## Voltage-Regulator Model

I love switching-regulator modules. They are efficient, you can configure them for many uses, and you can easily model them.

Figure 1 shows a typical characterization test for a regulator module—a Texas Instruments PTH08T220W switching-regulator module. The module is subject to an 8-A step load, with a maximum dI/dt of 2.5V/μsec. The plot shows the load current at the bottom and the voltage-regulator response to this current at the top.

To build a circuit model for this voltage regulator, you need no additional
information about the insides of the regulator. The step-response test reveals
enough information to form a simple circuit model (Figure 2). The
circuit model assumes a perfect voltage source, V_{REF}, connected
through components R_{1} and L_{1} to your V_{CC} plane.
Components R_{1} and L_{1} represent the action of the
regulator.

Component C_{2}, along with R_{2} and L_{2},
represent the bulk capacitor (or array of bulk capacitors) in your
application.

If,
by looking at the data sheet, you can discover values for R_{1} and
L_{1}, then you can build a circuit model such as the one in Figure 2 for
any application of the regulator.

The most straightforward parameter in this circuit is R_{1}. Over a
time period of more than 100 μsec, the circuit comes to rest at a steady-state
dc operating condition. After that time, capacitor C_{2} draws no
appreciable steady-state current, so you may replace it with an open circuit.
Similarly, replace inductor L_{1} with its dc equivalent: a short. The
only operative component remaining in the circuit is resistor R_{1},
which directly controls the output droop, or steady-state dc offset. The value
of R_{1} equals the ratio of droop to load current.

Over a medium scale of time, components C_{2} and L_{1} come
into play, creating a damped sinusoidal response. The application note for this
component shows a typical step-response waveform with 1200 μF of output
capacitance. Given that data point, you just set C_{2} equal to 1200 μF
and adjust L_{1} to match the width of the sinusoidal glitch. Now you
know L_{1}.

Last, given R_{1}, C_{2}, and L_{1}, adjust
R_{2} until you match the damping factor of each sinusoidal pulse. Now
you know what ESR (equivalent series resistance) that manufacturer used when it
snapped the step-response picture.

This simple circuit mimics the performance of the regulator at frequencies
from dc to approximately 100 KHz. Above that range, the ESL (equivalent series
inductance) of capacitor C_{2} comes into play, but this low-speed
step-response test doesn't provide enough information to determine
L_{2}. For a low-speed model, just leave L_{2} at zero.

This simple circuit model works for any voltage regulator with dominant-pole feedback, meaning that the regulator does not use a multipole phase-compensating feedback structure. (Most don't.)

Always follow the manufacturer's guidelines for minimum capacitance and
minimum ESR in your output capacitors. Failure to do so can produce unstable
oscillations in the feedback circuit, destroying your circuit. Figure 2 does *not* model that aspect of regulator behavior.