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A new instrument for DC voltage stability measurement and control
NUCLEAR
INSTRUMENTS
AND
METHODS
29
(I964) I4I-I48; © N O R T H - H O L L A N D
PUBLISHING
CO.
A NEW INSTRUMENT FOR DC VOLTAGE STABILITY MEASUREMENT AND CONTROL* W. K. BROOKSHIER and R. N. LEWIS
Argonne National Laboratory, Argonne, Illinois Received 12 January 1964 An instrument for the purpose of monitoring the stability of dc voltage sources, has been constructed and tested. The instrument is an operational invertor, which uses a vibrating reed electrometer and capacitors as input and feedback elements. This arrangement yields an output voltage signal which is an amplified version of the input voltage change, with the dc level subtracted out. The main advantages consist of the elimination of the usual resistance divider and reference voltage problems, as well as the
imposition of negligible steady-state loading on the source. Useful time intervals depend upon the magnitudes of the observed voltage fluctuations and range from a few minutes to a few days. The system has been tested in the voltage range up to 1 kV, and holds promise for applications to 10 kV or higher. Changes in the voltage source as small as I part in 107 can be displayed easily and with a minimum of ambiguity.
1. Introduction The d e m a n d for voltage sources o f exceptionally high stability has increased at A r g o n n e during the past few years. Desired stability figures have ranged f r o m 10 to 0.I p p m (parts per million) for time intervals f r o m a few seconds to a few hours and for voltage values f r o m a few volts to 50 kV. I n m a n y applications the absolute value o f voltage need not be k n o w n accurately, but the stability is o f prime importance. W h e n a voltage source is available with a suspected stability o f 10 p p m or better, the measurement o f the actual stability m a y become extremely difficult and expensive, particularly for the higher voltages. The usual m e t h o d for the measurement o f stability consists o f dividing the potential under question to a lower level with a resistance divider, to enable comparison against a voltage reference o f k n o w n stability, such as a saturated standard cell. A l t h o u g h a carefully handled saturated standard cell in an adequate constanttemperature enclosure will usually possess a stability in the range o f 1 to 0.1 ppm, the obtainment o f a similar stability figure for the resistance divider ratio m a y be a near-impossibility for high voltages. Some o f the formidable problems include: (1) temperature coefficient matching with high precision, (2) self-heating effects, (3) stability o f temperature environment, (4) source loading, and (5) leakage currents t h r o u g h medium surrounding resistors, whether it be gaseous, liquid, or solid. The system to be described was developed as an alternate m e t h o d o f making stability measurements, and offers the advantage o f negligible source loading. It involves a specially constructed capacitor, which replaces both voltage reference and resistance divider o f the conventional method. The system does not * Work performed under the auspices of the US Atomic Energy Commission.
measure total voltage values, but can easily indicate changes as small as 1 part in 107, or even smaller, when these changes occur over appropriate time intervals. Useful time intervals range f r o m a few minutes to a few days, depending u p o n the magnitudes o f the variations to be monitored and also u p o n the total voltage value. This system has been used with potentials up to 1 kV, with the possibility o f extension up to 10 kV, or perhaps higher. 2. Theory The circuit configuration is illustrated in fig. 1. The voltage under observation, vx is coupled to the input o f the vibrating reed electrometer t h r o u g h capacitor Ca. VIBRATING REED ELECTROMETER
el
I
I(
v°I
Vx C2
I( o"-o SHORTING SWITCH
Fig. 1. Block diagram of system for monitoring stability of voltage vz. The vibrating reed electrometer is connected as an integrator, with feedback capacitor C2. W h e n the shorting switch is open, we have Al')x C1 C1
C2
+---~C-~+ Avo~, + C2
or
141
_ Al)o
K
(1)
142
w . K . BROOKSHIER AND R. N. LEWIS
A v o _ C~ × Avx C2 - 1 + (Cl + C2)/KC2"
(2)
the shorting switch is open, the charges on the two capacitors are
If
Q1 = vxCl, KC 2 C 1 q- C 2
>> 1 then
C2"
Q2
=
/3oC2
and conservation of charge requires that
Arc ,~ Cl
Avx-
(5)
(3)
(4)
Thus changes Av x in the input voltage are amplified by the ratio Ca/C2, which may be made larger than unity providing condition (3) is maintained. During the application of a voltage vx, the shorting switch across the feedback capacitor is closed, permitting the initial charging of Ca without overdriving the electrometer. When the switch is opened thereafter, the variations in vo may be observed with a recorder connected to the normal recorder output terminals of the vibrating reed electrometer. Since the open-loop d.c. gain K of readily available commercial instruments is usually about 1000, capacitance ratios as large as I00 and over may be used. I f the capacitance ratio is 100 and the electrometer is on a 100 mV output scale, the full-scale sensitivity referred to the input is 1 mV, which would represent 1 ppm for an applied potential of 1000 V. Since commercial electrometers of this type possess ranges down to 1 or 10 mV, there is no lack of sensitivity. In practice, it is usually necessary to reduce the ratio Ca~C2 to 10 or 1 when higher voltages are under observation. If capacitor C~ were to pass a steady leakage current IL, there would be a steady drift in the output voltage given by IL/C 2. A similar effect occurs due to the background current of the vibrating reed electrometer, which acts in the manner of an external current signal flowing into the junction between C~ and C2. Since the background current of the electrometer is normally less than 5 × 10 -17 amperes, it is desirable that any leakage current adding to this figure be comparable or smaller. In order to obtain a leakage current of this value with a potential as high as 100 V, the leakage resistance required would be 0.2 x 10 z° ohms. This degree of perfection can only be achieved by the use of a guarded, vacuum-dielectric, capacitor. The capacitance stability requirements of Ca and C2 are of interest. Assuming that (3) holds, we may think of the circuit of fig. 1 as a perfect operational amplifier with a zero input error signal at the C 1, C 2 summing junction. In reality this junction does operate at a level of several millivolt due to the contact potential of the vibrating reed, but the drift rate of contact potential is low enough to be negligible in this application. When
dQa = dQ2.
