- Email: [email protected]
A new modification of the cockcroft-walton voltage multiplier circuit
NUCLEAR
A NEW
INSTRUMENTS
MODIFICATION
AND
METHODS
OF
THE
67 0969) 331-336;
©
NORTH-HOLLAND
PUBLISHING
CO.
C O C K C R O F T - W A L T O N VOLTAGE M U L T I P L I E R CIRCUIT W. G O E B E L * Received 9 September 1968
By introducing a transverse coil in the middle of a CockcroftWalton multiplier, thus forming a resonant circuit in series with the capacitors of the condenser columns, the limit of the obtainable high voltage, given by Greinacher in the expression V = nvo can be far exceeded. The economy of the modificated cascade rectifier voltage multipliers seems to be better compared with
conventional ones, which could be studied with a test model of 200 kV. The power factor was measured to be 1.0 and the overall efficiency to 76%. This gives new principles on the design of dc-accelerators with high power-output using Cockcroft-Walton multipliers.
1. I n t r o d u c t i o n
In the design of high-voltage particle accelerators different principles are used, dependent from the requirements. If averaged beam-currents above a few milliamperes are wanted and also voltages in the range up from 50 kV the Cockcroft-Walton voltage multiplier is suitable and often used. However there is a limitation in the development of this type towards increasing voltages and currents. Stray capacities cause a drop of the transverse voltage a n d - a s a c o n s e q u e n c e - a decrease of the output voltage even without load. The obtainable voltage according to the Greinacher formulas (fig. l a) is V = nVo,
(no load)
V = n V o - ~ - i n3 I / ( 6 f ) ,
(load, but squareterm
[
!"
c C
cT rv-ew~
l
....
J
Fig.la Oreinacher - circuil
Fig.lb Circuil with several Iransformers
Fig.It Symmelrical half wave
circuit
(1)
neglected),
~
:
(2)
where n is the number of rectifier branches (in the following designed as stage), Vo the peak-value of the ac input voltage, I the dc load current, f the operating frequency and C the series capacitors across two stages (fig. la). Numerous literature exists decribing the Cockcroft-Walton multiplier circuit in detaill'2). Several measures have been adopted in the past to eliminate the effect of stray capacities and to approximate the value of the ideal and nondissipative generator described above: Increase of the ac input voltage is limited by the break-through characteristics of the circuit elements involved and also results in exceptionally high and undesirable voltages within the generator. Increase of the operating frequency reduces the load
* Address: Burgkmairstr. 48, 8 MiJnchen 12, West-Germany.
331
2 o_o
15 I
o-"~
J
Fig.ld Fig.le Symmetrical full-wave High Pass ~-Filter circuil
Fig. I f transmission Line
Fig. 1. Some modifications o f the original Greinacher-circuit.
dependent voltage drop but not the one due to the reactive currents. Higher values of C improve the situation, but increase the stored energy which is undesirable, because heavy damages occur when sparks jump over which is alsmost inevitable in high voltage devices. Using several high voltage feed points for the
332
w. GOEBEL
cascade generator at various stages (fig. lb) avoids decreasing transverse voltage at upper stages3), but such generators seem to be expensive and voluminous. Grounding the center tap of the transformer and adding a separate smoothing condenser column (fig. l c) reduces the ripple. On addition it allows the duplication of the input voltage without obtaining a higher voltage at the grounded transformer core. However the stored energy increases adaequately by adding the smoothing condenser column. Applying a full wave rectification by using twice the number of rectifiers (fig. Id), both the load dependent voltage drop and the ripple are further reduced4). The inserting of high voltage coils between the capacitor columns (like fig. lc, center tap like ld) gives a compensation for the effects of stray capacities if tuned to them by a parallel resonant circuit. Every circuit, however, absorbs energy and thus increases the load. Designing the generator as a high-pass LC-filter (fig. le) or as a transmission line (fig. If) the circuit is terminated on its high voltage end by a matching resistor 5) or by a suitable chosen inductance6). In all these modified circuit arrangements the maximum voltage obtained may not exceed the theoretical level derived from formula (1). Contrary to this, by using a similar arrangement, but another operation mode, the limits of formula (1) are no more obligatory and voltages are obtainable which may be extended theoretically to infinity under ideal circumstances without load, as subsequently will be described. 2. A new modification: The resonant cascade
The resonant cascade is applicable to cascade generators with symmetrical or nonsymmetrical circuits and with half wave or full wave rectification. The only difference to these is the insertion of a transverse coil Lq with high Q-factor, the position of which is approximately in the middle of the condenser columns and which is connected between them (fig. 2). The operation mode may be explained in the following manner: The transverse coil, the high-voltage transformer and all the capacitors C between them, on both columns, form a series-resonant circuit having a resonant frequency equal to the ooerating frequency. If the circuit would not be damped, there would be a current in it extended to infinity, i f a voltage is applied. The transverse voltage vL across the coil vL =
I~oL,
(3)
would also run to infinity. The required ac input voltage v0 would be near zero.
