Control Loop Modeling of Switching Power Supplies

This paper presents techniques to assist the power supply designer in accurately modeling and designing the control loop of a switchmode DC/DC power supply. The three major components of the power supply control loop (i.e., the power stage, the pulse width modulator and the error amplifier) are presented with power stage modeling being the focus of this presentation. The power stage is modeled using the PWM Switch model, which greatly simplifies the analysis over state-space averaging methods. Voltage mode pulse-width-modulation is presented. Introduction There are many facets to the analysis and design of a switching power supply. The power supply designer must have a good understanding of basic analog circuit theory, a small but ever increasing grasp of digital circuits, at least a passing comprehension of electromagnetic fundamentals and a proficient knowledge of control system concepts. This paper deals with modeling the frequency response characteristics of a switching power supply control loop. A regulated switching power supply control loop consists of three major components; the power stage, the reference voltage/error-amplifier combination, and the pulse-widthmodulator. Figure 1 is a simple block diagram of a switching power supply showing these components. The power stage performs basic voltage conversion. Modeling the power stage presents the fundamental challenge to the power supply designer. A relatively new technique involves modeling only the switching elements of the power stage. An equivalent circuit for these elements is derived and is called the PWM Switch Model. This approach is presented here. Once an accurate and easy-to-use model for the power stage is obtained, the power supply designer can design the reference voltage/error-amplifier circuit so that a stable and fast-responding control loop results. The reference voltage and error-amplifier provide a signal which, roughly speaking, indicates the closeness of the output voltage to the desired value. Modeling this part of the control loop is easy because they are linear circuits and are easily represented mathematically. Finally, the pulse-width-modulator converts the analog output signal of the error-amplifier to a digital pulse train that is used by the power stage to produce the output voltage. The model for the pulse-width-modulator is relatively straightforward. It can be said that a regulated switching power supply has all the components of a classical control system: a plant, a reference input, and a feedback network. The techniques presented here can be used to analyze many of the various types of regulated switching power supplies. In order to limit the scope of this paper, the discussion will be limited to DC/DC converters.