Datasheet

VO
R
L
VC
fp
fz
Adc
gm
ps
R
ESR
C
OUT
VSENSE
COMP
VO
R1
R3
C1
C2
R2
CO RO
gm
225 uA/V
0.8 V
PowerStage
13.0 A/V
PH
R
ESR
C
OUT
R
L
b
a
c
TPS54318
SLVS975A –SEPTEMBER 2009–REVISED SEPTEMBER 2013 www.ti.com
SMALL-SIGNAL MODEL FOR LOOP RESPONSE
Figure 31 shows an equivalent model for the TPS54318 control loop which can be modeled in a circuit simulation
program to check frequency response and dynamic load response. The error amplifier is a transconductance
amplifier with a gm of 225 μA/V. The error amplifier is modeled using an ideal voltage controlled current source.
The resistor Ro and capacitor Co model the open-loop gain and frequency response of the amplifier. The 1-mV
AC voltage source between the nodes a and b effectively breaks the control loop for the frequency response
measurements. Plotting a/c shows the small signal response of the frequency compensation. Plotting a/b shows
the small signal response of the overall loop. The dynamic loop response is checked by replacing the R
L
with a
current source with the appropriate load step amplitude and step rate in a time domain analysis.
Figure 31. Small-Signal Model for Loop Response
SIMPLE SMALL-SIGNAL MODEL FOR PEAK-CURRENT-MODE CONTROL
Figure 31 is a simple small-signal model that is used to understand how to design the frequency compensation.
The TPS54318 power stage can be approximated to a voltage controlled current source (duty-cycle modulator)
supplying current to the output capacitor and load resistor. The control to output transfer function is shown in
Equation 7 and consists of a DC gain, one dominant pole, and one ESR zero. The quotient of the change in
switch current and the change in COMP pin voltage (node c in Figure 31) is the power-stage transconductance.
The gm for the TPS54318 is 13 A/V. The low frequency gain of the power-stage frequency response is the
product of the transconductance and the load resistance as shown in Equation 8. As the load current increases
and decreases, the low frequency gain decreases and increases, respectively. This variation with load may seem
problematic at first glance, but the dominant pole moves with load current (see Equation 9). The combined effect
is highlighted by the dashed line in the right half of Figure 32. As the load current decreases, the gain increases
and the pole frequency lowers, keeping the 0-dB crossover frequency the same for the varying load conditions
which makes it easier to design the frequency compensation.
Figure 32. Simple Small-Signal Model and Frequency Response for Peak-Current-Mode Control
16 Submit Documentation Feedback Copyright © 2009–2013, Texas Instruments Incorporated
Product Folder Links :TPS54318