Datasheet

VSENSE

COMP

CO RO

225 uA/V

0.8 V

PowerStage

13.0 A/V

ESR

OUT

TPS54218

SLVS974B –SEPTEMBER 2009–REVISED JULY 2013

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SMALL SIGNAL MODEL FOR LOOP RESPONSE

Figure 31 shows an equivalent model for the TPS54218 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 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

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 TPS54218 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 TPS54218 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.

Product Folder Links :TPS54218