innovation tower, hk polytechnic university … · 2016-03-07 · hong kong polytechnic university...

Hong Kong, February 2016

The Role of Circuit Theory in Power Electronics: Methods and Applications

Prof C K Michael Tse Dept. of Electronic and Information Engineering, Hong Kong Polytechnic University

Innovation Tower, HK Polytechnic University completed 2013, by Zahi Hadid

Michael Tse, Hong Kong Polytechnic University

Apple rumour

2


Moving computers

3


Opportunities in power electronics

❖ If 5% of our cars became electric, the demand on recharging systems would be tremendous!

❖ Portable devices may also change the way we power them.

❖ Lightings may drive future distribution to DC.

4


How do we make our work more effective?

❖ Circuit, control and system theories are central to power electronics development, but yet much of the basics has been forgotten. Efforts in reestablishing “new” methods and “concepts” were unnecessary.

5http://www.digdang.com/image/


Exposition through application examples

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Circuit and system theory Application example (current work)

Duality LED drivers

Input resistance PFC converters

Power flow analysis / 3-port circuit PFC power supplies

Kirchhoff’s laws Interconnected converters

Filter theory Deign for EMI

Resonant circuit analysis Wireless power transfer

Case 1

Circuit dualityA concept we learned in basic circuit course, but is mostly forgotten. Many unnecessary redevelopments could have been avoided if free use of duality has been borne in mind.


Duality: a forgotten tool

❖ Duality — A concept taught in undergraduate year 1 circuit theory course.

8

Circuit G Dual circuit G’

Voltage Current

Current Voltage

Resistor Conductor

Conductor Resistor

Inductor Capacitor

Capacitor Inductor

Open switch Closed switch

Closed switch Open switch

Duty cycle D 1 – D

GG’


DC-DC converters and their duals❖ Buck converter :

❖ Dual buck converter :

❖ All properties remain the same after duality transform.

9

+− IoutIinVin Vout

+

-

D =

output voltage

input voltage

=

Vout

Vin

1�D =

output current

input current

=

Iout

Iin

dual


Dual converters as current converters

10

+−

+−

+−

+

-

-

+

+

-

+

+

+

Buck

Buck-boost

Boost

Voltage converters Current converters


Dual operation

11

+−

+

-

+

DT(1−D)T

IL

DT(1−D)T

VC

filtering reactanceconverter

VcIL

ON becomes OFF; OFF becomes ON.


Voltage input termination / load termination

❖ Duty cycle is now controlling the current ratio of the input and output.

❖ The two terminating inductors are serving as filters, not energy storage in the converter sense.

❖ This is NOT a boost converter followed by a lowpass filter, unless the values of the L and C have been chosen wrongly!

12

++−

++−


LED as a voltage load❖ When the load is a voltage

source, e.g., solid-state lighting device, the driver should deliver controllable current to the load.

❖ Also, for LED, the current defines the brightness.

13

+−

+−

+−

driver driver

LED LED

http://duckhits.com/


+−

Kirchhoff’s law says no voltage source!

❖ KVL prohibits voltage sources connected around a loop.

❖ Current converters are relevant to LED driver design.

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X+−

+−

+−

driver driver

LED LEDX


+−

DC-DCconverter

LED

Some basic questions

❖ Can LED be driven by a voltage source?

❖ Can LED be driven by a dc-dc voltage converter (buck, buck-boost or boost converter)?

❖ Can intensity be changed by duty cycle adjustment using a dc-dc voltage converter?

15

?


+−

DC-DCconverter

LEDVoVIN

r

VLED

Inadequacy of one DC-DC converter

❖ Duty cycle controls the output voltage only!

❖ If input voltage is constant, then the duty cycle is already FIXED.

❖ Current control is almost impossible, or through a very small resistance

16

ILED =Vo

� VLED

r

Vo

= F (D)VIN

❖ A DC-DC converter is inadequate (unsuitable) for driving LED.


Dual (current) converter is the choice

❖ If a dual DC-DC converter is used, duty cycle now controls the output current directly.

❖ The question is how to supply an input current.

❖ The input source is mostly voltage.

❖ Feedback adjusts duty cycle for dimming.

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+− DC-DC

converter

LEDVIN VLEDDual

Io

IIN?

Io

= F (1�D)IIN

❖ Suppose at half brightness, output current is halved. If input is a voltage source, the input current will be halved as well.


Driving LED

❖ Suppose input voltage fluctuates. The duty cycle can be used to regulate output current.

❖ Suppose at half brightness, output current is required to be halved. If input is a constant voltage source, the input current should be halved as well.

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+− DC-DC

converter

LEDVIN VLEDDual

Io

IIN

Feedback

c

duty cycle control


LED power driver

❖ Two-stage power supply is the solution.

❖ A front stage provides a current source.

❖ A current converter stage drives the LED.

❖ This forms the basic guiding principle for design.

19

+−

+−

front stagedriver

LED

current converter


An old circuit revisited

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PFC converter based on current converters (2003) becomes relevant for LED loads

Reference: C.K. Tse, Y.M. Lai, R.J. Xie and M.H.L. Chow, "Application of duality principle to synthesis of single-stage power-factor-correction voltage regulators," International Journal of Circuit Theory and Applications, vol. 31, no. 6, pp. 555-570, November 2003.


Duality-based converter design for LED loads

❖ Duty cycle controls current output directly.

❖ DCM operation in current dual mode can achieve PFC, as proven.

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C.K. Tse, Y.M. Lai, R.J. Xie and M.H.L. Chow, "Application of duality principle to synthesis of single-stage power-factor-correction voltage regulators," International Journal of Circuit Theory and Applications, vol. 31, no. 6, pp. 555-570, November 2003.


Opportunity and challenge❖ The advent of solid-state lightings

and renewable sources has opened up new opportunities and created new challenges in the design of current source converters as well as deriving power from non-voltage sources.

❖ Converter design with different source terminations will be a topic fundamental to circuit theory which provides a very rich and effective set of tools.

22http://forceofthesun.com/category/renewable-energy

Case 2

Resistor propertyWe learned about Ohm’s law in secondary school, and yet it is just all we need to understand power factor correction.


Review of PFC

❖ Research in 1990s, through 2000s, and still continuing

❖ Major achievements:

❖ DCM achieves natural PFC

❖ CCM requires special current programming to make input current waveform follow the input voltage’s

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Converter

input current

input voltage


Back to Ohm’s law

❖ Voltage is proportional to current.

❖ If voltage is a sine wave, current will be the same sine wave, with zero phase difference!

❖ The resistor is a perfect unity power factor device.

25http://voltsnbolts.wordpress.com/2014/09/05


Resistor as input impedance❖ If we start with the basic

circuit requirement, then PFC is just pure resistive input impedance.

❖ Any PFC converter must therefore present itself as a resistor to the input voltage.

❖ This requirement is only relevant for the 50Hz sine input, and the pure resistance is only required for low-frequency range.

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input current

input voltage


DC-DC converters as PFC

❖ PFC can be achieved by

❖ any switching sequence that can prevent the input from “seeing” any inductive or capacitive element.

❖ The solution is to destroy the inductors and capacitors as reactive elements at low frequencies.

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Inductors and capacitors

❖ An inductor does not have jumped current as v = L di/dt must be finite.

❖ An inductor forming a cutset with open switch(es) cyclically at a much higher frequency than 50HZ is NOT an inductor at 50Hz because

❖ Similarly for capacitors.

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IL

IL = 0 periodically

cutset

open switch

open switch


DCM converters

❖ DC-DC converters in DCM are exactly having such an inductor.

❖ Therefore, DCM converters are natural PFC converters.

❖ For a buck-boost converter operating in DCM, the equivalent low-frequency input resistance is

29

+− IL

IL

t

Rin =2L

D2T

Reference: C.K. Tse, "Zero-Order Switching Networks and Their Applications to Power Factor Correction in Switching Converters," IEEE Transactions on Circuits and Systems I, vol. 44, no. 8, pp. 667-675, August 1997.


DCM boost converter❖ The boost converter is not as

perfect as the buck-boost converter because the input “sees” the output in some interval of time.

❖ Still it is a very good PFC converter as its low-frequency input resistance is

30

+−

IL

IL

t

Rin =2L

D2T

✓1� VIN

VO

◆


Direct destruction of inductor’s dynamics

❖ If we make the inductor current dependent on the input voltage (50Hz), the inductor is no longer reactive at 50Hz.

❖ The solution is direct current programming (CCM or DCM).

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Standard implementation

❖ CCM

❖ Current-programmed inductor, following the input voltage waveform, with power balance feedback.

❖ PFC is achieved.

32

CK Michael Tse, January 201124

Practical PFC system

Always require tightly regulated DC output, in addition to PFC.

Can one converter do the jobs of PFC and tight output regulation?

No!

because we need a low-frequency power buffer!€

ˆ v inˆ i in sin2ωm t Po

PFC converter with tightly

regulated output


Power buffer

In general we need a power buffer to achieve PFC and tight output regulation simultaneously.

3-port model

How many basic converters do we need?

Answer: TWO.(For a rigorous proof, seeC. K. Tse and M. H. L. Chow, “Theoretical study of Switching Converters with Power Factor Correction and Voltage Regulation,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 7, pp. 1047-1055, July 2000.)


A different question

Probably, the question of interest to the engineers is HOW THE TWO CONVERTERS ARE POSSIBLY ARRANGED?

Best known configuration:

PFC dc/dc

cascade structure

low-freq power buffer


Cascade structure

Obviously, the problem of the cascade structure is the double processing of power in the two stages, degrading the efficiency.

Naturally, we wish to examine the way power is being processed.

PFC dc/dc

cascade structure

Pin

η1 = 90% η2 = 90%0.81Pin

η1η2 = 81%


Power processing

Let’s start from the basics again.

In what ways power can flow within the 3-port model?

I II III


Power processing

Let’s try fitting in the three types of flows.

Type I and Type I


Power processing

Another try!

Type I , Type II


Power processing

Another try!

Type I , Type III


Power processing

Another try!

Type II , Type III


Power processing possibilities

To fulfill the power flow conditions of the 3-port model, we have 4 power flow possibilities.


Completing the structure

Finally, we place 1 converter to each path.

1 2 12

and 2 others!

12

and 2 others!

12

and 8 others!

CK Michael Tse, January 2011C. K. Tse: Circuit Theory of PFC 36

The sixteen configurationsFitting in the two basic converters, we clearly see 16 possible structures.


Theoretical efficiency

We can theoretically compare the efficiencies of the 16 structures. Obviously, the cascade (type I-I) is the poorest, and the others are always better since power is not doubly processed.

For example, consider the I-IIA structure.Suppose k is the ratio of power split.

€

efficiency = kη1η2 + (1− k)η2 = η1η2 + (1− k)η1(1−η2) > η1η2

k

1–k

We shall see that this k is a very important parameter. If k is too large, the circuit resembles the cascade structure, hence no efficiency advantage. But if it is too small, P.F. degrades.


Theoretical efficiency

We can theoretically compare the efficiencies of the 16 structures. Obviously, the cascade (type I-I) is the poorest, and the others are always better since power is not doubly processed.


Synthesis procedure

For a detailed procedure, seeC. K. Tse, M. H. L. Chow and M. K. H. Cheung, “A Family of PFC Voltage Regulator Configurations with Reduced Redundant Power Processing,” IEEE Transactions on Power Electronics, vol. 16, no. 6, pp. 794-802, November 2001. (IEEE Transactions Best Paper Award)

In brief, we insert suitable converters in

the respective positions (guided by certain

circuit rules), and we will end up with a PFC voltage regulator of the desired characteristics.


The choice

It turns out that not all converters can be inserted. No free choice! This table shows the allowable configurations.


Synthesis examples

Type I-IIB using a buck-boost and a buck converter.


Synthesis examples

Type I-IIA using a buck-boost and a buck converter.


and more…

Type I-IIIB using buck-boost converters. Type I-IIIA using a buck-boost and a buck converter.


Practical design

Various configurations tested experimentally, e.g., see C. K. Tse, M. H. L. Chow and M. K. H. Cheung, “A Family of PFC Voltage Regulator Configurations with Reduced Redundant Power Processing,” IEEE Transactions on Power Electronics, vol. 16, no. 6, pp. 794-802, November 2001.

MORE: M.K.H. Cheung, M.H.L. Chow and C.K. Tse, “Practical Design and Evaluation of a 1 kW PFC Power Supply Based on Reduced Redundant Power Processing Principle,” IEEE Transactions on Industrial Electronics, vol. 55, no. 2, pp. 665-673, February 2008.

CK Michael Tse, January 2011 48

Efficiency “claims”

Earlier on, we said that the non-cascade structure is supposed to be more efficient.

This is indeed true.Note we are not interested in the absolute efficiencies, but rather look at the comparisons with the cascade structure! Vin = 160 V Vin = 190 V

Vin = 230 VVin = 200 V


Problems

We have seen the comparison of the cascade (type I-I) and non-cascade (all other types) structures.

