12345

1. IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 48, NO. 3, JUNE 2001 535
A High-Voltage Power Supply Operating Under a
Magnetic Field
Yoshiaki Shikaze, Masatosi Imori, Hideyuki Fuke, Hiroshi Matsumoto, and Takashi Taniguchi
Abstract—This paper describes the performance of a
high-voltage power supply incorporating a ceramic transformer.
Since the transformer is constructed using a ceramic bar con-
taining no magnetic material, the power supply can operate under
a magnetic field of 1.5 Tesla with no degradation of performance.
Feedback is used to stabilize high-voltage output such that a
supply voltage of 3 V provides from 1500 to 2500 V at a load of
more than 10 M
with efficiency higher than 50%; and with
a supply voltage of 2 V, 3000 V is supplied at a load of 20 M
.
In fact, a supply voltage of 5 V is sufficient to provide 4000 V
at the same load. A network of high-voltage power supplies is
also described. Most functions of the power supply are thereby
monitored and controlled through the network.
I. INTRODUCTION
THIS paper describes a high-voltage power supply intended
to efficiently provide high-voltage output under a mag-
netic field. This is made possible by incorporating a ceramic
transformer that uses the piezoelectric effect to generate high-
voltage [1]. As the transformer contains no magnetic material,
there is no leakage of magnetic flux such that it can be oper-
ated under a magnetic field. An inductance element is needed
to obtain efficient voltage conversion, being implemented by an
air-core coil that can also be operated under a magnetic field.
We previously studied a high-voltage power supply incorpo-
rating these components [2]–[8], and have thus far improved
conversion efficiency and the amplitude ratio of the transformer
[2]–[6]. Here, we further evaluate its performance and measure
the effects of a 1.5-Tesla magnetic field, finding no degradation
of performance.
The high-voltage power supply includes feedback to stabilize
high-voltage output. The range of high-voltage output which
the power supply can efficiently provide depends on the supply
voltage. A supply voltage of 3 V can supply from 1500 to 2500
V at a load of more than 10 M with efficiency higher than 50%.
With a supply voltage of 2 V, 3000 V is supplied at a load of 20
M . In fact, a supply voltage of 5 V is sufficient to provide 4000
V at the same load.
This paper also describes a network of high-voltage power
supplies that we intend to implement. Each high-voltage power
supply is equipped with an interface chip supporting a network.
Manuscript received November 2, 2000; revised February 25, 2001 and
March 18, 2001.
Y. Shikaze and H. Fuke are with the Faculty of Science, University of Tokyo,
Tokyo 113-0033, Japan.
M. Imori and M. Matsumoto are with International Center for Elementary
Particle Physics (ICEPP), University of Tokyo, Tokyo 113-0033, Japan (e-mail:
imori@icepp.s.u-tokyo.ac.jp).
T. Taniguchi is with the National Laboratory for High Energy Physics (KEK),
Tsukuba-shi 305-0801, Japan.
Publisher Item Identifier S 0018-9499(01)04909-7.
Most functions of the power supply are maintained under the
control of the chip, and are then monitored and controlled
through the network.
II. CERAMIC PIEZOELECTRIC TRANSFORMER
Manufactured by NEC Corporation [2], the ceramic trans-
former is symmetrically shaped in the lengthwise direction and
operated in a third-order longitudinal vibration mode that fea-
tures low internal resistance. This mode locates electrodes, wire-
connected to input and output electronic terminals, at the nodes
of the vibration mode. The transformer input voltage is ampli-
fied at the output, with the input to output voltage ratio being an
amplitude ratio that shows a resonance as a function of a driving
frequency. The -value depends on the load connected to the
transformer, being about 2000 at no load and roughly a hundred
when loaded at a few hundred kilo-ohms [2], [5]. Voltage is am-
plified by about 120 times at a load of about 200 k . Maximum
output power is about 4 W.
A. Optimal Resistance
Efficiency of the ceramic transformer is determined using the
ratio of the power supplied to the transformer to the power dissi-
pated at the load. If is angular velocity of the driving frequency
and is output capacitance of the transformer, then assuming
that the load of the transformer is a resistor denoted by , the
efficiency of the transformer can be expressed as a simple func-
tion of , i.e., . Maximum efficiency is achieved
when , i.e., the resistance is equal to the impedance of the
output capacitor at the driving frequency [4], [9]. If is
the optimal resistance realizing maximum efficiency, then
(1)
B. Energy Reservoir
When energy is stored in inductance loaded with resistance
, the time constant is . To maintain voltage across the re-
sistance, energy is injected into the inductor at switching time
intervals roughly equal to the time constant. Accordingly, a large
resistance increases the switching frequency. Since the load re-
sistance of power supply tends to be large, the inductance is not a
good energy reservoir for the high-voltage power supply. When
energy is stored in capacitance C, the time constant is such
that the switching time required to maintain voltage becomes
longer as the resistance increases. The capacitance is therefore
a good energy reservoir for the high-voltage power supply. The
piezoelectric ceramic transformer stores energy as mechanical
0018–9499/01$10.00 © 2001 IEEE

2. 536 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 48, NO. 3, JUNE 2001
Fig. 1. Schematic circuit of the high-voltage supply incorporating an error amplifier implemented by INA122 and OPA234 and voltage controlled oscillator by
PD5555 and a flip–flop.
vibration, with energy dissipation at the load decaying the vibra-
tion. The transformer is similar to capacitance in that the time
constant of the decay is proportional to load resistance.
III. HIGH-VOLTAGE POWER SUPPLY
The high-voltage power supply is utilized in an experiment in
which the range of output voltage supplies photomultipliers, i.e.,
it provides 1500–2500 V against a load of about 10 M . This
load is a bleeder of the photomultipliers. From a power stand-
point, the ceramic transformer delivers sufficient power to drive
a load of 20 M up to 4000 V output. Note that simply changing
the ratio of the divider resistors will produce from 3000 to 4000
V.
A. Circuit
The high-voltage supply is composed of a reference voltage,
error amplifier, voltage controlled oscillator (VCO), driver cir-
cuit, ceramic transformer, Cockcroft–Walton (CW) circuit, and
divider resistors (Fig. 1). The high-voltage output is stabilized
by feedback, i.e., it is divided by divider resistors and fed back
to the error amplifier to be compared with the reference voltage.
The voltage difference between the input of the error amplifier is
amplified and fed to the VCO which produces a carrier wave that
carries the driving frequency for the ceramic transformer. The
carrier wave is frequency-modulated by the output of the error
amplifier and is applied to the ceramic transformer through the
driver circuit. The driver circuit generates a sinusoidal carrier
wave so that input capacitance of the ceramic transformer can be
efficiently driven. This carrier wave is amplified in voltage, and
the amplified voltage induced between the output terminals of
Fig. 2. Resonance curve of the ceramic transformer.
the ceramic transformer is then further amplified in voltage and
rectified by the CW circuit. Ideally the CW circuit multiplies the
input voltage by six times at the output, which reduces the dis-
crepancy in resistance between the optimal resistance and load
resistance. In this manner the CW circuit serves as an impedance
converter between the transformer and load [4]. The resistance
of the load viewed from the input of the CW circuit is about 200
k at a load of 20 M .
1) Error Amplifier: The transformer’s resonance frequency
is about 120 kHz (Fig. 2), and the driving frequency intervenes
between 120 and 130 kHz. Noise in the high-voltage output in-
cludes voltage ripples produced by cyclic charge/discharge of
capacitors. These ripples are a sawtooth component of the noise
synchronized with the driving frequency. To prevent amplifying
voltage ripples at the error amplifier, capacitance is used
across the amplifier input and output. , with a value of 1 nF,
limits the amplifier bandwidth between dc components to a few
tens of kilohertz, being sufficiently narrow to reduce the rip-
ples synchronized with driving frequency. Since a range of the

3. SHIKAZE et al.: A HIGH-VOLTAGE POWER SUPPLY OPERATING UNDER A MAGNETIC FIELD 537
Fig. 3. Delay circuits, MOSFETs, air-core coils, and supply voltage at the
driver circuit.
driving frequency utilized for feedback intervenes between dc to
a few kilohertz, a second zero is introduced by capacitance
connected in parallel with a 50-k resister at the amplifier input.
This reduces the phase shift in the frequency range and improves
feedback stability. has a value of 2 nF to prevent the second
zero from interfering with an amplitude response produced if
the second zero were not present.
2) Delay Circuits: Delay circuits (Fig. 3), added to the input
of TPS2811 to postpone rising edges of the flip–flop output,
delay turning off the MOSFETs (2SK2796Ls) to prevent both
FETs from simultaneously switching off, which would produce
a large voltage spike at the output of the driver circuit and sub-
sequently cause noise at the power supply high-voltage output.
B. Feedback
Feedback utilizes the frequency dependence of the amplitude
ratio of the transformer which depends on the driving fre-
quency whose range is designed to be higher than the resonance
frequency of the ceramic transformer. As shown in Fig. 2,
feedback increases the driving frequency when the output
voltage is higher than the reference voltage at the input of
the error amplifier. Similarly, the driving frequency decreases
when output voltage is lower than the voltage specified by the
reference voltage.
1) Breakdown of Feedback: If the load of the high-voltage
power supply falls within an allowable range, the driving fre-
quency is maintained higher than the resonance frequency such
that the feedback is negative as designed. The allowable range
of load is sufficient in most cases, but it cannot cover, for ex-
ample, short-circuiting the output high-voltage to ground. When
the load deviates beyond the allowable range, the driving fre-
quency may decrease below the resonance frequency; a condi-
tion that will not provide the required negative feedback, i.e.,
positive feedback locks the circuit such that it is independent
of load. In order to recover the negative feedback, the driving
frequency must be reset externally in addition to removing the
load.
2) Protection of Circuit: When the reference voltage is
shifted, the output high-voltage follows this shift. The capacitor
employed at the high-voltage output is charged or discharged
according to the voltage shift. If the voltage shift is too large in
amplitude, the load caused by the shift may flip the frequency
of the VCO beyond the resonance frequency. The flip of the
frequency, accompanied with the breakdown of the feedback,
lowers the output high-voltage. Thus the flip of the frequency
works as protection against, for example, a short circuit of
output high-voltage.
IV. IMPROVING EFFICIENCY
Since transformer performance is susceptible to stray capac-
itance, especially around the output terminals, it is important to
reduce the capacitance mainly due to the junction capacitance
of the diodes in the CW circuit. The diodes are therefore
vital for the efficiency of the high-voltage power supply [5],
[4]. The key to improving efficiency is realizing zero-voltage
switching (ZVS) at the driver circuit. Therefore, a range
of driving frequency was studied where ZVS occurs, being
maintained against a wide range of driving frequency [6]. It
is also important to match the resistance of the load viewed
from the input of the CW circuit to the optimal resistance of
the transformer, i.e., reducing the discrepancy of resistance
contributes to improving efficiency.
A. Diode
Efficiency of the ceramic transformer is susceptible to
stray capacitance, especially around the output terminal. The
output impedance of the transformer affects efficiency which
is degraded by the capacitance between the output terminal
and ground. Lower equivalent resistance of the transformer
provides lower impedance at the output, which reduces such
degradation. The diode in the CW circuit strongly influences
efficiency because its junction capacitance is loaded between
the output terminal of the transformer and ground. This diode
(ESJA98), a high-voltage diode featuring high speed switching
up to 1 MHz, was developed for high-voltage rectification
in the deflection system of high definition TV. The junction
capacitance is less than 2 pF at 1 MHz. Its characteristics have
been measured for Spice parameters which indicate that the
junction capacitance is smaller than 1 pF.
B. Zero-Voltage Switching
To efficiently drive the transformer, it is indispensable
to apply a sinusoidal carrier wave to the input terminals.
The driver circuit generates this wave which eliminates the
power consumed by the capacitance mainly produced by the
transformer. The driver circuit includes two identical reso-
nant circuits (Fig. 3), each of which consists of inductance
implemented by an air-core coil and MOSFET. The FETs are
simultaneously switched on and off alternately. When the FET
is off, the inductance in the resonant circuit resonates with
the capacitance; and when it is on, the inductance stores the
current. One resonant circuit produces a half sinusoidal wave,
while the other identical circuit alternately generates the other
half sinusoidal wave. Accordingly, the driver circuit generates a
quasisinusoidal carrier wave at the transformer input terminals.
ZVS is realized if the FETs switch over when the voltage
applied across them is close to 0 V. They are simultaneously

4. 538 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 48, NO. 3, JUNE 2001
Fig. 4. Plots of (a) output high-voltage and (b) efficiency against driving
frequency for each value of inductance.
driven by the driving frequency. If the ZVS frequency is de-
fined by a self-running frequency at which the inductance res-
onates with the capacitance autonomously, then ZVS is real-
ized when the driving frequency is equal to the ZVS frequency.
ZVS is also realized while the driving frequency is lower than
the ZVS frequency. Thus, the efficiency, being the ratio of the
power supplied to the driver circuit to the power dissipated at
the load resistance, should be fairly constant while the driving
frequency intervenes between the resonance frequency and ZVS
frequency.
C. Dependence of Efficiency on Inductance
With the supply voltage set at 3 V, power supply efficiency
was measured at several values of inductance. Fig. 4 shows the
output high-voltage and efficiency versus the driving frequency
for various values of inductance, where output high-voltage in-
creases as the driving frequency approaches the resonance fre-
quency. Similarly, efficiency increases, reaching a plateau at
about 50%. As expected, the plateau corresponds to a range of
driving frequency between the resonance and ZVS frequencies.
Since a smaller inductance causes a higher ZVS frequency, the
plateau shows a wider frequency range as inductance decreases.
Regarding efficiency versus output high-voltage (Fig. 5), note
that at smaller inductance values the plateau is again wider in
the range of output high-voltage and that at larger inductance
the efficiency reaches a higher plateau.
Since the ZVS frequency is a function of the inductance in the
resonator circuit, an inductance must not be used that locates the
ZVS frequency close to the resonance frequency. In other words,
placing the ZVS frequency at an adequate frequency contributes
to improving the efficiency of the power supply. The inductance
value should ensure sufficient tolerance to maintain the ZVS
against a wide range of driving frequency.
V. PERFORMANCE
At a load of 20 M , an equivalent load resistance viewed
from the input of the CW circuit is about 200 k . The amplitude
ratio of the ceramic transformer is accordingly expected to be
Fig. 5. Plot of efficiency versus output high-voltage for various values of
inductance.
Fig. 6. Plot of (a) efficiency and (b) output high-voltage versus driving
frequency for various values of supply voltage.
about 120 at the resonance frequency. In practice, the amplitude
ratio was found to be about 80 around the resonance frequency
[6].
A. Dependencies on Supply Voltage
When efficiency was plotted against the driving frequency
for various supply voltages, results showed that it is indepen-
dent of supply voltage and strongly dependent upon driving fre-
quency [Fig. 6(a)]. Similarly, output high-voltage was deter-
mined versus driving frequency for each supply voltage, with
results showing that the amplitude ratio at a specified driving
frequency is rather independent of the supply voltage [Fig. 6(b)].
The amplitude of the sinusoidal carrier wave applied to the ce-
ramic transformer is about three times the supply voltage, and
the transformer output voltage is then further multiplied by the
CW circuit by about six times. For example, at a supply voltage
of 2 V, the output high-voltage reaches 2800 V at a load of 20
M . In this case, the amplitude ratio around the resonance is
estimated to be about 80.

5. SHIKAZE et al.: A HIGH-VOLTAGE POWER SUPPLY OPERATING UNDER A MAGNETIC FIELD 539
Fig. 7. Plot of efficiency versus output high-voltage for various supply
voltages.
1) Efficiency Versus Output High-Voltage: Fig. 7 shows
efficiency plotted against output high-voltage for each supply
voltage, where correspondence between efficiency and output
high-voltage is identical among the supply voltages in the
sense that widening the correspondence at the 2-V supply
voltage by two times in a lengthwise direction produces the
correspondence at the 4-V supply voltage. The shape of the
correspondence is due to the dependence of efficiency on
driving frequency, which is defined by the inductance at the
driver circuit.
Fig. 7 shows that the efficiency for producing output high-
voltage depends on the supply voltage; thus the supply voltage
should be selected according to the range of output high-voltage.
For example, assuming a high-voltage power supply load of 20
M , a supply voltage of 2 V is efficient for output from 1000
to 2000 V, while a 3-V supply voltage for 1500 to 2500 V, and
a 5-V supply voltage for 3000 to 4000 V at wide range of load.
VI. EFFICIENCY UNDER A MAGNETIC FIELD
Efficiency under a 1.5-Tesla magnetic field was tested
at KEK, i.e., the output high-voltage and efficiency were
measured with respect to driving frequency. Fig. 8 shows the
results with and without the magnetic field present. Note that
the magnetic field shows no marked effect on either output or
efficiency. Fig. 9 shows efficiency versus output high-voltage,
where again the effect of the magnetic field is small. The
effect of the magnetic field is limited when precision of the
measurement is taken into account. For practical application,
however, long-term stability must be verified. This is left for
future work.
VII. NETWORK
The high-voltage power supply includes a “Neuron” chip1
which is a programming device possessing a variety of input and
output processing capabilities. It can also communicate over a
twisted-pair cable with other Neuron chips; a feature that allows
1Neuron is a registered trademark of Echelon Corporation.