(6)
Allowing for the possibility of capacitance changes as well as voltage changes C l d v x + v x d C 1 = C2dvo + v o d C 2.
(7)
We may determine the importance of the capacitance changes by calculating the equivalent input voltage change required to just counteract the capacitance changes, thus making dvo = 0. We then obtain from (7) dvx
vx -
Vo dC2
dC 1
vxC---S
ca"
(8)
Thus, a given fractional change in C1 is counteracted by the same magnitude of fractional change in Vx. This means that a given fractional change in G cannot be distinguished from the same fractional change in the applied potential and the required stability of capacitor C1 should be as good, or better, than that of the voltage source under observation. In contrast, it may be observed that the stability of Cz is exceedingly non-critical, since the ratio Vo/Vx always starts at zero when the shorting switch is opened and never rises above a very small value.
3. Preliminary designs of capacitor C1 In an initial experiment, a guarded air-dielectric capacitor with aluminum plates was fabricated and tried. As expected, the current through Cx due to collection of air ionization due to background radiation was much larger than the background current of the electrometer, thus severely limiting performance. Measured current values ranged from 0 . 5 x 1 0 -a4 to 4 x 10 -as amperes. In a second experiment, a guarded vacuum capacitor of commercial manufacture ~) was tried. Ion chamber action was absent, of course, but further measurements revealed a temperature coefficient of capacitance of about 60 ppm per degree C, with a thermal time constant of about one hour. A capacitor such as this, if carefully temperature regulated, would probably possess a useful degree of capacitance stability. However, the decision to design and fabricate a similar capacitor of greatly improved temperature stability was made.
INSTRUMENT
FOR DC VOLTAGE STABILITY
4. Capacitor construction The construction of capacitor C~ to meet the necessary requirements poses the only difficult problem, since the remainder of the system consists of very little more than the commercially available vibrating reed electrometer. The construction of capacitor C~ is illustrated in fig. 2. It consists of two sets of interleaved plates six inches square, with one set of plates rotated 45 degrees with respect to the other. The plates of both stacks are of gold-plated quartz, chosen for dimensional stability. If the spacers separating the plates were also of the same material, it can be shown that the combined effects of temperature-induced dimensional changes along all three axes would result in a temperature coefficient of capacitance equal to + 0.57 ppm per degree C, which is the coefficient of expansion for fused quartz. Since very little additional effort was required, the spacers were made of Vycor, which has a slightly greater coefficient of expansion and thus permits designing for a near-zero capacitance coefficient.
143
The capacitance value is proportional to the effective area A divided by the spacing ½ ( l - t), where lis the total length of the spacers, and t is the thickness of the quartz plates. It can be shown that the temperature coefficient of capacity will be zero if ~,t 1 =
2cq
(9) ct 2
-
where u~ and ~2 are the temperature coefficients of expansion of quartz and Vycor respectively. With t chosen as 0.25 inches, and using figures of 5.7 x 1 0 - 7 and 8.0 x 1 0 - 7 for ~ and ~2, the figure of 0.419 inches for the length of the Vycor spacer results. Another important precaution in the capacitor design involves minimizing the electric field produced by the input voltage at the surface of the insulators supporting the output plate stack. Such an electric field will result in a temporary charging effect upon the surfaces, with an equilibrium condition being reached only after the lapse of a time interval determined by the conductivity
50% COATED WITH STAINLESS STEEL
HOLD DOWN P L A T E ~ STAINLESS STEEL GOLD PLATED (4)~"DIA. X .187" VYCORTOP SURFACEUNPLATED
BELL JAR.12~'O.D. PYREX
(4) ~ DIA. X ,522%~--~ VYCOR. TOP SURFACE UNPLATED
(~,6.000"L005 SQ. X .250" ±~02 THICK QUARTZ PLATE GOLD PLATED
(68)SPACER ~' DIA.X .419" VYCOR GOLD PLATED
(84) ~"DIA. X~' QUARTZ ROD
(4) ~'DIA. X .2095 "...,,,, VYCOR
(4)~'DIA. X .IBT" QUARTZ GOLD PLATED
(4) I~'DIA. X .IBT~...... QUARTZ PLATE GOLD PLATED
~~(4)_-[p"DIA. X .500" QUARTZ GOLD PLATED
9"DIA. X I" QUART: GOLD PLATED
(B)7"DIA. X .IB?" THICK QUARTZ. TOP SURFACE UNPLATED
x
KOROSEAL GASKET GUIDESLEEVE-TO~ FIT VIBRATINGREED ELECTROMETER PREAMP INPUT
~'~ANCHOR _
PLATE
,4,,×
STA,NLESS STEEL
GOLD WIRE (2)ADVAC 500B TERMINAL
WIRE TO VACUUM SYSTEM
Fig. 2. Construction of input capacitor C1.
TO H.V INPUT"
IRASS FITTING WITH "0" RING
144
W. K. B R O O K S H I E R
of the insulator, typically as much as an hour. The charging currents involved in this action flow into the electrometer input, producing an erroneous indication of change in the applied voltage. The magnitudes of these currents can be much larger than the steady-sate leakage currents flowing between the output stack and ground and it is essential to minimize them. This is accomplished by keeping the amount of unplated surfaces to a minimum and locating the unplated surfaces so that they are shielded from the potential of the input stack by the potential of the output stack. In fig. 2 it may be observed that the stack of plates which includes the bottom plate is supported from the large quartz base plate by three cylindrical buttons of quartz at each corner, with the bottom two pieces recessed into a hole in the base plate. The insulating surface is formed by omitting the plating of the top surface of the bottom piece. The top piece, which is completely plated, acts as a shield against penetration of electric field from the input voltage. A similar arrangement is used at the top and bottom of both plate stacks, which makes it permissible to interchange the input and output terminals of the capacitor, should it be desired to do so. In order to shield the internal structure of the capacitor from the influence of external electric fields, the interior surface of the bell jar was coated with a semi-transparent conductive layer of stainless steel. This coating is grounded to the metal base plate with finger contacts not shown in fig. 2. The conductive gold coating on all the quartz and
SIA
A N D R. N. L E W I S
Vycor pieces was applied by a painting and baking process using DuPont's Liquid Bright Gold No. 4063. This coating is quite durable and cannot be scratched off easily. However, some difficulty was experienced in obtaining satisfactory electrical contact between plates and spacers with normal assembly pressure. This trouble was cured by applying small dabs of silver paint to bridge the gap across each junction. The choice of capacitance value is influenced by the effect of the background current of the system. The total background current of the system consists of the contribution from the electrometer, typically 5 x 10-17 amperes or so, plus the contribution from surface currents flowing from the insulating surfaces supporting the output plate stack. This total background current I b flows into the junction between C1 and (72, accumulating on C 2. The drift rate at the output is then Ib/C 2. When referred to the input by multiplication by C2/C 1, the drift rate becomes I J C I . This drift rate represents an uncertainty in the measurement of changes in the input voltage and is to be minimized. Thus the higher the value of capacitance for C 1, the smaller will be the input drift rate. The value of capacitance chosen, about 1500 pF, represents the largest value that could conveniently be assembled into a 12 inch bell jar with the desired constructional features.
5. Description of remainder of system The remainder of the electronic part of the system is indicated in the circuit of fig. 3. Switch $1 permits
$2
Vx
r--°0'""'T'/ ----
136V
,00
/ .,L
9r'..
I
I
I I
'
~-
APpL~Eo p,Ys,cs
--TMODEL 3oF
ws.A'r,NG
SIB
o,OvO o..
/
~,oM
2500n
5o. L. 4, HELiPOTh" ~27,~ RECOROER
REC.CAL.;
1"
lo0 IJA
Fig. 3. System for monitoring stability of voltage vz, with means for insertion of calibrating voltage steps.