2 ~
~..t_x..A..A_.r~
t. . . . .
7
]
Fig. 2. T h e resonant cascade, s h o w n as a 8-stage model.
Thus the transformer may be regarded as a current transformer which delivers the resonant current, the transverse coil may be regarded as voltage-generator. Currents in a nondissipative resonant circuit are reactance-currents like those of stray capacities. Contrary to the conventional devices, where they diminish the efficiency, in the new modification they are needed to produce a voltage across the rectifiers. The ac voltages are rectified and accumulated in the usual manner to the dc output voltage. The limitation of resonant current occurs by the dissipation factors of transformer, condensers and the transverse coil, but essentially by the load resistor which produces in-phase-components of the current. Such currents in an resonant circuit cause a damping and also a widening of the resonance curve. The real operation of the resonance cascade with load is a mixture between the mode just described and the conventional operation mode with an input voltage vo not being near zero. And the real output voltage is neither infinity nor Greinachers value, but between them.
COCKCROFT-WALTON
VOLTAGE
3. The mathematical model Because f o r m u l a ( i ) is no m o r e a p p l i c a b l e on r e s o n a n t circuits we have to use a n o t h e r m a t h e m a t i c a l model to d e t e r m i n e the o u t p u t voltage. F o r the case o f z e r o - l o a d the cascade m a y be regarded as a n e t w o r k o f reactances. There are c a p a c i t o r s C o f the c o n d e n s e r columns, a transformer, a transverse coil Lq a n d stray capacities Cq, which c o m p r i s e the j u n c t i o n capacities o f the rectifiers, the individual capacities interconnecting the c o n d e n s e r c o l u m n s a n d the capacities between the g e n e r a t o r a n d external devices such as a pressure t a n k housing the circuit. The rectifiers D itself need not be considered, because they show a very high reverse resistance in the static case without load. In a usual way - by t h e o r y o f the transmission line6), or by using a matrix - the ac transverse voltage across each rectifier-branch m a y be d e t e r m i n e d , if an inputvoltage on the b o t t o m - f e e d p o i n t is assumed. The dc voltage across every rectifier-branch is equal to the peak value o f the ac transverse voltage. By algebraic a d d i t i o n o f all the dc voltages a l o n g the rectifiers the o u t p u t dc voltage o f the cascade is determined. This way to calculate the t o p dc voltage was perf o r m e d in a c o m p u t e r for the test m o d e l described in ch. 4 and it a d d u c e d g o o d results. There are a lot o f further aspects to be n o t e d on the design o f resonance cascades, for e x a m p l e the linearity
MULTIPLIER
333
CIRCUIT
in potential gradient along the columns, the overall efficiency o f energy conversion, p o w e r factor, voltage d e p e n d e n c e o f l o a d current etc. I f the o p e r a t i n g frequency c a n n o t be varied easily, a variability o f transverse i n d u c t a n c e must be provided, which can be realized by changing the distance o f disks at air-coil-assemblies. To study the b e h a v i o r o f the r e s o n a n t cascade and to d e m o n s t r a t e the function o f it at lower voltages, a test model was built in one o f the l a b o r a t o r i e s o f a West-German company.
4. Design and final results of the low voltage model The cascade consists o f a high-voltage transformer, three identical c a p a c i t o r columns, rectifiers interconnecting two columns, and at least one transverse coil, the design being p r o t e c t e d by a spark gap which limits the o u t p u t voltage to 220 kV (fig. 3). F o r rectification silicon diodes o f 3 different m a n u f a c t u r e r s are used; the recovery time is less 4/lsec. The estimated straycapacities are simulated by ceramic capacitors. The load consists o f two resistor-columns, one o f which serves for measuring the output-voltage. The results are s u m m a r i z e d in table 1. In a d d i t i o n a high voltage cascade is designed using a voltage scale-factor o f 20, to get an o u t p u t voltage o f 4 MV and - equivalent to i t - an o u t p u t current o f 20 mA.
TABLE l
Specifications of the described low voltage model and extrapolation to a high voltage device, using a voltage scale factor of 20.
Model
Type of rectification Number of stages (= rectifier branches) Frequency Capacitors C between 2 stages Smoothing condensor column Ct Inserted stray capacity CQ per stage Transformer voltage v0 Rated output dc-voltage V Rated loading current I Rated acquivalent resistance R of load Inductivity of resonant coil L Q-factor of resonant coil Output-power Stored energy (at rated voltage V) Efficiency Power factor
one way Isymm.) 20 5.0 kcps
1.25/tF 0.125 pF 11 pF 2x3.7 kVpeak 200 kV 1 mA 200 M.Q 3.3 H 120 200 W 7.5 J 76% 1.0
Scale between model and high voltage design
High voltage design
-1: I 1: 1 1: 1 1: 1 1: 1 1:20 I: 20 I: 20 I: 1 1: I I: 1 1:400 1:400 I: I I: 1
one way (symm.) 20 5.0 kcps 1.25 pF 0.125/LF 11 pF 2x74 kV peak 4 MV 20 mA 200 M~ 3.3 H 120 80 kW 3 kJ 76% 1.0
334
w. GOEBEL
V
6
i
nvo
Dosttion OJ the
J coil b e t w e e n s t a g e s
I
/i
516
!~o i' 7/8
d/9
"
9~tO
and
1,2
IQ/ t l
SIslor
re ¢(~P
I ll 12
W
13 /14 o,8
15/t6 17/!8
0,4 q~
6'
Fig. 3. Design of the test model, shown as a 16-stage model but later enlarged to a 20-stage model. In the middle o f the columns there are three instead of two rectifiers serious-connected, because the voltage near the coil is higher than at the bottom or at the top.
5, Detailed test readings and method of plotting To get readings independent from the input voltage just applied, they are plotted in a normalized form by multiplicating with a factor containing l/v o. Because of special advantages in analysing the results, this f a c t o r - d u e to the nondissipative circuit of Greinacher - might be (nvo)- 1 Formula (2) will thus be modified in the following manner: viO~vo) = 1 - ~'-~- .2 q ( ¢ ' f v o ) .
(4)
As I is related to the resistance R by O h m ' s law, I--
V/t~,
(5)
we get replacing 1 by eq. (5)
~7(nvo) =
{ 1 + ,½ n 3/(CfR)}-~.
(6)
Normalized values of 1.0 correspond to the ideal
2
4
6
8
)0
~2
t.,)
t6
t6'
20
Fig. 4, Potential rise at various positions of the resonant coil. The inductance is tuned to a resonant frequency of 5.0 kcps. Rated load is 200 ME2. Greinacher circuit, higher values cannot be explained by conventional circuits, but they can by the resonant circuit principles. The position of a transverse coil affects the behavior of the circuit considerably. Variation in positioning the coil is shown in fig. 4 (measured at ~ rated load). The maximum slope of the curve is identical with maximum transverse ac voltage and will be seen at the stage, where the coil is located. This agrees exactly with the theory (ch. 2). The variation of the inductance of the coil affects the resonant frequency of the circuit and, in addition, it varies the slope of the curve because of eq. (3), if the resonant current is regarded as being constant. Lq has therefore to be matched to the requirements of linearity, while the resonant frequency is a result of Lq, Cq and C. The variation of load characterizes the special peculiarity of the resonant cascade. Because of the
COCKCROFT-WALTON
VOLTAGE MULTIPLIER CIRCUIT
335
Eeach parameter (linearity, efficiency, output voltage) has its own o p t i m u m different from the other. According to special requirements one may prefer the one or the other.
