Capacitor Engineering Bulletins

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1. Equivalent Series Resistance (ESR) . . . . . . . . . . . . . 2

2. Charging Capacitors: Polarization and Leakage Currents . . . . . 10

3. Metallized Electrode Capacitors for Pulsed Power Applications . . . 21

Engineering Bulletins

Capacitors

2

Many electrical engineers arefamiliar with a circuit model (Figure 1)of a non-ideal capacitor which includesa series inductance (the ESL) and a se-ries resistance (the ESR). This modelis very misleading because it often re-sults in the assumption that the equiva-lent resistance is actually a true resis-tance, having essentially constant valueover a wide range of conditions [7]. Intruth, the Equivalent Series Resistanceis the value of resistance which is equalto the total effect of a large and com-plex set of energy loss mechanismsoccuring under a particular set ofmeasurement or operating conditions.

General Atomics Energy Prod-ucts (GAEP) has attempted to avoid in-correct application of ESR informationby not listing an ESR value in its stan-dard product sales literature. Each cus-tomer who is concerned about this pa-rameter is asked how the ESR value isto be used in his or her calculations ormodels. This allows us to tailor a mea-surement method to the requirements ofa particular application. Although thisis more complex and time-consuming,it is the only way of assuring that thequoted ESR values have real mean-ing for the intended purpose.

Capacitor manufacturers oftendefine the ESR as the impedance mea-sured at the resonant frequency of thecapacitor, or the value of the ESR at aparticular AC frequency (e.g. 100 kHz),usually measured with a bridge, LCRmeter, or impedance analyzer at about1 V. These are definitions which makeit easy to measure the ESR but may beinadequate to describe the behavior ofa high voltage capacitor under actualoperating conditions.

Equivalent SeriesResistance (ESR)

Figure 1. AC voltage signal applied tocircuit below resonant frequency.

RS(ESR)

LS(ESL)

CS

I

V

RSI

ωCSδ

θ

3

In this Technical Note, we in-tend to briefly describe why the ESRdoes not behave like a simple resistanceas the result of the physics of a capaci-tor. We will then examine several meth-ods of measuring the ESR and how theexact test conditions affect the resultsof each. Finally, we will discuss howESR values are often used and suggesthow to specify the ESR and the propermeasurement technique for your appli-cation.

If we apply an AC voltage sig-nal to the circuit of Figure 1 at a fre-quency well below the resonant fre-quency, we observe a phase shift be-tween voltage and current which is lessthan 90 degrees. The difference be-tween the phase angle and 90 degrees isthe defect angle (δ), which can be usedto determine the effective resistive im-pedance using:

tangent (δ) = Zr/Zc= ESR.ω.C (1)

where Zr and Zc are the resistive andcapacitive impedances, ω is the angularfrequency, and C is the capacitance.Note that tangent δ is the same as thedissipation factor, or DF [4].

The energy loss in the circuit isproportional to the power factor, PF,which is given by the cosine of the phaseangle. The DF is approximately thesame as the PF for small values (e.g. DF< 0.1 or 10 %).

If we assume that the energydissipated is a constant fraction of the

energy stored over all frequencies (con-stant DF), the ESR decreases with in-creasing frequency, as can be seen byrearranging equation (1):

ESR = DF/ωC ~ 1/ω (2)

Figure 2 illustrates the hypo-thetical constant-DF case.

Capacitor Physicsand ESR

Figure 2. Hypothetical constant/DF case.

Figure 3. ESR as a function of frequency.

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

ESR

(Ohm

s)

Log (Frequency, HZ)

2 4 6 8 10

Dielectric LossMetal LossBoth

C = 1 µFDF = Constant = 0.001

.00002

.00018

.00016

.00014

.00012

.00010

.00008

.00006

.00004

.00002

.00000

ES

R (O

hms)

Log (Frequency, HZ)

2 4 8 10 14

C = 1 µFDF (dielectrric) = 0.001R (metal) = 0.00001Ω

Dielectric LossMetal LossBoth

SkinEffect

Total ESR

6 12

4

The ESR of a 1 µF capacitor hasbeen modelled assuming that the di-electric losses result in a constant DFof 0.001 or 0.1% and the ohmic resis-tance is 0.01 milliohm. The resultingESR is shown as a function of fre-quency in Figure 3. The ESR fallsfrom a value of 1.6 ohm at 100 Hz toa value of 0.01 milliohm at 5 MHz.Above this frequency the ESR islargely determined by the ohmic re-sistance of the conductors, and re-mains relatively constant until the skineffect begins to reduce the effectivethickness of the foil electrodes. TheESR then begins to increase in pro-portion to f 0.5 above about 30 MHz.

When examined more closely,the losses vary as a function of voltage,temperature, and other aspects of thewaveform. This is because there are avariety of energy loss mechanismswhich act within a capacitor. Some ofthese reside within the dielectric whileothers involve the conductors carryingthe current. Below we describe someof these mechanisms and the operatingparameters which strongly effect themagnitude of the losses which are asso-ciated with them.

Dielectric losses are usually themost important losses in a film capaci-tor. These losses are associated with thepolarization and relaxation of the dielec-tric material in response to the applica-tion and removal of voltage from thecapacitor. As such, the magnitude of thedielectric losses in a capacitor are, ingeneral, both frequency and temperaturedependent. In this case, the largestlosses occur at low temperatures or highfrequencies, where dipole orientation ismost hindered. Dielectric losses (asdefined here) are not voltage-dependent.

The dielectric losses of a givenmaterial can be described by its Dissi-pation Factor (DF). If the dielectric losswere the only loss mechanism operat-ing in a capacitor, then the DF of thecapacitor would be independent of itssize and geometry and internal configu-ration. Capacitors of any size made withthe same material would have the sameDF when measured under identical con-ditions. The ESR could then easily becomputed using equation (2). However,the capacitor DF and ESR do dependon the electrodes and their configura-tion, as described below.

Ferroelectric hysteresis lossesare observed in certain high dielectricconstant materials, most notably ceram-ics. These losses are a strong functionof applied voltage. This loss mechanismarises when the internal polarizationfield has the same order of magnitudeas the applied field. Under these condi-tions the dielectric response saturates.Capacitors made with such materialsexhibit permanent polarization, variablecapacitance as a function of voltage, andextreme sensitivity to reversals of voltage.

Dielectric conduction lossesare caused by the actual transport ofcharge across the volume of the dielec-tric or across internal dielectric inter-faces. These losses are largest at lowfrequencies and higher temperatures.Because conduction in a dielectric ma-terial can be strongly nonlinear (non-Ohmic), conduction losses are oftenstrongly dependent on the voltage ap-plied to the capacitor.

