## Research on PWM Power Converters

This research has followed several directions; selected published results are summarized below.

#### Modeling, control, and design of PWM power converters

- Robert Erickson, Slobodan Cuk, and R. D. Middlebrook, "Large Signal Analysis and Design of Switching Regulators,"
*IEEE Power Electronics Specialists Conference*, 1982 Record, pp. 240-250.

State-plane analysis of nonlinear switching regulators having state feedback. Solution for equilibrium points, and the effects of saturation and current limiting. - Robert Erickson and R. D. Middlebrook, "Origins of Harmonic Distortion in Switching Amplifiers,"
*Proceedings Fourth Annual International PCI '82 Conference*, pp. 567-582, March 1982.

A perturbation series analysis is employed to predict harmonic distortion in switching amplifiers. This leads to a series of equivalent circuits that predict approximate magnitudes and phases of each harmonic. - Robert Erickson, Bill Behen, R. D. Middlebrook, and Slobodan Cuk, "Characterization of Power MOSFET's in Switching Converters,"
*Proceedings Seventh National Solid-State Power Conversion Conference*(Powercon 7), pp. D4.1-D4.17, March 1980. - Slobodan Cuk and Robert Erickson, "A Conceptually New High-Frequency Switched-Mode Amplifier Technique Eliminates Current Ripple,"
*Proceedings Fifth National Solid-State Power Conversion Conference*(Powercon 5), pp. G3.1-G3.22, May 1978. - Robert Erickson, "Synthesis of Switched-Mode Converters,"
*IEEE Power Electronics Specialists Conference*, 1983 Record, pp. 9-22.

The first paper on systematic systhesis of switched-mode converter topologies. Additional papers on converter synthesis are listed on the rectifier page. - I. Horowitz, M. Sidi, and R. Erickson, "Quantitative Feedback Synthesis for Nonlinear Switched-Mode Uncertain Regulators,"
*International Journal of Electronics*, Vol. 57, No. 4, pp. 461-476, Oct. 1984. - I. Khan and R. W. Erickson, "Control of Switched-Mode Converter Harmonic-Free Terminal Waveforms through Internal Energy Storage,"
*IEEE Power Electronics Specialists Conference*, 1986 Record, pp. 13-26, June 1986. - Yungtaek Jang and Robert Erickson, "Physical Origins of Input Filter Oscillations in Current Programmed Converters,"
*IEEE Applied Power Electronics Conference*, 1991 Record, March 1991. - Yungtaek Jang and Robert Erickson, "Physical Origins of Input Filter Oscillations in Current Programmed Converters,"
*IEEE Transactions on Power Electronics*, vol 7, no. 4, pp. 725-733, October 1992. - R. Erickson, “Optimal Single-Resistor Damping of Input Filters,”
*IEEE Applied Power Electronics Conference*, March 1999.

This paper extends Middlebrook's original work on optimum damping of input filters to several additional cases. This material was later incorporated into the textbook chapter on input filter damping. - R. Erickson, “DC-DC Power Converters,” article in
*Wiley Encyclopedia of Electrical and Electronics Engineering*, vol. 5, pp. 53-63, 1999. - J. Chen, R. Erickson, and D. Maksimovic, "Averaged Switch Modeling of Boundary Conduction Mode DC-to-DC Converters,"
*Proc. IEEE Industrial Electronics Society Annual Conference*(IECON 01), Nov. 2001. - A. Prodic, D. Maksimovic, and R. Erickson, "Design and Implementation of a Digital PWM Controller for a High- Frequency Switching DC-to-DC Power Converter,"
*Proc. IEEE Industrial Electronics Society Annual Conference*(IECON 01), Nov. 2001. - P. Athalye, D. Maksimovic, and R. Erickson, "Averaged Switch Modeling of Active-Clamped Converters,"
*Proc. IEEE Industrial Electronics Society Annual Conference (IECON 01)*, Nov. 2001. - Y. Zhang, R. Zane, A. Prodic, R. Erickson, and D. Maksimovic, "Online Calibration of MOSFET On-State Resistance For Precise Current Sensing,"
*IEEE Power Electronics Letters*, vol. 2, no. 3, pp. 100-103, September 2004. - P. Athalye, D. Maksimovic, and R. Erickson, "Variable-Frequency Predictive Digital Current Mode Control,"
*IEEE Power Electronics Letters*, vol. 2, no. 4, pp. 113-116, December 2004. - D. Maksimović, R. Zane, R. Erickson, “Advances in practical high-performance digital control,” invited paper,
*Digital Power Forum*, September 2005. - D. Friedrichs, R. Erickson, and J. Gilbert, “A New System Architecture Improves Output Power Regulation in Electrosurgical Generators,”
*33rd Annual International IEEE Engineering In Medicine and Biology Society Conference*, Aug. 2011. - Robert W. Erickson, “Advances in Averaged Switch Modeling,”
*SOBRAEP/IEEE Fourth Brazilian Power Electronics Conference*, December 1997, invited paper and tutorial seminar. - Dragan Maksimovic and Robert Erickson, "Advances in Averaged Switch Modeling and Simulation,"
*IEEE Power Electronics Specialists Conference*, 1999, tutorial seminar. - Robert Erickson and Dragan Maksimovic, "A primer on simulation, modeling, and design of the control loops of switching regulators,"
*IEEE Applied Power Electronics Confernce*, March 2003, tutorial seminar. - R. White, G. Miller, B. Dudman, and R. Erickson, "Recent Developments in GaAs Power Switching Devices Including Device Modeling,"
*IEEE Applied Power Electronics Conference*, March 2014.

