19.3 Soft switching in resonant convertersecee.colorado.edu/~ecen5817/lectures/L5_ECEN5817_notes.pdf · 19.3 Soft switching in resonant converters ... Resonant Inverter Design

ECEN5817, ECEE Department, University of Colorado at Boulder

ECEN 58171

19.3 Soft switching in resonant converters

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,

e.g. due to diode reverse recovery

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 converters based on MOSFETs

ECEN 58172

19.3.1 Operation of the full bridge below resonance:

Zero-current switching

Series resonant converter example

L

+–

Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

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


ECEN 58173

Tank input impedance

1ωC

Re

|| Zi ||

f0

ωL

R0

Qe = R

0 /R

e

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

ECEN 58174

Switch network waveforms, below resonanceZero-current switching

L CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Conduction sequence: Q1–D1–Q2–D2

Q1 is turned off during D1 conduction interval, without loss (same for Q4/D4)

Q2 is turned off during D2 conduction interval, without loss (same for Q3/D3)


ECEN 58175

Turn-on transitions: significant switching losses

L CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

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.

ECEN 58176

More on Diode Stored Charge and Reverse Recovery

Typical test circuit

and parameter

definitions in diode

data sheets


ECEN 58177

Diode stored charge during recovery

ECEN 58178

“Snappy” and “soft-recovery” diodes

Also see textbook Section 4.3.2 and HW 1 problem 3 solution


ECEN 58179

Example

Reverse recovery time trr, maximum reverse recovery current IRRM, and

reverse recovery charge Qrr depend on diode forward current IF prior to

turn off, rate of current decay dif/dt, and junction temperature TJ

Diode in IRGP50B60 (IGBT+diode): ultra-fast, “soft recovery”

ECEN 581710

Review of HW1 problem 3 example

gs

g

t

t

Ts

+–

D

it

ids

M

Ms

Ds

Ls

id

iL = I

+

V

_

+

vds

_

iLs

its

g gs

L

C


ECEN 581711

19.3.2 Operation of the full bridge above resonance:

zero-voltage switching

Series resonant converter example

L

+–

Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Operation above resonance: input tank current lags voltage

Zero-voltage switching (ZVS) occurs

ECEN 581712

Tank input impedance

1ωC

Re

|| Zi ||

f0

ωL

R0

Qe = R

0 /R

e

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


ECEN 581713

Switch network waveforms, above resonanceZero-voltage switching

L CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

Conduction sequence: D1–Q1–D2–Q2

Q1 is turned on during D1 conduction interval, without loss

ZVS turn-on transitions for all transistors

Turn-off transitions are at non-zero current

ECEN 581714

Turn-off transition at non-zero current: hard switching?

L CQ1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

– is(t)

+

vds1(t)

–iQ1(t)

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 …


ECEN 581715

Soft switching at the turn-off transition

L

+–

Vg

Q1

Q2

Q3

Q4

D1

D2

D3

D4

+

vs(t)

–

is(t)

+

vds1(t)

–to remainderof converter

Cleg

Cleg

Cleg

Cleg

Conductingdevices:

t

Vg

vds1(t)

Q1

Q4

D2

D3

Turn offQ

1, Q

4

Commutationinterval

X

• 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.

Note: with IGBTs, substantial Cleg may be

required

ECEN 581716

Resonant Inverter Design

Applications:

Resonant inverters for lamp ballasts

DC-AC side of resonant DC-DC 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!)


ECEN 581717

19.4 Load-dependent properties of resonant converters

ECEN 581718

Inverter output characteristics


ECEN 581719


ECEN 581720


This result is valid provided that (i) the resonant network is purely reactive, and (ii) the load is purely resistive.


ECEN 581721

Matching output characteristic

to application requirements

Electronic ballast Electrosurgical generator

ECEN 581722

Input impedance of the resonant tank networkAppendix C: Section C.4.4

where

Expressing the tank input impedance as a function of the load resistance R:


ECEN 581723

ZN and ZD

ZD is equal to the tank output impedance under the condition that the tank input source vs1 is open-circuited. ZD = Zo∞

ZN is equal to the tank output impedance under the condition that the tank input source vs1 is short-circuited. ZN = Zo0

ECEN 581724

Reciprocity


ECEN 581725

Relations

ECEN 581726


ECEN 581727

Relating transistor current variations

to load resistance R

Theorem 1: If the tank network is purely reactive, then its input impedance || Zi ||

is a monotonic function of the load resistance R.

So as the load resistance R varies from 0 to ∞, the resonant network input

impedance || Zi || varies monotonically from the short-circuit value

|| Zi0 || to the open-circuit value || Zi∞ ||.

The impedances || Zi∞ || and || Zi0 || are easy to construct.

If you want to minimize the circulating tank currents at light load, maximize ||

Zi∞ ||.

Note: for many inverters, || Zi∞ || < || Zi0 || ! The no-load transistor current is

therefore greater than the short-circuit transistor current.

ECEN 581728

Derivation


ECEN 581729

Example: || Zi || of LCC

• for f < f m, || Zi || increases

with increasing R .

• for f > f m, || Zi || decreases

with increasing R .

• at a given frequency f, || Zi ||

is a monotonic function of

R.

• It’s not necessary to draw

the entire plot: just construct

|| Zi0 || and || Zi∞ ||.

ECEN 581730

Discussion: LCC

|| Zi0 || and || Zi∞ || both represent series

resonant impedances, whose Bode

diagrams are easily constructed.

|| Zi0 || and || Zi∞ || intersect at frequency

fm.

For f < fm

then || Zi0 || < || Zi∞ || ; hence

transistor current decreases as

load current decreases

For f > fm

then || Zi0 || > || Zi∞ || ; hence

transistor current increases as load

current decreases, and transistor

current is greater than or equal to

short-circuit current for all R

LCC example


ECEN 581731

Discussion —series and parallel

• No-load transistor current = 0, both above

and below resonance.