Interfacial polarization lossesare closely related to dielectric conduc-tion. Many high voltage capacitors con-tain two or three different materials

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within their dielectric systems – filmand oil or paper, film and oil. Eachmaterial has different conduction prop-erties and permittivity. As a result, theapplication of a DC voltage over a pe-riod of time will result in a build-up ofconducted charge at the internal inter-faces between materials. This polariza-tion of the dielectric is largely a low-frequency phenomenon and the energystored in this way is not available fordischarge at high frequency. Again,since the conduction is nonlinear, inter-facial polarization will also generally benonlinearly voltage dependent.

This loss mechanism can be es-pecially important in pulse dischargeapplications, where the capacitor ischarged over a relatively long period oftime and then discharged much morerapidly.

Partial discharge losses canoccur within gas-filled or defective solidcapacitors or even in liquid-filled ca-pacitors at high voltages. It is also com-mon to have external corona on capaci-tor terminals (which can be considereda capacitor energy loss mechanism).Partial discharges are most energetic athigh rates of change of voltage (high dV/dt), such as during a capacitor pulse dis-charge. Also, reversal of the voltagesuch as in a highly oscillatory ringingcapacitor discharge will cause more nu-merous, energetic, partial discharges.

Electromechanical losses re-sult from the electrostriction (and some-times piezoelectricity) acting within thecapacitor dielectric itself and the flex-ing of internal wiring due to the Lorentzforces.

Ohmic resistance losses occur

within the metallic electrodes, the inter-nal wiring, and the terminals of the ca-pacitor. (In electrolytic capacitors,ohmic resistance in the electrolyte itselfrepresents the largest loss mechanism.)The resistance losses in the metal arequite constant as a function of tempera-ture and frequency (until the skin depthin the electrodes becomes important,usually at several megahertz or higher).Losses in the internal wiring and the ter-minal can be important in high currentapplications, and should not be ignored.When high voltage capacitors are inter-nally configured as a series string oflower voltage capacitor windings orunits, the ohmic resistance within agiven container size increases at thesquare of the voltage (or as the numberof series elements).

Sparking between conductorsor different points on the same conduc-tor during the discharge has been re-ported to occur in pulse capacitors [3].For example, capacitors manufacturedwith an inserted tab connection to theelectrode foil which is only a pressurecontact have been found to exhibitpoints of localized melting after pulsedischarge operation resulting fromsparks between the adjacent metallicsurfaces [3]. This phenomenon probablyis related to a high rate of change of thecurrent (dI/dt) during the discharge, andtherefore to both frequency and voltage.

Eddy current losses are impor-tant in Pulse Forming Networks (PFNs)or other situations where a high mag-netic field can couple into any ferromag-netic materials used in the capacitor.These losses will depend strongly onfrequency. Usually the internal induc-tance in a capacitor is small and will notgenerate significant eddy currents.

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Measuring ESR

There are several techniqueswhich can be used to measure the ESRunder different conditions. Below wedescribe these methods and discuss whatthey actually are measuring in terms ofthe mechanisms discussed previously.

AC Bridge measurements in-volve the application of a sinusoidal ACsignal to the capacitor at a particular fre-quency and the measurement of thephase angle. Note that this measurementof the ESR is equivalent to measuringthe DF.

In practice, most manufacturersuse a low voltage bridge, LCR meter,or impedance analyzer to make this mea-surement. High voltage AC bridge mea-surements are possible [5], but usuallycannot be performed at the rated DCvoltage due to capacitor stress limits.

One major drawback of thebridge measurement technique is thatmeasurements are made at a discrete fre-quency, whereas pulse discharge appli-cations typically involve two wide bandsof frequency involved in charging anddischarging. Some improvement can bemade by measuring and reporting theESR over a wide range of frequencies.

Another drawback is that thesignal is sinusoidal, whereas pulse dis-charge applications generally involvecharging to a DC voltage and either no

reversal or less than 100% reversal ondischarge.

Biased AC Bridge measure-ments are a possible solution to the highvoltage DC application versus low volt-age AC measurement problem. In theoryit would be possible to bias the applied1 V AC signal and measure the differ-ential ESR at high DC voltage. By it-self, this technique offers no advantage,but by making a continuous series ofmeasurements over the full range ofvoltage and using computer-basedanalysis the data could be integrated toobtain the total effective ESR. Thiscould be repeated over a range of fre-quencies to map out the behavior in thefrequency and bias voltage domains.

This approach seems promisingfor a future line of research, but to ourknowledge, has not been previously de-scribed or tested.

Short-circuit discharge of thecapacitor is a technique which has beenfrequently used at GAEP. The methodinvolves charging the capacitor to a volt-age at which it is acceptable for a ring-ing discharge to occur without damag-ing the capacitor. The capacitor is thendischarged through a low inductance,low resistance short circuit and the dis-charge waveform captured using aRogowski coil or other sensor. Both thecircuit inductance and resistance can becalculated from the period and thedamping factor measured using thistechnique.

To improve the accuracy andsensitivity of this method, it is oftennecessary to connect multiple capacitorsin series in the discharge circuit. Onethen replaces one of the capacitors with

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a direct short so as to determine the dif-ference in the circuit resistance and in-ductance due to a single capacitor. Thismethod allows the elimination of theresidual resistance in the externalbuswork and switch [2]. It assumes thatthe difference in the resonant frequencyof the circuit with different numbers ofcapacitors is not significant to the mea-surement.

A similiar method, developedfor measuring low values of capacitorparasitic inductance, involves perform-ing a series of ringing discharges whilevarying a small added external induc-tance. The dI/dt at the start of the dis-charge is estimated for each pulse andprojected to zero external inductance[1].

These methods suffer becausethe resonant frequency of the capacitoris generally well above the frequencyrange of interest to the user. Also, theyinvolve a high reversal discharge whichmay not be representative of the appli-cation, and measure only the energylosses occuring during the discharge.Although such techniques can be usedat higher voltages than the AC bridge,they often cannot be used above halfrated voltage due to capacitor stresslimitations.

Standing wave measurementsusing, for example, a Q-meter, can bemade to determine the Q at the self-reso-nant frequency. The Q is just 1/DF, andso the ESR at the self-resonant fre-quency can be calculated. This methodis a low voltage measurement techniqueand is restricted to the self-resonant fre-quency [1].

Calorimetric measurement of

the heat generated in a capacitor underclosely simulated operating conditionsis relatively difficult, but yields directinformation about the total energy lossesin the capacitor which will result in self-heating. This method measures the to-tal energy losses which discharging thecapacitor [3],[6].

Energy efficiency measure-ments can be made under simulated op-erating conditions by measuring the in-put current and voltage and the outputcurrent and voltage as functions of time,calculating the power, and integratingto obtain the energy input and output.This method has been used to charac-terize nonlinear ferroelectric capacitorswhich have relatively low efficiencies.The precision necessary to measure theefficiency of very low loss capacitorshas not been demonstrated [6].

Like the calorimetric method,the energy losses measured in this wayresult from both the charging and dis-charging portions of the cycle, and arenot directly applicable to discharge cir-cuit modelling.

How the ESR is Applied

Engineers specifying the ESRof a capacitor are usually concernedabout either energy delivery to a lowimpedance load, self-heating of the ca-pacitor under high average power con-ditions, or quality assurance.

In many instances, users ofpulse discharge capacitors are concernedwith efficient energy delivery from thecapacitor to the load. In order to model

8

the circuit and estimate the energy de-livered, these engineers seek to estimatethe resistance in the various componentsof the pulse circuit. Alternatively, theengineer may specify a maximum resis-tance budgeted to each componentwhich will insure that the required en-ergy is delivered.

In this case the user is only con-cerned about how much the deliveredenergy will be reduced by the energyloss mechanisms occuring in the capaci-tor during the discharge itself. Gener-ally this will involve a wide band of fre-quencies proximate to the ringing fre-quency of the discharge. The most im-portant of the possible loss mechanismswill be dielectric, ferroelectric (in ce-ramic and PVDF capacitors), electrome-chanical, partial discharge, ohmic con-duction, and sparking.

As previously discussed, theESR measured at the resonant frequencyis not the worst-case value. The ESR ishigher at lower frequencies.

To take this into account, GAEPrecommends measuring the ESR at theresonant frequency using the high volt-age short-circuit discharge technique.The equivalent dissipation factor canthen be calculated using equation (1).This is constant over the range of fre-quencies of interest, and the effectiveESR can be calculated from this usingequation (2). If a single value of ESR isdesired, this could be a weighted aver-age using the spectral content of thepulse, calculated using Fourier or an-other transform method. Simpler alter-natives would be to use the maximumvalue of ESR, or the value at the ring-ing frequency, in the circuit model.

When specifying the maximumallowable ESR, clearly it is most impor-tant to include the frequency or rangeof frequencies over which the limits areapplicable.

Self-heating of capacitors is animportant concern in high repetition-ratepulse discharge, AC, and other applica-tions where the RMS current and aver-age power are high. Limits on the ESRare sometimes specified as a means ofassuring that thermal runaway, overheat-ing, and capacitor failure are avoided.

For non-sinusoidal waveforms,GAEP recommends specifying limits onthe dissipation factor rather than the ESRdue to the large variation in ESR with fre-quency. Either the two frequency bandsor the charging and discharging wave-forms should also be specified.

To be absolutely certain that thecapacitor will not overheat, the calori-metric or energy efficiency measure-ment techniques should be used undervoltage, waveform, repetition rate, andenvironmental conditions which closelyapproximate those of the application.

ESR is sometimes specified asa quality assurance parameter to be in-cluded in the acceptance testing of eachcapacitor. A limitation may be placedon the value of the ESR in order to in-sure that no "deviant" capacitors passthe acceptance test. In this case, the testmethod and parameters should also bedefined, but the choice of method maybe considered less critical.

For simplicity, reproducibility,and economy, the low voltage bridgetechnique is usually preferable for thispurpose. However, GAEP recommendsspecifying the dissipation factor rather

9

than the ESR if this measurement tech-nique is acceptable. (This will help toavoid improper use of the specifiedvalue by other engineers.) It may bedesireable to measure the DF at twowidely separated frequencies (e.g. 120Hz and 10 kHz) in order to detect a widerrange of potential defects or variations.

If another ESR measurementtechnique is to be specified, GAEP rec-ommends calling out the short-circuitdischarge method at a specified voltage.

Summary

The Equivalent Series Resis-tance is one of the most misunderstoodand misapplied parameters used inspecifying or describing capacitors. TheESR is often used as though it were anideal resistance, constant over frequencyand voltage. In reality, the ESR repre-sents a complex set of loss mechanisms,many of which are strongly dependenton the measurement conditions. A num-ber of measurement techniques areavailable depending on the intended usefor the information.

References[1] B.R. Hayworth, "How to Tell a Nanohenry from a Microfarad", Elec-tronic Instrumentation, April 1972, pp. 36-39.

[2] W.C. Nunnally, et al, "Differential Measurement of Fast Energy Dis-charge Capacitor Inductance and Resistance", IEEE Tansactions on In-strumentation and Measurement, Vol. 24, (2), June 1975, pp.112-114.

[3] J.B. Ennis and R.S. Buritz, Advanced Capacitors, USAF TechnicalReport AFWAL-TR-84-2058, Hughes Aircraft Company Report FR84-76-621, October 1984.

[4] Rene Seeberger, "Capacitance and Dissipation Factor Measurements",IEEE Electrical Insulation Magazine, Vol. 2, (1), January 1986, pp. 27-36.

[5] P. Osvath and S. Widmer, "A High Voltage High-Precision Self-Bal-ancing Capacitance and Dissipation Factor-Measuring Bridge", IEEE Trans-actions on Instrumentation and Measurement, Vol. IM-35, (1), March 1986,pp. 19-23.

[6] K. Rust and G. McDuff, "Calorimetric Measurement of the 'EquivalentSeries Resistance' of Low-Loss, High-Repetition Rate Pulse Discharge Ca-pacitors", Proceedings of the 17th IEEE Power Modulator Symposium,June 1986, pp. 202-206.

[7] D.J. McDonald, "A Method of Characterizing High Energy DensityCapacitors for Power Conditioning Systems", Proceedings of the 18th IEEEPower Modulator Symposium, June 1988, pp. 345-348.

[8] M. Honda, The Impedance Measurement Handbook: A Guide to Mea-surement Technology and Techniques, Yokagawa-Hewlett-Packard LTD,1989.

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It is an unfortunate fact that“real” capacitors differ from idealcapacitors in many respects. Realcapacitors include parasitic inductanceand resistance, and vary in capacitancewith temperature, frequency andvoltage. This is especially true in highenergy density capacitors, wheredielectric materials and currentconductors are highly stressed.

The behavior of real capacitorsdeviates farthest from the ideal capacitormodel during low-frequency transientssuch as during DC charging. This canimpact the selection or design of

compact charging power supplies, timedelays between the connection ofcharging circuits and discharge of thecapacitor or bank, or systemperformance.

General Atomics EnergyProducts (GAEP) manufacturescapacitors, charging power supplies anda variety of pulse power systems whichutilize capacitors as energy storage,pulse discharge devices. Due to thisexperience, GAEP has a uniqueunderstanding of the physical behaviorof capacitors and the problemsassociated with capacitor applications.

Charging Capacitors:Polarization and

Leakage Currents

11

This experience has beenimportant both in developing newcapacitor technology and in assisting ourcustomers in their applications.

Here we will describe thegeneral behavior of real capacitorsduring charging and steady-state voltageconditions. We will examine the reasonsfor this behavior in terms of physicalprocesses occurring within the capacitordielectric. We will discuss possibleimpacts on system design. Finally, wewill discuss measurement andcharacterization techniques.