INSTRUMENT FOR DC VOLTAGE STABILITY
145
reed electrometer and the insulator current from the output plate stack of C~. The average slope of the initial part of this recording is about 17 ~V/sec, corresponding to a current of 1.7 x 10 -16 amperes. Since the voltage gain is about 150, the drift rate referred to the input is 17/150 = 0.11/~V per second. The 100#V calibrating step super-imposed in the middle of the run verifies the sensitivity, which is further indicated by observing the amplitude of the voltage change produced by a 500 megohm load on the standard cells. Although this system was not intended for application at voltage levels as low as 4 volt, some usefulness does exist at that level. The entire amount of the drift rate due to total background current need not be taken as an uncertainty, since the value of the background current normally remains fairly constant for periods of time ranging up to an hour or more. If the recording of an unknown voltage is sandwiched between two recordings with zero volt applied, as was done in fig. 6
Fig. 4. Photograph of input capacitor C1. convenient switching from zero volt to the voltage under test and $2 makes possible the addition of known voltage steps, from 100#V through 1 volt, in series with the applied voltage. A 10 megohm resistor is placed in series with the input end of C1 to act as a current limiter in the event of an internal breakdown. This resistor also serves to limit the peak charging current flowing from the source into C1 upon application of a voltage. Capacity values used for C2 ranged from 10 to 1000 pF. The value of 10 pF is built into the vibrating reed electrometer circuit. Higher values were obtained by paralleling the built-in capacitor with an external polystyrene capacitor. The bell jar containing the capacitor C1 was evacuated to a pressure of about 10 -4 mm Hg for all of the experimental results to follow. Fig. 4 is a photograph of the special capacitor assembly out of the bell jar and fig. 5 is a photograph of the entire assembled apparatus. 6. Results
Fig. 6 indicates a recording of an applied voltage of about 4 volt from four series-connected saturated standard cells2). In this run, as in all others, a relatively steady drift appears in the output recording, produced by the sum of the background current of the vibrating
Fig. 5. Photograph of complete system.
146
W. K. B R O O K S H I E R
Fig. 6. Stability recording of saturated standard cells. and if the slopes of the two zero runs are nearly equal, the uncertainty of the A Vmeasurements of the unknown becomes a small fraction of the total drift over the measurement period. Fig. 7. represents a zero run followed by a recording of a 300 volt battery. The slope of this zero run corresponds to a total background current of about 2.2 x 10 - 1 6 amperes. The calibration voltage step of 1 millivolt represents 3 ppm of the applied potential. The effect of applying a load of 10 ~ ohms across the battery can be examined in some detail. There is an
A N D R. N. L E W I S
initial potential drop of about 0.3 ppm, followed by a further decrease over the following 2 minutes. If the zero run is projected onward through the 300 volt run and the variations in battery potential noted with respect to this projection, it can be stated with reasonable certainty that the battery maintained a potential to within about 5 ppm for a time interval of 1½ hours. This degree of stability is not typical of this type of battery, but was achieved only after a long stabilization period and recovery from the initial loading of the battery caused by the charging current into C1. During the 4 hour period following initial application of the voltage, the potential drifted upward by a total amount several times the full-scale span of the recording. It is possible, of course, to pre-charge C1 to match the potential of the unknown and avoid most of the otherwise-long recovery time. However, this is a problem associated with the voltage source under test and has little to do with the accuracy of the measurement technique. Fig. 8 is a recording of a 1000 volt potential from a Fluke Model 412A power supply. It serves to illustrate the difference between the very short term stability (1 minute or so) of an electronically regulated supply, in comparison with a battery source. The observed stability is consistent with the manufacturer's specification of 50 ppm per hour.
Fig. 7. Stability recording of a 300 volt battery.
INSTRUMENT FOR DC VOLTAGE STABILITY
147
Fig. 8. Stability recording of 1000 volt potential from a Fluke 412A supply. Fig. 9 is a recording of the 100V output of a Princeton Applied Research Model TC100.2R supply. The peak-to-peak noise level on the supply over a one minute time interval is about 3 p p m and the change in output due to application of a 100 m A load is about 1 ppm. These recordings indicate that the system is capable of displaying changes in voltage source as small as
0.1 p p m over time intervals of usefully long duration. For higher values of voltage, even this figure is not a sensitivity limit, and it should be quite feasible to display changes of 0.01 p p m over correspondingly shorter time intervals. A logical extension of application for the system would consist of incorporating it as an error detector in a feedback system for controlling the output of a voltage source. In such an application, it
Fig. 9. Stability recording of 100 volt potential from a Princeton Applied Research TC100.2R supply.
148
w. K. BROOKSHIER AND R. N. LEWIS
should be possible to obtain a controlled voltage source stability corresponding to the input-referred drift rate of this system of about 0.1 #V/sec, or 360 #V/h. For a source potential of 1000 V, the stability would then be 0.36 ppm per hour and correspondingly better for higher source potentials. The capacitor was designed for use with potentials up to 10 kV. Due to limitations in associated equipment, the highest level used to date is I kV.
