*This article is the first in a three-part series. Part 2, Estimating the Frequency Response of a Power Electronic Model: Sinestream vs. Pseudo-Random Binary Sequence (PRBS), compares FRE for an open-loop buck converter with sinestream and with PRBS, focusing on estimation time, number of estimated frequency points, and estimation accuracy. Part 3, Cascade Digital PID Control Design for Power Electronics Models, describes a frequency-response-estimation based control design workflow for tuning the controller gains of a switch-mode buck converter with inner current control loop and outer voltage control loop.*

Power electronics systems rely on feedback control to convert voltages and currents from the power source to those needed by the load. For example, a DC-DC power converter uses a control system to achieve the desired output voltage level and to maintain that level as the source voltage and load resistance change.

Power electronics engineers base their control designs on classic control theory. Since the theory is based on linear time-invariant (LTI) systems such as transfer functions and state-space models, to apply it to a power electronics system, engineers need to find an LTI representation of such a system.

Frequency response estimation (also known as an AC sweep) is commonly used to compute an LTI representation of a power electronics model. Frequency response estimation involves superimposing a small perturbation signal of controllable amplitude and frequency onto the input of the system operating in steady state and measuring the system response to this perturbation. Measured input and output signals can be then used to compute either the frequency response or a transfer function—that is, the LTI system that represents the system dynamics around the operating point.

This article describes a six-step workflow for estimating the frequency response of an open-loop boost converter.

## The Open-Loop Boost Converter Model

A boost converter is a well-known switch-mode converter that is capable of producing a DC output voltage greater than the DC input voltage. It is used to connect a lower-voltage source to a higher-voltage load in many applications, including consumer electronics products, electric automobiles, more-electric ships and aircraft, renewables, and LED drivers.

Our switch-mode open-loop boost converter model is built with Simscape Electrical™ components (Figure 1). It is assumed that the converter operates in continuous conduction mode (CCM), which means that the inductor current never goes to zero when the converter is operating in steady state. The input perturbation and output measurement points for frequency response estimation are set for the duty cycle and output voltage, respectively. The control-to-output transfer function will then have the duty cycle as control input and the output voltage as output.

- Frequency sweep analysis
- Bode plot analysis
- Transfer function estimation