Fig. 8. Efficiency versus output high-voltage at various supply voltages.
Fig. 9. Efficiency versus output high-voltage for various supply voltages.
establishing a network consisting of a number of power supplies
that respectively incorporate the chip. The functions of a chip-
controlled power supply are managed via the network, i.e., it
monitors and controls all connected power supplies.
A. Output High-voltage
The reference voltage is generated by a digital-to-analog con-
verter controlled by the chip such that the reference voltage and
therefore output high-voltage can be controlled by the network.
B. Recovery from Feedback Breakdown
The VCO voltage, being the output of the error amplifier, is
supplied to the VCO and controls the driving frequency. A fre-
quency flip is produced by deviation of the VCO voltage from
its normal range. This deviation is detected by voltage com-
parators which interrupt the Neuron chip. Once awakened the
chip reports the frequency flip through the network. While under
network control the chip recovers from the frequency flip, i.e.,
the reference voltage is reset, which initializes the driving fre-
quency, and the chip increases the reference voltage to a pre-
scribed value and restores the output high-voltage.
C. Current Monitor
If the output high-voltage is assigned, the frequency at which
the transformer is driven depends on the supply voltage, which
if known beforehand, allows the output current to be estimated
from the driving frequency. The VCO outputs the driving fre-
quency on a square wave, thus a simple logic circuit enables

6. 540 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 48, NO. 3, JUNE 2001
the chip to count pulses. The driving frequency, obtained by
counting pulses over a fixed time interval, allows calculating
the output current based on output high-voltage and the supply
voltage.
ACKNOWLEDGMENT
The authors are grateful to NEC Corporation. for providing
the ceramic transformers, without which it would have been im-
possible to develop the presented device, and to NEC employees
T. Zaitsu, Y. Sasaki, and A. Ochi for their valuable support. They
also thank Prof. A. Yamamoto for making available the mag-
netic field testing facility, and members and supporters of the
BESS collaboration for encouraging us to employ the ceramic
transformer.
REFERENCES
[1] C. A. Rosen, Solid State Magnetic and Dielectric Devices. New York:
Wiley, 1959, pp. 87–197.
[2] S. Kawashima, O. Ohnishi, H. Hakamata, S. Tagami, A. Fukuoka, T.
Inoue, and S. Hirose, “Third order longitudinal mode piezoelectric ce-
ramic transformer and its application to high-voltage power inverter,” in
IEEE Ultrasonic Sympo., Pro., Cannes, France, Nov. 1994, pp. 525–530.
[3] M. Imori, T. Taniguchi, and H. Matsumoto, “A photomultiplier
high-voltage power supply incorporating a piezoelectric ceramic
transformer,” IEEE Trans. Nucl. Sci., vol. 43, pp. 1427–1431, June
1996.
[4] M. Imori, T. Taniguchi, and H. Matsumoto, “A photomultiplier high-
voltage power supply incorporating a ceramic transformer driven by fre-
quency modulation,” IEEE Trans. Nucl. Sci., vol. 45, pp. 777–781, June
1998.
[5] , “Performance of a photomultiplier high-voltage power supply
incorporating a piezoelectric ceramic transformer,” IEEE Trans. Nucl.
Sci., vol. 47, pp. 2045–2049, Dec. 2000.
[6] Y. Shikaze, M. Imori, H. Fuke, H. Matsumoto, and T. Taniguch, “Per-
formance of a high-voltage power supply incorporating a ceramic trans-
former,” in Pro. 6th Workshop on Electronics for LHC Experiments,
Krakov, Poland, Sept. 2000, pp. 371–375.
[7] T. Zaitsu, T. Inoue, O. Onishi, and A. Iwatani, “2 M Hz power converter
with piezoelectric transformer,” in INTELEC’92, Pro., Oct. 1992, pp.
430–437.
[8] O. Onishi, Y. Sasaki, T. Zaitsu, H. Kishie, and T. Inoue, “Piezoelec-
tric ceramic transformer for power supply operating in thickness exten-
sional vibration mode,” IEICE Trans. Fundamentals, vol. E77-A, pp.
2098–2105, Dec. 1994.
[9] C. Y. Lin and F. C. Lee, “Design of piezoelectric transformer converters
using single-ended topologies,” in 1994 VPEC Seminar, Proc., pp.
107–112.