The authors wish to express appreciation for the fabrication of the special capacitor performed by the Central Shops Division of Argonne and to D. J. Keefe for his assistance in gold-plating the capacitor parts. References 1) Jennings JCCG-500 vacuum capacitor, 500 pF. a) Sensitive Research Type 4305 in Type 9152 constant tempera ture enclosure.
INSTRUMENTS
AND
METHODS
29
(I964) I4I-I48; © N O R T H - H O L L A N D
PUBLISHING
CO.
A NEW INSTRUMENT FOR DC VOLTAGE STABILITY MEASUREMENT AND CONTROL* W. K. BROOKSHIER and R. N. LEWIS
Argonne National Laboratory, Argonne, Illinois Received 12 January 1964 An instrument for the purpose of monitoring the stability of dc voltage sources, has been constructed and tested. The instrument is an operational invertor, which uses a vibrating reed electrometer and capacitors as input and feedback elements. This arrangement yields an output voltage signal which is an amplified version of the input voltage change, with the dc level subtracted out. The main advantages consist of the elimination of the usual resistance divider and reference voltage problems, as well as the
imposition of negligible steady-state loading on the source. Useful time intervals depend upon the magnitudes of the observed voltage fluctuations and range from a few minutes to a few days. The system has been tested in the voltage range up to 1 kV, and holds promise for applications to 10 kV or higher. Changes in the voltage source as small as I part in 107 can be displayed easily and with a minimum of ambiguity.
1. Introduction The d e m a n d for voltage sources o f exceptionally high stability has increased at A r g o n n e during the past few years. Desired stability figures have ranged f r o m 10 to 0.I p p m (parts per million) for time intervals f r o m a few seconds to a few hours and for voltage values f r o m a few volts to 50 kV. I n m a n y applications the absolute value o f voltage need not be k n o w n accurately, but the stability is o f prime importance. W h e n a voltage source is available with a suspected stability o f 10 p p m or better, the measurement o f the actual stability m a y become extremely difficult and expensive, particularly for the higher voltages. The usual m e t h o d for the measurement o f stability consists o f dividing the potential under question to a lower level with a resistance divider, to enable comparison against a voltage reference o f k n o w n stability, such as a saturated standard cell. A l t h o u g h a carefully handled saturated standard cell in an adequate constanttemperature enclosure will usually possess a stability in the range o f 1 to 0.1 ppm, the obtainment o f a similar stability figure for the resistance divider ratio m a y be a near-impossibility for high voltages. Some o f the formidable problems include: (1) temperature coefficient matching with high precision, (2) self-heating effects, (3) stability o f temperature environment, (4) source loading, and (5) leakage currents t h r o u g h medium surrounding resistors, whether it be gaseous, liquid, or solid. The system to be described was developed as an alternate m e t h o d o f making stability measurements, and offers the advantage o f negligible source loading. It involves a specially constructed capacitor, which replaces both voltage reference and resistance divider o f the conventional method. The system does not * Work performed under the auspices of the US Atomic Energy Commission.
measure total voltage values, but can easily indicate changes as small as 1 part in 107, or even smaller, when these changes occur over appropriate time intervals. Useful time intervals range f r o m a few minutes to a few days, depending u p o n the magnitudes o f the variations to be monitored and also u p o n the total voltage value. This system has been used with potentials up to 1 kV, with the possibility o f extension up to 10 kV, or perhaps higher. 2. Theory The circuit configuration is illustrated in fig. 1. The voltage under observation, vx is coupled to the input o f the vibrating reed electrometer t h r o u g h capacitor Ca. VIBRATING REED ELECTROMETER
el
I
I(
v°I
Vx C2
I( o"-o SHORTING SWITCH
Fig. 1. Block diagram of system for monitoring stability of voltage vz. The vibrating reed electrometer is connected as an integrator, with feedback capacitor C2. W h e n the shorting switch is open, we have Al')x C1 C1
C2
+---~C-~+ Avo~, + C2
or
141
_ Al)o
K
(1)
142
w . K . BROOKSHIER AND R. N. LEWIS
A v o _ C~ × Avx C2 - 1 + (Cl + C2)/KC2"
(2)
the shorting switch is open, the charges on the two capacitors are
If
Q1 = vxCl, KC 2 C 1 q- C 2
>> 1 then
C2"
Q2
=
/3oC2
and conservation of charge requires that
Arc ,~ Cl
Avx-
(5)
(3)
(4)
