2 Loop Gain Measurement

Step-down converters have basic blocks that contribute to the closed loop system. Figure 2-1 shows a closed loop system for a generic step-down converter.

Figure 2-1 Closed Loop System for a Generic Step-down Converter

$Z_o^{ol}\left(s\right)$ is the open loop output impedance of the power stage loop gain and $T\left(s\right)$ is defined as the product of all gains around the loop. When the loop is open, the power stage is running at a constant operating point meaning the controller signal stays constant.

When the loop is closed, converter is running in normal operation. The closed loop output impedance is $Z_o^{cl}\left(s\right)$:

From this equation we can deduct that the higher the loop gain is, the more the output impedance is reduced by the feedback loop. While designing a power supply, reducing the output impedance is possible by adding output capacitance to lower the open loop impedance. Especially for high-current operation, making sure that the output impedance is low across the frequencies is important to enable good load transients. Though, this method comes to a size and bill of material cost, it might also degrade performance for some designs where a maximum output capacitance should not be exceeded.

From the previous formula we can derive the loop gain: