Abstract—Power transformer is one of the most complex partsof power converters. The complicated behavior of the transformeris usually neglected in the power converter analysis and a simplemodel is mostly used to analyze the converter. This paper presentsa precise analysis of a fifth-order resonant converter which has in-corporated the resonant circuit into the transformer. The derivedmodel, which is based on the accurate model of the power trans-former, can fully predict the behavior of the fifth-order resonantconverter. The proposed fifth-order resonant converter is able toeffectively reduce the range of phase-shift angle from no load to fullload for a fixed-frequency phase-shift control approach. Therefore,the converter is able to operate under zero voltage switching dur-ing entire load range with a fixed-frequency control method. Also,the proposed converter offers a high gain which leads to a lowertransformer turns ratio. A 10-kVDC, 1.1-kW prototype has beenprepared to evaluate the performance of the proposed converter.The experimental results exhibit the excellent accuracy of the pro-posed model and the superiority of the performance compared tothe lower order resonant converters, especially for high-voltageapplications.
Index Terms—Fifth-order resonant converter, high-voltage dcpower supply, phase-shift fixed-frequency control approach, steadystate analysis, zero voltage switching (ZVS) operation.
NOMENCLATURE
Cn Resonant capacitance ratio (Cn = Cp/Cs).CP Parallel resonant capacitance (F).CS Series resonant capacitance (F).Cw,s Winding capacitance of a transformer secondary
side (transferred to the primary) (F).d Duty cycle (in percent).f0 Series resonant frequency (Hz).fs Switching frequency (Hz).
Manuscript received December 21, 2011; revised March 3, 2012 and April10, 2012; accepted May 4, 2012. Date of current version September 11, 2012.Recommended for publication by Associate Editor M. Vitelli.
N. Shafiei is with the Department of Electrical Engineering, Na-jafAbad Branch, Islamic Azad University, Isfahan 81966-75954, Iran (e-mail:[email protected]).
M. Pahlevaninezhad, A. Bakhshai, and P. Jain are with the ePOWER, Depart-ment of Electrical and Computer Engineering, Queens University, Kingston, ONK7L 3N6, Canada (e-mail: [email protected]; [email protected];[email protected]).
H. Farzanehfard is with the Department of Electrical and Computer Engi-neering, Isfahan University of Technology, Isfahan 84156-83111, Iran (e-mail:[email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPEL.2012.2200301
ILPPeak current of the parallel resonant inductance(A).
ILP ,A Coefficient of the Fourier sinusoidal term of ILP
at fs .ILP ,B Coefficient of the Fourier cosinusoidal term of ILp
at fs .ILS 1 Peak current of the first series resonant inductance
(A).ILS 1 ,A Coefficient of the Fourier sinusoidal term of ILS 1
at fs .ILS 1 ,B Coefficient of the Fourier cosinusoidal term of ILS 1
at fs .ILS 2 Peak current of the second series resonant induc-
tance (A).ILS 2 , A
Coefficient of the Fourier sinusoidal term of ILS 2
at fs .ILS 2 ,B Coefficient of the Fourier cosinusoidal term of ILS 2
at fs .I ′out DC output current (A).Lext External series inductance (H).Llk,p Transformer primary leakage inductance (H).Llk,s Transformer secondary leakage inductance (H).Lm Transformer magnetizing inductance (H).Ln Resonant inductance ratio (Ln = LS1/LP ).Loc-P Reflected inductance of the transformer secondary
side under the primary open-circuit condition.Loc-S Inductance of the transformer primary side under
the secondary open-circuit condition.LP Parallel resonant inductance (H).Ls Series resonant inductance ratio (Ls = LS1/LS2).Lsc-S Inductance of the transformer primary side under
the secondary short-circuit condition.LS1 First series resonant inductance (H).LS2 Second series resonant inductance (H).m Slope of the transformer frequency response at low
frequencies.n Transformer turns ratio (Ns/Np).QL Loaded quality factor.R′
L Load resistance (kΩ).s Laplace frequency domain.VCP
Clamped voltage of parallel capacitor (V).V̂CP
Fundamental harmonic component of parallel res-onant capacitance voltage.
VCP ,A Coefficient of the Fourier sinusoidal term of V̂CP
at fs .VCP ,B Coefficient of the Fourier cosinusoidal term of V̂CP
86 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013
Vin DC input voltage (V).V ′
out DC output voltage (kV).Z0 Characteristic impedance (Ω).δ Second series inductance current angle.ϕ First series inductance current angle.φ Parallel inductance current angle.ψ Rectifier nonconduction angle.σ ZVS angle.
I. INTRODUCTION
R ESONANT converters are widely used in different appli-cations where soft switching is of great importance [1],
[2]. Especially in high-voltage applications, resonant convert-ers are suitable topologies since they can effectively absorb andtake advantage of parasitic components, which are considerabledue to the high-voltage transformers used to provide the volt-age gain and galvanic isolation [3]–[9]. The power transformer,used in switching converters, is one of the most complicatedcomponents in the converter analysis. In order to analyze theconverter, this transformer is usually modeled by an equiva-lent circuit based on the operating frequency of the converterand transformer configuration. Fig. 1 shows different standardequivalent circuits of the transformer that have been used in theliterature for converter analysis. Fig. 1(a) shows the first-ordermodel of the transformer which consists of a leakage inductancein series with an ideal transformer. This model is widely usedfor converters with low switching frequency or with low out-put voltage [10], [11]. In [12]–[16], the magnetizing inductanceis considered in the transformer model to form a second-ordermodel for the transformer as shown in Fig. 1(b). In [17] and [18],the third-order model as shown in Fig. 1(c) is adopted to ana-lyze the transformer. This equivalent circuit separately modelsboth the leakage inductance of the primary side and the sec-ondary side. In [18], the impacts of the secondary-side leakageinductance on a resonant converter are analyzed. The equivalentcircuit, shown in Fig. 1(c), is mostly used for analysis of LLCresonant converters [19], [20]. The three equivalent circuits ofthe transformer, illustrated in Fig. 1(a)–(c), are accurate enoughto predict the behavior of a converter operating in low-frequencyor low-voltage applications. However, these models fail to pre-cisely predict the behavior of the transformer in high-frequency,high-voltage power converters. In [4] and [6], a second-orderequivalent circuit is used to analyze the behavior of the trans-former in high-voltage applications. This equivalent circuit isshown in Fig. 1(d). The aforementioned references confirm thatthe equivalent capacitance of the transformer has considerableimpact on the behavior of the converter especially for high-voltage applications. Another third-order equivalent circuit ofa transformer, shown in Fig. 1(e), is used in [9] to analyze afourth-order resonant converter with a capacitive output filter.
The most comprehensive equivalent circuit of the transformeris shown in Fig. 2(a), which is the IEEE standard model [21],[22]. This model is adopted in order to analyze a pulse trans-former for a rectangular pulse shape with very fast rise time. Inaddition, this model is utilized for electromagnetic interference(EMI) analysis in high-frequency power converters [23].
In high-voltage applications, due to the structure of the trans-former, a very large turns ratio is inevitable. This leads to ahigh value of the equivalent secondary capacitance. Further-more, the primary winding and the secondary winding are notperfectly coupled due to the distance imposed by the requiredhigh-voltage insulation. The weak coupling leads to a largeleakage inductance that must be modeled on both sides of thetransformer. In this paper, the fourth-order equivalent circuitof the transformer, as shown in Fig. 2(b), is adopted to ana-lyze the proposed converter. This equivalent circuit takes intoaccount the effects of the primary leakage inductance and thesecondary leakage inductance separately. Also, the magnetiz-ing inductance and the equivalent parallel capacitance are in-corporated in this equivalent circuit. The proposed converteris a fifth-order resonant converter, which fully incorporates thetransformer parasitic components into the resonant circuit. Fig. 3shows the fifth-order resonant converter with a capacitive outputfilter. This topology uses a purely capacitive filter at the outputside. This is a great advantage in high-voltage applications, dueto the fact that there are so many issues with the fabrication ofthe inductor at high-voltage output in terms of insulation [4]and [6].
There are two main control techniques used to regulate theoutput voltage of the resonant converters. The first method is thevariable-frequency (VF) control method and the second methodis the fixed-frequency phase-shift control method [1], [24]. Inhigh-voltage applications, the VF technique is not preferablesince the breakdown voltage of the insulation materials used inthe converter significantly degrades with the increase in the fre-quency [25]. Therefore, the fixed-frequency phase-shift controltechnique is well suited for this application. In addition, sincethe range of load variations is very wide in this application(from absolutely no load to full load), the converter should beable to maintain ZVS for the entire range. Thus, the converterrequires the circulating current even at light loads in order tohave ZVS. This imposes a little extra conduction losses imposedby the reactive current, which is more pronounced in light loads.However, maintaining ZVS for light loads is essential in orderto have a reliable operation and a noise-free control/drive cir-cuitry. Also, since the voltage is pretty high in the primary side,the current is pretty low, and the extra conduction losses arenegligible.
The mathematical analysis derived in this paper proves thatthe proposed fifth-order resonant converter can effectively re-duce the range of the phase-shift angle required from no-loadto full-load conditions. Thus, the full-bridge switches in theproposed converter operate under the ZVS condition for the alloperating conditions. The other aspect that should be consid-ered in high-voltage applications is the maximum achievablegain that is produced by the resonant circuit. The analysis ofthe proposed converter demonstrates that the fifth-order reso-nant converter has an inherent gain of more than unity. In thispaper, the precise model of the fifth-order resonant converter isderived. This model is able to accurately describe the behaviorof the converter and proves the features of the converter tailoredfor high-voltage applications.
SHAFIEI et al.: ANALYSIS OF A FIFTH-ORDER RESONANT CONVERTER FOR HIGH-VOLTAGE DC POWER SUPPLIES 87
Fig. 1. First-, second-, and third-order models of the transformer.
Fig. 2. (a) IEEE standard equivalent circuit of a transformer. (b) Simplifiedfourth-order model of the transformer.
This paper is organized as follows. The steady-state analy-sis of the fifth-order resonant converter with a capacitive outputfilter is described in Section II. High-voltage transformer and in-tegrated magnetics are explained in Section III. Soft-switchinganalysis of the proposed fifth-order resonant converter is dis-cussed in Section IV. In Section V, performance and features ofthe proposed converter are verified through experimental results.Also, Section V contains some practical descriptions for imple-mentation of the high-voltage converter. Finally, the features ofthe fifth-order resonant converter for high-voltage applicationsare summarized in Section VI.
II. STEADY-STATE ANALYSIS
Fig. 4 shows the general block diagram of a typical dc/dcresonant converter. According to Fig. 4, the dc/dc resonant con-verter mainly consists of two parts, namely a high-frequencyresonant inverter (high-frequency inverter and resonant circuit)and a high-frequency rectifier.
The resonant inverter is fed by a dc voltage source and actsas a high-frequency sine-wave voltage or current source. Thehigh-frequency rectifier rectifies the high-frequency ac volt-age/current and is driven by a high-frequency ac energy source.If the resonant inverter and high-frequency rectifier are com-patible with each other (the voltage and current waveforms of
the rectifier are in phase), the high-frequency rectifier, outputfilter, and load can be modeled by an equivalent resistance. Theequivalent resistances of the voltage-driven and current-drivenrectifiers are summarized in Fig. 4. In both cases, the dc/acresonant inverter can be analyzed through the first harmonicapproximation (FHA) [1].
However, the FHA method is not quite straightforward forthe proposed resonant converter shown in Fig. 3, because thevoltage of the parallel capacitor is clamped to the output voltageof the converter transferred to the primary side of the trans-former while the power is transferred from the resonant circuitto the output [26]–[29]. In [4], [6], [9], and [27], a mathemati-cal model is proposed for LCC and LCLC resonant converterswith a capacitive output filter. They have used a rectifier com-pensated first harmonic approximation (RCFHA) technique tomodel the output side of the converter. In this technique, insteadof using a purely resistive impedance, a resistive impedance inseries with an imaginary impedance is used to model the com-bination of the rectifier, output filter, and load. The results givenin the aforementioned papers verify the excellent accuracy ofthe RCFHA technique. In this paper, the RCFHA technique isused to analyze the proposed converter. Fig. 5 shows the keywaveforms of the proposed converter.
In all equations, the transformer secondary-side variables(with an apostrophe) are transferred to the primary side (withoutapostrophe). The procedure in this analysis is to find the equiv-alent impedance viewed from different points of the resonanttank through the FHA of the currents and voltages. The FHA ofiLS 1 (t), iLP
(t), and iLS 2 (t) are given by [9]
iLS 1 (t) = ILS 1 sin(ωst − ϕ) (1)
iLP(t) = ILP
sin(ωst − φ) (2)
iLS 2 (t) = iLS 1 − iLP= ILS 2 sin(ωst + δ). (3)
According to Fig. 5, the magnitude of iLS 2 (t) reaches zero atωt = ζ and there is no power flowing to the load. The noncon-duction interval ψ is started from this point as shown in Fig. 5.During this interval, the voltage across the parallel capacitor isgiven by
vCP(θ) = vCP
(ζ) +1
CP ωs
∫ θ
ζ
ILS 2 sin(θ + δ)dθ. (4)
88 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013
Fig. 3. Fifth-order resonant converter with a capacitive output filter.
Fig. 4. DC–DC resonant converter block diagram.
During the nonconduction mode, the voltage across CP is dis-charging from VCP
to −VCP. Once the voltage across CP has
reached −VCPat ωt = ζ + ψ, the output diodes are forward
biased and start conducting; therefore, ψ can be calculated asfollows [18]:
cos ψ = 1 − 2VCPCP ωs
IL S 2
. (5)
According to Fig. 5, while the power is being transferred tothe load through the output rectifier, vCP
(t) is clamped to thereflected output voltage in the primary side of the transformer,whereas vCP
(t) is changed to a sinusoidal form during non-conduction interval. This nonlinear behavior is modeled by anequivalent impedance. Fig. 6 shows the schematic of the out-put side of the converter (including the output rectifier, outputfilter, and load) which is transferred to the primary side of thetransformer along with the three resonant components.
In order to determine the equivalent impedance of this circuitZeq , the first coefficients of the Fourier series of iLS 1 (t), iLP
(t),iLS 2 (t), and vCP
(t) are given by [6]
iLS 1 (t) = ILS 1 ,A sin(ωst) + ILS 1 ,B cos(ωst) (6)
iLP(t) = ILP ,A sin(ωst) + ILP ,B cos(ωst) (7)
iLS 2 (t) = iLS 1 (t) − iLP(t) = ILS 2 ,A sin(ωst)
+ ILS 2 ,B cos(ωst) (8)
vCP(t) = VCP ,A sin(ωst) + VCP ,B cos(ωst). (9)
The first coefficient of the Fourier series of V̂CPis calculated
as
VCP ,A =1π
∫ 2π+ξ
ξ
vCpsin(ωst)d(ωst) (10)
VCP ,A =1
πCP ωs
× (ILS 2 ,A sin2 ψ − ILS 2 ,B (sin ψ cos ψ − ψ)) (11)
VCP ,B =1π
∫ 2π+ξ
ξ
vCpcos(ωst)d(ωst) (12)
VCP ,B =1
πCP ωs
× (ILS 2 ,B sin2 ψ + ILS 2 ,A (sin ψ cos ψ − ψ)). (13)
The equivalent impedance from the parallel capacitor Z ′eq (as
shown in Fig. 6) is calculated using (8), (11), and (13) [6]
Z ′eq =
VCP ,A + jVCP ,B
ILS 2 ,A + jILS 2 ,B= R′
eq + jX ′eq (14)
R′eq =
sin2 ψ
πCP ωs(15)
X ′eq =
πCP
ψ − sin ψ cos ψ. (16)
Now the equivalent impedance of Fig. 6 is calculated asfollows:
Zeq = Req + jXeq = jωsLP
∥∥∥∥(
jωsLS2 + R′eq +
1jωsC ′
eq
).
(17)The final equation is shown in (A1). The equivalent circuit
of the fifth-order resonant converter is shown in Fig. 7. In thiscircuit, the fundamental component of the input voltage vAB 1(t)is given by [1]
vAB 1(t) =4Vin
πsin
(π
2d)
sin(ωst). (18)
SHAFIEI et al.: ANALYSIS OF A FIFTH-ORDER RESONANT CONVERTER FOR HIGH-VOLTAGE DC POWER SUPPLIES 89
Fig. 5. Key waveforms of the proposed converter.
The steady-state analysis of the fifth-order resonant converteris carried out by using the equivalent circuit. The normalizedinput impedance Zin/Z0 is calculated using (A1) and the defini-tions given in (19). The derivation for the normalized impedanceis shown in (A2)
Z0 =√
LS1
CS, ω0 =
1√LS1CS
, ωn =ωs
ω0. (19)
Fig. 6. Output rectifier along with three resonant elements.
Fig. 7. Equivalent circuit of the fifth-order resonant converter with a capacitiveoutput filter.
The amplitude of the input resonant circuit current (switchescurrent) is obtained using (18) and (A2) as follows:
|ILS 1 | =4Vin sin (πd/2)π |Zin(jωn )| . (20)
The output current is the average value of the output rectifiercurrent. Thus, the output current and the output voltage are givenby
Iout =12π
(∫ π+ζ
ζ+ψ
iLS 2 d(ωst) +∫ 2π+ζ
π+ζ+ψ
iLS 2 d(ωst))
(21)
Iout =ILS 2
π(1 + cos ψ) (22)
Vout = RL.Iout =RLILS 2
π(1 + cos ψ). (23)
In order to calculate the output voltage, ILS 2 and ψ are re-quired. The value of ψ is calculated using the normalized pa-rameters given in (19) as follows [18]:
cos ψ =π − 2CnQLωn
π + 2CnQLωn(24)
QL =RL
Z0. (25)
The voltages across the parallel resonant inductor vLP(t) and
the Fourier series of vLP(t) are given by
vLP(t) = LS2
diLS 2
dt+ vCP
(t) (26)
vLP(t) = VLP ,A sin(ωst) + VLP ,B cos(ωst). (27)
According to (6)–(9), and (26) and (27), the following equal-ities are derived:{
ILS 1 ,A = ILP ,A + ILS 2 ,A
ILS 1 ,B = ILP ,B + ILS 2 ,B(28)
{VLP , A
=−LS2ωsILS 2 , B+VCP , A
, VLP , A=−LP ωsILP , B
VLP , B=LS2ωsILS 2 , A
+VCP , B, VLP , B
=LP ωsILP , A.
(29)
The first-order Fourier series coefficients of the amplitude ofiLS 2 (t) are obtained using (11), (13), (28), and (29). The final
90 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013
equations are shown in (A3)–(A5). Having both coefficients ofthe amplitude in (A4) and (A5), ILS 2 is calculated as follows:
ILS 2 =√
(I2LS 2 ,A + I2
LS 2 ,B ). (30)
Now, it is possible to analyze the fifth-order resonant converterwith the capacitive output filter by using the equivalent circuitof Fig. 7 and (18)–(30).
III. HIGH-VOLTAGE TRANSFORMER
Power transformer is the most challenging part of a high-voltage converter. A transformer with a very high turns ratiois inevitable in a high-voltage dc/dc converter. The high turnsratio results in a considerable amount of parasitic componentsin the high-voltage transformer. Significant amount of para-sitic components considerably deteriorates the performance ofpulsewidth modulation (PWM) converters. Therefore, the useof PWM converters is very limited in high-voltage applica-tions. Also, in low-frequency PWM converters, the magnetiz-ing current should be as small as possible in order to mini-mize the circulating current imposed by the magnetizing cur-rent. Therefore, the transformer should be designed such thatthe magnetizing inductance is much bigger than the series in-ductances. However, in high-frequency resonant converters, inwhich the resonant circuit includes a parallel inductance, themagnetizing inductor is utilized to implement the resonant cir-cuit [8], [9], [12]–[15], [17]–[20]. The smaller value of the mag-netizing inductance is achieved by having a small air gap in thetransformer core [9], [19], [20]. In fact, the transformer with airgap is able to provide enough reactive current to maintain ZVSfor light loads. The magnetizing current actually guarantees thelagging current required for ZVS for the entire range of loadvariations. This air gap not only produces enough parallel in-ductance, but also linearizes the BH curve of the high-frequencytransformer, which is very advantageous in high-frequency ap-plications [30]–[33].
Due to the considerable amount of parasitic components inhigh-voltage transformers, the transformer equivalent circuitused to analyze the performance of the converter should bevery accurate. In Section I, different standard equivalent cir-cuits of the transformer have been presented (shown in Figs.1 and 2) and the most precise equivalent circuit is shown inFig. 2(a). In this equivalent circuit, the only capacitor, which canaffect the converter behavior in the switching frequency range,is the parallel capacitance of the secondary winding reflectedto the primary side. The other capacitances have minor effectson the steady-state behavior of the converter in the switchingfrequency range and they should be incorporated for EMI anal-ysis of the converter [23]. Therefore, a fourth-order equivalentcircuit can be considered as an accurate model of the trans-former to describe the steady-state behavior of the converter. Inorder to calculate the parasitic components of the transformerpresent in the fourth-order model, the well-known open-circuitand short-circuit tests should be applied to the transformer. Theequivalent circuit of the transformer in the open-circuit test isshown in Fig. 8(a). The transformer input impedance under the
Fig. 8. Equivalent circuit of the fourth-order model of the transformer.(a) Secondary-side open-circuit condition. (b) Secondary-side short-circuitcondition.
Fig. 9. Transformer frequency response for an open-circuit test.
According to (31), the input impedance has two complex con-jugate poles at ωp , one zero at zero and two complex conjugatezeros at ωz , where
ωP =1√
(Llk,s + Lm )Cw,s
(32)
ωZ =1√
((Llk,pLm /Llk,p + Lm ) + Llk,s)Cw,s
. (33)
The frequency response of the transformer is shown in Fig. 9[34]. At low frequency range, the capacitive impedance is neg-ligible. Therefore, the slop of the frequency response, for a low-frequency range, represents the open-circuit inductance givenby [35]
Loc-S = Llk,p + Lm (34)
Loc-P = Llk,s + Lm . (35)
Fig. 8(b) shows the equivalent circuit of the transformer in theshort-circuit test. According to this figure, the input impedanceis given by
Zin,Tr,sc-S = (Llk,p + Lm ‖Llk,s )s. (36)
SHAFIEI et al.: ANALYSIS OF A FIFTH-ORDER RESONANT CONVERTER FOR HIGH-VOLTAGE DC POWER SUPPLIES 91
Fig. 10. (a) High-voltage transformer structure. (b) Prototype of the transformer.
The slope of the input impedance curve at low frequencyrange under the short-circuit condition is obtained as follows:
Lsc-S = Llk,p +Lm Llk,s
Lm + Llk,s. (37)
The parasitic components of the transformer can be calculatedthrough (32), (34), (35), and (37)
Lm =√
(Loc,p − Lsc,p)Loc,s (38)
Llk,p = Loc-S − Lm (39)
Llk,s = Loc-P − Lm (40)
Cw,s =1
(Llk,s + Lm )ω2p
. (41)
The design of the high-voltage transformer is highly challengingand has been the area of interest in many papers Also, resonantconverters can effectively absorb the parasitic components ofthe converter specially the ones related to the high-frequencytransformer [5], [6], [9], [36].
However, in this paper, the transformer is specifically de-signed to accommodate the resonant components. Integratingthe resonant components into the high-frequency transformercan significantly increase the power density of the converterand reduce the total number of reactive components requiredto implement the resonant tank. There are different structuresproposed for the high-voltage transformer. In this paper, thestar core transformer is used to fabricate the high-voltage trans-former; therefore, primary winding and the secondary windingare wound on the legs of an UU core [36]. The first step isto choose a core, which has enough winding area to transferthe maximum power and also guarantee the isolation require-ments. In this application, the isolation requirement determinesthe size of the core. Therefore, OP45917UC from Magnetics,Inc., is selected for this application. After choosing the core,the number turns in the primary side should be determined suchthat the losses of the transformer are minimized. The numberturns determines the maximum flux density allowed inside the
core. The optimal point for the maximum flux density is whenthe core losses and copper losses are equal [37]–[39].
The transformer structure and the prototype are shown inFig. 10. In this transformer, the primary and the secondary arewound on separate bobbins in order to provide the requiredisolation. The material used for the bobbin is PTFE Teflon,which can provide a very good insulation between the wind-ings and the transformer core. The Kapton film is used as aninsulator between the transformer windings. The Kapton film iswidely used in high-voltage transformers to guarantee the insu-lation requirements. In order to provide enough insulation andalso prevent partial discharge, different kinds of insulator ma-terials are used in high-voltage, high-frequency transformers.For example, mineral oil, Askaler oil, and sulfur hexafluoride(SF6) are the common materials that can be used in high-voltagetransformers. Although it may be possible to use dry and cleanair at normal atmospheric pressure for prototype power sup-plies, in industrial applications high-voltage transformers aresubmerged in the oil or sealed with SF6 gas. [40]. Table I showsdifferent parameters of the high-voltage transformer prototype.The transformer, used in this application, employs an air-gappedcore. Therefore, the BH curve of the transformer is dominatedby the air gap and is pretty linear. Therefore, in the analysis ofthe fifth-order resonant converter, the BH curve is consideredlinear, imposed by the air gap in the transformer structure.
IV. SOFT-SWITCHING ANALYSIS
In a few kilowatt power range, MOSFETs are usually usedto realize the semiconductor switches in power circuits. In thisrange of power, MOSFETs are able to safely work up to 20 kHz,under the hard-switching condition. As switching frequency in-creases, the switching losses increase considerably and the con-verter is not able to perform efficiently. Therefore, soft switchingis necessary for safe and efficient performance of the MOSFETs.
In addition, ZVS provides a noise-free environment for thecontrol circuit to safely produce the MOSFET gating pulses. Inhigh-voltage applications, ZVS is even more crucial. Since a
92 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013
transformer with a high turns ratio is inevitable in high-voltageapplications, the voltage spikes due to the hard switching willbe amplified and deteriorate the quality of the output voltage.In addition, output bridge diodes are the main victims of thevoltage spikes in high-voltage applications. Because the leakageinductance of the high-voltage transformer is quite high, thevoltage spikes across the output diodes are very high. This makesthe hard-switching impractical for high-voltage applications.
Fig. 12. ZVS angle versus loaded quality factor for ±50% variation in eachnormalized parameter. (a) Resonant inductance ratio Ln . (b) Series resonantinductance ratio Ls . (c) Resonant capacitance ratio Cn .
ZVS is guaranteed for variable-frequency resonant converters,if the switching frequency is greater than the resonant frequency.Equivalently, MOSFETs are operating under zero voltage whilethe resonant circuit shows inductive impedance. This meansthat the resonant current is lagging the output voltage of thefull-bridge inverter [1].
SHAFIEI et al.: ANALYSIS OF A FIFTH-ORDER RESONANT CONVERTER FOR HIGH-VOLTAGE DC POWER SUPPLIES 93
Fig. 13. Analysis of the fifth-order resonant converter with a capacitive outputfilter in a fixed-frequency phase-shift control approach for Ln = 1, Ls = 2, Cn
= 0.25, ωn = 0.9, and constant values of normalized load resistance QL . (a)Phase of the input impedance ϕ versus normalized frequency ωn . (b) Amplitudeof the normalized series inductance current ILs 1∗Z0 /Vin versus duty cycle. (c)Magnitude of the voltage transfer function Vout /Vin versus duty cycle.
TABLE IIANALYSIS RESULTS OF THE FIFTH-ORDER RESONANT CONVERTER IN A
PHASE-SHIFT CONTROL APPROACH
Fig. 14. Performance analysis of the fifth-order resonant converter with acapacitive output filter in a frequency control approach for Ln = 1, Ls = 2, Cn =0.25, and constant values of normalized load resistance QL . (a) Amplitude of thenormalized series inductance current ILs 1∗Z0 /Vin versus normalized frequency.(b) Magnitude of the voltage transfer function Vout /Vin versus normalizedfrequency.
TABLE IIIRESULTS OF THE FIFTH-ORDER RESONANT CONVERTER FOR A
VARIABLE-FREQUENCY CONTROL APPROACH
However, for fixed-frequency phase-shift resonant converters,not only the switching frequency should be higher than theresonant frequency, but also the zero crossings of the resonantcurrent must be within the full-bridge output voltage pulse [41].Therefore, ZVS depends on the pulse width of the full-bridgeoutput voltage. This fact makes it harder to maintain ZVS for awide range of operating conditions. One of the main setbacksof the fixed-frequency phase-shift series–parallel LCC resonantconverters is that the range of operating conditions, in whichthe converter is working under ZVS, is very limited. Therefore,
94 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013
Fig. 15. Analysis of the fourth-order resonant converter with a capacitiveoutput filter in a fixed-frequency phase-shift control approach for Ln = 1, Cn
= 0.25, ωn = 0.9, and constant values of normalized load resistance QL . (a)Phase of the input impedance ϕ versus normalized frequency ωn . (b) Amplitudeof the normalized series inductance current IL s1∗Z0 /Vin versus duty cycle. (c)Magnitude of the voltage transfer function Vout /Vin versus duty cycle.
the converter loses ZVS for a wide range of loads [24]. Thesoft-switching analysis in this section shows that the proposedfifth-order resonant converter is able to considerably extend theZVS operating range. The angle between the rising edge of thefull-bridge output voltage and the zero crossing of the resonantcurrent, σ (shown in Fig. 5) is the true measure for the ZVSrange in fixed-frequency phase-shift resonant converters. The
TABLE IVANALYSIS RESULTS OF THE FOURTH-ORDER RESONANT CONVERTER IN A
PHASE-SHIFT CONTROL APPROACH
Fig. 16. Output diode voltage and current waveforms.
angle of σ is defined as follows [41]:
σ = ϕ − 1 − d
2π. (42)
If this angle is positive, ZVS is guaranteed for the full-bridgepower MOSFETs. Therefore, the comparison of this angle for athird-order LCC resonant converter and the proposed fifth-orderresonant converter is carried out to show that the fifth-orderresonant converter is able to effectively extend the ZVS range. In[24], a thorough analysis for a fixed-frequency phase-shift LCCresonant converter is carried out. The converter specificationsare as follows:
Ls = 315 μH, Cs = 55 nF,
Cp = 28 nF, RL = 18.9 Ω
Vin = 120 VDC , V ′out = 48 VDC ,
Pout = 500 W, fs = 40 kHz. (43)
The converter is controlled through a fixed-frequency phase-shift modulator. The ZVS angle for this LCC resonant con-verter versus QL is shown in Fig. 11(a). The ZVS angle for theproposed fifth-order resonant converter is shown in Fig. 11(b)for the normalized parameters shown in the figure. When theZVS angle is positive, the full-bridge MOSFETs are turned ONunder zero voltage. Therefore, according to these figures, thefifth-order resonant converter is able to maintain the ZVS anglepositive for a wide range of load variations and largely extendthe ZVS range.
