Resonant and Soft-Switching Techniques in Power Electronics ECEN 5817 Instructors: Mariko Shirazi Professor Robert Erickson ECEE 1B65A 303-492-1661 mariko.shirazi@colorado.edu Course web site: http://ece.colorado.edu/~ecen5817 Lecture schedule Lecture slides and supplementary materials Homework assignments and solutions Announcements Textbook: Erickson and Maksimovic, Fundamentals of Power Electronics, second edition, Chapters 19 and 20 Extensive supplementary notes and chapters on course web site

Preliminaries Prerequisites ECEN 5797 Introduction to Power Electronics is a required prerequisite to this course Note that ECEN 5807 is not a prerequisite Grading Homework 50% Approximately 12 weekly assignments Assignments posted each week on course web page Midterm exam 17% One-week take-home exam Final exam 33%

For off-campus students Delivery options Web: lectures posted on web site within 24 hours. High resolution. Students electing this option will typically run 1-2 days behind the on-campus students. VHS or DVD: lectures mailed to off-campus students. Low resolution (NTSC: conventional analog TV). Students electing this option will typically run one week behind the on-campus students. With either approach: set a schedule for yourself — a regular time when you will watch the lectures, that is a fixed time behind the on-campus schedule. You will be expected to mail or fax your homework on the day that you would normally watch the lecture where the homework of the on-campus students is collected. Ditto for exams. Final grades for off-campus students are due 7-10 days after the on-campus grades. If you decide to quit the course, please submit the paperwork to formally drop.

Homework: off-campus students On the day you would normally watch the lecture in which the homework assignment is due, mail or fax your completed homework to: Mariko Shirazi ECE Department Campus Box 425 University of Colorado Boulder, CO 80309-0425 Fax: 303-492-2758 (cover page should list Mariko Shirazi as the recipient) Please don’t scan and email your homework. Homework solutions will be posted on the course web site, and solution passwords will be sent to you with your graded homework (if you put an email address on the first page of your homework, we will email the password when we receive your homework).

Office hours Thursdays, 12:00 - 2:00 pm ECEE 1B65 Telephone office hour: Thursdays, 2:00 to 3:00 pm Mountain time Off-campus students are welcome to call at this time or at other times; I’ll at least be there to answer the phone at the above time. Questions via email are also encouraged. I will try to respond to them within a day.

Acknowledgement Most of the material for this class has been developed by Professor Robert Erickson and/or taken directly from the course textbook Fundamentals of Power Electronics by Professor Erickson and Professor Dragan Maksimovic.

Introduction to Resonant Conversion Resonant power converters contain resonant L-C networks whose voltage and current waveforms vary sinusoidally during one or more subintervals of each switching period. These sinusoidal variations are large in magnitude, and the small ripple approximation does not apply. Some types of resonant converters: Dc-to-high-frequency-ac inverters Resonant dc-dc converters Another application of resonant techniques: Soft-switched PWM converters Resonant switch converters Other soft-switching converters

A basic class of resonant inverters Basic circuit Several resonant tank networks

Input impedance

Tank network responds only to fundamental component of switched waveforms Tank current and output voltage are essentially sinusoids at the switching frequency fs. Output can be controlled by variation of switching frequency, closer to or away from the tank resonant frequency

Derivation of a resonant dc-dc converter Rectify and filter the output of a dc-high-frequency-ac inverter The series resonant dc-dc converter

Quasi-resonant converters Buck converter example In a conventional PWM converter, replace the PWM switch network with a switch network containing resonant elements. Two switch networks:

Applications of resonant and soft-switching converters Electronic ballasts for gas-discharge lamps Produce high-frequency ac Other high-frequency ac applications Electrosurgical generators Induction heaters Piezoelectric transformers High-frequency high-density dc–dc converters Reduce switching loss and improve efficiency High-voltage and other specialized converters Transformer nonidealities lead to ringing waveforms Converters using IGBTs Mitigate switching loss caused by current tailing Low-harmonic rectifiers Mitigate switching loss caused by diode stored charge

