1 Engineering Bulletins Capacitors

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

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

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

1 Equivalent Series Resistance (ESR)

Many electrical engineers are General Atomics Energy Prod- familiar with a circuit model (Figure 1) ucts (GAEP) has attempted to avoid in- of a non-ideal capacitor which includes correct application of ESR information a series inductance (the ESL) and a se- by not listing an ESR value in its stan- ries resistance (the ESR). This model dard product sales literature. Each cus- is very misleading because it often re- tomer who is concerned about this pa- sults in the assumption that the equiva- rameter is asked how the ESR value is lent resistance is actually a true resis- to be used in his or her calculations or tance, having essentially constant value models. This allows us to tailor a mea- over a wide range of conditions [7]. In surement method to the requirements of truth, the Equivalent Series Resistance a particular application. Although this is the value of resistance which is equal is more complex and time-consuming, to the total effect of a large and com- it is the only way of assuring that the plex set of energy loss mechanisms quoted ESR values have real mean- occuring under a particular set of ing for the intended purpose. measurement or operating conditions. Capacitor manufacturers often define the ESR as the impedance mea-

CS LS RS sured at the resonant frequency of the (ESL) (ESR) capacitor, or the value of the ESR at a

V particular AC frequency (e.g. 100 kHz), usually measured with a bridge, LCR meter, or impedance analyzer at about I 1 V. These are definitions which make δ ωCS it easy to measure the ESR but may be θ inadequate to describe the behavior of a high voltage capacitor under actual

RSI operating conditions. Figure 1. AC voltage signal applied to circuit below resonant frequency. 2 In this Technical Note, we in- energy stored over all frequencies (con- tend to briefly describe why the ESR stant DF), the ESR decreases with in- does not behave like a simple resistance creasing frequency, as can be seen by as the result of the physics of a capaci- rearranging equation (1): tor. We will then examine several meth- ods of measuring the ESR and how the ESR = DF/ωC ~ 1/ω (2) exact test conditions affect the results of each. Finally, we will discuss how Figure 2 illustrates the hypo- ESR values are often used and suggest thetical constant-DF case. how to specify the ESR and the proper C = 1 µF measurement technique for your appli- DF = Constant = 0.001 cation. 1.6 1.4 Capacitor Physics 1.2 and ESR 1.0 Dielectric Loss 0.8 Metal Loss If we apply an AC voltage sig- Both nal to the circuit of Figure 1 at a fre- ESR (Ohms) 0.6 quency well below the resonant fre- 0.4 quency, we observe a phase shift be- 0.2 tween voltage and current which is less than 90 degrees. The difference be- 0.0 tween the phase angle and 90 degrees is 246810 the defect angle (δ), which can be used Log (Frequency, HZ) to determine the effective resistive im- pedance using: Figure 2. Hypothetical constant/DF case. tangent (δ) = Zr/Zc . . C = 1 µF = ESR ω C (1) DF (dielectrric) = 0.001 R (metal) = 0.00001Ω .00002 where Zr and Zc are the resistive and .00018 capacitive impedances, ω is the angular frequency, and C is the capacitance. .00016 Note that tangent δ is the same as the .00014 Skin dissipation factor, or DF [4]. .00012 Effect .00010

The energy loss in the circuit is .00008 ESR (Ohms) ESR proportional to the power factor, PF, .00006 which is given by the cosine of the phase Total ESR Dielectric Loss .00004 Metal Loss angle. The DF is approximately the Both same as the PF for small values (e.g. DF .00002 < 0.1 or 10 %). .00000 24612 810 14 If we assume that the energy Log (Frequency, HZ) dissipated is a constant fraction of the Figure 3. ESR as a function of frequency. 3 The ESR of a 1 µF capacitor has The dielectric losses of a given been modelled assuming that the di- material can be described by its Dissi- electric losses result in a constant DF pation Factor (DF). If the dielectric loss of 0.001 or 0.1% and the ohmic resis- were the only loss mechanism operat- tance is 0.01 milliohm. The resulting ing in a capacitor, then the DF of the ESR is shown as a function of fre- capacitor would be independent of its quency in Figure 3. The ESR falls size and geometry and internal configu- from a value of 1.6 ohm at 100 Hz to ration. Capacitors of any size made with a value of 0.01 milliohm at 5 MHz. the same material would have the same Above this frequency the ESR is DF when measured under identical con- largely determined by the ohmic re- ditions. The ESR could then easily be sistance of the conductors, and re- computed using equation (2). However, mains relatively constant until the skin the capacitor DF and ESR do depend effect begins to reduce the effective on the electrodes and their configura- thickness of the foil electrodes. The tion, as described below. ESR then begins to increase in pro- portion to f 0.5 above about 30 MHz. Ferroelectric hysteresis losses are observed in certain high dielectric When examined more closely, constant materials, most notably ceram- the losses vary as a function of voltage, ics. These losses are a strong function temperature, and other aspects of the of applied voltage. This loss mechanism waveform. This is because there are a arises when the internal polarization variety of energy loss mechanisms field has the same order of magnitude which act within a capacitor. Some of as the applied field. Under these condi- these reside within the dielectric while tions the dielectric response saturates. others involve the conductors carrying Capacitors made with such materials the current. Below we describe some exhibit permanent polarization, variable of these mechanisms and the operating capacitance as a function of voltage, and parameters which strongly effect the extreme sensitivity to reversals of voltage. magnitude of the losses which are asso- ciated with them. Dielectric conduction losses are caused by the actual transport of Dielectric losses are usually the charge across the volume of the dielec- most important losses in a film capaci- tric or across internal dielectric inter- tor. These losses are associated with the faces. These losses are largest at low polarization and relaxation of the dielec- frequencies and higher temperatures. tric material in response to the applica- Because conduction in a dielectric ma- tion and removal of voltage from the terial can be strongly nonlinear (non- capacitor. As such, the magnitude of the Ohmic), conduction losses are often dielectric losses in a capacitor are, in strongly dependent on the voltage ap- general, both frequency and temperature plied to the capacitor. dependent. In this case, the largest losses occur at low temperatures or high Interfacial polarization losses frequencies, where dipole orientation is are closely related to dielectric conduc- most hindered. Dielectric losses (as tion. Many high voltage capacitors con- defined here) are not voltage-dependent. tain two or three different materials

4 within their dielectric systems – film within the metallic electrodes, the inter- and oil or paper, film and oil. Each nal wiring, and the terminals of the ca- material has different conduction prop- pacitor. (In electrolytic capacitors, erties and permittivity. As a result, the ohmic resistance in the electrolyte itself application of a DC voltage over a pe- represents the largest loss mechanism.) riod of time will result in a build-up of The resistance losses in the metal are conducted charge at the internal inter- quite constant as a function of tempera- faces between materials. This polariza- ture and frequency (until the skin depth tion of the dielectric is largely a low- in the electrodes becomes important, frequency phenomenon and the energy usually at several megahertz or higher). stored in this way is not available for Losses in the internal wiring and the ter- discharge at high frequency. Again, minal can be important in high current since the conduction is nonlinear, inter- applications, and should not be ignored. facial polarization will also generally be When high voltage capacitors are inter- nonlinearly voltage dependent. nally configured as a series string of lower voltage capacitor windings or This loss mechanism can be es- units, the ohmic resistance within a pecially important in pulse discharge given container size increases at the applications, where the capacitor is square of the voltage (or as the number charged over a relatively long period of of series elements). time and then discharged much more rapidly. Sparking between conductors or different points on the same conduc- Partial discharge losses can tor during the discharge has been re- occur within gas-filled or defective solid ported to occur in pulse capacitors [3]. capacitors or even in liquid-filled ca- For example, capacitors manufactured pacitors at high voltages. It is also com- with an inserted tab connection to the mon to have external corona on capaci- electrode foil which is only a pressure tor terminals (which can be considered contact have been found to exhibit a capacitor energy loss mechanism). points of localized melting after pulse Partial discharges are most energetic at discharge operation resulting from high rates of change of voltage (high dV/ sparks between the adjacent metallic dt), such as during a capacitor pulse dis- surfaces [3]. This phenomenon probably charge. Also, reversal of the voltage is related to a high rate of change of the such as in a highly oscillatory ringing current (dI/dt) during the discharge, and capacitor discharge will cause more nu- therefore to both frequency and voltage. merous, energetic, partial discharges. Eddy current losses are impor- Electromechanical losses re- tant in Pulse Forming Networks (PFNs) sult from the electrostriction (and some- or other situations where a high mag- times piezoelectricity) acting within the netic field can couple into any ferromag- capacitor dielectric itself and the flex- netic materials used in the capacitor. ing of internal wiring due to the Lorentz These losses will depend strongly on forces. frequency. Usually the internal induc- tance in a capacitor is small and will not Ohmic resistance losses occur generate significant eddy currents.

5 reversal or less than 100% reversal on discharge.

Biased AC Bridge measure- ments are a possible solution to the high voltage DC application versus low volt- Measuring ESR age AC measurement problem. In theory it would be possible to bias the applied 1 V AC signal and measure the differ- There are several techniques ential ESR at high DC voltage. By it- which can be used to measure the ESR self, this technique offers no advantage, under different conditions. Below we but by making a continuous series of describe these methods and discuss what measurements over the full range of they actually are measuring in terms of voltage and using computer-based the mechanisms discussed previously. analysis the data could be integrated to obtain the total effective ESR. This AC Bridge measurements in- could be repeated over a range of fre- volve the application of a sinusoidal AC quencies to map out the behavior in the signal to the capacitor at a particular fre- frequency and bias voltage domains. quency and the measurement of the phase angle. Note that this measurement This approach seems promising of the ESR is equivalent to measuring for a future line of research, but to our the DF. knowledge, has not been previously de- scribed or tested. In practice, most manufacturers use a low voltage bridge, LCR meter, Short-circuit discharge of the or impedance analyzer to make this mea- capacitor is a technique which has been surement. High voltage AC bridge mea- frequently used at GAEP. The method surements are possible [5], but usually involves charging the capacitor to a volt- cannot be performed at the rated DC age at which it is acceptable for a ring- voltage due to capacitor stress limits. ing discharge to occur without damag- ing the capacitor. The capacitor is then One major drawback of the discharged through a low inductance, bridge measurement technique is that low resistance short circuit and the dis- measurements are made at a discrete fre- charge waveform captured using a quency, whereas pulse discharge appli- Rogowski coil or other sensor. Both the cations typically involve two wide bands circuit inductance and resistance can be of frequency involved in charging and calculated from the period and the discharging. Some improvement can be damping factor measured using this made by measuring and reporting the technique. ESR over a wide range of frequencies. To improve the accuracy and Another drawback is that the sensitivity of this method, it is often signal is sinusoidal, whereas pulse dis- necessary to connect multiple capacitors charge applications generally involve in series in the discharge circuit. One charging to a DC voltage and either no then replaces one of the capacitors with

6 a direct short so as to determine the dif- the heat generated in a capacitor under ference in the circuit resistance and in- closely simulated operating conditions ductance due to a single capacitor. This is relatively difficult, but yields direct method allows the elimination of the information about the total energy losses residual resistance in the external in the capacitor which will result in self- buswork and switch [2]. It assumes that heating. This method measures the to- the difference in the resonant frequency tal energy losses which discharging the of the circuit with different numbers of capacitor [3],[6]. capacitors is not significant to the mea- surement. Energy efficiency measure- ments can be made under simulated op- A similiar method, developed erating conditions by measuring the in- for measuring low values of capacitor put current and voltage and the output parasitic inductance, involves perform- current and voltage as functions of time, ing a series of ringing discharges while calculating the power, and integrating varying a small added external induc- to obtain the energy input and output. tance. The dI/dt at the start of the dis- This method has been used to charac- charge is estimated for each pulse and terize nonlinear ferroelectric capacitors projected to zero external inductance which have relatively low efficiencies. [1]. The precision necessary to measure the efficiency of very low loss capacitors These methods suffer because has not been demonstrated [6]. the resonant frequency of the capacitor is generally well above the frequency Like the calorimetric method, range of interest to the user. Also, they the energy losses measured in this way involve a high reversal discharge which result from both the charging and dis- may not be representative of the appli- charging portions of the cycle, and are cation, and measure only the energy not directly applicable to discharge cir- losses occuring during the discharge. cuit modelling. Although such techniques can be used at higher voltages than the AC bridge, they often cannot be used above half rated voltage due to capacitor stress limitations. How the ESR is Applied Standing wave measurements using, for example, a Q-meter, can be Engineers specifying the ESR made to determine the Q at the self-reso- of a capacitor are usually concerned nant frequency. The Q is just 1/DF, and about either energy delivery to a low so the ESR at the self-resonant fre- impedance load, self-heating of the ca- quency can be calculated. This method pacitor under high average power con- is a low voltage measurement technique ditions, or quality assurance. and is restricted to the self-resonant fre- In many instances, users of quency [1]. pulse discharge capacitors are concerned with efficient energy delivery from the Calorimetric measurement of capacitor to the load. In order to model

7 the circuit and estimate the energy de- When specifying the maximum livered, these engineers seek to estimate allowable ESR, clearly it is most impor- the resistance in the various components tant to include the frequency or range of the pulse circuit. Alternatively, the of frequencies over which the limits are engineer may specify a maximum resis- applicable. tance budgeted to each component which will insure that the required en- Self-heating of capacitors is an ergy is delivered. important concern in high repetition-rate pulse discharge, AC, and other applica- In this case the user is only con- tions where the RMS current and aver- cerned about how much the delivered age power are high. Limits on the ESR energy will be reduced by the energy are sometimes specified as a means of loss mechanisms occuring in the capaci- assuring that thermal runaway, overheat- tor during the discharge itself. Gener- ing, and capacitor failure are avoided. ally this will involve a wide band of fre- quencies proximate to the ringing fre- For non-sinusoidal waveforms, quency of the discharge. The most im- GAEP recommends specifying limits on portant of the possible loss mechanisms the dissipation factor rather than the ESR will be dielectric, ferroelectric (in ce- due to the large variation in ESR with fre- ramic and PVDF capacitors), electrome- quency. Either the two frequency bands chanical, partial discharge, ohmic con- or the charging and discharging wave- duction, and sparking. forms should also be specified.

As previously discussed, the To be absolutely certain that the ESR measured at the resonant frequency capacitor will not overheat, the calori- is not the worst-case value. The ESR is metric or energy efficiency measure- higher at lower frequencies. ment techniques should be used under voltage, waveform, repetition rate, and To take this into account, GAEP environmental conditions which closely recommends measuring the ESR at the approximate those of the application. resonant frequency using the high volt- age short-circuit discharge technique. ESR is sometimes specified as The equivalent dissipation factor can a quality assurance parameter to be in- then be calculated using equation (1). cluded in the acceptance testing of each This is constant over the range of fre- capacitor. A limitation may be placed quencies of interest, and the effective on the value of the ESR in order to in- ESR can be calculated from this using sure that no "deviant" capacitors pass equation (2). If a single value of ESR is the acceptance test. In this case, the test desired, this could be a weighted aver- method and parameters should also be age using the spectral content of the defined, but the choice of method may pulse, calculated using Fourier or an- be considered less critical. other transform method. Simpler alter- For simplicity, reproducibility, natives would be to use the maximum and economy, the low voltage bridge value of ESR, or the value at the ring- technique is usually preferable for this ing frequency, in the circuit model. purpose. However, GAEP recommends specifying the dissipation factor rather

8 than the ESR if this measurement tech- nique is acceptable. (This will help to avoid improper use of the specified References value by other engineers.) It may be [1] B.R. Hayworth, "How to Tell a Nanohenry from a Microfarad", Elec- desireable to measure the DF at two tronic Instrumentation, April 1972, pp. 36-39. widely separated frequencies (e.g. 120 [2] W.C. Nunnally, et al, "Differential Measurement of Fast Energy Dis- Hz and 10 kHz) in order to detect a wider charge Capacitor Inductance and Resistance", IEEE Tansactions on In- range of potential defects or variations. strumentation and Measurement, Vol. 24, (2), June 1975, pp.112-114.

If another ESR measurement [3] J.B. Ennis and R.S. Buritz, Advanced Capacitors, USAF Technical Report AFWAL-TR-84-2058, Hughes Aircraft Company Report FR84-76- technique is to be specified, GAEP rec- 621, October 1984. ommends calling out the short-circuit discharge method at a specified voltage. [4] Rene Seeberger, "Capacitance and Dissipation Factor Measurements", IEEE Electrical Insulation Magazine, Vol. 2, (1), January 1986, pp. 27-36. Summary [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, The Equivalent Series Resis- pp. 19-23. tance is one of the most misunderstood and misapplied parameters used in [6] K. Rust and G. McDuff, "Calorimetric Measurement of the 'Equivalent Series Resistance' of Low-Loss, High-Repetition Rate Pulse Discharge Ca- specifying or describing capacitors. The pacitors", Proceedings of the 17th IEEE Power Modulator Symposium, ESR is often used as though it were an June 1986, pp. 202-206. ideal resistance, constant over frequency and voltage. In reality, the ESR repre- [7] D.J. McDonald, "A Method of Characterizing High Energy Density sents a complex set of loss mechanisms, Capacitors for Power Conditioning Systems", Proceedings of the 18th IEEE Power Modulator Symposium, June 1988, pp. 345-348. many of which are strongly dependent on the measurement conditions. A num- [8] M. Honda, The Impedance Measurement Handbook: A Guide to Mea- ber of measurement techniques are surement Technology and Techniques, Yokagawa-Hewlett-Packard LTD, available depending on the intended use 1989. for the information.

9 Charging Capacitors: Polarization and Leakage Currents

It is an unfortunate fact that compact charging power supplies, time “real” capacitors differ from ideal delays between the connection of capacitors in many respects. Real charging circuits and discharge of the capacitors include parasitic inductance capacitor or bank, or system and resistance, and vary in capacitance performance. with temperature, frequency and voltage. This is especially true in high General Atomics Energy energy density capacitors, where Products (GAEP) manufactures dielectric materials and current capacitors, charging power supplies and conductors are highly stressed. a variety of pulse power systems which utilize capacitors as energy storage, The behavior of real capacitors pulse discharge devices. Due to this deviates farthest from the ideal capacitor experience, GAEP has a unique model during low-frequency transients understanding of the physical behavior such as during DC charging. This can of capacitors and the problems impact the selection or design of associated with capacitor applications.

10 This experience has been one to five minutes after charging the important both in developing new capacitor. This model predicts that the capacitor technology and in assisting our leakage current is directly proportional customers in their applications. to voltage and independent of time. To charge the capacitor (C) at some ramp Here we will describe the rate (dV/dt), one would therefore supply general behavior of real capacitors a current (I): during charging and steady-state voltage conditions. We will examine the reasons for this behavior in terms of physical I = I(capacitive) + I(leakage) processes occurring within the capacitor dielectric. We will discuss possible = C (dV/dt) + V/Rp. (1) impacts on system design. Finally, we will discuss measurement and characterization techniques. In reality, this current would be insufficient to charge a real capacitor at the desired ramp rate. In addition, if one were to attempt to hold the voltage at some level by just supplying the leakage Behavior Of Real current (V/Rp), the capacitor voltage would drop to some measurably lower Capacitors value before stabilizing.

Capacitors are often modeled These phenomena are mainly using the “equivalent circuit” shown in the result of time-dependent polarization Figure 1. This circuit includes a currents within the capacitor dielectric. conductance or parallel resistance (Rp) In addition, the assumption that the which represents a current leakage path steady-state leakage current is directly through the dielectric. The value of Rp proportional to voltage is not generally is usually determined by measuring the true. insulation resistance or leakage current If we apply a square wave C voltage pulse to a capacitor, and measure the total charge input versus time by integrating the current, we observe the behavior seen in Figure 2. There is an ESL ESR initial steep rise in the absorbed charge corresponding to fast polarization processes. This is followed by a more RP gradual rise in total charge which is the result of slower polarization processes. Finally there is a continuous, linear increase in the total charge at a relatively Figure 1. Circuit model of a capacitor which is commonly used. low rate which is due to steady-state conduction.

11 The time scale in Figure 2 is not indicated because there are several different polarization mechanisms Leakage which act on different time scales. Thus, Relaxation the charge-time graph on one time scale looks qualitatively the same as the "Fast" Polarization charge-time graph on a much longer or

Charge (Coulombs) much shorter time scale, whether in microseconds or thousands of seconds.

Ignoring the leakage current and considering only the polarization of the 0 Time dielectric, the graph of Figure 3 is the Figure 2. Typical dielectric response time-dependence of the capacitance. to a square wave voltage pulse. The capacitance (C) is equal to the charge stored (Q) divided by the applied voltage (V):

"Static Capacitance" C = Q/V (2)

so that Figure 3 is similar to Figure 2 in form. If we transform this to a capacitance versus frequency plot, we

Cap aci t an ce "Instantaneous" Capacitance would obtain a curve like that shown in Figure 4.

If we measure the current drawn by the capacitor when charged with a 0 square voltage pulse, we obtain the Figure 3. Effective capacitance versus time in Figure 1. result shown in Figure 5. Alternatively, if we charge the capacitor rapidly and then disconnect it from the power supply, we will observe a rapid initial voltage drop as the polarization

"Static Capacitance" continues and the capacitance increases, as illustrated by Figure 6. This drop cannot be fit to a pure exponential decay. After the static capacitance value has been reached, the voltage drop due to

Capacitance leakage current is at a much smaller "Instantaneous" Capacitance pace, and can usually be fit to a pure exponential decay.

The effect of this time- Frequency dependent capacitance is mostly seen during charging of the capacitor. The Figure 4 Capacitance versus frequency in Figure 2.

12 energy and charge which must be supplied to bring the capacitor to some voltage over a period of seconds or minutes is often greater than expected based on the value of capacitance measured at a higher frequency (60, 120, Current or 1000 Hz are typical). Yet the energy available for a fast discharge is very close to that predicted from the measured capacitance. The difference is certainly an energy loss, but it is not 0 due to leakage current alone. Time Figure 5. Charging current for square voltage pulse. Another way of observing this phenomenon is to charge a capacitor with a constant current power supply, for which the output current is set to be Initial Rapid Voltage Decay the ideal minimum value given by Equation 1. The resulting voltage ramp Normal Decay Due To Leakage Current will look something like that shown in

Figure 7. The rate of voltage rise will Voltage tend to roll-off toward the end of charge. This may be at first attributed to nonlinear conduction, but it may in fact be a stronger function of the charge time than of the charge voltage. 0 Time There is another effect of the Figure 6. Voltage decay after disconnecting power supply. time-dependent capacitance, known as dielectric absorption, which is observed after discharging the capacitor. If the capacitor is charged slowly, so that the static capacitance has been charged, and then discharged rapidly, followed by opening of the circuit, a residual voltage will appear across the capacitor terminals. The voltage is usually a small fraction of a percent of the peak charge Voltage Ideal Capacitor voltage, but can be several percent in Practical Capacitor some types of capacitors with polar dielectrics. This residual voltage is due to the energy which was stored in the slow polarization mechanisms that was not released during the fast pulse Time discharge. This energy will redistribute itself amongst all of the available Figure 7. Charging ramp with ideal current. 13 polarization mechanisms after the Figure 8 shows the frequency circuit is opened, so that a fast discharge dependence of the dielectric permittivity from this residual voltage is then and loss which is expected from these possible. In high voltage systems, this polarization mechanisms. effect can create a safety hazard. For this reason, capacitors should normally Note that electronic and atomic be kept shorted when not in operation. polarizations occur at optical frequencies, while dipole orientation Clearly the charging behavior of and interfacial polarization occur in the capacitors is more complicated than electrical/electronic frequency regime. indicated by the simple model commonly used. In the next section we Electronic polarization is due will explore why this is true. to the distortion of electron orbits within the atom by the applied field.

Atomic or deformation polarization is due to the displacement Dielectric Physics of atomic nuclei relative to one another in response to the applied field. There are four basic mechanisms of polarization which can Permanent dipole orientation be taking place within the dielectric of polarization is due to the rotation and a capacitor: electronic, atomic or alignment with the field of molecules distortion, permanent dipole orientation, or parts of molecules which have a and interfacial. Each process has its own permanent dipole moment. characteristic frequency regime and loss characteristics.

12 2 ∈'s 8

' or n ∈' ∈ 4 n2 0

-4 Interfacial Dipolar

Permitivity -6 Relaxation Relaxation Atomic (Resonance) Conduction Electronic (Resonance) '' ∈ Visible Loss

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

Log10 Frequency Figure 8. Generic frequency dependence of dielectric permittivity and loss.

14 Interfacial (or Maxwell- mechanism and response time constant, Wagner) polarization is due to as shown in Figure 9. Note that the differences in the conductivities of parallel resistance included in this different materials or phases within a schematic is considered to be variable, dielectric system, causing charge to depending on voltage and temperature. accumulate at interfaces. Examples of different materials and phases found in capacitor dielectrics include epoxy and RP mica paper; liquid, paper, and film in C0 impregnated mixed-dielectric capacitors; the crystals and boundary ESL R R layers in a ceramic, and crystalline and M C1 1 amorphous regions within polymers. There may also be interfacial C2 R2 polarization at the electrode-dielectric interface. Figure 9. An improved circuit We also must mention model of a capacitor. ferroelectric behavior, such as that observed in barium titanate perovskite ceramics, which is due to dipoles Conduction in a dielectric may aligning and creating a polarization field be non-ohmic at high fields such as those of the same magnitude as the applied applied in energy storage capacitors. field. Since the dipoles respond to the The conductivity at the operating local field, which is a combination of voltage can be much larger than the both the applied and polarization fields, conductivity measured at lower voltage. the dielectric behavior is no longer This can result in different interfacial proportional to the applied field, and polarization behavior at different various nonlinear effects can be voltages. The conductivity of dielectrics observed. These effects include generally increases with temperature, saturation of the polarization at high exacerbating the non-ideal behavior. fields, permanent polarization, and high A variety of non-ohmic conduction losses in AC voltage applications. processes in dielectrics have been described, including Joule heating, Very slow polarization over space-charge-limited conduction, Poole- seconds or minutes is generally due to Frenkel trap-barrier lowering, Schottky interfacial polarization. The smaller the emission and Fowler-Nordheim difference in conductivity between the tunneling. Non-ohmic behavior may be phases, the slower the polarization observed in polymers at applied fields process. In some extreme cases, the exceeding 0.1 MV/cm [1]. Note that steady-state leakage current value is not typical applied fields in film capacitors reached for months. at rated voltage range from 0.4 MV/cm to 1.6 MV/cm. The highest fields are Thus, a better circuit model of experienced in limited life, high energy a capacitor involves several parallel density, energy storage capacitors. capacitances, each with its own loss

15 We have shown that the test regimen is likely to provide charging behavior of capacitors is insufficient power to charge a capacitor dominated by the intrinsic properties of or bank of capacitors at the desired rate. their dielectrics. In the next section, we The prime energy store (fuel or battery) describe how capacitor charging may be insufficient to provide the behavior can impact systems and circuit number of charge/discharge cycles design. specified. This is especially true in designing with little or no capability beyond the specified ratings.

This type of problem is related to the energy efficiency of the capacitor, Implications For Systems defined as the ratio of energy output to energy input. In repetitively pulsing The advancement of technology applications, capacitors which are leads to continuous reduction in design inefficient will generate more heat margins and a need for greater accuracy internally and may fail as a result. In and precision in design and pulsed power applications, capacitor manufacturing. In terms of design, it is energy efficiency is often much lower necessary to improve models of than expected based on power factor or components which are to be used in a dissipation factor measurements made system to account for behavior which at low voltage using an AC signal. Some might previously have been ignored or engineers may be surprised to learn that perhaps even unobservable. true capacitor energy efficiencies may be as low as 70 to 90 percent in pulsed There is a definite need to power operations. improve models of capacitor behavior currently being used in circuit and The key here is to measure the systems design. This is evidenced by joules and the coulombs actually the increasing number of reported required to charge the capacitor to deviations of actual behavior from voltage in the specified time frame. For expected behavior in completed large capacitors or banks, this can be systems. Though these are usually done using a small model capacitor minor in impact today, they represent made with exactly the same dielectric weaknesses of the existing models system as in the full-size capacitor, and which may have major impacts in the then scaling with capacitance. (A future. We base the following technique used by GAEP is outlined in discussion on actual reports of problems the next section.) or “curiosities”. Voltage decay is another Undersized power supplies are significant issue. Using a traditional already a major concern. As we have measurement of insulation resistance already pointed out, a power supply (made minutes after charging), an specified using a capacitance value engineer may predict a voltage drop a measured at 1kHz and an insulation few seconds after the power supply is resistance measured using a traditional disconnected which is much smaller

16 than that which actually occurs. The energy efficiency will improve over the result is that the system may not deliver first few cycles in a DC application, the current, power, and energy expected whereas it would first decrease in an AC at a given charge voltage. This may be application where polarity is reversed overcome by increasing the charge on each charge cycle. voltage or the charge and hold time, but this may impact capacitor life or other These examples of the potential aspects of system performance. impacts on systems of not properly characterizing capacitor behavior are A related issue is the current drawn from actual experiences in the required to maintain voltage on a industry. The need to upgrade our capacitor once it has been charged. In existing models is becoming some applications, it is desirable to have increasingly apparent. two separate power supplies; one charges the capacitor, the other provides a small current to maintain the voltage. If the specified rating of the sustaining Measurement and power supply is based on the wrong assumptions, it may be unable to Characterization maintain the desired voltage. Techniques

Again, the prevention is a The best way to determine measurement of the actual behavior of whether a capacitor is suitable for an the proposed capacitor (or a scale application is to test it under model) under simulated operation conditions which simulate the actual conditions, including voltage, charge operation required. Traditional time, hold time (power supply methods for characterizing the connected), and delay time (power charging behavior of capacitors have supply disconnected). These aspects of some definite weakness in this regard. system operation should be defined at GAEP has developed improved test the time the capacitor is being specified. techniques which are useful to better define capacitor behavior for critical Dielectric absorption is both a applications. safety concern and a technical concern. From a safety standpoint, high voltage Traditional measurement systems should be designed to maintain procedures [2] which relate to the a short-circuit between terminals of a charging behavior of capacitors include capacitor when the system is not in use. “insulation resistance” tests, “leakage Otherwise, dangerous voltages may current” tests, and “dielectric appear across the capacitor terminals absorption” tests. These tests are long after the power supply is shut performed as required for certain down. From a technical standpoint, a military and other specifications. They capacitor displaying absorption will are useful as qualification tests for a new behave slightly differently from one design or a new manufacturer, but are cycle to the next, until an equilibrium seldom used as acceptance tests or for condition is reached. Generally the screening.

17 The insulation resistance (self- specification. Generally the insulation discharge or bleed down) measurement resistance measured increases with begins by charging a capacitor to a operation time or voltage aging until the specified voltage and maintaining that dielectric begins to degrade late in the voltage for a specified period of time life of the capacitor. The insulation (typically 1-5 minutes). The power resistance may decrease if the capacitor supply is then disconnected from the is stored for a long period without use; capacitor, leaving the capacitor high it will recover after being tested or voltage terminal connected only to a operated at voltage. high impedance voltage probe. The voltage is measured either at one point The “leakage current” may be in time or at various time intervals (e.g. measured in a similar test regime. In 10, 20, 30, 60, 90, 120 seconds) after this case, the power supply is not the disconnection. The voltage versus disconnected, and the current provided time data is fit to an exponential decay by the supply to maintain a constant voltage is measured. The measurement -t/RC V(t) = Voe (3) is made after a specified period of time (typically 60 seconds). Depending on and the “insulation resistance” is equal the capacitance, the DC leakage current to the RC time constant, often expressed will be in the picoampere to milliampere in megohm-microfarads (seconds). The range. Note that the power supply must equivalent resistance itself can be be extremely stable; AC ripple will calculated by dividing out the measured generate a relatively large AC current. capacitance. Instruments are commercially available to do this specific type of testing on The obvious problem with this small capacitances. technique is that it assumes (as will engineers using the capacitor The leakage current test suffers specification) that the voltage decay fits from the same limitations as those of the an exponential - that there is a constant insulation resistance test. Generally the parallel resistance value causing the current measured in the first few minutes decay. In fact, closer examination of the will include not only the true leakage early portions of the decay curve (which current but also a capacitive charging may be of most interest to the user) often component, which may dominate. A shows that it does not fit a pure exponential plot of the current versus time would for the reasons already described. A reveal this. second concern is that the result will vary depending on the previous operational or “Dielectric absorption” of test history of the capacitor. capacitors may be characterized by using a test regime which begins by The measured value may charging the capacitor to a specified depend very strongly upon the voltage voltage (Vo ) and holding that voltage for and times specified. To maximize a specified period of time. The capacitor catalog ratings, some manufacturers will is then disconnected from the power minimize the voltage and maximize the supply and discharged through a hold and measurement times in their test specified load for a specified time. The

18 discharge switch is then opened for a This methodology allows us to period equal to the hold time. The specify the optimum power supply to recovery voltage (Vr) on the capacitor charge a capacitor or bank in a given is then measured using a high impedance amount of time. Variations on this probe. The dielectric absorption is defined technique can be used to generate plots as the ratio of the voltages (Vr / Vo). of voltage decay versus time which occurs when the power supply is The results of this test will vary disconnected from the capacitor or bank, if any of the specified times are changed. or the current required to maintain a Generally, the longer the hold time at given voltage. The tests are normally voltage, the greater the recovery voltage. performed at rated or operating voltage. The shorter the discharge time, the Since the behavior is dominated by the greater the recovery voltage. The delay intrinsic properties of the dielectric time before measurement is also critical. system, it is generally sufficient to test The recovery voltage will gradually a small “model” capacitor to very increase with the delay time until the accurately predict the behavior of larger delay time equals the hold time, beyond capacitors or even large banks of which the recovery voltage must capacitors. decline. Another point is that the capacitor terminals should have been shorted for a time prior to beginning the Summary test which is at least equal to the total duration of the test, or else prior voltage Capacitor application engineers history may have an effect on the results. are frequently asked why capacitors are not behaving as expected, indicating that Scientists in GAEP’s Capacitor the deviations of actual capacitor Research and Development Laboratory behavior from the models successfully have developed a technique to measure used in the past are becoming the energy and coulombic charge measurable and significant today. required to charge a capacitor to a given GAEP is responding to the needs of voltage, and the energy and charge industry by providing understanding of delivered by the capacitor in discharging the fundamental dielectric physics through a specified load. This technique involved and developing new test involves simultaneously measuring the methods which simulate specified current and voltage during both phases operations and measure capacitor of the cycle, calculating the response. instantaneous power, and then integrating to obtain the energy and the charge. Using this technique we can References [1] R. Bartnikas and R.M. Eichhorn (editors), measure the energy efficiency of Engineering Dielectrics, Volume IIA: “Electrical Properties of Solid capacitors under accurately simulated Insulating Materials: Molecular Structure and Electrical Behavior,” operating conditions. A similar American Society for Testing and Materials, 1983. technique, used to measure an effective [2] MIL-STD-202 Method 302 “Insulation Resistance.” equivalent series resistance (ESR) was [3] J.E. Dolan and H.R. Bolton, “Capacitor ESR Measurement described in reference [3]. Technique,” Proceedings of the 8th IEEE International Pulsed Power Conference, 1991, pp. 228-231.

