the converter delivers 80 W at 78-percent efficiency with a power den- sity, excluding heat sink, ..... F. William Stephenson (M'75-SM'79-F'88) re- ceived the B.Sc.
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Hybridized Off-Line 2-MHz Zero-Current-Switched Quasi-Resonant Converter DOUGLAS C. HOPKINS, MEMBER, IEEE, MILAN M. JOVANOVIC, FRED c. Y. LEE, SENIOR MEMBER, IEEE, AND F. WILLIAM STEPHENSON, FELLOW, IEEE
Abstract-Thick-film hybrid technology is used to develop a halfbridge, half-wave, zero-current-switched quasi-resonant converter for 300-V dc off-line application. With a conversion frequency of 2 MHz the converter delivers 80 W at 78-percent efficiency with a power density, excluding heat sink, of 21 W/in3. The operation and detailed electrical and hybrid design of the circuit are described. Also described is a 2-MHz hybridized gate drive.
I. INTRODUCTION HE ADVANCEMENT of very large scale integration (VLSI) technology continues to reduce the size and increase the speed of information processing circuits. Consequently, power supplies for such circuits must meet ever increasing demands for power, yet simultaneously decrease in size. This need for higher power density in the supplies can be met through proper selection of circuit topology, operation at higher frequencies, and by using high-density circuit fabrication techniques [ 13. Generally, with MOSFET switches, when the conversion frequency of conventional pulsewidth-modulated (PWM) supplies approaches 1 MHz, the switching loss becomes excessive. This sharply reduces the efficiency of the supply. A quasi-resonant topology reduces much of this loss. In a zero-current-switched (ZCS) quasi-resonant converter (QRC) the turn-off loss is nearly eliminated [2]. It has been shown [3] that when comparing the flyback, forward, and half-bridge ZCS-QRC topologies for off-line applications, the half-bridge topology operating in halfwave mode with secondary-side resonance is preferred. The topology has fewer components, more efficient operation, and provides better core utilization and automatic flux reset of the transformer. The operation of any converter at megahertz frequencies is strongly influenced by the effects of parasitic ele-
T
Manuscript received April 7 , 1987; revised July 22, 1988. This work was supported by Digital Equipment Corporation and Virginia Center for Innovative Technology. D. C. Hopkins is with the Department of Electrical Engineering, 200 Broun Hall, Auburn University, Auburn, AL 36849-5201. M. M. JovanoviC is with the Virginia Power Electronics Center, Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, on leave from the Institute for Power and Electronics, University of Novi Sad, Novi Sad, Yugoslavia. F. C . Y. Lee and F. W. Stephenson are with Bradley Department of Electrical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061. IEEE Log Number 8824 134.
MEMBER, IEEE,
ments such as interconnect and leakage inductances, parasitic and junction capacitances, and skin effect in conductors. Some parasitics such as the leakage inductance of the transformer can be constructively used as a part of the circuit. Other parasitics may have adverse effects on the circuit performance and should be minimized. Many concerns, such as minimizing interconnect parasitics, can be resolved by using thick-film hybrid techniques. This paper presents design rules and hybridization techniques used to develop an 80-W (5-V / 16-A) off-line, halfbridge, half-wave ZCS-QRC operating with secondaryside resonance and with a conversion frequency of 2 MHz.
11. OPERATION OF IDEAL HALF-BRIDGE ZCS CIRCUIT For this development, the half-bridge, half-wave, ZCSQRC topology using the leakage inductance of the transformer for secondary-side resonance was chosen (Fig. 1). The circuit operation is described with the aid of four topological stages as shown in Fig. 2. For ease of explanation, assume that a) all components are ideal except the transformer which has leakage inductance; b) the circuit uses a diode to freewheel the output current; c) the inductance of the output filter is large and, in steady state, the output filter acts as a current source with a value equal to the output current, IO. At initial time to = To, SI is turned on and the converter enters the inductor-charging stage. Inductor-Charging Stage [To, T I ] (Fig. 2a): When SI turns on, current iLl begins flowing through the upper secondary of the transformer. Prior to turn-on the currents through both secondaries are zero, and the output current freewheels through diode DFW (Fig. 1). The current starts increasing linearly while resonant capacitor voltage vc is zero for the duration of this stage, i.e.,
vc(t) = 0
(1b)
where LRis the leakage inductance of the transformer, V,,, = V s / 2 N is the secondary voltage, V, is the supply volt-
0885-8993/89/0100-0147$01 .OO @ 1989 IEEE
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 4. NO. 1 , JANUARY 1989
I
U&)
=
v,,
10
- -t
CR where VcB is the capacitor voltage at the end of the resonant stage. . This stage ends when uC becomes zero. The duration of the stage is
Fig. 1. Ideal half-bridge zero-current-switched converter with secondaryside resonance operating in half-wave mode.
Freewheeling Stage [T,,T4](Fig. 2d): At time T, the freewheeling diode starts to conduct. Conduction continues until switch S2 is turned on, thus repeating the same sequence of operations but involving the lower secondary of the transformer. The duration of the stage is
Td4 = T4 - T3 = Ts - Tdl - Td2 - Td3 where Tsis the period of a switching cycle.
(C) (d) Fig. 2. Equivalent circuits of ideal half-bridge circuit in four topological stages.
age, and N is the turns ratio. This stage ends when iL1 equals Io. The duration of the stage is
Resonant Stage [T,,T2](Fig. 2b): At time TI,DFW is commutated off and current i L 1 (t ) - Io charges the resonant capacitor, CR. The equations for this stage are i L l ( t )= Io U C ( t )=
VS,, +sin (coot) Zn
VS [ 1 - cos 2N
-
(wet)]
(3a) (3b)
where wo = 1/ J L ~ C is the ~ angular resonant frequency is the characteristic impedance. Zeroand Z,, = current switching requires, from (3a),
(8)
Waveforms of ideal circuit operation are shown in Fig. 3 while Fig. 4 shows the ideal voltage-conversion ratio as a function of the conversion frequency [4].For a given normalized current ,Z = ZoZ,,/Vsec,the characteristics in Fig. 4 are straight lines. For maximum load (IoN = l ) ,
(9) where&,, is the conversion frequency and f o is the resonant frequency. 111. ELECTRICAL CIRCUITDESIGN The basic circuit design procedure for an off-line, halfbridge, half-wave ZCS-QRC with secondary-side resonance, shown in Fig. 5, is given in [3]. Applying this procedure, the input design data are
supply voltage, V, = 300 V k 50 V; output current, 1.5 A < Io < 16 A; output voltage, Vo = 5 V; conversion frequency, f ,","," = 2 MHz; transformer turns ratio, N = 12. Assuming cy = 0.8, the following component values and circuit parameters can be calculated. The calculated value of the resonant capacitor is
(4) This stage ends when resonant current i L 1 becomes zero. At this time the drive to the switch should be turned off. The duration of the stage is
Td2
=
T2
-
TI
=
ff -
(5)
WO
where a = sin-' ( -ZoZn/Vsec)and T Ia I3 ~ / 2 . Capacitor-Discharge Stage [T2,T,] (Fig. 2c): Since unidirectional switch S I prevents current reversal through the resonant inductor, the resonant capacitor begins discharging with constant output current Io through the outer loop, and vC decreases linearly. Thus,
The standard value of 82 nF is used which ensures zerocurrent switching. It is important that the capacitor be stable with temperature, able to operate with bipolar voltages, and have a very low equivalent series resistance (ESR). Therefore, an NPO ceramic capacitor was selected. The calculated value of the resonant inductance referred to the secondary is obtained from
149
HOPKINS et a l . : HYBRIDIZED OFF-LINE QUASI-RESONANT CONVERTER
"GSl
t
,-,
0
0.2
0.4
06
0.8
d. C
Fig. 4. DC voltage-conversion ratio of ideal half-bridge converter as function of normalized conversion frequency; ION = l o / (V,,,/Z,, ) is normalized output current.
I
L
L
/rg CP5
r
f
Lf = 5pH L, = 30nH R = 220KLl RpS = 470n
RS C 5
C, = 110,rF C,'= 82°F
C = O 12nF C p s = 68pF Rs = 160 C5 = 2 2°F QI IRF720 D I l 28CTQ40 DFW USDC845 Tr TDK LP23/8 H,Cd N = 12
Fig. 5. Circuit diagram of hybridized half-bridge converter
Fig. 3. Circuit waveforms of ideal half-bridge converter.
This inductance is composed of the leakage inductance of the transformer and any interconnect inductances in the tank circuit. Since the interconnect inductance in a hybrid circuit is negligible, LR depends almost entirely on the transformer. However, a specific leakage inductance is not readily attainable from a transformer design. Therefore, if the actual LR is too low, an external inductance can be added in the center leg of the transformer secondary. If it is too high, either the transformer should be redesigned or the resonant frequency of the converter decreased. The leakage inductance calculated in (1 1) is less than the 30 nH that was attained from the transformer constructed for this design. Therefore, a lower resonant frequency was used. The transformer was designed with a TDK low-profile H7C4material and an LP23/8 core and bobbin. The primary has two parallel windings of twentyfour turns each wound with 25 strand #42 AWG Litz wire. Two secondary turns of copper foil are inserted between
the primary windings. The turns ratio N of the transformer is 12. Measured magnetizing and leakage inductances from the primary and secondary side, at 100 kHz, are: L i p = .462 mH, Lih = 4.25 pH, LsOp = 3.2 pH, LZh = 30 nH. The superscripts indicate either the open- or shortcircuit state of the terminals that are not being measured, e.g., L:h is the leakage measured at the secondary. The resonant frequency of the circuit is then 1 f"
= 27r.\/L,cR
= 3.4 MHz.
(12)
Proper selection of the transistor switches is important in achieving high-efficiency operation. Unlike zero-voltage-switched circuits [5], the input switching device of a ZCS circuit turns on when a terminal voltage is applied. This voltage causes energy to be stored in the terminal capacitance of the device and is subsequently lost to device heating during turn-on. A low capacitance device is therefore desired. As shown in [3] a trade-off between onresistance and output capacitance exists for MOSFET transistor switches and an optimum on-resistance can be
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 4. NO. I , JANUARY 1989
calculated to assist in proper device selection. For this circuit design the optimum on-resistance is Ri$(on)
=
2NVy 631,"""
=
1.9 Q
(13)
where k = 50 ps for the IRF 700 family. The switches used in this circuit are IRF 720 devices rated at 400 V and 3.3 A with an on-resistance of 1.8 Q . A snubber is used across the primary winding of the transformer to reduce oscillations that occur when the magnetizing inductance of the transformer interacts with the junction capacitances of the switches. The component values selected are Rps = 470 Q and Cps= 68 pF. Selection of the rectifier diodes is critical since a 100mV change in the forward voltage drop changes the efficiency by two percentage points. For a low output voltage of 5 V, Schottky diodes are used. The maximum peak forward current through each diode is equal to the maximum peak resonant current, i.e.,
Pax 1 ; ~= 11;""+ 2 = 40 A 2NZ,
v;;
3 vy 2N
= -=
44 v
(14)
(15)
The diode current rating can be less than half of Zgr since each diode has less than a 50-percent conduction cycle. The freewheeling diode can also be a source for significant power loss if it has a high forward voltage drop. Therefore, a Schottky is used with I;& = 1, = 16 A
VEyw
=
(16)
Vy
- = 30 V N
(17)
Snubber circuits are used to prevent dangerous voltage oscillations that develop at diode turn-off due to secondary inductances and diode-junction capacitances. The snubber resistance and capacitance, Rs = 10 Q and Cs = 2.2 nF, are !,elected to critically damp the oscillations. The output filter is designed with a comer frequency, fp = 7 kHz, using LF = 5 pH and C, = 110 pF. The capacitance is obtained from 68 pF and 33 pF tantalum capacitors and two 3.3 pF NPO ceramic capacitors. The input capacitors foiming the half bridge are selected to ensure that their midpoint voltage varies less than 10 percent of Vs at full load, i.e., C >
10 v & y x
V f EX v
32
where 17 is the converter efficiency. IV. HYBRIDCIRCUIT DESIGN Material selection [6] is critical to the design of a highfrequency off-line thick-film hybrid converter since electrical conductivity, high-field metal migration, and ther-
mal conductivity are influenced by the frequency and power density [7]. There are four categories for materials used in the thickfilm hybrid design: substrates, conductors and interconnects, coatings and insulators, and attachments. Substrate materials such as aluminum nitride, beryllia and porcelainized steel were considered but not selected because of high cost, poor availability or unproven reliability. Conductor materials such as copper and gold were also considered but not selected for similar reasons. An alumina substrate (96 percent) and a silver-based metal conductor were selected because of their suitable electrical and thermal characteristics and commercial compatibility. For a power hybrid circuit the electrical conductance of the conductors, which depends on geometry, composition, firing temperature, and frequency of operation, is of major concern, particularly at frequencies of 1 MHz and above. Table I shows empirical resistivity results for different silver-based pastes. The change in the dc resistivity of the conductor is nearly linear with temperature; temperature coefficients calculated from the data are given. The measured change in ac resistivity versus frequency does not follow the theoretical square-root relationship as for a homogeneous medium. The conductance in an infinite slab of conductor varies inversely as the one-half power of frequency. However, in a strip conductor, as used in hybrid circuits having finite dimensions, finite impedance, and which is close to other conductors (i.e., closer than a distance equal to three times the surface circumference of the conductor [SI), edge and proximity effects redistribute the electromagnetic fields within and between conductors. This redistribution causes the ac resistance of the conductor to deviate from the square-root law. Empirical data were obtained using a serpentine conductor pattern with a 0.51 mm (20mils) wide conductor separated 0.51 mm (20mils). The data indicates a nearexponential relationship between the effective resistivity and frequency for most of the low-resistivity materials as shown in Fig. 6. Table I records coefficients U and 6, used in the following resistivity equation to approximate these curves. Resistivity
=
a . exp ( b f )[ mQ
*
mil]
( 19)
where f is frequency in megahertz. At 2 MHz the resistance of the conductor material used (ESL 9601) increases three percent above the dc resistance due to the edge, proximity, and skin effects. The above results show that in a hybridized gate-drive circuit where frequency components may be above 2 MHz and conductor widths less than 0.51 mm (20mils), the ac resistance can be quite large compared to the dc resistance. This is of particular concern in the high-pulsedcurrent output circuitry of the driver. These results are not applicable to the power stage where the high-voltage circuitry at the input has conductors widely separated or at the high-current output where wide conductors will appear as slabs.
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HOPKINS er al.: HYBRIDIZED OFF-LINE QUASI-RESONANT CONVERTER
TABLE 1 MATERIALS AND PROPERTIES Resistivity (mn-mil) drldf
Manufacturer
Material
@ 25OC
a
b
DuPont
6160 (Ag) 6134 (Pd-Ag) 5704
3.4 x 1 0 - ~ 0.86 20.7 X IO-’ 0.89 12.4 9.06 x 1 0 - ~ 12 7.32 x IO-) dielectric composition for use as an insulating layer
Electro-Science
9562 (Pd-Ag)
2.25 1.84
Laboratories
4904 9601 (Pd-Ag)
14.4 x io-) 4.5 x IO-’ 2.0 15.8 x IO-) 4.1 x 1.76 migration protecting glass overglaze
2.44
13.4 x IO-) 4.9 x 1 0 - ~ 2.37 7.8 x 10-3 7.69 8.4 x io-) SILICA-SEAL glass composition
3424 (Pd-Ag) 3745 (Pt-Ag) 1151
Ferro
-
1 - 1 2 0
dr/dt (“C)
10
20
30
40
50
Fmqusncy [MHz]
Fig. 6 . Experimental data and curve fit of resistivity versus frequency for different thick-film conductors.
Coatings are important when using a silver-based conductor because of silver migration [9]. When a conductor is exposed to high-electric fields and oxidizing atmospheres metal dendrites form, migrate from the conductor and, eventually, short the conductor. This phenomenon can be nearly eliminated by removing either or both adverse conditions [ lo], [ 111. A glass-based overcoat designed to abate migration is used to cover the circuit’s conductors except where solder attachment is made. Parasitic capacitances occurring between conductors because of electrostatic coupling through the metal heat sink are negligible at 2 MHz. Less than 1 pF/mil’ (of conductor surface) has been calculated for the hybrid circuit. Capacitances created by coupling across the surface are even less. V. HYBRIDCIRCUITFABRICATION A thick-film silver-based conductor pattem using Electro-Science Laboratories’ ESL 9601, Pd-Ag was successively printed and fired with a 900°C profile on 3M Company’s 96-percent alumina substrates. The circuit is overglazed and solder dammed with ESL 4904 “Migration Protecting Overglaze. ” Components are attached with DuPont’s Formon 8523 silver-bearing solder. The substrate is attached to a 4.75 mm (187 mils) thick copper
heatsink with Ablestik Company’s’Albefilm 561 K glass supported, modified-epoxy adhesive film. The final conductor thickness is 28 pm (1.1 mils) with a resistivity of 2 mQ/square area. A small portion of the output conductor path is reinforced with a tinned copper preform to assure low resistivity. High thermal conductivities necessary to keep components, such as semiconductors, at reasonable temperatures are achieved using substrate and heat spreader materials of alumina and copper, respectively. Interface materials are solders and epoxy. The semiconductors are mounted in modified TO-220 packages. The packages are surface mounted to fired-conductor substrate pads using solder. The modified packages act as copper heat spreaders for the silicon devices. The substrate is mounted to a copper plate with a 75 pm (3 mils) thick, thermally conductive epoxy preform. The calculated thermal resistance from junction to ambient is 4.1 “ C / W . The total dissipative area is 25 cm’ (3.8 in’). The circuit layout allows for high current densities and high electric fields. UL and VDE Standards are considered in the layout. Spacings of conductors and component terminations for primary-to-secondary , uncoated and coated reinforced insulation is 8 mm (3 15 mils) and 2 mm (79 mils), respectively, for both clearance and creepage. The transformer, including end tums, also conforms to the standards. The circuit without the transformer attached or the output conductors reinforced is shown in Fig. 7. VI. CIRCUITPERFORMANCE The power hybrid circuit operates at 80 W ( 5 V / 16 A ) with 78-percent efficiency from a 300 V dc input. The measured peak-to-peak output voltage ripple of the converter at full power is 40 mV. With inclusion of a gate drive the delivered power density is 21 W/in3. The oscillogram of the primary current of the transformer (switch current) and switch voltage at full output power is shown in Fig. 8. The resonant peak current is 2.4 A and the conversion frequency, as shown, is 2 MHz. The zero-current-switching property can be seen in Fig.
152
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 4, NO. I , JANUARY 1989 N
-E z F
D
% 0
20
40
60
80
Po (WI
Fig. 7 . Photograph of hybridized power circuit.
Fig. 9. Efficiency versus output power of hybridized half-bridge converter for three input line voltages, and constant output voltage, Vo = 5 V .
Fig. 8. Gate-drive voltage, primary current, and switch-voltage waveforms of hybridized half-bridge converter for Vo = 5 V and lo= 16 A . Scales: 10 V/div; 1 A/div; 100 V/div; 200 ns/div.
8. At turn-off the switch current is zero and, therefore, there is no turn-off loss. During turn-on with the junction capacitance initially charged to approximately 150 V, there is a loss as the charge dissipates within the device. At higher switching frequencies this turn-on loss reduces circuit efficiency. Figure 8 also shows a parasitic primarycircuit resonance that occurs between the magnetizing inductance of the transformer and the junction capacitances of the switches when both switches are off. This undesirable resonance is minimized with a snubber (as shown). The measured converter efficiency is shown in Fig. 9 for nominal high-line and low-line voltages. The conversion frequency as a function of the output power is shown in Fig. 10. The frequency is varied to maintain the output voltage at 5 V.
VII. 2-MHz HYBRIDIZED GATEDRIVE A two-channel isolated gate drive using the Unitrode UC3825 control chip was designed for driving the halfbridge ZCS-QRC. The UC3825 is intended for control of PWM converters, however, it has been adapted for quasiresonant circuits. The basic circuit diagram of the gate drive with constant on-time and variable frequency is shown in Fig. 11, and a detailed circuit diagram is shown in Fig. 12. A discrete NOR circuit activates Q to discharge a small capacitor, Con.When Q is off, i.e., when one of the two outputs A or B is high, the capacitor charges through Ron. The
Po IWJ
Fig. 10. Conversion frequency versus output power of hybridized halfbridge converter for three input line voltages, V, = 300 V, and constant output voltage, Vo = 5 V .
L O U T A
Fig. 11. Basic circuit diagram of 2-MHz gate drive.
capacitor is connected to the RAMP input of the UC3825. Whenever the ramp voltage reaches a value that is 1.25 V less than that at pin NI, the high voltage at active output A or B terminates. Simultaneously, Q is switched on to reset the ramp and prepare the circuit for the next pulse. On-time is determined by the time constant of the integrator circuit consisting of capacitor Conand resistor Ron.
HOPKINS
f’f
153
u l . : HYBRIDIZED OFF-LINE QUASI-RESONANT CONVERTER
Fig. 13. Gate-drive waveforms at 2 MHz
Frequency control is accomplished by using a voltagecontrolled current source connected to the RT pin (timing resistor for the internal oscillator) of the UC3825. The capacitor, at the CT input, controls the dead time between the termination of a pulse at one output and the commencement of a pulse at the other. Isolation for the drive is provided by two pulse transformers wound on very small cores (Magnetics 55266) with a 1 : 1 turns ratio (20 turns of #30 AWG). The primary sides arc capacitively decoupled with relatively large capacitors (0.1 pF) to prevent core saturation. The drive can operate from 50 kHz to 2 MHz and vary the on-time duration from 0.2 ps to 1 ps. Typical gate-pulse waveforms arc shown in Fig. 13. The measured power dissipation of the drive is plotted as a function of frequency and load, and is shown in Fig. 14. The circuit dissipates approximately 1 W when driving the ZCS-QRC at 80 W. The drive is hybridized on a 2.54 cm (1.0 in) by 3.8 cm (1.5 in) substrate as shown in Fig. 15. VIII. SUMMARY A half-bridge 300-V dc off-line zero-current-switched quasi-resonant converter (ZCS-QRC) operating in halfwave mode was designed and fabricated using thick-film hybrid techniques. Using the leakage inductance of the
Frequency [MHzl
Fig. 14. Power dissipation versus frequency of 2-MHz gate drive for three capacitive loads, C, = 1000. 560. 100 pF; and for gate-drive supply voltage VGD = 13 V.
Fig. 15. Photograph of hybrid gate drive
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 4, NO. I , JANUARY 1989
transformer and secondary-side resonance, the circuit delivered 8o ( 5 ‘/I6 A ) at 78-percent efficiency with a power density, excluding heat sink, Of 21 W/in3. A 2-MHz gate-drive circuit, designed with Unitrode’s 3825 PWM control chip, was also hybridized and its loss at full-power operation was approximately 1 W . For the hybrid design, skin effect in the thick-film conductors must be considered when power circuit operation is above 1 MHz. The data presented indicates that the of resistivity and frequency is approximately exponential in nature for conductors in close proximity. This is of concern for conductor design in the output circuitry of the gate drive. However, there is no appreciable effect at 2 MHz in the power circuit where conductors have large separations or widths.
[9] D. E. Reimer, “Material selection and design guidelines for migration-resistant thick-film circuits with silver-bearing conductors,” IEEE Electronic Components Con$ Proc,, pp, 287-292, 1981, [io] H. M. Naguib and B. K. MacLaurin, “Silver migration and the reliability of Pd/Ag conductors in thick-film dielectric crossover structures,” IEEE Trans. Components, Hybrids, Manuf. Technol., vol. CHMT-2, pp, 196-207, June 1979, [ 111 A. DerMarderosian, “The electrochemical migration of metals,” Proc. ISHM Internat. Symp. Microelectronics, pp. 134-141, 1978.
Douglas c. Hopkins (S’74-M’78). for a PhotOgraPh and biography Please see page 145 of this issue.
Milan M. JovanoviC ( s ’ 8 6 - ~ ’ 8 9 ) ,for a photograph and biography please see page 145 ofthis issue.
Fred C. Y. Lee (S’72-M’74-M’774M’87), for a photograph and biography please see page 146 of this issue.
REFERENCES [ l ] C. B. Jones and 1. P. Vergez, “Application of PWM techniques to realize a 2 MHz off-line switching regulator with hvbrid imolementation,” Proc. IEEE Applied Pow& Ecctronics Conj., New Orleans, pp, 221-227, 1986. K. H. Liu, R. Oruganti, and F. C. Lee, “Resonant switches-Topologies and characteristics,” IEEE Power Electronics Specialists Conf. Rec., Toulouse, France, pp. 106-116, 1985. M. M. JovanoviC, D. C. Hopkins, and F. C. Y. Lee, “Evaluation and design of megahertz-frequency off-line zero-current-switched quasi-resonant converters,” IEEE Trans. Power Electronics, vol. 4, pp. 136-146, Jan. 1989. [41 M. M. JovanoviC, K. H . Liu, R. Oruganti, and F. C. Y. Lee, “Stateplane analysis of quasi-resonant converters,” IEEE Trans. Power Electron.. vol. PE-2. DD. 36-44. Jan. 1987. [ 5 ] K. H. Liu’and F. C. Lie‘, “Zero-voltage switching technique in dc/dc converters,” IEEE Power Electronics Specialists Conf. Rec., Vancouver, Canada, pp. 58-70, 1986. [6] R. D. Gold, “Material selection in hybrid design,” Solid State Technology, pp. 31-35, Jan. 1977. 171 J. K. Baxter and J. W. Andow, “High temperature thermal characteristics of microelectronics packages,” IEEE Trans. Parrs, Hybrids, Packaging, vol. PHP-13, pp. 385-389, 1977. [8] R. W. Burton, “Proximity effects for parallel rectangular conductors in nontransmission-line mode,” IEEE Trans. Antennas Propagat., vol. AP-21, pp. 583-585, July 1973. (Note: Eq. 5 should be 1 [(B/A)/(2 + B/A)I.)
+
F. William Stephenson (M’75-SM’79-F’88) received the B.Sc. Engineering in 1961 from the University of Durham, UK, and the Ph.D. degree in electrical engineering in 1965 from the University of Newcastle upon Tyne, UK. He is currently a Professor of Electrical Engineering and Associate Dean for Research and Graduate Studies in the College of Engineering at Virginia Polytechnic Institute and State University, Blacksburg. He has held industrial appointments with Welwyn Electric and the Microelectronics Division of Electrosil, both in England. While with Electrosil, he worked on the applications of both monolithic and hybrid integrated circuits. His main research interests are in the areas of hybrid microelectronics, RC active and switched-capacitor filter design. Prior to joining Virginia Tech in 1978, he taught at the Universities of Hull (UK) and Rochester, NY, where he was the RT French Visiting Professor in 19761977. He is the coauthor of Linear Microelectronics Systems (Macmillan, 1973), and Active Filters for Communications and Instrumentation (McGraw Hill (UK), 1979), and the editor of RC Active Filter Design Handbook (John Wiley & Sons, 1985). He has published research results in such journals as IEEE Transactions (CHMT and CAS), Int. Journal of Circuit Theory and Applications, Microelectronics, and others.