Thus changes Av x in the input voltage are amplified by the ratio Ca/C2, which may be made larger than unity providing condition (3) is maintained. During the application of a voltage vx, the shorting switch across the feedback capacitor is closed, permitting the initial charging of Ca without overdriving the electrometer. When the switch is opened thereafter, the variations in vo may be observed with a recorder connected to the normal recorder output terminals of the vibrating reed electrometer. Since the open-loop d.c. gain K of readily available commercial instruments is usually about 1000, capacitance ratios as large as I00 and over may be used. I f the capacitance ratio is 100 and the electrometer is on a 100 mV output scale, the full-scale sensitivity referred to the input is 1 mV, which would represent 1 ppm for an applied potential of 1000 V. Since commercial electrometers of this type possess ranges down to 1 or 10 mV, there is no lack of sensitivity. In practice, it is usually necessary to reduce the ratio Ca~C2 to 10 or 1 when higher voltages are under observation. If capacitor C~ were to pass a steady leakage current IL, there would be a steady drift in the output voltage given by IL/C 2. A similar effect occurs due to the background current of the vibrating reed electrometer, which acts in the manner of an external current signal flowing into the junction between C~ and C2. Since the background current of the electrometer is normally less than 5 × 10 -17 amperes, it is desirable that any leakage current adding to this figure be comparable or smaller. In order to obtain a leakage current of this value with a potential as high as 100 V, the leakage resistance required would be 0.2 x 10 z° ohms. This degree of perfection can only be achieved by the use of a guarded, vacuum-dielectric, capacitor. The capacitance stability requirements of Ca and C2 are of interest. Assuming that (3) holds, we may think of the circuit of fig. 1 as a perfect operational amplifier with a zero input error signal at the C 1, C 2 summing junction. In reality this junction does operate at a level of several millivolt due to the contact potential of the vibrating reed, but the drift rate of contact potential is low enough to be negligible in this application. When
dQa = dQ2.
(6)
Allowing for the possibility of capacitance changes as well as voltage changes C l d v x + v x d C 1 = C2dvo + v o d C 2.
(7)
We may determine the importance of the capacitance changes by calculating the equivalent input voltage change required to just counteract the capacitance changes, thus making dvo = 0. We then obtain from (7) dvx
vx -
Vo dC2
dC 1
vxC---S
ca"
(8)
Thus, a given fractional change in C1 is counteracted by the same magnitude of fractional change in Vx. This means that a given fractional change in G cannot be distinguished from the same fractional change in the applied potential and the required stability of capacitor C1 should be as good, or better, than that of the voltage source under observation. In contrast, it may be observed that the stability of Cz is exceedingly non-critical, since the ratio Vo/Vx always starts at zero when the shorting switch is opened and never rises above a very small value.
3. Preliminary designs of capacitor C1 In an initial experiment, a guarded air-dielectric capacitor with aluminum plates was fabricated and tried. As expected, the current through Cx due to collection of air ionization due to background radiation was much larger than the background current of the electrometer, thus severely limiting performance. Measured current values ranged from 0 . 5 x 1 0 -a4 to 4 x 10 -as amperes. In a second experiment, a guarded vacuum capacitor of commercial manufacture ~) was tried. Ion chamber action was absent, of course, but further measurements revealed a temperature coefficient of capacitance of about 60 ppm per degree C, with a thermal time constant of about one hour. A capacitor such as this, if carefully temperature regulated, would probably possess a useful degree of capacitance stability. However, the decision to design and fabricate a similar capacitor of greatly improved temperature stability was made.
INSTRUMENT
FOR DC VOLTAGE STABILITY
4. Capacitor construction The construction of capacitor C~ to meet the necessary requirements poses the only difficult problem, since the remainder of the system consists of very little more than the commercially available vibrating reed electrometer. The construction of capacitor C~ is illustrated in fig. 2. It consists of two sets of interleaved plates six inches square, with one set of plates rotated 45 degrees with respect to the other. The plates of both stacks are of gold-plated quartz, chosen for dimensional stability. If the spacers separating the plates were also of the same material, it can be shown that the combined effects of temperature-induced dimensional changes along all three axes would result in a temperature coefficient of capacitance equal to + 0.57 ppm per degree C, which is the coefficient of expansion for fused quartz. Since very little additional effort was required, the spacers were made of Vycor, which has a slightly greater coefficient of expansion and thus permits designing for a near-zero capacitance coefficient.