19 Metallized Electrode Capacitors for Pulsed Power Applications

Metallized paper capacitors relatively slow (millisecond) discharges were first developed in Germany during are the norm. The advantages of using World War II. The use of metallized metallized electrodes in such electrodes in capacitors has since applications include higher energy become very widespread in low to density and longer life, greater reliability medium voltage applications. For many and safety, and reduced costs. years, metallized electrodes were not used in high voltage or high energy General Atomics Energy capacitor applications due to the very Products (GAEP) has pioneered the use limited current-carrying capacity of the of metallized electrode capacitors in electrode and termination in comparison pulsed power applications, achieving to discrete foils. This barrier gradually both record energy densities and broke down, beginning first with large unprecedented cost reductions. In the DC filter capacitors and then laboratory we have demonstrated 2.7kJ/ encompassing power factor correction kg capacitors delivering 100's of Joules, capacitors (1). and larger capacitors at somewhat reduced energy densities. Capacitors More recently, metallized with energy densities of up to 1.5kJ/kg capacitors have been introduced in some in sizes ranging from 10's of Joules up pulsed power applications including to 50kJ and beyond are now available medical cardiac defibrillators and commercially. electromagnetic launchers, where 21 This bulletin will compare the metallized electrode technology to Metallized Versus Foil discrete foils and provide an Electrodes understanding of the advantages and disadvantages of each in capacitor design. Finally, typical applications for Most pulsed power capacitors metallized electrode capacitors will be have been built using discrete aluminum described. foil electrodes with a thickness ranging Solder from about 4 microns (0.15 mil) to more Bus than 12 microns (0.48 mil). Extended Foil Terminations are normally made by either soldering directly to extended + Solder foils or by inserting flag-shaped taps during the winding process, as Foil illustrated in Figure 1.

Metallized electrodes are made Dielectric by vacuum vapor deposition of +- aluminum, zinc, or an alloy directly on the surface of a dielectric material such as paper or film. The nominal thickness WINDING CROSS-SECTION of the metal layer is in the range from (not to scale) about 250 to 1000 Angstroms or 0.025 to 0.1 micron. This results in a surface (a) Extended foil termination resistivity ranging from a fraction of an ohm to about 10 ohms per square. Since typical high voltage capacitor dielectric thicknesses range from 12 to 60 microns, + metallized electrodes have negligible - thickness in comparison. Tap Ribbon Masks are used during the metallized process to provide "margins" Foil on opposite edges of the two opposing polarity electrodes. The margins Foil "Flag" prevent a flashover between the two electrodes at the ends of the winding. Dielectric During the capacitor winding operation, the two electrodes are extended from opposite edges of the winding by a small amount to expose some of the electrode WINDING AS WOUND for purposes of termination. This is (b) Inserted tap termination similar to the extended foil construction. Figure 2 illustrates these features.

Figure 1. Foil capacitor terminations. 22 Dielectric Film spraying or arc-spraying a solderable alloy onto each end of the winding. Metallization Masks may be used to leave gaps in the sprayed metal layer for subsequent drying and impregnation.

There are many variations of the metallized electrode concept which have End Spray Terminations been used in various capacitor products. Offset One of these is a double-metallized paper used like a discrete foil; Figure 2. Cross-section of a typical commonly known as "soggy foil" [2]. metallized electrode capacitor Kraft paper is metallized on both sides (not to scale). to provide twice the current-carrying capacity. The natural roughness of the For higher current applications, paper aids in impregnation. This the thickness of the metallization at the technology was developed for use in AC termination edges can be increased or power capacitors. Figure 3 is a reinforced during the metallizing schematic cross-section of this type of process. This reduces the surface capacitor. resistivity in this most critical region by a factor of 3-4. Many pulse power Double Metallized Paper applications require such "heavy edge" or "reinforced edge" patterns. Dielectric Film

The substrate for the metallization can be virtually any of the common dielectrics used in capacitors. Kraft paper which is of high density or lacquered to provide a smooth surface can be metallized after sufficient pre- End Spray drying. Films such as polypropylene Terminations and polytetrafluoroethylene (PTFE or Figure 3. Cross-section of a “soggy- "Teflon") can be metallized after foil” (double metallized) capacitor treatment of the surface to enhance (not to scale). adhesion. Many other polymer films require no pre-treatment, including Another variation which is poloycarbonate or polyethylene becoming popular is the segmentation of terephthalate (PET). The processing of the metallized layer to provide what are metallized capacitors is designed to essentially fusible links within the minimize changes in dimension by capacitor. This technology has the shrinkage or swelling which could potential of improving the safety of disrupt the metal layer. metallized polypropylene capacitors used in low to medium voltage AC applications. Termination of the metallized Segmented electrodes are discussed in electrode is done by either flame- more detail in the next section.

23 Self-healing or "clearing" metallized electrode which has been cleared or removed, resulting in a One of the advantages of small loss of capacitance. The area metallized capacitors over discrete foil cleared depends on voltage and other capacitors is their ability to self-heal in design and manufacturing variables, the event of a dielectric breakdown. but is typically between a few square This improves reliability, permits higher millimeters and a few square stresses and therefore higher energy centimeters. In large capacitors, it densities to be achieved, and results in takes hundreds or thousands of a "soft" failure mode rather than a clearings to cause a few percent loss catastrophic short-circuit. of capacitance. Figure 4 is a photograph of the site of a clearing on If a dielectric breakdown metallized paper, magnified about occurs, current flows from surrounding 10X. areas of the capacitor through the breakdown arc. In a foil capacitor, virtually all of the stored energy is dissipated in the arc itself, resulting in significant damage to the capacitor. A breakdown in a large energy storage capacitor may rupture its container.

In a metallized capacitor, the current flowing into the arc has a high enough current density to heat and vaporize the metallization immediately surrounding the breakdown arc. There is a rapid rise in the local gas pressure from the pyrolization of the organic substrate, and the arc length increases as the area of the metallization that is Figure 4. Photograph of a clearing being vaporized increases. Finally the site (~10x). arc is extinguished by this process, which is essentially the same as that which occurs in a fuse. Each clearing generates small amounts of chemical byproducts The energy dissipated in the including gases, water, and carbon. clearing process is in the range of These byproducts may have a negative microjoules to joules [3]. A sound effect on capacitor electrical parameters which may be described as a "snap" can such as insulation resistance (IR) and some-times be heard. The capacitor dissipation factor (DF). Again, the continues to operate normally during effect is usually not measurable until a and after the clearing event. very large number of clearings have occurred. A buildup of internal gas As a result of a dielectric pressure may also be observed at the end breakdown, there is an area of the of the capacitor's life.

