Loop Gain Reconstruction of a Step-Down Converter from Output Impedance Measurement
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1 Introduction
The loop gain measurement shows the stability and robustness of the control loop of a power supply and provides insight to improve output transient response. For the characterization of the loop, the open loop gain is commonly measured by using the voltage injection method.
Figure 1-1 shows a common method to measure loop gain of a DC-DC converter, the voltage injection method. This method consists of breaking the control loop in a single place with a resistor and injecting into the loop a sinusoidal disturbance at different frequencies with an injection transformer. Relative magnitudes and phase of the input signal and output signal versus frequency will be subsequently measured.
The voltage injection method approach ensures correct quiescent operating conditions in the system and avoids a common difficulty in systems having a large DC loop gain. However, the limitation is that the voltage injection method requires breaking the control loop by placing an additional resistor at a suitable point.
Figure 1-1 Output Impedance Setup for TPS62816Adding additional components could weaken the noise immunity of a device by making the feedback signal trace longer. Thus, making control loop more sensitive to fast switching signals. Besides, the voltage injection approach might not be an acceptable method for space-limited designs.
To avoid breaking the feedback loop, an alternative method is proposed to obtain the loop gain from the output impedance measurements of a DC-DC converter.
The output impedance is an important parameter to characterize a switching voltage regulator and help evaluate how the converter will respond to load changes at different frequencies. Valuable information such as control loop stability, decoupling networks powering the device, dynamic load response and the susceptibility of the power supply to complex loads can be derived from an output impedance measurement.
This application report shows the details of the loop gain measurement of a switching voltage regulator using output impedance measurements and results obtained with TPS62816.
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 Converteris the open loop output impedance of the power stage loop gain and 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 :
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:
