### Title page for ETD etd-11092010-235021

Type of Document Master's Thesis
Author Yan, Yingyi
URN etd-11092010-235021
Title Unified Three-terminal Switch Model for Current Mode Controls
Degree Master of Science
Department Electrical and Computer Engineering
Lee, Fred C. Committee Chair
Boroyevich, Dushan Committee Member
Mattavelli, Paolo Committee Member
Keywords
• modeling
• current-mode control
• equivalent circuit
• three-terminal switch model
Date of Defense 2010-11-08
Availability unrestricted
Abstract
Current-mode control architectures with different implementation approaches have been an indispensable technique in many applications, such as voltage regulator, power factor correction, battery charger and LED driver. Since the inductor current ramp, one of state variables influenced by the input voltage and the output voltage, is used in the modulator in current-mode control without any low pass filter, high order harmonics play important role in the feedback control. This is the reason for the difficulty in obtaining the small-signal model for current-mode control in the frequency domain. A continuous time domain model was recently proposed as a successful model for current-mode control architectures with different implementation. However, the model was derived by describing function method, which is very arithmatically complicated, not to mention time consuming. Although an equivalent circuit for a current mode control Buck converter was proposed to help designers to use the model without involving complicated math, the equivalent circuit is not a complete model. Moreover, no equivalent circuit for other topologies is available for designers. In this thesis, the primary objective is to develop a unified three-terminal switch model for current-mode control with different implementation methods, which are applicable in all the current mode control power converters.

First, the existing model for current mode control is reviewed. The limitation of average models and the discrete time model for current-mode control is identified. The continuous time model and its equivalent circuit of Buck converter is introduced. The deficiency of the equivalent circuit is discussed.

After that, a unified three-terminal switch model for current mode control is presented. Based on the observation, the PWM switch and the closed current loop is taken as an invariant sub-circuit which is common to different DC/DC converter topologies. A basic small signal relationship between terminal currents is studied and the result shows that the PWM switch with current feedback preserves the property of the PWM switch in power stage. A three-terminal equivalent circuit is developed to represent the small signal behavior of this common sub-circuit. The proposed model is a unified model, which is applicable in both constant frequency modulation and variable frequency modulation. The physical meaning of the three-terminal equivalent circuit model is discussed. The model is verified by SIMPLIS simulation in commonly used converters for both constant frequency modulation and variable frequency modulation.

Then, based on the proposed unified model, a comparison between different current mode control implementations is presented. In different applications, different implementations have their unique benefit on extending control bandwidth. The properties of audio susceptibility and output impedance are discussed. It is found that, for adaptive voltage positioning design, constant on-time current mode control can simplifies the outer loop design.

Next, since multiphase interleaving structure is widely used in PFC, voltage regulator and other high current applications, the model is extended to multiphase current mode control. Some design concerns are discussed based on the model.

As a conclusion, a unified three-terminal switch model for current mode controls is investigated. The proposed model is quite general and not limited by implementation methods and topologies. All the modeling results are verified through simulation and experiments.

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