#### Magnetics modeling

This series of papers is concerned with modeling switching converter waveforms in multiple-winding transformers and coupled-inductors. It specifically addresses prediction of cross-regulation in multiple-output flyback converters, a problem previously considered intractable. An approach is found in which every model parameter can be directly measured in the laboratory, and that explains the observed waveforms and converter performance.

- K. Changtong, R. Erickson, and D. Maksimovic, "A Comparison of the Ladder and Full- Order Models,"
*IEEE Power Electronics Specialists Conference*, June 2001.

The ladder model of multiple-winding transformers has been employed by multiple authors, based on the physical geometry of the windings. It is shown here that this model does not predict the first-order behavior of multiple-output flyback converters: regardless of the winding geometry, a full-order model is required. The extended cantilever model correctly predicts observed waveforms and gives a physical explanation of the relevant phenomena. - R. Erickson and D. Maksimovic, "Cross regulation mechanisms in multiple-output forward and flyback converters,"
*IEEE Applied Power Electronics Conference*, March 1999, tutorial seminar. - D. Maksimovic and R. Erickson, “Modeling of Cross Regulation in Multiple-Output Flyback Converters,”
*IEEE Applied Power Electronics Conference,*March 1999.

This paper applies the multiple-winding magnetics models of other papers listed here, to the difficult problem of predicting cross-regulation in multiple-output flyback converters. These converters are notorious for exhibiting very poor cross-regulation. This paper explains how winding geometry governs cross-regulation, and it suggests solutions to improve cross regulation. - R. Erickson and D. Maksimovic, “A Multiple-Winding Magnetics Model Having Directly Measurable Parameters,”
*IEEE Power Electronics Specialists Conference*, May 1998.

This paper describes the modeling of the flyback transformer of a multiple-output flyback converter, with a methodology in which every model parameter is directly measured in the laboratory. The resulting model is shown to accurately predict converter waveforms and cross-regulation performance. - D. Maksimovic, R. Erickson, and C. Griesbach, “Modeling of Cross-Regulation in Converters Containing Coupled Inductors,”
*IEEE Applied Power Electronics Conference*, pp. 350-356, Feb. 1998. - D. Maksimovic, R. Erickson, and C. Griesbach, “Modeling of Cross-Regulation in Converters Containing Coupled Inductors,”
*IEEE Transactions on Power Electronics*, vol. 15, no. 4, pp. 607-615, July 2000.

#### Power conservative networks

While it has been well understood that the transformer and gyrator are the only linear power-conservative two-port networks, in the power electronics field we have found applications that require new nonlinear power-conservative systems. These papers explore the fundamentals of these networks. The *dependent power source* and sink are basic nonlinear elements that arise in the models of these systems whenever *buffering* conditions are met. The *loss-free resistor* is a power-conservative network that arises in a number of applications including low-harmonic rectification and DCM converters.

- S. Singer and R. Erickson, “On the buffering condition implied by the stabilization of the output of switched-mode converters,”
*IEEE Power Electronics Specialists Conference*, 1992 Record, pp. 1197-1201, vol. 2, June 1992. - S. Singer and R. Erickson, “Control-implied input/output buffering of power conservative two-port networks,”
*IEEE International Symposium on Circuits and Systems (ISCAS ’92)*, pp. 1911-1913, vol. 4, 1992. - S. Singer and R.W. Erickson, “Power-Source Element and Its Properties,”
*IEE Proceedings - Circuits Devices and Systems*, vol. 141, no. 3, pp. 220-226, June 1994. - S. Singer and R. Erickson, “Canonical Modeling of Power Processing Circuits Based on the POPI Concept,”
*IEEE Transactions on Power Electronics*, vol. 7, no. 1, January 1992.