Behavior Of RealCapacitors

Capacitors are often modeledusing the “equivalent circuit” shown inFigure 1. This circuit includes aconductance or parallel resistance (Rp)which represents a current leakage paththrough the dielectric. The value of Rpis usually determined by measuring theinsulation resistance or leakage current

one to five minutes after charging thecapacitor. This model predicts that theleakage current is directly proportionalto voltage and independent of time. Tocharge the capacitor (C) at some ramprate (dV/dt), one would therefore supplya current (I):

I = I(capacitive) + I(leakage)

= C (dV/dt) + V/Rp. (1)

In reality, this current would beinsufficient to charge a real capacitor atthe desired ramp rate. In addition, if onewere to attempt to hold the voltage atsome level by just supplying the leakagecurrent (V/Rp), the capacitor voltagewould drop to some measurably lowervalue before stabilizing.

These phenomena are mainlythe result of time-dependent polarizationcurrents within the capacitor dielectric.In addition, the assumption that thesteady-state leakage current is directlyproportional to voltage is not generallytrue.

If we apply a square wavevoltage pulse to a capacitor, and measurethe total charge input versus time byintegrating the current, we observe thebehavior seen in Figure 2. There is aninitial steep rise in the absorbed chargecorresponding to fast polarizationprocesses. This is followed by a moregradual rise in total charge which is theresult of slower polarization processes.Finally there is a continuous, linearincrease in the total charge at a relativelylow rate which is due to steady-stateconduction.

RP

C

ESRESL

Figure 1. Circuit model of acapacitor which is commonly used.

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The time scale in Figure 2 is notindicated because there are severaldifferent polarization mechanismswhich act on different time scales. Thus,the charge-time graph on one time scalelooks qualitatively the same as thecharge-time graph on a much longer ormuch shorter time scale, whether inmicroseconds or thousands of seconds.

Ignoring the leakage current andconsidering only the polarization of thedielectric, the graph of Figure 3 is thetime-dependence of the capacitance.The capacitance (C) is equal to thecharge stored (Q) divided by the appliedvoltage (V):

C = Q/V (2)

so that Figure 3 is similar to Figure 2 inform. If we transform this to acapacitance versus frequency plot, wewould obtain a curve like that shown inFigure 4.

If we measure the current drawnby the capacitor when charged with asquare voltage pulse, we obtain theresult shown in Figure 5. Alternatively,if we charge the capacitor rapidly andthen disconnect it from the powersupply, we will observe a rapid initialvoltage drop as the polarizationcontinues and the capacitance increases,as illustrated by Figure 6. This dropcannot be fit to a pure exponential decay.After the static capacitance value hasbeen reached, the voltage drop due toleakage current is at a much smallerpace, and can usually be fit to a pureexponential decay.

The effect of this time-dependent capacitance is mostly seenduring charging of the capacitor. The

Figure 2. Typical dielectric responseto a square wave voltage pulse.

Figure 3. Effective capacitance versus time in Figure 1.

Figure 4 Capacitance versus frequency in Figure 2.

Cha

rge

(Cou

lom

bs)

Time0

"Fast" Polarization

RelaxationLeakage

"Static Capacitance"

"Instantaneous" Capacitance

Cap

acita

nce

Frequency

0

"Static Capacitance"

"Instantaneous" CapacitanceCapa

cita

nce

13

energy and charge which must besupplied to bring the capacitor to somevoltage over a period of seconds orminutes is often greater than expectedbased on the value of capacitancemeasured at a higher frequency (60, 120,or 1000 Hz are typical). Yet the energyavailable for a fast discharge is veryclose to that predicted from themeasured capacitance. The differenceis certainly an energy loss, but it is notdue to leakage current alone.

Another way of observing thisphenomenon is to charge a capacitorwith a constant current power supply,for which the output current is set to bethe ideal minimum value given byEquation 1. The resulting voltage rampwill look something like that shown inFigure 7. The rate of voltage rise willtend to roll-off toward the end of charge.This may be at first attributed tononlinear conduction, but it may in factbe a stronger function of the charge timethan of the charge voltage.

There is another effect of thetime-dependent capacitance, known asdielectric absorption, which isobserved after discharging the capacitor.If the capacitor is charged slowly, so thatthe static capacitance has been charged,and then discharged rapidly, followed byopening of the circuit, a residual voltagewill appear across the capacitorterminals. The voltage is usually a smallfraction of a percent of the peak chargevoltage, but can be several percent insome types of capacitors with polardielectrics. This residual voltage is dueto the energy which was stored in theslow polarization mechanisms that wasnot released during the fast pulsedischarge. This energy will redistributeitself amongst all of the available

Figure 5. Charging current for square voltage pulse.

Figure 7. Charging ramp with ideal current.

Figure 6. Voltage decay after disconnecting power supply.

Time

Cur

rent

0

Initial Rapid Voltage Decay

Normal Decay Due To Leakage Current

Vol

tage

Time0

Vol

tage

Time

Ideal CapacitorPractical Capacitor

14

polarization mechanisms after thecircuit is opened, so that a fast dischargefrom this residual voltage is thenpossible. In high voltage systems, thiseffect can create a safety hazard. Forthis reason, capacitors should normallybe kept shorted when not in operation.

Clearly the charging behavior ofcapacitors is more complicated thanindicated by the simple modelcommonly used. In the next section wewill explore why this is true.

Dielectric PhysicsThere are four basic

mechanisms of polarization which canbe taking place within the dielectric ofa capacitor: electronic, atomic ordistortion, permanent dipole orientation,and interfacial. Each process has its owncharacteristic frequency regime and losscharacteristics.

Figure 8 shows the frequencydependence of the dielectric permittivityand loss which is expected from thesepolarization mechanisms.

Note that electronic and atomicpolarizations occur at opticalfrequencies, while dipole orientationand interfacial polarization occur in theelectrical/electronic frequency regime.

Electronic polarization is dueto the distortion of electron orbits withinthe atom by the applied field.

Atomic or deformationpolarization is due to the displacementof atomic nuclei relative to one anotherin response to the applied field.

Permanent dipole orientationpolarization is due to the rotation andalignment with the field of moleculesor parts of molecules which have apermanent dipole moment.

Figure 8. Generic frequency dependence of dielectric permittivity and loss.

InterfacialRelaxation

DipolarRelaxation

Conduction

Log10 Frequency

Loss

∈''

Vis

ible

Per

miti

vity∈

' or n

2

-6 -4 -2 0 2 4 6 8 10 12 14 16

12

8

4

0

-4-6 Atomic

(Resonance)Electronic

(Resonance)

∈'s

∈'

n2

15

Interfacial (or Maxwell-Wagner) polarization is due todifferences in the conductivities ofdifferent materials or phases within adielectric system, causing charge toaccumulate at interfaces. Examples ofdifferent materials and phases found incapacitor dielectrics include epoxy andmica paper; liquid, paper, and film inimpregnated mixed-d ie lec t r iccapacitors; the crystals and boundarylayers in a ceramic, and crystalline andamorphous regions within polymers.There may also be interfacialpolarization at the electrode-dielectricinterface.