A family of ZVS angle curves is shown in Fig. 12. Accordingto these figures, the ZVS angle of the proposed converter re-mains positive for±50% variation in each normalized parameterexcept for an increase in Cn . Basically, increasing Cn (parallelcapacitor) has a double negative effect on zero voltage switchingbecause it increases the gain of the converter and decreases thephase of the input impedance [9]. Fig. 13 shows different graphsof the proposed fifth-order resonant converter with a capacitiveoutput filter that are derived by MATLAB software. Fig. 13(a)
SHAFIEI et al.: ANALYSIS OF A FIFTH-ORDER RESONANT CONVERTER FOR HIGH-VOLTAGE DC POWER SUPPLIES 95
Fig. 17. Schematic of the fifth-order resonant converter.
TABLE VCONVERTER PARAMETERS
shows the phase of the input impedance of the resonant tankversus the normalized frequency. According to this figure, theinput impedance remains inductive for a wide range of loadvariations. Fig. 13(b) shows the normalized input current of theresonant circuit versus the duty cycle and Fig. 13(c) shows thevoltage transfer function of the converter versus the duty cycle.Fig. 13(c) illustrates that the range of change in duty cycle is notvery large under different load conditions. This helps the con-verter to maintain zero voltage switching for different loads. Theresults of converter analysis are summarized in Table II. Accord-ing to Table II, the amplitude of series inductance current dropsby half for a decade decreasing in the output load. Therefore, theconduction losses in light loads deteriorate the efficiency. In or-der to compare the conduction losses in both variable-frequencyand fixed-frequency phase-shift control methods, the amplitudeof normalized series inductance current and the magnitude ofvoltage transfer function versus frequency variations are shownin Fig. 14, for normalized parameter in Fig. 13. Also, the re-sults for a variable-frequency control method are presented inTable III. It is essential to note that in the variable-frequencycontrol method, the switching frequency is changed for dif-ferent load conditions. In light loads, the switching frequencyincreases to maintain the series resonant current lagging angle.An increase in the switching frequency results in more lossesin the magnetics and drive circuit. According to the results, thelosses are almost the same for both variable-frequency and fixed-
frequency phase-shift control methods. In order to examine theaccuracy of the converter model used for the fifth-order resonantconverter, the accuracy of the fifth-order model is compared tothat of the fourth-order model presented in [9].
Fig. 15 shows different graphs of the resonant converter ob-tained with the fourth-order model with the same normalizedparameters as presented in Fig. 13. Fig. 15(a) shows the phaseof the input impedance versus normalized frequency, Fig. 15(b)illustrates the normalized amplitude of the resonant input currentversus duty cycle, and, finally, Fig. 15(c) depicts the magnitudeof voltage transfer function of the converter versus duty cycle.Also, Table IV shows the summary of the parameters for dif-ferent quality factors. Comparing this table with Table II, it isevident that the results obtained from the fifth-order model aredifferent, and more precise, from the ones obtained from thefourth-order model.
Another main advantage of the proposed converter is softswitching of the output diodes. Fig. 16 shows the current andvoltage waveforms of the output diode. According to the oper-ating modes of the converter, once iLS 1 (t) reaches iLP
(t), theoutput diode current smoothly reaches zero and naturally turnsOFF. This causes zero current switching (ZCS) at turn-off andavoids any reverse recovery losses in the output diodes. In ad-dition, the voltage across the diodes is smooth and sinusoidalduring the switching transitions. Therefore, placing diodes inseries is possible without any resistive or capacitive voltagedividers to divide the voltage equally between the diodes. Softswitching of the output diodes highly enhances the performanceof the converter at the secondary side.
V. EXPERIMENTAL RESULTS
In order to verify the performance of the proposed fifth-orderresonant converter, a 1.1-kW, 10-kV prototype has been pre-pared. Fig. 17 shows the schematic of the converter. The dc-busvoltage is produced through a bridge rectifier, which rectifies the110-VAC line voltage along with a capacitive filter. A full-bridgeinverter is used to convert the dc voltage to a high-frequencyac voltage. Four MOSFETs are used to realize the full-bridgeinverter. The part number of the MOSFETs is FA57SA50LCfrom International Rectifier. This MOSFET has a very low
96 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013
Fig. 18. Output voltage of full-bridge inverter (square wave, 50 V/Div) andfirst series inductance current (sin wave, 10 A/Div) for (a) full load, (b) 50%load, (c) 25% load, and (d) 10% load.
TABLE VIEXPERIMENTAL RESULTS
Fig. 19. Series inductance current (Channel 1) along with series resonantcapacitor voltage (Channel 2).
ON-resistance, which reduces the conduction losses of the con-verter. The resonant tank consists of an external capacitor, anexternal inductor (Lext = 20 μH), and the parasitic componentsof the transformer. The external capacitor is a film-type capac-itor, which is able to withstand high value of a current rippleat high frequency. The output diodes are realized based on theseries connection of BYT56M. Thus, the high-voltage diode isthe series connection of 1000 V diodes placed in a Teflon PTFEbox for the required high insulation purpose.
The resonant tank is designed based on the analysis curves ofthe fifth-order resonant converter and the transformer parame-ters that are shown in Fig. 13 and Table I. Considering the ohmiclosses and voltage drops across the inverter switches and outputdiodes, the gain of the inverter along with the resonant circuit isselected as MV = 1.4. Therefore, VCP
is given by
VCP= MV × Vin ⇒ VCP
= 1.4 × 150 = 210 VDC . (44)
According to the quality factor at full load, the characteristicimpedance is calculated as
Z0 =V 2
CP
Pout × QL⇒ Z0 = 26.7 Ω. (45)
The normalized parameters of the converter are as follows:
LS = 2, Ln = 1, Cn = 0.25, ωn = 0.9. (46)
Therefore, the resonant components and switching frequencyare obtained as follows:
LS1 = 30 μH, LS2 = Llk,S = 15 μH
LP = Lm = 30 μH, CP = Cw,s = 10.5 nF (47)
SHAFIEI et al.: ANALYSIS OF A FIFTH-ORDER RESONANT CONVERTER FOR HIGH-VOLTAGE DC POWER SUPPLIES 97
TABLE VIICOMPARING THEORETICAL AND EXPERIMENTAL RESULTS
CS =CP
Cn⇒ CS = 42 nF (48)
ω0 =1√
LS1 × CS
⇒ ω0 = 283.6π × 103 rad/s
ωs = ωn × ω0 ⇒ fs = 127 kHz. (49)
The converter parameters are summarized in Table V. Fig. 18shows the experimental results of the fifth-order resonant con-verter. The output voltage of the full-bridge inverter and the firstseries inductor current (MOSFET’s current) are illustrated forfull load, 50% load, 25% load, and 10% load in Fig. 18(a)–(d)respectively. Also, voltage across series resonant capacitor VCS
is presented in Fig. 19. According to Fig. 18, the full-bridgeswitches are fully turned ON under zero voltage. The phase ofthe input impedance and σ are measured through experimentalresults, which are shown in Table VI.
In Table VI, the efficiency is calculated based on the measure-ment of the converter input/output power. In order to approx-imately calculate the efficiency from the theoretical analysis,it is necessary to incorporate the ohmic losses in the theoret-ical equations. However, this highly increases the complexityof the derived equations. Therefore, in order to have an empiri-cal method to calculate the efficiency, the conduction losses ofthe converter can be calculated using (20) and (30). From thesecurrents, the conduction losses of the MOSFETs as well as theohmic losses of the converter can be calculated. The switchinglosses are almost negligible due to the soft-switching duringturn-on and turn-off of the semiconductor elements.
The theoretical and experimental results are compared inTable VII. It is clear from this table that the values obtained fromthe theoretical analysis (see Table II) and ones obtained fromthe experimental results are very close and the proposed modelcan precisely predict the behavior of the fifth-order resonantconverter with capacitive output filter for a wide load range.
The voltage waveform of a diode in the output rectifier isshown in Fig. 20. According to this figure, the output diodevoltage is similar to Fig. 16; therefore, the ZCS condition isprovided for the output diodes and robust operation of the outputrectifier is guaranteed.
In order to illustrate the accuracy of the RCFHA techniqueused to describe the behavior of the fifth-order resonant con-verter, some performance parameters, such as different harmon-ics, total harmonic distortion (THD), and distortion factor (DF),are calculated from the simulations and experimental results.Fig. 21 shows the amount of harmonics in the series resonantcurrent waveform derived from experimental results. Also, InTable VIII, the THD and DF of the series resonant current aregiven, derived from the simulation and experimental results.
Fig. 20. Voltage waveforms of a diode in an output rectifier for the full-loadcondition.
Fig. 21. FFT analysis of series inductance current.
TABLE VIIIPERFORMANCE PARAMETERS
Fig. 21 and Table VIII confirm that the RCFHA technique isvery accurate and is able to effectively describe the behavior ofthe converter.
VI. CONCLUSION
A fifth-order resonant converter which is controlled by afixed-frequency phase-shift control approach is presented in thispaper. The proposed converter is able to significantly extend thezero voltage switching from no load to full load. Also, a precisemodel is proposed for the converter, which is able to accuratelypredict the behavior of the converter. Theoretical and experi-mental results verify the performance of the proposed converterin terms of soft switching under various load conditions. Softswitching of the full-bridge MOSFETs and soft switching ofhigh-voltage output diodes make this topology a very good can-didate for high-voltage applications. As a summary, the featuresof the proposed converter for high-voltage applications are asfollows:
98 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013
Zeq =
[π CP L2
P ω3s sin2 ψ + jLP ωs(−2ψ sin ψ cos ψ + π CP LP ω2
s sin ψ cos ψ + 2π CP LS2ω2s sin ψ cos ψ
−2πCP LS2ψω2s + ψ2 − πCP LP ψω2
s + π2C2P LP LS2ω
4s + π2C2
P L2S2ω
4s − cos2 ψ + 1)
]
[−2ψ sinψ cos ψ + 2π CP LS2 ω2
s sin ψ cos ψ + 2π CP LP ω2s sinψ cos ψ + ψ2 + π2C2
P L2S2ω
4s
−2π CP LP ψ ω2s − 2π CP LS2ψ ω2
s + 2π2 C2P LP LS2 ω4
s + π2C2P L2
P ω4s − cos2 ψ + 1
] (A1)
Zin (jωn )Z0
= j
(ωn − 1
ωn
)
+
[(πCnω3
n sin2 ψ/Ln ) + jωn (−2ψ sinψ cos ψ + (πCnω2n sinψ cos ψ/Ln ) + (2πCnω2
n sin ψ cos ψ/Ls)
−(2πCnψω2n/Ls) + ψ2 − (πCnψω2
n/Ln ) + (π2C2nω4
n/LnLs) + (π2C2nω4
n/L2s ) − cos2 ψ + 1)
]
Ln
[−2ψ sin ψ cos ψ + (2πCnω2
n sinψ cos ψ/Ls) + (2πCnω2n sinψ cos ψ/Ln ) + ψ2 + (π2C2
nω4n/L2
s )
−(2πCnψω2n/Ln ) − (2πCnψω2
n/Ls) + (2π2C2nω4
n/LnLs) + (π2C2nω4
n/L2n ) − cos2 ψ + 1
] (A2)
{−LP ωs(ILS 1 , B
− ILS 2 , B) = −LS2ωsILS 2 , B
+ 1πCP ωs
(ILS 2 ,A sin2 ψ − ILS 2 ,B (sin ψ cos ψ − ψ))
LP ωs(ILS 1 , A− ILS 2 , A
) = LS2ωsILS 2 , A+ 1
πCP ωs(ILS 2 ,B sin2 ψ + ILS 2 ,A (sin ψ cos ψ − ψ))
(A3)
ILS 2 ,A =πCnω2
n
[−ILS 1 ,B sin2 ψ + (πCnω2
nILS 1 ,A/Ln ) + (πCnω2nILS 1 ,A/Ls) + sinψ cos ψILS 1 ,A − ψILS 1 ,A
]
Ln
⎡⎢⎣
(π2C2nω4
n/L2n ) + (2π2C2
nω4n/LnLs) + (2πCnω2
n sinψ cos ψ/Ln )
−(2πCnψω2n/Ln ) + (π2C2
nω4n/L2
s ) + (2πCnω2n sin ψ cos ψ/Ls) − (2πCnψω2
n/Ls)
+ sin2 ψ cos2 ψ − 2ψ sin ψ cos ψ + ψ2 + sin4 ψ
⎤⎥⎦
(A4)
ILS 2 ,B =πCnω2
n
[ILS 1 ,A sin2 ψ + (πCnω2
nILS 1 ,B /Ln ) + (πCnω2nILS 1 ,B /Ls) + sin ψ cos ψILS 1 ,B − ψILS 1 ,B
]
Ln
[(π2C2
nω4n/L2
n ) + (2π2C2nω4
n/LnLs) + (2πCnω2n sinψ cos ψ/Ln ) − (2πCnψω2
n/Ln ) + (π2C2nω4
n/L2s )
+(2πCnω2n sin ψ cos ψ/Ls) − (2πCnψω2
n/Ls) + sin2 ψ cos2 ψ − 2ψ sin ψ cos ψ + ψ2 + sin4 ψ
]
(A5)
1) a very narrow range of pulse width variations from noload to full load that results in ZVS operation using afixed-frequency phase-shift control approach;
2) higher resonant circuit gain that reduces the transformerturns ratio and facilitates manufacturing of the trans-former;
3) the converter takes advantage of the integrated transformerfor high-voltage applications;
4) the converter absorbs all parasitic components of the high-voltage transformer;
5) the resonant circuit is realized by only two external com-ponents;
6) pure capacitive output filter which makes it suitable forhigh-voltage applications.
APPENDIX
As (A1–A5) shown at the top of the page.
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Navid Shafiei (S’11–M’12) was born in Isfahan,Iran, in 1981. He received the B.S degree fromKashan University, Kashan, Iran, and the M.S degreefrom NajafAbad Branch, Islamic Azad University,Iran, in 2005 and 2011, respectively, both in electricalengineering.
In 2005, he joined as a Researcher in Informationand Communication Technology Institute (ICTI), Is-fahan University of Technology, Isfahan, Iran. He iscurrently working as a technical designer at Informa-tion and Communication Technology Institute (ICTI)
in Isfahan, Iran. His current research interests include application of novel res-onant inverters in dc–dc and dc–ac power supply, power modulators, and pulsepower applications.
Majid Pahlevaninezhad (S’07–M’12) received theB.S and M.S. degrees in electrical engineering fromthe Isfahan University of Technology, Isfahan, Iran,and the Ph.D. degree from Queen’s University,Kingston, Canada.
He is currently a Postdoctoral Research Asso-ciate with the Department of Electrical and ComputerEngineering, Queen’s University. He was a Techni-cal Designer in the Information and CommunicationTechnology Institute (ICTI), Isfahan University ofTechnology, from 2003 to 2007, where he was in-
volved in the design and implementation of high-quality resonant converters.He also collaborated with Freescale Semiconductor, Inc., where he was theLeader of a research team involved in the design and implementation of thepower converters for a pure electric vehicle from 2008 to 2012. He is the authorof more than 32 journal and conference proceeding papers and the holder of4 U.S. patents. His current research interests include robust and nonlinear con-trol in power electronics, advanced soft-switching methods in power converters,plug-in pure electric vehicles, and PV microinverters.
Dr. Pahlevaninezhad is a member of the IEEE Power Electronics Society andIndustrial Electronics Society. He was also the recipient of the distinguishedgraduate student award from the Isfahan University of Technology.
Hosein Farzanehfard (M’08) was born in Isfahan,Iran, in 1961. He received the B.S. and M.S. de-grees in electrical engineering from the University ofMissouri, Columbia, in 1983 and 1985, respectively,and the Ph.D. degree from Virginia Tech, Blacksburg,in 1992.
Since 1993, he has been a Faculty Member at theDepartment of Electrical and Computer Engineering,Isfahan University of Technology, Isfahan, Iran. Heis the author of more than 100 papers in journalsand conference proceedings. His research interests
include high-frequency soft-switching converters, pulse power applications,power factor correction, active power filters, and electromagnetic interference.
100 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 1, JANUARY 2013
Alireza Bakhshai (M’04–SM’09) received the B.Sc.and M.Sc. degrees from the Isfahan University ofTechnology, Isfahan, Iran, in 1984 and 1986, respec-tively, and the Ph.D. degree from Concordia Univer-sity, Montreal, QC, Canada, in 1997.
From 1986 to 1993 and from 1998 to 2004, he wasa Faculty Member with the Department of Electri-cal and Computer Engineering, Isfahan University ofTechnology. From 1997 to 1998, he was a Postdoc-toral Fellow with Concordia University. He is cur-rently with the Department of Electrical and Com-
puter Engineering, Queen’s University, Kingston, ON, Canada. His researchinterests include high-power electronics and applications in distributed genera-tion and wind energy, control systems, and flexible ac transmission services.
Praveen K. Jain (S’86–M’88–SM’91–F’02) re-ceived the B.E. degree (Hons.) in electrical engi-neering from the University of Allahabad, Allahabad,India, in 1980 and the M.A.Sc. and Ph.D. degrees inelectrical engineering from the University of Toronto,Toronto, ON, Canada, in 1984 and 1987, respectively.
He is the Founder of CHiL Semiconductor, Tewks-bury, MA, and SPARQ System, Kingston, ON. Hewas a Production Engineer with Crompton Greaves(1980), a Design Engineer with ABB (1981), a SeniorSpace Power Electronics Engineer with Canadian As-
tronautics Ltd. (1987–1990), a Technical Advisor with Nortel (1990–1994), anda Professor with Concordia University, Montreal, QC, Canada (1994–2000). Inaddition, he has been a Consultant with Astec, Ballard Power, Freescale Semi-conductors, Inc., General Electric, Intel, and Nortel. He is currently a Professorand a Canada Research Chair with the Department of Electrical and ComputerEngineering, Queen’s University, Kingston, where he is also the Director of theQueen’s Centre for Energy and Power Electronics Research. He has securedmore than $20 million cash and $20 million in kind in external research fundingto conduct research in the field of power electronics. He has supervised morethan 75 graduate students, postdoctoral fellows, and research engineers. He haspublished more than 350 technical papers (including more than 90 IEEE Trans-actions papers). He is the holder of more than 50 patents (granted and pending).
Dr. Jain is a Fellow of the Engineering Institute of Canada and the CanadianAcademy of Engineering. He was the recipient of the 2004 Engineering Medal(R&D) from the Professional Engineers of Ontario and the 2011 IEEE WilliamNewell Power Electronics Field Award. He is an Editor of the InternationalJournal of Power Electronics. He is an Associate Editor of the IEEE TRANS-ACTIONS ON POWER ELECTRONICS. He is also a Distinguished Lecturer of theIEEE Industry Applications Society.
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