All non-cascade structures involve a power split. The design parameter is k.

We observe that there is a trade off of PFC performance and efficiency. We mentioned (in slide #37) that the power split ratio k is important!

Can we optimize the design? What k gives best trade-off?

k

1–k


Can we optimize?

• Yes, for some, and no for some others

C. K. Tse: Circuit Theory of PFC 50

Regulation can be optimized, but pf sacrificed.

Pf can be optimized,but regulation sacrificed.

M.K.H. Cheung, M.H.L. Chow and C.K. Tse, “Practical Design and Evaluation of a 1 kW PFC Power Supply Based on Reduced Redundant Power Processing Principle,” IEEE Transactions on Industrial Electronics, vol. 55, no. 2, pp. 665-673, February 2008.

M.K.H. Cheung, M.H.L. Chow and C.K. Tse, “Design and performance considerations of PFC switching regulators based on noncascading structures,” IEEE Transactions on Power Electronics, vol. 57, no. 11, pp. 3730-3745, November 2010.

Case 3

Kirchhoff’s lawsKirchhoff’s laws are fundamental in circuit theory, and they form guiding principles for connecting between converters.


Parallel-parallel Series-parallel

Parallel-series Series-series

Inter-connected converters❖ Interconnected converters ❖ Parallel - lower current

stress ❖ Input parallel

connected ❖ Output parallel

connected ❖ Series - lower voltage

stress ❖ Input series connected ❖ Output series

connected

57

Question: How to control individual converters?


Converters are voltage or current sources

❖ Basics:

❖ Converters with regulated output voltage are voltage sources.

❖ Converters with controlled output current are current sources.

58

+−=DC-DC

DC-DCC

=


The problem of paralleling

59

❖ Design problem:

❖ Parallel converters to supply larger current to the load, hence reducing current stress in individual converters.

❖ How to connect converters in parallel?

❖ Current sharing among converters. I1 = I2 = I3

converter 1

converter 2

converter 3

I1

I3

I2Vo

+

-


KVL and KCL

❖ KVL implies:

❖ Voltage sources are not allowed to be connected in parallel.

❖ KCL implies:

❖ Current sources are not allowed to be connected in series.

60

+−

+−

+−

+−

+−+−

+−+−

+−

✔

✘

✔

✔

✔

✘


Parallel-connected converters

❖ Parallel connected converters for high current output applications

❖ Control challenge is: sharing of output currents

❖ PROBLEM: If each converter attempts to produce a regulated output voltage, we are trying put voltage sources in parallel ! This is a fundamental conflict!

61

Perfectly regulated voltage converter is like an independent voltage source. Connecting voltage sources in parallel violates KVL, and should not be allowed. Even if the voltages have the same voltage magnitude, currents are theoretically not solvable.

+−

+−

+−

+−

????load

vovin converter


What should be prohibited?

❖ Putting “more than one converters having regulated output voltages” in parallel is theoretically faulty and should be prohibited!

62

VM

convertervo

vin

VM

convertervo

vin

VM

convertervo

vin

tightly regulated output voltage

load

+−

+−

+−

voltage-modeconverters

✘


Still tolerable in practice❖ Conventional connection (used widely

in practice called droop method):

❖ Each converter is output regulated.

❖ Parallel connection of two or more converters to deliver large currents.

❖ Current sharing control is applied mandatorily.

63

+−

+−

+−

+−

load

converters

Current sharing is controlled and maintained in individual converters through the simple voltage feedback which automatically detects the voltage drops across the resistances and regulates the output voltage slightly. This is the simple DROOP METHOD, involving just connecting the “poorly” voltage-regulated converters.

feedback control


Connection re-examined

64

...

V1Vo

+

-

V2 Vn

✔ ✔

✘

✤ How should we connect the converters if they are controlled as voltage/current sources?

✤ Then, it would become straightforward to select the appropriate control strategies.


Possible configurations

65

Type I

Type II

Type III

✔

✔

✔


General classification

66

Definition: Current sharing loop is defined as one that takes output current information from one or more constituent converters to produce a current control signal which is used for controlling an individual converter.


Type I Control without current sharing loop, i.e., droop method


Type I Control with current sharing loop

68


Type II Control without current sharing loop

• For Type II connection, only one converter serves as a voltage source (more precisely a Thevenin source), and all others behave as current (Norton) sources.

• There is a main voltage controller to regulate the output voltage tightly. • All current sources only need to follow a common current control signal to achieve current sharing.