V n~-o
I i
6. Discussion
C o m p a r i n g the conventional and the modified circuit there are some properties which differ from each other and are more or less profitable. The more advantageous are: - - higher voltage and current output by resonance method ; - - smaller volume because of using smaller capacities; - - lower energy because o f using smaller capacities; - - power factor near 1 because o f using a resonant system : - - higher efficiency; - - the linearity o f potential distribution is nearly independent from load ; - - no harmful effect by stray capacities by involving them in the resonance system;
~,o
3,o - - - - -
2,0
1,o
I i so .
.
.
.
.
.
.
'
.
'
.
I
- - ~
i 0
2
4
G
8
lO
12
t4
J6
18
20
Stages
Fig. 5. Potential rise at various loadings, if t'o remains constant. 20
dependence o f output voltage from the resonant current running through the coil and this being dependent from circuit damping, the output voltage varies strongly with load fluctuation (fig. 5). However if the current is controlled at a constant value, the output voltage does not fluctuate remarkably with variable load. It should be noted that neither the linearity of potential along the columns depends essentially from load (fig. 6), nor the resonant frequency does. The model just described has proved to be a reliable and rugged system. It was driven during the test-time (several hours) without disturbances, even 20% overtension did not make any trouble. G r o u n d i n g tests from rated voltage were made (fig. 7); when sparkover was finished the voltage built up instantly to exact the same value measured before.
--
) 200 Md
X/ /I '
/
2
d
4
I 6
r
lO
12
~4
IG
18
20
Stages
Fig. 6. Potential rise at various loadings, the output voltage being regulated to 30 kV by variation of v0. The dotted line shows exact linearity for comparison.
336
W. GOEBEL TABLE 2 Deviation of power factor if the operating frequency varies around the resonant frequency.
f (kcps)
Input real power (W) Input apparent power (VA) Power factor (cos q~)
--
4.90
283 305 0.93
the output dc voltage is not limited in principle and the designer may decide whether he prefers a maximum of dc voltage, an optimum of linearity of potential along the column, a minimum of stored energy, a maximum of current output, a maximum of efficiency or a well weighted compromise between them according to the requirements.
4.95
283 284 1.0
5.00
5.10
270 276 0.98
274 285 0.96
The less advantageous are: - - the frequency may not be chosen independent from the circuit-design; - - the circuit must be exactly tuned to the operating frequency; - - i f load fluctuation happens, not the input voltage, but the input current has to be controlled constant to get an output-voltage nearly independent from load. Ripple voltage has not been investigated, because of no requirements. Obviously it must be lower than the ac-voltage and the percentage portion therefore decreases with higher multiplication factor dc to ac. If smaller values are requested, usually a smoothing column is provided, which reduces the load-dependent ripple to bl/r, p = I / ( f C t )
and
~SVpp= -~-l/(JCt),
(7)
for half-wave, resp. full-wave rectification, corresponding with conventional circuits. Ct is the total capacity of the smoothing capacitors. Ripples due to reactance-currents become zero at symmetrical circuits (fig. I c - 1f).
The task of developing a high voltage design of low volume and low stored energy was put from the Brown Boveri & Cie in Mannheim, West-Germany. i wish to express my thanks to this company for help in the construction of this device and for release this patent in the United States of America to be applicated by me. References
Fig. 7. The low voltage model during grounding experiments. Just having finished the sparkover, exactly the original voltage appears.
1) 2) :3) 4) 5)
A. Bouwers und A. Kuntke, Z. Teclln. Physik 18 (1937) 209. E. Baldinger, Kaskadengeneratoren, in Handbuch der Physik 44. G. Reiche, Dissertation (TH-Aachen, 1959). W. Heilpern, Helv. phys. Acta 28 (1955) 485. E. M. Balabanov und G. A. Vasilev, J. Nucl. Energy, Plasma Physics C 4 (1962) 65. 6) E. Everhart and P. Lorrain, Rev. Sci. Instr. 24 (1953) 221.
A NEW
INSTRUMENTS
MODIFICATION
AND
METHODS
OF
THE
67 0969) 331-336;
©
NORTH-HOLLAND
PUBLISHING
CO.
C O C K C R O F T - W A L T O N VOLTAGE M U L T I P L I E R CIRCUIT W. G O E B E L * Received 9 September 1968
By introducing a transverse coil in the middle of a CockcroftWalton multiplier, thus forming a resonant circuit in series with the capacitors of the condenser columns, the limit of the obtainable high voltage, given by Greinacher in the expression V = nvo can be far exceeded. The economy of the modificated cascade rectifier voltage multipliers seems to be better compared with
conventional ones, which could be studied with a test model of 200 kV. The power factor was measured to be 1.0 and the overall efficiency to 76%. This gives new principles on the design of dc-accelerators with high power-output using Cockcroft-Walton multipliers.
1. I n t r o d u c t i o n
In the design of high-voltage particle accelerators different principles are used, dependent from the requirements. If averaged beam-currents above a few milliamperes are wanted and also voltages in the range up from 50 kV the Cockcroft-Walton voltage multiplier is suitable and often used. However there is a limitation in the development of this type towards increasing voltages and currents. Stray capacities cause a drop of the transverse voltage a n d - a s a c o n s e q u e n c e - a decrease of the output voltage even without load. The obtainable voltage according to the Greinacher formulas (fig. l a) is V = nVo,
(no load)
V = n V o - ~ - i n3 I / ( 6 f ) ,
(load, but squareterm
[
!"
c C
cT rv-ew~
l
....
J
Fig.la Oreinacher - circuil
Fig.lb Circuil with several Iransformers
Fig.It Symmelrical half wave
circuit
(1)
neglected),
~
:
(2)
where n is the number of rectifier branches (in the following designed as stage), Vo the peak-value of the ac input voltage, I the dc load current, f the operating frequency and C the series capacitors across two stages (fig. la). Numerous literature exists decribing the Cockcroft-Walton multiplier circuit in detaill'2). Several measures have been adopted in the past to eliminate the effect of stray capacities and to approximate the value of the ideal and nondissipative generator described above: Increase of the ac input voltage is limited by the break-through characteristics of the circuit elements involved and also results in exceptionally high and undesirable voltages within the generator. Increase of the operating frequency reduces the load
* Address: Burgkmairstr. 48, 8 MiJnchen 12, West-Germany.
331
2 o_o
15 I
o-"~
J
Fig.ld Fig.le Symmetrical full-wave High Pass ~-Filter circuil
Fig. I f transmission Line
Fig. 1. Some modifications o f the original Greinacher-circuit.
dependent voltage drop but not the one due to the reactive currents. Higher values of C improve the situation, but increase the stored energy which is undesirable, because heavy damages occur when sparks jump over which is alsmost inevitable in high voltage devices. Using several high voltage feed points for the
332
w. GOEBEL
cascade generator at various stages (fig. lb) avoids decreasing transverse voltage at upper stages3), but such generators seem to be expensive and voluminous. Grounding the center tap of the transformer and adding a separate smoothing condenser column (fig. l c) reduces the ripple. On addition it allows the duplication of the input voltage without obtaining a higher voltage at the grounded transformer core. However the stored energy increases adaequately by adding the smoothing condenser column. Applying a full wave rectification by using twice the number of rectifiers (fig. Id), both the load dependent voltage drop and the ripple are further reduced4). The inserting of high voltage coils between the capacitor columns (like fig. lc, center tap like ld) gives a compensation for the effects of stray capacities if tuned to them by a parallel resonant circuit. Every circuit, however, absorbs energy and thus increases the load. Designing the generator as a high-pass LC-filter (fig. le) or as a transmission line (fig. If) the circuit is terminated on its high voltage end by a matching resistor 5) or by a suitable chosen inductance6). In all these modified circuit arrangements the maximum voltage obtained may not exceed the theoretical level derived from formula (1). Contrary to this, by using a similar arrangement, but another operation mode, the limits of formula (1) are no more obligatory and voltages are obtainable which may be extended theoretically to infinity under ideal circumstances without load, as subsequently will be described. 2. A new modification: The resonant cascade
The resonant cascade is applicable to cascade generators with symmetrical or nonsymmetrical circuits and with half wave or full wave rectification. The only difference to these is the insertion of a transverse coil Lq with high Q-factor, the position of which is approximately in the middle of the condenser columns and which is connected between them (fig. 2). The operation mode may be explained in the following manner: The transverse coil, the high-voltage transformer and all the capacitors C between them, on both columns, form a series-resonant circuit having a resonant frequency equal to the ooerating frequency. If the circuit would not be damped, there would be a current in it extended to infinity, i f a voltage is applied. The transverse voltage vL across the coil vL =
I~oL,
(3)
would also run to infinity. The required ac input voltage v0 would be near zero.
2 ~
~..t_x..A..A_.r~
t. . . . .
7
]
Fig. 2. T h e resonant cascade, s h o w n as a 8-stage model.
Thus the transformer may be regarded as a current transformer which delivers the resonant current, the transverse coil may be regarded as voltage-generator. Currents in a nondissipative resonant circuit are reactance-currents like those of stray capacities. Contrary to the conventional devices, where they diminish the efficiency, in the new modification they are needed to produce a voltage across the rectifiers. The ac voltages are rectified and accumulated in the usual manner to the dc output voltage. The limitation of resonant current occurs by the dissipation factors of transformer, condensers and the transverse coil, but essentially by the load resistor which produces in-phase-components of the current. Such currents in an resonant circuit cause a damping and also a widening of the resonance curve. The real operation of the resonance cascade with load is a mixture between the mode just described and the conventional operation mode with an input voltage vo not being near zero. And the real output voltage is neither infinity nor Greinachers value, but between them.
COCKCROFT-WALTON
VOLTAGE
3. The mathematical model Because f o r m u l a ( i ) is no m o r e a p p l i c a b l e on r e s o n a n t circuits we have to use a n o t h e r m a t h e m a t i c a l model to d e t e r m i n e the o u t p u t voltage. F o r the case o f z e r o - l o a d the cascade m a y be regarded as a n e t w o r k o f reactances. There are c a p a c i t o r s C o f the c o n d e n s e r columns, a transformer, a transverse coil Lq a n d stray capacities Cq, which c o m p r i s e the j u n c t i o n capacities o f the rectifiers, the individual capacities interconnecting the c o n d e n s e r c o l u m n s a n d the capacities between the g e n e r a t o r a n d external devices such as a pressure t a n k housing the circuit. The rectifiers D itself need not be considered, because they show a very high reverse resistance in the static case without load. In a usual way - by t h e o r y o f the transmission line6), or by using a matrix - the ac transverse voltage across each rectifier-branch m a y be d e t e r m i n e d , if an inputvoltage on the b o t t o m - f e e d p o i n t is assumed. The dc voltage across every rectifier-branch is equal to the peak value o f the ac transverse voltage. By algebraic a d d i t i o n o f all the dc voltages a l o n g the rectifiers the o u t p u t dc voltage o f the cascade is determined. This way to calculate the t o p dc voltage was perf o r m e d in a c o m p u t e r for the test m o d e l described in ch. 4 and it a d d u c e d g o o d results. There are a lot o f further aspects to be n o t e d on the design o f resonance cascades, for e x a m p l e the linearity
MULTIPLIER
333
CIRCUIT
in potential gradient along the columns, the overall efficiency o f energy conversion, p o w e r factor, voltage d e p e n d e n c e o f l o a d current etc. I f the o p e r a t i n g frequency c a n n o t be varied easily, a variability o f transverse i n d u c t a n c e must be provided, which can be realized by changing the distance o f disks at air-coil-assemblies. To study the b e h a v i o r o f the r e s o n a n t cascade and to d e m o n s t r a t e the function o f it at lower voltages, a test model was built in one o f the l a b o r a t o r i e s o f a West-German company.
4. Design and final results of the low voltage model The cascade consists o f a high-voltage transformer, three identical c a p a c i t o r columns, rectifiers interconnecting two columns, and at least one transverse coil, the design being p r o t e c t e d by a spark gap which limits the o u t p u t voltage to 220 kV (fig. 3). F o r rectification silicon diodes o f 3 different m a n u f a c t u r e r s are used; the recovery time is less 4/lsec. The estimated straycapacities are simulated by ceramic capacitors. The load consists o f two resistor-columns, one o f which serves for measuring the output-voltage. The results are s u m m a r i z e d in table 1. In a d d i t i o n a high voltage cascade is designed using a voltage scale-factor o f 20, to get an o u t p u t voltage o f 4 MV and - equivalent to i t - an o u t p u t current o f 20 mA.
TABLE l
Specifications of the described low voltage model and extrapolation to a high voltage device, using a voltage scale factor of 20.
Model
Type of rectification Number of stages (= rectifier branches) Frequency Capacitors C between 2 stages Smoothing condensor column Ct Inserted stray capacity CQ per stage Transformer voltage v0 Rated output dc-voltage V Rated loading current I Rated acquivalent resistance R of load Inductivity of resonant coil L Q-factor of resonant coil Output-power Stored energy (at rated voltage V) Efficiency Power factor
one way Isymm.) 20 5.0 kcps
1.25/tF 0.125 pF 11 pF 2x3.7 kVpeak 200 kV 1 mA 200 M.Q 3.3 H 120 200 W 7.5 J 76% 1.0
Scale between model and high voltage design
High voltage design
-1: I 1: 1 1: 1 1: 1 1: 1 1:20 I: 20 I: 20 I: 1 1: I I: 1 1:400 1:400 I: I I: 1
one way (symm.) 20 5.0 kcps 1.25 pF 0.125/LF 11 pF 2x74 kV peak 4 MV 20 mA 200 M~ 3.3 H 120 80 kW 3 kJ 76% 1.0
334
w. GOEBEL
V
6
i
nvo
Dosttion OJ the
J coil b e t w e e n s t a g e s
I
/i
516
!~o i' 7/8
d/9
"
9~tO
and
1,2
IQ/ t l
SIslor
re ¢(~P
I ll 12
W
13 /14 o,8
15/t6 17/!8
0,4 q~
6'
Fig. 3. Design of the test model, shown as a 16-stage model but later enlarged to a 20-stage model. In the middle o f the columns there are three instead of two rectifiers serious-connected, because the voltage near the coil is higher than at the bottom or at the top.
5, Detailed test readings and method of plotting To get readings independent from the input voltage just applied, they are plotted in a normalized form by multiplicating with a factor containing l/v o. Because of special advantages in analysing the results, this f a c t o r - d u e to the nondissipative circuit of Greinacher - might be (nvo)- 1 Formula (2) will thus be modified in the following manner: viO~vo) = 1 - ~'-~- .2 q ( ¢ ' f v o ) .
(4)
As I is related to the resistance R by O h m ' s law, I--
V/t~,
(5)
we get replacing 1 by eq. (5)
~7(nvo) =
{ 1 + ,½ n 3/(CfR)}-~.
(6)
Normalized values of 1.0 correspond to the ideal
2
4
6
8
)0
~2
t.,)
t6
t6'
20
Fig. 4, Potential rise at various positions of the resonant coil. The inductance is tuned to a resonant frequency of 5.0 kcps. Rated load is 200 ME2. Greinacher circuit, higher values cannot be explained by conventional circuits, but they can by the resonant circuit principles. The position of a transverse coil affects the behavior of the circuit considerably. Variation in positioning the coil is shown in fig. 4 (measured at ~ rated load). The maximum slope of the curve is identical with maximum transverse ac voltage and will be seen at the stage, where the coil is located. This agrees exactly with the theory (ch. 2). The variation of the inductance of the coil affects the resonant frequency of the circuit and, in addition, it varies the slope of the curve because of eq. (3), if the resonant current is regarded as being constant. Lq has therefore to be matched to the requirements of linearity, while the resonant frequency is a result of Lq, Cq and C. The variation of load characterizes the special peculiarity of the resonant cascade. Because of the
COCKCROFT-WALTON
VOLTAGE MULTIPLIER CIRCUIT
335
Eeach parameter (linearity, efficiency, output voltage) has its own o p t i m u m different from the other. According to special requirements one may prefer the one or the other.