We also must mentionferroelectric behavior, such as thatobserved in barium titanate perovskiteceramics, which is due to dipolesaligning and creating a polarization fieldof the same magnitude as the appliedfield. Since the dipoles respond to thelocal field, which is a combination ofboth the applied and polarization fields,the dielectric behavior is no longerproportional to the applied field, andvarious nonlinear effects can beobserved. These effects includesaturation of the polarization at highfields, permanent polarization, and highlosses in AC voltage applications.

Very slow polarization overseconds or minutes is generally due tointerfacial polarization. The smaller thedifference in conductivity between thephases, the slower the polarizationprocess. In some extreme cases, thesteady-state leakage current value is notreached for months.

Thus, a better circuit model ofa capacitor involves several parallelcapacitances, each with its own loss

mechanism and response time constant,as shown in Figure 9. Note that theparallel resistance included in thisschematic is considered to be variable,depending on voltage and temperature.

Conduction in a dielectric maybe non-ohmic at high fields such as thoseapplied in energy storage capacitors.The conductivity at the operatingvoltage can be much larger than theconductivity measured at lower voltage.This can result in different interfacialpolarization behavior at differentvoltages. The conductivity of dielectricsgenerally increases with temperature,exacerbating the non-ideal behavior.A variety of non-ohmic conductionprocesses in dielectrics have beendescribed, including Joule heating,space-charge-limited conduction, Poole-Frenkel trap-barrier lowering, Schottkyemission and Fowler-Nordheimtunneling. Non-ohmic behavior may beobserved in polymers at applied fieldsexceeding 0.1 MV/cm [1]. Note thattypical applied fields in film capacitorsat rated voltage range from 0.4 MV/cmto 1.6 MV/cm. The highest fields areexperienced in limited life, high energydensity, energy storage capacitors.

Figure 9. An improved circuitmodel of a capacitor.

R2

RM

C0

C1

C2

ESL R1

RP

16

We have shown that thecharging behavior of capacitors isdominated by the intrinsic properties oftheir dielectrics. In the next section, wedescribe how capacitor chargingbehavior can impact systems and circuitdesign.

Implications For Systems

The advancement of technologyleads to continuous reduction in designmargins and a need for greater accuracyand precision in design andmanufacturing. In terms of design, it isnecessary to improve models ofcomponents which are to be used in asystem to account for behavior whichmight previously have been ignored orperhaps even unobservable.

There is a definite need toimprove models of capacitor behaviorcurrently being used in circuit andsystems design. This is evidenced bythe increasing number of reporteddeviations of actual behavior fromexpected behavior in completedsystems. Though these are usuallyminor in impact today, they representweaknesses of the existing modelswhich may have major impacts in thefuture. We base the followingdiscussion on actual reports of problemsor “curiosities”.

Undersized power supplies arealready a major concern. As we havealready pointed out, a power supplyspecified using a capacitance valuemeasured at 1kHz and an insulationresistance measured using a traditional

test regimen is likely to provideinsufficient power to charge a capacitoror bank of capacitors at the desired rate.The prime energy store (fuel or battery)may be insufficient to provide thenumber of charge/discharge cyclesspecified. This is especially true indesigning with little or no capabilitybeyond the specified ratings.

This type of problem is relatedto the energy efficiency of the capacitor,defined as the ratio of energy output toenergy input. In repetitively pulsingapplications, capacitors which areinefficient will generate more heatinternally and may fail as a result. Inpulsed power applications, capacitorenergy efficiency is often much lowerthan expected based on power factor ordissipation factor measurements madeat low voltage using an AC signal. Someengineers may be surprised to learn thattrue capacitor energy efficiencies maybe as low as 70 to 90 percent in pulsedpower operations.

The key here is to measure thejoules and the coulombs actuallyrequired to charge the capacitor tovoltage in the specified time frame. Forlarge capacitors or banks, this can bedone using a small model capacitormade with exactly the same dielectricsystem as in the full-size capacitor, andthen scaling with capacitance. (Atechnique used by GAEP is outlined inthe next section.)

Voltage decay is anothersignificant issue. Using a traditionalmeasurement of insulation resistance(made minutes after charging), anengineer may predict a voltage drop afew seconds after the power supply isdisconnected which is much smaller

17

than that which actually occurs. Theresult is that the system may not deliverthe current, power, and energy expectedat a given charge voltage. This may beovercome by increasing the chargevoltage or the charge and hold time, butthis may impact capacitor life or otheraspects of system performance.

A related issue is the currentrequired to maintain voltage on acapacitor once it has been charged. Insome applications, it is desirable to havetwo separate power supplies; onecharges the capacitor, the other providesa small current to maintain the voltage.If the specified rating of the sustainingpower supply is based on the wrongassumptions, it may be unable tomaintain the desired voltage.

Again, the prevention is ameasurement of the actual behavior ofthe proposed capacitor (or a scalemodel) under simulated operationconditions, including voltage, chargetime, hold time (power supplyconnected), and delay time (powersupply disconnected). These aspects ofsystem operation should be defined atthe time the capacitor is being specified.

Dielectric absorption is both asafety concern and a technical concern.From a safety standpoint, high voltagesystems should be designed to maintaina short-circuit between terminals of acapacitor when the system is not in use.Otherwise, dangerous voltages mayappear across the capacitor terminalslong after the power supply is shutdown. From a technical standpoint, acapacitor displaying absorption willbehave slightly differently from onecycle to the next, until an equilibriumcondition is reached. Generally the

energy efficiency will improve over thefirst few cycles in a DC application,whereas it would first decrease in an ACapplication where polarity is reversedon each charge cycle.

These examples of the potentialimpacts on systems of not properlycharacterizing capacitor behavior aredrawn from actual experiences in theindustry. The need to upgrade ourexisting models is becomingincreasingly apparent.

Measurement andCharacterizationTechniques

The best way to determinewhether a capacitor is suitable for anapplication is to test i t underconditions which simulate the actualoperation required. Traditionalmethods for characterizing thecharging behavior of capacitors havesome definite weakness in this regard.GAEP has developed improved testtechniques which are useful to betterdefine capacitor behavior for criticalapplications.

Traditional measurementprocedures [2] which relate to thecharging behavior of capacitors include“insulation resistance” tests, “leakagecurrent” tests, and “dielectricabsorption” tests. These tests areperformed as required for certainmilitary and other specifications. Theyare useful as qualification tests for a newdesign or a new manufacturer, but areseldom used as acceptance tests or forscreening.

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The insulation resistance (self-discharge or bleed down) measurementbegins by charging a capacitor to aspecified voltage and maintaining thatvoltage for a specified period of time(typically 1-5 minutes). The powersupply is then disconnected from thecapacitor, leaving the capacitor highvoltage terminal connected only to ahigh impedance voltage probe. Thevoltage is measured either at one pointin time or at various time intervals (e.g.10, 20, 30, 60, 90, 120 seconds) afterthe disconnection. The voltage versustime data is fit to an exponential decay

V(t) = Voe-t/RC (3)

and the “insulation resistance” is equalto the RC time constant, often expressedin megohm-microfarads (seconds). Theequivalent resistance itself can becalculated by dividing out the measuredcapacitance.