69


Type II Control with current sharing loop


Type III Control without current sharing loop

For Type III connection, all converters are current (Norton) sources.

71


Type III Control with current sharing loop


Results

✤ Output voltage versus output current for Type I scheme without a current-sharing loop. (a) Vref1 = Vref2 = 2.5 V, rcon1 = 0.001Ω, rcon2 = 0.05Ω, RCS1 = RCS2 = 150 kΩ; (b) Vref1 = Vref2 = 2.5 V, rcon1 = 0.001Ω, rcon2 = 0.05Ω, RCS1 = RCS2 = 50 kΩ; (c) Vref1 = 2.4 V, Vref2 = 2.5 V, rcon1 = rcon2 = 0.025Ω, RCS1 = RCS2 = 150 kΩ; (d) Vref1 =2.4 V, Vref2 = 2.5 V, rcon1 = rcon2 = 0.025Ω, RCS1 = RCS2 = 50 kΩ.

73


Results

✤ Output voltage versus output current for Type I scheme with a current-sharing loop. (a) Vref1 = Vref2 = 2.5 V, rcon1 = 0.001 Ω, rcon2 = 0.05 Ω; (b) Vref1 = 2.4 V, Vref2 = 2.5 V, rcon1 = rcon2 = 0.001 Ω.

74


Results

✤ Output voltage versus output current for Type II scheme at Vref = 2.5 V, rcon1 = 0.001 Ω, rcon2 = 0.05 Ω, (a) without a current-sharing loop; (b) with a current-sharing loop.

75


Results

✤ Output voltage versus output current for Type III scheme at Vref = 2.5 V, rcon1 = 0.001 Ω, rcon2 = 0.05 Ω, (a) without a current-sharing loop; (b) with a current-sharing loop.

76


General comparison❖ Type I schemes are simple but suffer fundamentally from paralleling voltage

sources. The adjustment range for current sharing is small since each constituent converter is designed primarily to regulate its output voltage.

❖ Type II schemes are theoretically more viable as there is only one voltage source paralleling with current sources. The dynamics of the voltage regulation thus depends on the control method being employed by the voltage regulating loop. Current-sharing performance is generally much better and the control implementation is simpler, compared to Type I schemes.

❖ Type III schemes are generally best in terms of current sharing as all converters are fundamentally current controlled. The voltage regulation is only executed at the load side (only one voltage loop to keep tight regulation). Both voltage regulation and current sharing are excellent.

77


Further reading❖ Y. Huang and C.K. Tse, "Circuit theoretic

classification of parallel connected dc/dc converters," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 54, no. 5, pp. 1099-1108, May 2007 (nominated for Best Paper prize).

❖ Y. Huang, C.K. Tse and X. Ruan, "General control considerations for input-series connected dc/dc converters," IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 56, no. 6, pp. 1286-1296, June 2009.

78

Case 4

LCR circuitsInductors, capacitors and resistors form resonant circuits that are relevant to a wide range of design applications


Inductive power transfer

❖ IPT is a recent hot topic in research.

❖ But its analytical root is very old:

❖ the transformer theory

80

https://www.youtube.com/watch?v=2ODW-ntPHSU


Transformer

❖ The ideal transformer is simply transforming voltage and current:

❖ but the real device has magnetising and leakage inductances.

81

v2i2

�=

n 00 1/n

� v1i1

�

v1 v2+

−

+

− 1:n

i2i1

v2v1++

− −

i1 i2

ideal transformer

coupled inductors


Equivalent model

82

M = mutual inductance

k = coupling coe�cient =

MpLsLp

+−jωMis

LpRp ip

+− jωMip

RsLsisM

Ns

Np= n = turns ratio =

sLs

Lp


Power transfer

❖ Problem 1: If leakage is large, not much voltage can be transferred to the load!

❖ Problem 2: There is resistive loss in the circuit. Can efficiency be maximised?

83

v1 v2+

−

+

− 1:n

R/n2

R

R/n2

rloss

v1 v2+

−

+

− 1:n

transformer reflected to primary


LC circuit❖ An inductor has its reactance

proportional to frequency, whereas a capacitor has its reactance inversely proportional to frequency. They are opposite in sign.

❖ If an L and a C are connected in series, the reactance can be cancelled (zero) at a particular frequency.