V n~-o
I i
6. Discussion
C o m p a r i n g the conventional and the modified circuit there are some properties which differ from each other and are more or less profitable. The more advantageous are: - - higher voltage and current output by resonance method ; - - smaller volume because of using smaller capacities; - - lower energy because o f using smaller capacities; - - power factor near 1 because o f using a resonant system : - - higher efficiency; - - the linearity o f potential distribution is nearly independent from load ; - - no harmful effect by stray capacities by involving them in the resonance system;
~,o
3,o - - - - -
2,0
1,o
I i so .
.
.
.
.
.
.
'
.
'
.
I
- - ~
i 0
2
4
G
8
lO
12
t4
J6
18
20
Stages
Fig. 5. Potential rise at various loadings, if t'o remains constant. 20
dependence o f output voltage from the resonant current running through the coil and this being dependent from circuit damping, the output voltage varies strongly with load fluctuation (fig. 5). However if the current is controlled at a constant value, the output voltage does not fluctuate remarkably with variable load. It should be noted that neither the linearity of potential along the columns depends essentially from load (fig. 6), nor the resonant frequency does. The model just described has proved to be a reliable and rugged system. It was driven during the test-time (several hours) without disturbances, even 20% overtension did not make any trouble. G r o u n d i n g tests from rated voltage were made (fig. 7); when sparkover was finished the voltage built up instantly to exact the same value measured before.
--
) 200 Md
X/ /I '
/
2
d
4
I 6
r
lO
12
~4
IG
18
20
Stages
Fig. 6. Potential rise at various loadings, the output voltage being regulated to 30 kV by variation of v0. The dotted line shows exact linearity for comparison.
336
W. GOEBEL TABLE 2 Deviation of power factor if the operating frequency varies around the resonant frequency.
f (kcps)
Input real power (W) Input apparent power (VA) Power factor (cos q~)
--
4.90
283 305 0.93
the output dc voltage is not limited in principle and the designer may decide whether he prefers a maximum of dc voltage, an optimum of linearity of potential along the column, a minimum of stored energy, a maximum of current output, a maximum of efficiency or a well weighted compromise between them according to the requirements.
4.95
283 284 1.0
5.00
5.10
270 276 0.98
274 285 0.96
The less advantageous are: - - the frequency may not be chosen independent from the circuit-design; - - the circuit must be exactly tuned to the operating frequency; - - i f load fluctuation happens, not the input voltage, but the input current has to be controlled constant to get an output-voltage nearly independent from load. Ripple voltage has not been investigated, because of no requirements. Obviously it must be lower than the ac-voltage and the percentage portion therefore decreases with higher multiplication factor dc to ac. If smaller values are requested, usually a smoothing column is provided, which reduces the load-dependent ripple to bl/r, p = I / ( f C t )
and
~SVpp= -~-l/(JCt),
(7)
for half-wave, resp. full-wave rectification, corresponding with conventional circuits. Ct is the total capacity of the smoothing capacitors. Ripples due to reactance-currents become zero at symmetrical circuits (fig. I c - 1f).
The task of developing a high voltage design of low volume and low stored energy was put from the Brown Boveri & Cie in Mannheim, West-Germany. i wish to express my thanks to this company for help in the construction of this device and for release this patent in the United States of America to be applicated by me. References
Fig. 7. The low voltage model during grounding experiments. Just having finished the sparkover, exactly the original voltage appears.
1) 2) :3) 4) 5)
A. Bouwers und A. Kuntke, Z. Teclln. Physik 18 (1937) 209. E. Baldinger, Kaskadengeneratoren, in Handbuch der Physik 44. G. Reiche, Dissertation (TH-Aachen, 1959). W. Heilpern, Helv. phys. Acta 28 (1955) 485. E. M. Balabanov und G. A. Vasilev, J. Nucl. Energy, Plasma Physics C 4 (1962) 65. 6) E. Everhart and P. Lorrain, Rev. Sci. Instr. 24 (1953) 221.