMP to SW transfer function is simply the gain of the PWM modulator.
where
• ΔV
RAMP
is the oscillator peak-to-peak ramp voltage (nominally 0.8 V) (9)
The SW to COMP transfer function includes the output inductor, output capacitor, and output load resistance.
The inductor and capacitor create two complex poles at a frequency described by:
(10)
In addition to two complex poles, a left half plane zero is created by the output capacitor ESR located at a
frequency described by:
(11)
A Bode plot showing the power train response can be seen below.
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