84

Zs = j!L+1

j!C= j

✓!L� 1

!C

◆

Zs = 0 if ! =1pLC

❖ If an L and a C are connected in parallel, the admittance can be cancelled (zero) at a particular frequency.

Yp = j!C +1

j!L= j

✓!C � 1

!L

◆

Yp = 0 if ! =1pLC

Zs Yp

L

C

L C


Compensation

❖ Add C to cancel the leakage at a specific frequency, so that the entire voltage can be applied to the load.

❖ Reactive power reduces to zero. No wasted current component.

❖ All active power goes to the load.

85

L

RVin

CIin

Vs

VR

Vs = 0 at !p


General configuration

❖ Primary side and secondary side compensations to achieve minimum reactive power.

❖ Other parameters:

❖ Quality factors of windings

❖ Circuit resistance

❖ Coupling coefficient of transformer

86

primarycompensation

secondarycompensation

compensated at !p compensated at !s


Efficiency

87

+−

ωMis

LpRpCpip

+−

ωMip

CsRsLs

R

is

⌘p =<{Zr}

Rp + <{Zr}⌘s =

<{Zs}�Rs

<{Zr}

where Zr is the total impedance on the primary side

where Zs is the total impedance on the secondary side

⌘ = ⌘p⌘s


The optimization problem❖ Optimization problem

❖ Find the operating frequency that achieves compensation, i.e., minimizes reactive power

❖ AND optimizes efficiency.

88

d⌘

d!= 0 ) ! = !M

! = !s

!M =!sq

1� 12Q2

o

Qo

=Q

s

QLS

Qs

+QLS

QLS

=1

R

rLs

Cs

where

and Qs is sec. winding quality factor.

Reference: W. Zhang, S.C. Wong, C.K. Tse and Q. Chen, "Design for efficiency optimization and voltage controllability of series-series compensated inductive power transfer systems," IEEE Transactions on Power Electronics, vol. 29, no. 1, pp. 191-200, Jan 2014.

For series compensation:


Further optimisation

❖ For low coupling (k < 0.5), optimal efficiency changes with load.

❖ Is there an optimal point where the frequency does not change with the load?

89

Efficiency at ! = !M

heavier load (smaller RL)

optimal efficiency


Compensation at max efficiency

❖ We do have a range of loads, near the point of peak efficiency, for which the choice of can overlap with

90

!s ⇡ !M

!M

!s


Challenge

❖ LED loads

❖ Constant current output OR constant transconductance

❖ Can we design the circuit such that we can achieve optimal efficiency, compensation, and constant transconductance (load independent)?

91


Further IPT research❖ In view of renewable sources and solid state loads, input sources

can be V or I, and output loads can be V or I. Hence, four cases should be considered for optimization:

❖ Voltage to voltage

❖ Voltage to current

❖ Current to current

❖ Current to voltage

92

VIN VOUT

IOUTIIN

+−

loosely coupled


Further reading❖ W. Zhang, S.C. Wong, C.K. Tse and Q. Chen, "Load-

independent duality of current and voltage outputs of a series or parallel compensated inductive power transfer converter with optimized efficiency," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 3, no. 1, pp. 137-146, March 2015.

❖ W. Zhang, S.C. Wong, C.K. Tse and Q. Chen, "Analysis and comparison of secondary series and parallel compensated inductive power transfer systems operating for optimal efficiency and load-independent voltage- transfer ratio," IEEE Transactions on Power Electronics, vol. 29, no. 6, pp. 2979–2990, June 2014.

❖ J. Hou, Q. Chen. X. Ren, X. Ruan, S. C. Wong and C. K. Tse, “Precise characteristics analysis of series/series- parallel compensated contactless resonant converter,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 3, no. 1, 101-110, March 2015.

❖ J. Hou, Q. Chen,S.C. Wong,C.K. Tse and X. Ruan, “Analysis and control of series/series-parallel compensated resonant converters for contactless power transfer,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 3, no. 1, pp. 124–136, March 2015.

93


Volume 14, Number 3Third Quarter 2014ISSN 1531-636X

Conclusion❖ University curricula are densely

packed with applications, and foundational circuit training is often sacrificed so as to release more curriculum space for other purposes.

❖ New applications continue to emerge, requiring creative design and analysis methods. Circuits and systems theory provides the foundation of developing the essential concepts.

❖ It is essential that circuits and systems theories are taught to the needed level of relevance to support developments of new applications.

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Thank You

innovation tower, hk polytechnic university … · 2016-03-07 · hong kong polytechnic university...

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