• ZCS below resonance, ZVS above

resonance

• Above resonance: no-load transistor current

is greater than short-circuit transistor

current. ZVS.

• Below resonance: no-load transistor current

is less than short-circuit current (for f <fm),

but determined by || Zi∞ ||. ZCS.

ECEN 581732

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!)


ECEN 581733

Relation between ZVS/ZCS boundary and load R

Theorem 2: If the tank network is purely reactive, then the boundary between zero-

current switching and zero-voltage switching occurs when the load resistance R is

equal to the critical value Rcrit, given by

It is assumed that zero-current switching (ZCS) occurs when the tank input

impedance is capacitive in nature, while zero-voltage switching (ZVS) occurs when

the tank is inductive in nature. This assumption gives a necessary but not sufficient

condition for ZVS when significant semiconductor output capacitance is present.

ECEN 581734

Derivation


ECEN 581735

Discussion —Theorem 2

Again, Zi∞, Zi0, and Zo0 are pure imaginary quantities.

If Zi∞ and Zi0 have the same phase (both inductive or both capacitive), then

there is no real solution for Rcrit.

Hence, if at a given frequency Zi∞ and Zi0 are both capacitive, then ZCS occurs

for all loads. If Zi∞ and Zi0 are both inductive, then ZVS occurs for all loads.

If Zi∞ and Zi0 have opposite phase (one is capacitive and the other is inductive),

then there is a real solution for Rcrit. The boundary between ZVS and ZCS

operation is then given by R = Rcrit.

Note that R = || Zo0 || corresponds to operation at matched load with maximum

output power. The boundary is expressed in terms of this matched load

impedance, and the ratio Zi∞ / Zi0.

ECEN 581736

LCC example

f > f∞: ZVS occurs for all R

f < f0: ZCS occurs for all R

f0 < f < f∞, ZVS occurs for

R< Rcrit, and ZCS occurs for

R> Rcrit.

Note that R = || Zo0 ||

corresponds to operation at

matched load with maximum

output power. The boundary is

expressed in terms of this

matched load impedance, and

the ratio Zi∞ / Zi0.


ECEN 581737

LCC example, continued

Typical dependence of Rcrit and matched-load impedance || Zo0 || on frequency f, LCC example.

Typical dependence of tank input impedance phase vs. load R and frequency, LCC example.

ECEN 581738

19.4.4 Design Example

Select resonant tank elements to design a resonant inverter that meets the following

requirements:

• Switching frequency fs = 100 kHz

• Input voltage Vg = 160 V

• Inverter is capable of producing a peak open circuit output voltage of 400 V

• Inverter can produce a nominal output of 150 Vrms at 25 W


ECEN 581739

Solve for the output characteristic (ellipse)

that meets requirements

ECEN 581740

Numerical values

The required short-circuit current can be found by solving the elliptical output characteristic for Isc:

hence

Use the requirements to evaluate the above:


ECEN 581741

Open circuit magnitude response

The requirements imply that the inverter tank circuit have an open-circuit

magnitude response:

Note that Voc need not have been given as a requirement, we can solve the elliptical relationship, and therefore find Voc given any two required operating points of ellipse. E.g. Isc could have been a requirement instead of Voc

ECEN 581742

Solve for matched load

(output impedance magnitude)

Matched load therefore occurs at the operating point

Hence the tank should be designed such that its output impedance is


ECEN 581743

Solving for the tank elements

to give required ||Zo0|| and ||Hinf||

Design an LCC tank network for this example

The impedances of the series and shunt branches can be represented by the reactances

ECEN 581744

Analysis in terms of Xs and Xp

The transfer function is given by the voltage divider equation:

The output impedance is given by the parallel combination:

Solve for Xs and Xp:


ECEN 581745

Discussion

Choice of series branch elements

The series branch is comprised of two elements L and Cs, but there is only one

design parameter: Xs = 733 Ω. Hence, there is an additional degree of

freedom, and one of the elements can be arbitrarily chosen.

This occurs because the requirements are specified at only one operating

frequency. Any choice of L and Cs, that satisfies Xs = 733 Ω will meet the

requirements, but the behavior at switching frequencies other than 100 kHz

will differ.

Given a choice for Cs, L must be chosen according to:

For example, Cs = 3Cp = 3.2 nF leads to L = 1.96 mH

ECEN 581746

Rcrit

For the LCC tank network chosen, Rcrit is determined by the parameters of the

output ellipse, i.e., by the specification of Vg, Voc, and Isc. Note that Zo∞ is

equal to jXp. One can find the following expression for Rcrit:

Since Zo0 and H ∞ are determined uniquely by the operating point requirements, then Rcrit is also. Other, more complex tank circuits may have more degrees of freedom that allow Rcrit to be independently chosen.

Evaluation of the above equation leads to Rcrit = 1466 Ω. Hence ZVS for R < 1466 Ω, and the nominal operating point with R = 900 Ω has ZVS.


ECEN 581747

Ellipse again with Rcrit, Rmatched, and Rnom

showing ZVS and ZCS

ECEN 581748

Converter performance

For this design, the salient tank frequencies are

(note that fs is nearly equal to fm, so the transistor

current should be nearly independent of load)

The open-circuit tank input impedance is

So when the load is open-circuited, the transistor current is

Similar calculations for a short-circuited load lead to


ECEN 581749

Extending ZVS range

Documents

19.3 Soft switching in resonant convertersecee.colorado.edu/~ecen5817/lectures/L5_ECEN5817_notes.pdf · 19.3 Soft switching in resonant converters ... Resonant Inverter Design