ECEN 5817 Housekeeping I plan on indicating for each lecture(s) of this year the equivalent lecture(s) from Spr. 06. This will make it easy if you choose to watch those lectures to stay in synch with this years class if we should run at a slightly different pace. I will also indicate if there is any new material for this year not covered in Spr. 06 so you will know to watch / attend that particular lecture this year. Similarly, any material covered in Spr. 06 but not covered this year will not show up as an equivalent lecture so you will know you can skip it. Today (lecture 4) we will cover material covered in lecture 7 of the Spr. 06 class. You may wish to watch some of Spring 06 lectures 1 to 3 for some valuable insight and historical perspective on resonant power conversion techniques.

2 different ways to construct transfer function H

Dc conversion ratio of the PRC At resonance, this becomes PRC can step up the voltage, provided R > R0 PRC can produce M approaching infinity, provided output current is limited to value less than Vg / R0

Model: series resonant converter

Comparison of approximate and exact characteristics Series resonant converter Below resonance: 0.5 < F < 1 Above resonance: 1 < F

Comparison of approximate and exact characteristics Parallel resonant converter Exact equation: solid lines Sinusoidal approximation: shaded lines

Chapter 19 Resonant Conversion Introduction 19.1 Sinusoidal analysis of resonant converters 19.2 Examples Series resonant converter Parallel resonant converter 19.3 Soft switching Zero current switching Zero voltage switching 19.4 Load-dependent properties of resonant converters 19.5 Exact characteristics of the series and parallel resonant converters

19.3 Soft switching Soft switching can mitigate some of the mechanisms of switching loss and possibly reduce the generation of EMI Losses due to high voltage and high current present in switch during transitions, Losses due to shorting device capacitances Semiconductor devices are switched on or off at the zero crossing of their voltage or current waveforms: Zero-current switching: transistor turn-off transition occurs at zero current. Zero-current switching eliminates the switching loss caused by IGBT current tailing and by stray inductances. It can also be used to commutate SCR’s. Zero-voltage switching: transistor turn-on transition occurs at zero voltage. Diodes may also operate with zero-voltage switching. Zero-voltage switching eliminates the switching loss induced by diode stored charge and device output capacitances. Zero-voltage switching is usually preferred in modern converters, including soft-switching PWM converters.

19.3.1 Operation of the full bridge below resonance: Zero-current switching Series resonant converter example Current bi-directional switches ZCS vs. ZVS depends on tank current zero crossings with respect to transistor switching times = tank voltage zero crossings Operation below resonance: input tank current leads voltage Zero-current switching (ZCS) occurs

Tank input impedance Operation below resonance: tank input impedance Zi is dominated by tank capacitor. Zi is negative, and tank input current leads tank input voltage. Zero crossing of the tank input current waveform is(t) occurs before the zero crossing of the voltage vs(t) – before switch transitions

Switch network waveforms, below resonance Zero-current switching Conduction sequence: Q1–D1–Q2–D2 Tank current is negative at the end of each half interval – antiparallel diodes conduct after their respective switches Q1 is turned off during D1 conduction interval, without loss

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

Switch network waveforms, below resonance Zero-current switching Conduction sequence: Q1–D1–Q2–D2 Q1 is turned off during D1 conduction interval, without loss Note on terminology:

ZCS turn-on transition: hard switching Q1 turns on while D2 is conducting. Stored charge of D2 and of semiconductor output capacitances must be removed. Transistor turn-on transition is identical to hard-switched PWM, and switching loss occurs.

More on diode reverse recovery Circuits with diode and switch in loop – when turn on switch diode turns off (unless ZVS)

More on diode reverse recovery Diode equations : Stored minority charge profile under forward-biased conditions In steady-state:

Induced losses Stored charge is exponential function of voltage - require large change in q to get small change in vD vD remains > 0 until all stored charge removed – holding voltage across MOSFET = Vg while MOSFET is providing not only iL, but diode reverse current as well. Induces losses in MOSFET This energy loss is MUCH greater than the energy stored in diode in the form of stored charge as well as across depletion capacitance

19.3.2 Operation of the full bridge above resonance: Zero-voltage switching Series resonant converter example Operation above resonance: input tank current lags voltage Zero-voltage switching (ZVS) occurs

Tank input impedance Operation above resonance: tank input impedance Zi is dominated by tank inductor. Zi is positive, and tank input current lags tank input voltage. Zero crossing of the tank input current waveform is(t) occurs after the zero crossing of the voltage vs(t) – after switch transitions

Switch network waveforms, above resonance Zero-voltage switching Conduction sequence: D1–Q1–D2–Q2 Tank current is negative at the beginning of each half-interval – antiparallel diodes conduct before their respective switches Q1 is turned on during D1 conduction interval, without loss – D2 already off!

ZVS turn-off transition: hard switching? When Q1 turns off, D2 must begin conducting. Voltage across Q1 must increase to Vg. Transistor turn-off transition is identical to hard-switched PWM. Switching loss may occur… but….

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

Soft switching at the ZVS turn-off transition Introduce small capacitors Cleg across each device (or use device output capacitances). Introduce delay between turn-off of Q1 and turn-on of Q2. Tank current is(t) charges and discharges Cleg. Turn-off transition becomes lossless. During commutation interval, no devices conduct. So zero-voltage switching exhibits low switching loss: losses due to diode stored charge and device output capacitances are eliminated.

19.4 Load-dependent properties of resonant converters Resonant inverter design objectives: 1. Operate with a specified load characteristic and range of operating points With a nonlinear load, must properly match inverter output characteristic to load characteristic 2. Obtain zero-voltage switching or zero-current switching Preferably, obtain these properties at all loads Could allow ZVS property to be lost at light load, if necessary 3. Minimize transistor currents and conduction losses To obtain good efficiency at light load, the transistor current should scale proportionally to load current (in resonant converters, it often doesn’t!)