Resonant inverter: An electronic ballast Must produce controllable high-frequency (50 kHz) ac to drive gas discharge lamp DC input is typically produced by a low-harmonic rectifier Similar to resonant dc-dc converter, but output-side rectifier is omitted Half-bridge, driving LCC tank circuit and gas discharge lamp

Motivation for resonant DC-DC converters and soft-switching techniques Increasing switching frequency reduces value and size of filter inductances and capacitances Up to a point, increasing switching frequency reduces transformer size Increasing switching frequency increases switching loss Much R&D effort has been devoted to increasing the switching frequency and reducing the loss in high-density power supplies Approaches to achieve these goals include use of resonant converters and soft switching techniques

Reducing the size of a dc-dc converter

Effect of switching frequency on transformer size Ferrite core for Cuk converter example As switching frequency is increased from 25 kHz to 250 kHz, core size is dramatically reduced As switching frequency is increased from 400 kHz to 1 MHz, core size increases

High power density requires high efficiency A goal of current converter technology is to construct converters of small size and weight, which process substantial power at high efficiency High density power conversion

4.3. Switching loss Energy is lost during the semiconductor switching transitions, via several mechanisms: Transistor switching times Diode stored charge Energy stored in device capacitances and parasitic inductances Semiconductor devices are charge controlled – controlling charge must be inserted or removed to switch a device

Classical but misleading example: Transistor switching with clamped inductive load (4.3.1) Buck converter example transistor turn-off transition Loss:

4.3.4. Efficiency vs. switching frequency Add up all of the energies lost during the switching transitions of one switching period: Average switching power loss is Total converter loss can be expressed as where Pfixed = fixed losses (independent of load and fsw) Pcond = conduction losses

Efficiency vs. switching frequency Switching losses are equal to the other converter losses at the critical frequency This can be taken as a rough upper limit on the switching frequency of a practical converter. For fsw > fcrit, the efficiency decreases rapidly with frequency.

Soft switching: Zero-voltage and zero-current switching Soft switching can mitigate some of the mechanisms of switching loss and possibly reduce the generation of EMI Semiconductor devices are switched on or off at the zero crossing of their voltage or current waveforms Conduction sequence: D1–Q1–D2–Q2 Q1 is turned on during D1 conduction interval, without loss

Soft switching in a PWM converter Example: forward converter with active clamp circuit Switching transitions are resonant, remainder of switching period is not resonant Transistors operate with zero voltage switching Beware of patent issues

Classical but misleading example: Transistor switching with clamped inductive load (4.3.1) Buck converter example transistor turn-off transition Loss:

Analysis of resonant converters Series resonant dc-dc converter example Complex! Small ripple approximation is not valid Need new approaches: Sinusoidal approximation State plane analysis

Outline of course 1. Analysis of resonant converters using the sinusoidal approximation Classical series, parallel, LCC, and other topologies Sinusoidal model Zero voltage and zero current switching Resonant converter design techniques based on frequency response 2. Sinusoidal analysis: small-signal ac behavior with frequency modulation Spectra and envelope response Phasor transform method 3. State-plane analysis of resonant converters Fundamentals of state-plane and averaged modeling of resonant circuits Exact analysis of the series and parallel resonant dc-dc converters

Outline, p. 2 4. State plane analysis of resonant switch and other soft-switching converters Quasi-resonant topologies and their analysis via state-plane approach Quasi-square wave converters Zero voltage transition converter Soft switching in forward and flyback converters Multiresonant and class E converter 5. Server systems, portable power, and green power issues (time permitting) Modeling efficiency vs. load, origins of loss Variable frequency approaches to improving light-load efficiency DCM Burst mode Effects of parallel modules DC transformers

Upcoming Assignments Preparation for next lecture: Read Section 19.1, Sinusoidal analysis of resonant converters Preparation for Lecture 3: Read Section 19.2, Examples Homework assignment, due Lecture 5: Homework set #1, Review