The obvious problem with thistechnique is that it assumes (as willengineers using the capacitorspecification) that the voltage decay fitsan exponential - that there is a constantparallel resistance value causing thedecay. In fact, closer examination of theearly portions of the decay curve (whichmay be of most interest to the user) oftenshows that it does not fit a pure exponentialfor the reasons already described. Asecond concern is that the result will varydepending on the previous operational ortest history of the capacitor.

The measured value maydepend very strongly upon the voltageand times specified. To maximizecatalog ratings, some manufacturers willminimize the voltage and maximize thehold and measurement times in their test

specification. Generally the insulationresistance measured increases withoperation time or voltage aging until thedielectric begins to degrade late in thelife of the capacitor. The insulationresistance may decrease if the capacitoris stored for a long period without use;it will recover after being tested oroperated at voltage.

The “leakage current” may bemeasured in a similar test regime. Inthis case, the power supply is notdisconnected, and the current providedby the supply to maintain a constantvoltage is measured. The measurementis made after a specified period of time(typically 60 seconds). Depending onthe capacitance, the DC leakage currentwill be in the picoampere to milliampererange. Note that the power supply mustbe extremely stable; AC ripple willgenerate a relatively large AC current.Instruments are commercially availableto do this specific type of testing onsmall capacitances.

The leakage current test suffersfrom the same limitations as those of theinsulation resistance test. Generally thecurrent measured in the first few minuteswill include not only the true leakagecurrent but also a capacitive chargingcomponent, which may dominate. Aplot of the current versus time wouldreveal this.

“Dielectric absorption” ofcapacitors may be characterized byusing a test regime which begins bycharging the capacitor to a specifiedvoltage (Vo ) and holding that voltage fora specified period of time. The capacitoris then disconnected from the powersupply and discharged through aspecified load for a specified time. The

19

discharge switch is then opened for aperiod equal to the hold time. Therecovery voltage (Vr) on the capacitoris then measured using a high impedanceprobe. The dielectric absorption is definedas the ratio of the voltages (Vr / Vo).

The results of this test will varyif any of the specified times are changed.Generally, the longer the hold time atvoltage, the greater the recovery voltage.The shorter the discharge time, thegreater the recovery voltage. The delaytime before measurement is also critical.The recovery voltage will graduallyincrease with the delay time until thedelay time equals the hold time, beyondwhich the recovery voltage mustdecline. Another point is that thecapacitor terminals should have beenshorted for a time prior to beginning thetest which is at least equal to the totalduration of the test, or else prior voltagehistory may have an effect on the results.

Scientists in GAEP’s CapacitorResearch and Development Laboratoryhave developed a technique to measurethe energy and coulombic chargerequired to charge a capacitor to a givenvoltage, and the energy and chargedelivered by the capacitor in dischargingthrough a specified load. This techniqueinvolves simultaneously measuring thecurrent and voltage during both phasesof the cycle, calculating theinstantaneous power, and thenintegrating to obtain the energy and thecharge. Using this technique we canmeasure the energy efficiency ofcapacitors under accurately simulatedoperating conditions. A similartechnique, used to measure an effectiveequivalent series resistance (ESR) wasdescribed in reference [3].

This methodology allows us tospecify the optimum power supply tocharge a capacitor or bank in a givenamount of time. Variations on thistechnique can be used to generate plotsof voltage decay versus time whichoccurs when the power supply isdisconnected from the capacitor or bank,or the current required to maintain agiven voltage. The tests are normallyperformed at rated or operating voltage.Since the behavior is dominated by theintrinsic properties of the dielectricsystem, it is generally sufficient to testa small “model” capacitor to veryaccurately predict the behavior of largercapacitors or even large banks ofcapacitors.

SummaryCapacitor application engineers

are frequently asked why capacitors arenot behaving as expected, indicating thatthe deviations of actual capacitorbehavior from the models successfullyused in the past are becomingmeasurable and significant today.GAEP is responding to the needs ofindustry by providing understanding ofthe fundamental dielectric physicsinvolved and developing new testmethods which simulate specifiedoperations and measure capacitorresponse.

References [1] R. Bartnikas and R.M. Eichhorn (editors),Engineering Dielectrics, Volume IIA: “Electrical Properties of SolidInsulating Materials: Molecular Structure and Electrical Behavior,”American Society for Testing and Materials, 1983.[2] MIL-STD-202 Method 302 “Insulation Resistance.”[3] J.E. Dolan and H.R. Bolton, “Capacitor ESR MeasurementTechnique,” Proceedings of the 8th IEEE International Pulsed PowerConference, 1991, pp. 228-231.

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21

Metallized paper capacitorswere first developed in Germany duringWorld War II. The use of metallizedelectrodes in capacitors has sincebecome very widespread in low tomedium voltage applications. For manyyears, metallized electrodes were notused in high voltage or high energycapacitor applications due to the verylimited current-carrying capacity of theelectrode and termination in comparisonto discrete foils. This barrier graduallybroke down, beginning first with largeDC filter capacitors and thenencompassing power factor correctioncapacitors (1).

More recently, metallizedcapacitors have been introduced in somepulsed power applications includingmedical cardiac defibrillators andelectromagnetic launchers, where

relatively slow (millisecond) dischargesare the norm. The advantages of usingmetallized electrodes in suchapplications include higher energydensity and longer life, greater reliabilityand safety, and reduced costs.

General Atomics EnergyProducts (GAEP) has pioneered the useof metallized electrode capacitors inpulsed power applications, achievingboth record energy densities andunprecedented cost reductions. In thelaboratory we have demonstrated 2.7kJ/kg capacitors delivering 100's of Joules,and larger capacitors at somewhatreduced energy densities. Capacitorswith energy densities of up to 1.5kJ/kgin sizes ranging from 10's of Joules upto 50kJ and beyond are now availablecommercially.

MetallizedElectrode Capacitors

for Pulsed PowerApplications

22

This bulletin will compare themetallized electrode technology todiscrete foils and provide anunderstanding of the advantages anddisadvantages of each in capacitordesign. Finally, typical applications formetallized electrode capacitors will bedescribed.

Metallized Versus FoilElectrodes

Most pulsed power capacitorshave been built using discrete aluminumfoil electrodes with a thickness rangingfrom about 4 microns (0.15 mil) to morethan 12 microns (0.48 mil).Terminations are normally made byeither soldering directly to extendedfoils or by inserting flag-shaped tapsduring the winding process, asillustrated in Figure 1.

