TPS54319_1 Datasheet, PDF (17/35 Pages) Texas Instruments – 2.95-V to 6-V Input, 3-A Output, 2-MHz, Synchronous Step-Down Switcher With Integrated FETs ( SWIFT™)

TPS54319
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SLVSA83 – JUNE 2010
SMALL SIGNAL MODEL FOR LOOP RESPONSE
Figure 32 shows an equivalent model for the TPS54319 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 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 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.
c
C2
COMP
R3
C1
Power Stage
18.0 A/V
PH
VO
a
b
R1
R_ESR
R_L
CO RO
0.827 V ^VSENSE
gm
245 µA/V
R2
C_OUT
Figure 32. Small Signal Model for Loop Response
SIMPLE SMALL SIGNAL MODEL FOR PEAK CURRENT MODE CONTROL
Figure 32 is a simple small signal model that can be used to understand how to design the frequency
compensation. The TPS54319 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 32) is the power stage
transconductance. The gm for the TPS54319 is 18.0 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 33. 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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