143
The capacitance value is proportional to the effective area A divided by the spacing ½ ( l - t), where lis the total length of the spacers, and t is the thickness of the quartz plates. It can be shown that the temperature coefficient of capacity will be zero if ~,t 1 =
2cq
(9) ct 2
-
where u~ and ~2 are the temperature coefficients of expansion of quartz and Vycor respectively. With t chosen as 0.25 inches, and using figures of 5.7 x 1 0 - 7 and 8.0 x 1 0 - 7 for ~ and ~2, the figure of 0.419 inches for the length of the Vycor spacer results. Another important precaution in the capacitor design involves minimizing the electric field produced by the input voltage at the surface of the insulators supporting the output plate stack. Such an electric field will result in a temporary charging effect upon the surfaces, with an equilibrium condition being reached only after the lapse of a time interval determined by the conductivity
50% COATED WITH STAINLESS STEEL
HOLD DOWN P L A T E ~ STAINLESS STEEL GOLD PLATED (4)~"DIA. X .187" VYCORTOP SURFACEUNPLATED
BELL JAR.12~'O.D. PYREX
(4) ~ DIA. X ,522%~--~ VYCOR. TOP SURFACE UNPLATED
(~,6.000"L005 SQ. X .250" ±~02 THICK QUARTZ PLATE GOLD PLATED
(68)SPACER ~' DIA.X .419" VYCOR GOLD PLATED
(84) ~"DIA. X~' QUARTZ ROD
(4) ~'DIA. X .2095 "...,,,, VYCOR
(4)~'DIA. X .IBT" QUARTZ GOLD PLATED
(4) I~'DIA. X .IBT~...... QUARTZ PLATE GOLD PLATED
~~(4)_-[p"DIA. X .500" QUARTZ GOLD PLATED
9"DIA. X I" QUART: GOLD PLATED
(B)7"DIA. X .IB?" THICK QUARTZ. TOP SURFACE UNPLATED
x
KOROSEAL GASKET GUIDESLEEVE-TO~ FIT VIBRATINGREED ELECTROMETER PREAMP INPUT
~'~ANCHOR _
PLATE
,4,,×
STA,NLESS STEEL
GOLD WIRE (2)ADVAC 500B TERMINAL
WIRE TO VACUUM SYSTEM
Fig. 2. Construction of input capacitor C1.
TO H.V INPUT"
IRASS FITTING WITH "0" RING
144
W. K. B R O O K S H I E R
of the insulator, typically as much as an hour. The charging currents involved in this action flow into the electrometer input, producing an erroneous indication of change in the applied voltage. The magnitudes of these currents can be much larger than the steady-sate leakage currents flowing between the output stack and ground and it is essential to minimize them. This is accomplished by keeping the amount of unplated surfaces to a minimum and locating the unplated surfaces so that they are shielded from the potential of the input stack by the potential of the output stack. In fig. 2 it may be observed that the stack of plates which includes the bottom plate is supported from the large quartz base plate by three cylindrical buttons of quartz at each corner, with the bottom two pieces recessed into a hole in the base plate. The insulating surface is formed by omitting the plating of the top surface of the bottom piece. The top piece, which is completely plated, acts as a shield against penetration of electric field from the input voltage. A similar arrangement is used at the top and bottom of both plate stacks, which makes it permissible to interchange the input and output terminals of the capacitor, should it be desired to do so. In order to shield the internal structure of the capacitor from the influence of external electric fields, the interior surface of the bell jar was coated with a semi-transparent conductive layer of stainless steel. This coating is grounded to the metal base plate with finger contacts not shown in fig. 2. The conductive gold coating on all the quartz and
SIA
A N D R. N. L E W I S
Vycor pieces was applied by a painting and baking process using DuPont's Liquid Bright Gold No. 4063. This coating is quite durable and cannot be scratched off easily. However, some difficulty was experienced in obtaining satisfactory electrical contact between plates and spacers with normal assembly pressure. This trouble was cured by applying small dabs of silver paint to bridge the gap across each junction. The choice of capacitance value is influenced by the effect of the background current of the system. The total background current of the system consists of the contribution from the electrometer, typically 5 x 10-17 amperes or so, plus the contribution from surface currents flowing from the insulating surfaces supporting the output plate stack. This total background current I b flows into the junction between C1 and (72, accumulating on C 2. The drift rate at the output is then Ib/C 2. When referred to the input by multiplication by C2/C 1, the drift rate becomes I J C I . This drift rate represents an uncertainty in the measurement of changes in the input voltage and is to be minimized. Thus the higher the value of capacitance for C 1, the smaller will be the input drift rate. The value of capacitance chosen, about 1500 pF, represents the largest value that could conveniently be assembled into a 12 inch bell jar with the desired constructional features.
5. Description of remainder of system The remainder of the electronic part of the system is indicated in the circuit of fig. 3. Switch $1 permits
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Fig. 3. System for monitoring stability of voltage vz, with means for insertion of calibrating voltage steps.
INSTRUMENT FOR DC VOLTAGE STABILITY
145
reed electrometer and the insulator current from the output plate stack of C~. The average slope of the initial part of this recording is about 17 ~V/sec, corresponding to a current of 1.7 x 10 -16 amperes. Since the voltage gain is about 150, the drift rate referred to the input is 17/150 = 0.11/~V per second. The 100#V calibrating step super-imposed in the middle of the run verifies the sensitivity, which is further indicated by observing the amplitude of the voltage change produced by a 500 megohm load on the standard cells. Although this system was not intended for application at voltage levels as low as 4 volt, some usefulness does exist at that level. The entire amount of the drift rate due to total background current need not be taken as an uncertainty, since the value of the background current normally remains fairly constant for periods of time ranging up to an hour or more. If the recording of an unknown voltage is sandwiched between two recordings with zero volt applied, as was done in fig. 6
Fig. 4. Photograph of input capacitor C1. convenient switching from zero volt to the voltage under test and $2 makes possible the addition of known voltage steps, from 100#V through 1 volt, in series with the applied voltage. A 10 megohm resistor is placed in series with the input end of C1 to act as a current limiter in the event of an internal breakdown. This resistor also serves to limit the peak charging current flowing from the source into C1 upon application of a voltage. Capacity values used for C2 ranged from 10 to 1000 pF. The value of 10 pF is built into the vibrating reed electrometer circuit. Higher values were obtained by paralleling the built-in capacitor with an external polystyrene capacitor. The bell jar containing the capacitor C1 was evacuated to a pressure of about 10 -4 mm Hg for all of the experimental results to follow. Fig. 4 is a photograph of the special capacitor assembly out of the bell jar and fig. 5 is a photograph of the entire assembled apparatus. 6. Results
Fig. 6 indicates a recording of an applied voltage of about 4 volt from four series-connected saturated standard cells2). In this run, as in all others, a relatively steady drift appears in the output recording, produced by the sum of the background current of the vibrating
Fig. 5. Photograph of complete system.
146
W. K. B R O O K S H I E R
Fig. 6. Stability recording of saturated standard cells. and if the slopes of the two zero runs are nearly equal, the uncertainty of the A Vmeasurements of the unknown becomes a small fraction of the total drift over the measurement period. Fig. 7. represents a zero run followed by a recording of a 300 volt battery. The slope of this zero run corresponds to a total background current of about 2.2 x 10 - 1 6 amperes. The calibration voltage step of 1 millivolt represents 3 ppm of the applied potential. The effect of applying a load of 10 ~ ohms across the battery can be examined in some detail. There is an
A N D R. N. L E W I S
initial potential drop of about 0.3 ppm, followed by a further decrease over the following 2 minutes. If the zero run is projected onward through the 300 volt run and the variations in battery potential noted with respect to this projection, it can be stated with reasonable certainty that the battery maintained a potential to within about 5 ppm for a time interval of 1½ hours. This degree of stability is not typical of this type of battery, but was achieved only after a long stabilization period and recovery from the initial loading of the battery caused by the charging current into C1. During the 4 hour period following initial application of the voltage, the potential drifted upward by a total amount several times the full-scale span of the recording. It is possible, of course, to pre-charge C1 to match the potential of the unknown and avoid most of the otherwise-long recovery time. However, this is a problem associated with the voltage source under test and has little to do with the accuracy of the measurement technique. Fig. 8 is a recording of a 1000 volt potential from a Fluke Model 412A power supply. It serves to illustrate the difference between the very short term stability (1 minute or so) of an electronically regulated supply, in comparison with a battery source. The observed stability is consistent with the manufacturer's specification of 50 ppm per hour.
Fig. 7. Stability recording of a 300 volt battery.
INSTRUMENT FOR DC VOLTAGE STABILITY
147
Fig. 8. Stability recording of 1000 volt potential from a Fluke 412A supply. Fig. 9 is a recording of the 100V output of a Princeton Applied Research Model TC100.2R supply. The peak-to-peak noise level on the supply over a one minute time interval is about 3 p p m and the change in output due to application of a 100 m A load is about 1 ppm. These recordings indicate that the system is capable of displaying changes in voltage source as small as
0.1 p p m over time intervals of usefully long duration. For higher values of voltage, even this figure is not a sensitivity limit, and it should be quite feasible to display changes of 0.01 p p m over correspondingly shorter time intervals. A logical extension of application for the system would consist of incorporating it as an error detector in a feedback system for controlling the output of a voltage source. In such an application, it
Fig. 9. Stability recording of 100 volt potential from a Princeton Applied Research TC100.2R supply.
148
w. K. BROOKSHIER AND R. N. LEWIS
should be possible to obtain a controlled voltage source stability corresponding to the input-referred drift rate of this system of about 0.1 #V/sec, or 360 #V/h. For a source potential of 1000 V, the stability would then be 0.36 ppm per hour and correspondingly better for higher source potentials. The capacitor was designed for use with potentials up to 10 kV. Due to limitations in associated equipment, the highest level used to date is I kV.
The authors wish to express appreciation for the fabrication of the special capacitor performed by the Central Shops Division of Argonne and to D. J. Keefe for his assistance in gold-plating the capacitor parts. References 1) Jennings JCCG-500 vacuum capacitor, 500 pF. a) Sensitive Research Type 4305 in Type 9152 constant tempera ture enclosure.