Metallized electrodes are madeby vacuum vapor deposition ofaluminum, zinc, or an alloy directly onthe surface of a dielectric material suchas paper or film. The nominal thicknessof the metal layer is in the range fromabout 250 to 1000 Angstroms or 0.025to 0.1 micron. This results in a surfaceresistivity ranging from a fraction of anohm to about 10 ohms per square. Sincetypical high voltage capacitor dielectricthicknesses range from 12 to 60 microns,metallized electrodes have negligiblethickness in comparison.

Masks are used during themetallized process to provide "margins"on opposite edges of the two opposingpolarity electrodes. The marginsprevent a flashover between the twoelectrodes at the ends of the winding.During the capacitor winding operation,the two electrodes are extended fromopposite edges of the winding by a smallamount to expose some of the electrodefor purposes of termination. This issimilar to the extended foil construction.Figure 2 illustrates these features.

(a) Extended foil termination

(b) Inserted tap termination

Figure 1. Foil capacitor terminations.

Extended Foil

SolderBus

Dielectric

WINDING CROSS-SECTION(not to scale)

Foil

Solder

-

+

++

WINDING AS WOUND

Tap Ribbon

Foil

Foil "Flag"

Dielectric

+-

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For higher current applications,the thickness of the metallization at thetermination edges can be increased orreinforced during the metallizingprocess. This reduces the surfaceresistivity in this most critical region bya factor of 3-4. Many pulse powerapplications require such "heavy edge"or "reinforced edge" patterns.

The substrate for themetallization can be virtually any of thecommon dielectrics used in capacitors.Kraft paper which is of high density orlacquered to provide a smooth surfacecan be metallized after sufficient pre-drying. Films such as polypropyleneand polytetrafluoroethylene (PTFE or"Teflon") can be metallized aftertreatment of the surface to enhanceadhesion. Many other polymer filmsrequire no pre-treatment, includingpoloycarbonate or polyethyleneterephthalate (PET). The processing ofmetallized capacitors is designed tominimize changes in dimension byshrinkage or swelling which coulddisrupt the metal layer.

Termination of the metallizedelectrode is done by either flame-

spraying or arc-spraying a solderablealloy onto each end of the winding.Masks may be used to leave gaps in thesprayed metal layer for subsequentdrying and impregnation.

There are many variations of themetallized electrode concept which havebeen used in various capacitor products.One of these is a double-metallizedpaper used like a discrete foil;commonly known as "soggy foil" [2].Kraft paper is metallized on both sidesto provide twice the current-carryingcapacity. The natural roughness of thepaper aids in impregnation. Thistechnology was developed for use in ACpower capacitors. Figure 3 is aschematic cross-section of this type ofcapacitor.

Another variation which isbecoming popular is the segmentation ofthe metallized layer to provide what areessentially fusible links within thecapacitor. This technology has thepotential of improving the safety ofmetallized polypropylene capacitors usedin low to medium voltage AC applications.Segmented electrodes are discussed inmore detail in the next section.

Metallization

Offset

Dielectric Film

End SprayTerminations

Figure 2. Cross-section of a typicalmetallized electrode capacitor

(not to scale).

Double Metallized Paper

Dielectric Film

End SprayTerminations

Figure 3. Cross-section of a “soggy-foil” (double metallized) capacitor

(not to scale).

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Self-healing or "clearing"One of the advantages of

metallized capacitors over discrete foilcapacitors is their ability to self-heal inthe event of a dielectric breakdown.This improves reliability, permits higherstresses and therefore higher energydensities to be achieved, and results ina "soft" failure mode rather than acatastrophic short-circuit.

If a dielectric breakdownoccurs, current flows from surroundingareas of the capacitor through thebreakdown arc. In a foil capacitor,virtually all of the stored energy isdissipated in the arc itself, resulting insignificant damage to the capacitor. Abreakdown in a large energy storagecapacitor may rupture its container.

In a metallized capacitor, thecurrent flowing into the arc has a highenough current density to heat andvaporize the metallization immediatelysurrounding the breakdown arc. Thereis a rapid rise in the local gas pressurefrom the pyrolization of the organicsubstrate, and the arc length increasesas the area of the metallization that isbeing vaporized increases. Finally thearc is extinguished by this process,which is essentially the same as thatwhich occurs in a fuse.

The energy dissipated in theclearing process is in the range ofmicrojoules to joules [3]. A soundwhich may be described as a "snap" cansome-times be heard. The capacitorcontinues to operate normally duringand after the clearing event.

As a result of a dielectricbreakdown, there is an area of the

metallized electrode which has beencleared or removed, resulting in asmall loss of capacitance. The areacleared depends on voltage and otherdesign and manufacturing variables,but is typically between a few squaremillimeters and a few squarecentimeters. In large capacitors, ittakes hundreds or thousands ofclearings to cause a few percent lossof capacitance. Figure 4 is aphotograph of the site of a clearing onmetallized paper, magnified about10X.

Each clearing generates smallamounts of chemical byproductsincluding gases, water, and carbon.These byproducts may have a negativeeffect on capacitor electrical parameterssuch as insulation resistance (IR) anddissipation factor (DF). Again, theeffect is usually not measurable until avery large number of clearings haveoccurred. A buildup of internal gaspressure may also be observed at the endof the capacitor's life.

Figure 4. Photograph of a clearingsite (~10x).

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Figure 5 shows the typical behavior ofvarious parameters of a metallizedcapacitor during the life of the capacitor.

Figure 5. Typical variation ofelectrical parameters during life of ametallized electrode capacitor.

Some metallized capacitorshave been developed which provide anadditional safety feature beyond that ofclearing. These capacitors have ametallized electrode which is segmentedto force current to flow along prescribedpaths. In the event of a dielectricbreakdown, the current flow into thatparticular segment will be high enough

to cause a fusing action of themetallization at the entry point to thatpath and away from the actualbreakdown site [4]. Figure 6 illustratesthis approach.

Figure 6. Segmented metallizationpattern and fusing operation

Advantages ofMetallized Capacitors

In applications which permit theuse of metallized electrodes, they offermany advantages over foils. Energydensity is significantly higher inmetallized capacitors than in foilcapacitors for two reasons: (1) thereduced volume occupied by theelectrodes themselves, and (2) the higherdielectric stress levels which may besafely applied to achieve a given lifetimeand reliability.

The reduced electrode volumeis especially important in low voltage(<1000 V) applications where thethickness of a discrete foil would be thesame or even greater than that of theoptimum dielectric.

+5%

-5%

0

∆C C

(%)

Log (Time)

0.010

0

0.005

DF

(tanδ)

10.0

0.1

1.0

IR (

MΩ−µF

)

Log (Time)

Log (Time)

End of Life

"T" Margins Fused Link

Connection Edge

Breakdown SiteMetallization Normal Edge Margin

26

Reliability of metallizedcapacitors is improved over foil capacitorsbecause of the elimination of the largestsource of single-point failures. Whereasin a foil capacitor the first dielectricbreakdown produces a catastrophic failure,in a metallized capacitor hundreds tothousands of such events must occur tocause a capacitance loss which brings thedevice out of tolerance.

