Download Design of a Modified Cockcroft Walton Generator

PHY 492: Final Report
Design of a modified Cockcroft Walton Generator
Fidel Tewolde
April 25, 2014
Abstract
A modified design of Cockcroft Walton voltage multiplier was studied in this paper. This
modification was implemented using symmetric version of the original Cockcroft Walton
voltage multiplier. Experimentally various input voltages were studied for up to three stage
symmetric Cockcroft Walton voltage multiplier and the results were compared with the
theoretically expected values. Circuit simulation software called Circuit Maker was used to
simulate output waveforms from input of 120 V peak to peak sinusoidal a.c voltage operating at
60 Hz for up to four stages of symmetrically modified circuit.
1 Introduction
British and Irish physicists John Douglas Cockcroft and Ernest Thomas Sinton Walton in 1932
used high dc voltage generated from low voltage ac input to power their particle accelerator [1].
Cockcroft and Walton had won the Nobel Prize for Transmutation of atomic nuclei by artificially
accelerated atomic particles. It should be noted that the circuit they used was discovered first by
Swiss physics Heinrich Greinacher in 1919. Since then there had been various improvements in
circuit design resulting in doubling of output voltage, tripling, quadrupling and so on in different
ways. However, various studies and publications show the efficiency of Cockcroft-Walton
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voltage multiplier (CWVM) failed to continually raise the value of output voltage when the
number of stages increase or when the operating frequency and capacitance are not sufficiently
high to avoid voltage drop in coupling capacitors at each stage. Complete understanding of the
working principle of CWVM requires consideration of transient behavior and analysis under
various load current. Zi-Feng He, Jin-Ling Zhang, Yong-Hao Liu, Yu-Tian Zhang and Yin
Zhang (2011) [5] found that the voltage drop with in the ciruit increases linearly as the load
current increases. The voltage ripple of the output also increases linearly as a percentage of the
output voltage as the load current increases. Haibo Zhang et al. (1995) also found that the upper
and lower end diodes suffer most during load short circuit [2].
This method of raising voltage is cheaper than using a transformer. The components needed are
only two capacitors and two diodes (three capacitors four diodes for symmetric CWVM),
cheaper. The difference in the output of each stages is an integer multiple of the original input,
thus allowing for the possibility of multi-tapping. However as the number of stages increase the
voltage is reduced. This is primarily due to ac impedance of capacitors and the internal resistance
of diodes.
In our project only the case of voltage multiplication when there is no load current (open circuit
characteristics) were investigated. The work was done both experimentally and in simulation
modes.
2 Applications
CWVM was used in various scientific and industrial applications. The most common
applications are in CRT televisions, laser systems, traveling wave tube amplifiers, high voltagelow current power supplies, x-ray systems, LCD backlighting, ion pumps, electrostatic systems,
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air ionizers, particle accelerators, copy machines, scientific instrumentation, oscilloscopes, and
many other application requiring high voltage dc [4].
3 How does it work?
Eout=2N(Vin-Vdrop);
However the value of Vdrop=0 under no load [5].
Let’s build the circuit beginning by Figure1: which consists of only only ac voltage source, one
capacitor C1 and one diode D1. After a short time the capacitor will be charged to a value equal
to the maximum input voltage V1.Note that the capacitors used in the experiment were rated at a
maximum of 1kV, which was well inside the range of the experiment. If we compare the input
voltage measured at the input side of C1 seen at Figure 2 with the voltage measured at the other
end of capacitor C1 (Figure 4:), we can see that after a short initial time needed to charge the
capacitor C1, the output voltage is effectively shifted up from the negative values. This is
explained as follows. Let’s begin when the capacitor is fully charged and the voltage is at its
peak positive value. The net voltage at the out of the capacitor is the addition of both the input
voltage and the voltage of the capacitor, thus we have twice the input voltage. And when the
voltage is at its lowest point we can see that the two voltages (voltage of the source and voltage
across C1) are equal in magnitude but opposite in direction, thus the voltage at the output of the
capacitor is zero. Other values that are between these two extreme points can then be deduced to
have values between the value of 2V1 and 0 volts
3
.
Figure 1: Series Capacitor diode circuit
Figure 2: Measured input of capacitor diode
circuit
Figure 3: Measuring output of C1
Figure 4: Measured output of C1
But the output voltage is still very much sinusoidal, though not alternating any more. Thus a
smoothing circuit is required which was achieved using the circuit below at Figure 5. Since our
measuring instrument was measuring the voltage across C2 for all times, we can assume that the
voltage was only going to increase from 0 to the maximum possible value (assuming the input
voltage to C2 did not exceed the peak operational voltage of that capacitor which is a reasonable
assumption in our case). Note that we did not have any load and there would not be any draining
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of voltage from C2. Thus when voltage was pumped in to C2 the voltage across C2 would rise to
the maximum which in our case was 2V1 giving us our steady and smooth dc voltage. Note that
D2 will prevent any reduction in the value of the peak voltage across C2 when the voltage coming
from the input drops in the sinusoidal fashion.
Figure 5: Addition of smoothing circuit
Figure 6: smoothed dc output
Figure 5 is the conventional CWVM. By cascading more stages we can repeat the process and
ideally add additional voltage of V1 after each stage. For the modified CWVM the same process
is repeated the only difference being the reversed polarity of input voltage of V1. By making the
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CWVM circuit symmetric we are effectively adding another stage thus doubling the voltage
multiplication factor of the circuit.
3.1 Limitations of the Cockcroft-Walton voltage multiplier
There a critical practical limitations on how we can go with this method of voltage
multiplication. The first limitation is our diodes. The diode was assumed to be open when
reverse biased but there is a small reverse bias voltage which could be considerable when we use
low values of voltage. The effect of the reverse biase voltage is to effectively pull the output
voltage by that specific amount (of reverse bias voltage) below the zero voltage line.
More significantly though is the effect of frequency on voltage across the capacitor. We know
that a capacitor is charged after opposing charges migrate to opposing plates. This migration
which is also called electric current in turn builds voltage across the plates. However if the input
frequency is low there is a high capacitive reactance which in turn this reactance lowers the
current or charge build up thus reducing the voltage across the capacitor. With each additional
stage stage the effect is amplified further. To avoid this effect we can use high frequency input
supply.
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4. Experimental Setup
IN4007 diode and 0.1uF capacitor were used in the construction of symmetrical CWVM circuit.
Variable ac voltage generator with a range of 0 to 40V was used. An Oscilloscope was used to
observe the voltage at various stages and the measurement was done using digital multimeter
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5. Simulation
Figure 7: Input signal of 120V peak to peak at 60 Hz
Figure 8: One stage CWVM
Figure 9: Output of one stage
CWVM
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Figure 10: Two stage CWVM
Figure 11: Output of two stage CWVM
Figure 12: Three stage CWVM
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Figure 13: output of three stage CWVM
Figure 14: Four stage CWVM
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Figure 15: Output of four stage CWVM
6, Experimental Data
For single stage symmetrical CWVM, the theoretical output voltage was twice the input voltage,
however the measured ratio of output to input voltage was only 1.7599.
One stage symmetrical CW voltage multiplier
80
y = 1.7599x
70
60
50
40
30
20
10
0
0
5
10
15
20
25
30
35
40
45
Figure 16: Input Vs Output voltage of one stage symmetrical CWVM
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For two stage symmetrical CWVM, the theoretical ratio of output voltage to input voltage was 4,
however a ratio of 3.4018 was measured in the experiment
Two stage symmetrical CW voltage multiplier
160
140
y = 3.4018x
120
100
80
60
40
20
0
0
5
10
15
20
25
30
35
40
45
Figure 17: Input Vs Output voltage of two stage symmetrical CWVM
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For symmetrical three stage CWVM multiplier the ratio of output voltage to input voltage was 6
however the data from the experiment showed a ratio of only 4.2255.
Three stage symmetrical CW voltage multiplier
180
y = 4.2255x + 1.4687
160
140
120
100
80
60
40
20
0
0
5
10
15
20
25
30
35
40
45
Figure 18: Input Vs Output voltage of three stage symmetrical CWVM
Figure 19: Input and output voltage of CWVM as seen by an Oscilloscope.
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7 Results and Conclusion
Based on the experimental data and simulations, we could see that the CWVM circuit raised low
voltage ac input in to high values of dc voltage. However theoretical expectations and
experimental differ by a constant multiple of the measured output voltage. The simulated open
circuit output voltage similarly differed from the theoretical value of output voltage of the
symmetric CWVM. The only explanation for this discrepancy was ac impedance of capacitors
especially the coupling capacitors on both sides of the symmetric circuit and resistance
associated with each diode. Based on our measurement the resistance of each diode was about
0.9k ohm.
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8. References
[1] D. Cockcroft and E.T.S Walton, Proc. R Soc. London 136 (830), 619 (1932)
[2] Haibo Zhang, Akio Takaoka, and Katsumi Ura. Transient analysis of Cockroft-Walton
cascade rectifier circuit after load short circuit. (1995)
[3] Reinhold G. and Gleyvod R. Megawatt hv dc power supplies. IEEE transaction on nuclear
science, 22(3), 1975.p. 1289-92
[4] Suematsu S, Suganomata S, and Oshima Y. Nuclear instruments and methods. 52(1967), p.
206-212
[5] Zi-Feng He, Jin-Ling Zhang, Yong-Hao Liu, Yu-Tian Zhang and Yin Zhang. Characterstics
of a Symmetrical Cockcroft Walton power supply of 50 Hz 1.2 V/50mA (2011)
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