Datasheet

VSENSE
COMP
VO
R1
R3
C1
C2
R2
C0 R0
gm
245 µA/V
0.800 V
PowerStage
14 A/V
PH
R
ESR
C
OUT
R
L
b
a
c
TPS57112-Q1
SLVSAL8 –DECEMBER 2010 www.ti.com
SMALL SIGNAL MODEL FOR LOOP RESPONSE
Figure 31 shows an equivalent model for the TPS57112-Q1 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 245 mA/V. The error amplifier can be modeled using an ideal voltage
controlled current source. The resistor R0 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 can be 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 can be used to understand how to design the frequency
compensation. The TPS57112-Q1 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 11 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 TPS57112-Q1 is 14 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 12. 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 13].
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.
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