Lifetime of metallized capacitorsis significantly greater than that of foilcapacitors of comparable or event greatersize and weight. Factors of two to tenimprovements are easily achieved.

The soft failure mode ofmetallized capacitors is usually preferableto a catastrophic short circuit. Thecapacitance begins to measurably decreasenear the end of life, and the insulationresistance and dissipation factor maydegrade as well. It is even possible toutilize the buildup of internal gas pressureto provide a disconnect feature.

Cost of metallized capacitorscan be smaller than that of comparablefoil capacitors due to reductions in thevolume of raw material used inmanufacturing the capacitor.

These advantages have resultedin the introduction of metallizedcapacitor technology in virtually everyfilm capacitor market.

Limitations ofMetallized Capacitors

Unfortunately, metallizedelectrodes cannot be used in everyapplication due to significant

performance limitations imposed by theuse of very thin electrodes.

The peak power and "action"(defined as the integral of the square ofthe current with respect to time) per unitlength of the connected edge of themetallized electrode must be limited toprevent damage. The end connections arethe weak links in the capacitor due to therelatively high resistivity at this interface.Peak power in excess of the rating cancause the end connections to physicallyseparate from the ends of the winding.

The limitation on current meansthat a metallized capacitor is lesstolerant to external faults or short-circuitconditions than a foil capacitor. It alsomeans that metallized capacitors cannotbe used in applications which requirecombinations of high voltage and highpeak current.

The range of voltage which canbe provided with metallized electrodecapacitors is considerably more limitedthan in discrete foil capacitors. Whereasmetallized capacitors are optimal at lowvoltage, the internal resistance of theirelectrodes limits series connectioncapability and restricts the high voltageend of the range to below 50 kV. Incomparison, foil capacitors have beenbuilt for fast pulse peaking circuits withratings above one megavolt.

The metallized electrode hasgreater resistivity than a foil electrode.At low frequency (into the kilohertzrange) the parasitic resistance of acapacitor is dominated by the losses inits dielectric, and the resistance of themetallization is negligible. At higherfrequencies the resistance in themetallization will dominate and the

27

equivalent series resistance (ESR) ordissipation factor (DF) will besignificantly greater than in a foilcapacitor. Most metallized capacitorsare safely used in DC filteringapplications, 60 Hz-400 Hz AC, andpulse discharges with millisecond pulsewidth. GAEP engineers have developedspecial designs which allow metallizedelectrodes to be used in someapplications at considerably higherfrequency and shorter pulse width, butthe fastest discharge capacitors stillrequire discrete foils.

Another important limitation ofmetallized capacitors is their relativelypoor thermal conductivity. In foilcapacitors, the metal foils provide asignificant conduction path out of thewinding not only for current but also forheat. By comparison, the metallizedelectrode is a very poor thermalconductor. This is important incontinuous duty, high RMS currentapplications such as AC or repetitivepulsing, where losses in the dielectricand the metallization itself can generatesignificant heat. The worst case resultis a large temperature buildup at thecenter of the capacitor which can resultin bulk dielectric failure.

Metallized capacitors used forhigh average power applications mustbe designed to minimize the heatgenerated internally through the choiceof dielectric materials. In addition, thegeometry of the capacitor must be suchas to minimize the distance that heatmust travel to exit.

Gas generation due to self-healing in metallized capacitors,sometimes resulting in internalpressurization and distortion of the

container at the end of life, is considereda disadvantage in some applications. Asalready mentioned, in such situations theinternal pressure can be used to providea disconnect safety feature to thecapacitor, or can be sensed externallyusing a mechanical switch or sensor totrigger a safety interlock device.

ApplicationsMetallized electrode capacitors

have become the standard for low dutyapplications involving low frequency(<1000 Hz) pulse discharges andrequiring high energy densities. Twoexamples are medical cardiacdefibrillators and electric guns.

Defibrillator capacitors aretypically rated at voltages less than 6 kVand store up to 500 Joules of energy.Discharge frequencies are of the order100 Hz, and typical peak currents areless than 200 Amps. The application isessentially "single shot," with less thanfive cycles required over a period ofminutes. Lifetimes of thousands ofshots are required with high reliability.

Early defibrillator capacitorswere essentially DC filter capacitorswhich were re-rated for the requiredreliability and life. Later, specialdesigns incorporating polyvinylidenefluoride (PVDF) achieved the energydensities needed for portabledefibrillators used by paramedics.These capacitors were not onlyexpensive, but suffered from low energyefficiency and restricted operatingtemperature range due to theferroelectric properties of PVDF.

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Metallized electrode capacitorshave now displaced PVDF capacitors inthis market, by offering not only higherenergy density (up to 1 J/cc) and lowercost (1/3 the cost of PVDF units), butalso improved reliability. GAEP hasdelivered more than 200,000 suchcapacitors to defibrillator manufacturersworldwide.

Electric gun testbeds built in thelast few years have often utilizedmetallized electrode capacitors. Thecapacitor banks in these systemstypically store 10-50 MJ at 15-24 kV anddeliver pulses of several millisecondsduration. The higher energy density ofmetallized capacitors has allowedsmaller facilities to be used to house thecapacitor banks, at significant overallcost savings. GAEP has supplied over52 MJ of metallized energy storagecapacitors for this particular application.

Metallized energy storagecapacitor banks are also being utilizedin Inertial Confinement Fusion (ICF)experiments such as those being

conducted by the Department of Energyat Lawrence Livermore NationalLaboratory (Beamlet) and the Universityof Rochester (OMEGA).Other applications include mobile hardrock mining (shock wave generation)systems, flashlamp drivers used in foodprocessing and xerography, and laserrangefinders.

Summary

Metallized electrode capacitorsoffer many advantages over foilcapacitors in low average powerapplications. Higher energy density,longer life, and higher reliability are afew of the benefits of this technology.General Atomics Energy Products issupplying large numbers of thesecapacitors for medical defibrillator,electric gun, and other pulse dischargeand DC applications. We invite you toinquire how GAEP's metallizedelectrode capacitors can benefit yourapplication.

References [1] D.G. Shaw, S.W. Cichanowski, A. Yializis, "A ChangingCapacitor Technology - Failure Mechanisms and Design Innovations," IEEE Transac-tions on Electrical Insulation, Vol. EI-16, No. 5, Oct. 1981, pp. 399-413.

[2] Mark A. Carter, "Paper and Film Energy Discharge Capacitors: An Introduction,"Proceedings of the Capacitor and Resistor Technology Symposium (CARTS), 1988.

[3] H. Heywang, "Physikalische und chemische Vorgange in selbstheileaden kundstoff-kindensatoren," Colloid & Polymer Science, Vol. 254, pp. 139-147, 1976. (Englishtranslation available through GAEP).

[4] H. Wada, K. Unami, S. Okino, K. Sudoh, "Dry Type Low Voltage Power Capacitorwith Safety Mechanism," CIGRE 15-05, 1992.

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