24 Figure 5 shows the typical behavior of to cause a fusing action of the various parameters of a metallized metallization at the entry point to that capacitor during the life of the capacitor. path and away from the actual breakdown site [4]. Figure 6 illustrates +5% this approach.

Connection Edge

(%) 0

C Fused Link

C "T" Margins ∆

En d o f Li f e -5%

Log (Time)

0.010 )

δ Breakdown Site Metallization 0.005 Normal Edge Margin DF (tanDF

Figure 6. Segmented metallization 0 pattern and fusing operation Log (Time)

10.0

F) Advantages of

Ω−µ 1.0 Metallized Capacitors IR (M IR In applications which permit the 0.1 use of metallized electrodes, they offer Log (Time) many advantages over foils. Energy density is significantly higher in metallized capacitors than in foil Figure 5. Typical variation of capacitors for two reasons: (1) the electrical parameters during life of a reduced volume occupied by the metallized electrode capacitor. electrodes themselves, and (2) the higher dielectric stress levels which may be Some metallized capacitors safely applied to achieve a given lifetime have been developed which provide an and reliability. additional safety feature beyond that of clearing. These capacitors have a The reduced electrode volume metallized electrode which is segmented is especially important in low voltage to force current to flow along prescribed (<1000 V) applications where the paths. In the event of a dielectric thickness of a discrete foil would be the breakdown, the current flow into that same or even greater than that of the particular segment will be high enough optimum dielectric.

25 Reliability of metallized performance limitations imposed by the capacitors is improved over foil capacitors use of very thin electrodes. because of the elimination of the largest source of single-point failures. Whereas The peak power and "action" in a foil capacitor the first dielectric (defined as the integral of the square of breakdown produces a catastrophic failure, the current with respect to time) per unit in a metallized capacitor hundreds to length of the connected edge of the thousands of such events must occur to metallized electrode must be limited to cause a capacitance loss which brings the prevent damage. The end connections are device out of tolerance. the weak links in the capacitor due to the relatively high resistivity at this interface. Lifetime of metallized capacitors Peak power in excess of the rating can is significantly greater than that of foil cause the end connections to physically capacitors of comparable or event greater separate from the ends of the winding. size and weight. Factors of two to ten improvements are easily achieved. The limitation on current means that a metallized capacitor is less The soft failure mode of tolerant to external faults or short-circuit metallized capacitors is usually preferable conditions than a foil capacitor. It also to a catastrophic short circuit. The means that metallized capacitors cannot capacitance begins to measurably decrease be used in applications which require near the end of life, and the insulation combinations of high voltage and high resistance and dissipation factor may peak current. degrade as well. It is even possible to utilize the buildup of internal gas pressure The range of voltage which can to provide a disconnect feature. be provided with metallized electrode capacitors is considerably more limited Cost of metallized capacitors than in discrete foil capacitors. Whereas can be smaller than that of comparable metallized capacitors are optimal at low foil capacitors due to reductions in the voltage, the internal resistance of their volume of raw material used in electrodes limits series connection manufacturing the capacitor. capability and restricts the high voltage end of the range to below 50 kV. In These advantages have resulted comparison, foil capacitors have been in the introduction of metallized built for fast pulse peaking circuits with capacitor technology in virtually every ratings above one megavolt. film capacitor market. The metallized electrode has greater resistivity than a foil electrode. Limitations of At low frequency (into the kilohertz range) the parasitic resistance of a Metallized Capacitors capacitor is dominated by the losses in its dielectric, and the resistance of the Unfortunately, metallized metallization is negligible. At higher electrodes cannot be used in every frequencies the resistance in the application due to significant metallization will dominate and the

26 equivalent series resistance (ESR) or container at the end of life, is considered dissipation factor (DF) will be a disadvantage in some applications. As significantly greater than in a foil already mentioned, in such situations the capacitor. Most metallized capacitors internal pressure can be used to provide are safely used in DC filtering a disconnect safety feature to the applications, 60 Hz-400 Hz AC, and capacitor, or can be sensed externally pulse discharges with millisecond pulse using a mechanical switch or sensor to width. GAEP engineers have developed trigger a safety interlock device. special designs which allow metallized electrodes to be used in some applications at considerably higher frequency and shorter pulse width, but the fastest discharge capacitors still Applications require discrete foils. Metallized electrode capacitors Another important limitation of have become the standard for low duty metallized capacitors is their relatively applications involving low frequency poor thermal conductivity. In foil (<1000 Hz) pulse discharges and capacitors, the metal foils provide a requiring high energy densities. Two significant conduction path out of the examples are medical cardiac winding not only for current but also for defibrillators and electric guns. heat. By comparison, the metallized electrode is a very poor thermal Defibrillator capacitors are conductor. This is important in typically rated at voltages less than 6 kV continuous duty, high RMS current and store up to 500 Joules of energy. applications such as AC or repetitive Discharge frequencies are of the order pulsing, where losses in the dielectric 100 Hz, and typical peak currents are and the metallization itself can generate less than 200 Amps. The application is significant heat. The worst case result essentially "single shot," with less than is a large temperature buildup at the five cycles required over a period of center of the capacitor which can result minutes. Lifetimes of thousands of in bulk dielectric failure. shots are required with high reliability.

Metallized capacitors used for Early defibrillator capacitors high average power applications must were essentially DC filter capacitors be designed to minimize the heat which were re-rated for the required generated internally through the choice reliability and life. Later, special of dielectric materials. In addition, the designs incorporating polyvinylidene geometry of the capacitor must be such fluoride (PVDF) achieved the energy as to minimize the distance that heat densities needed for portable must travel to exit. defibrillators used by paramedics. These capacitors were not only Gas generation due to self- expensive, but suffered from low energy healing in metallized capacitors, efficiency and restricted operating sometimes resulting in internal temperature range due to the pressurization and distortion of the ferroelectric properties of PVDF.

27 Metallized electrode capacitors conducted by the Department of Energy have now displaced PVDF capacitors in at Lawrence Livermore National this market, by offering not only higher Laboratory (Beamlet) and the University energy density (up to 1 J/cc) and lower of Rochester (OMEGA). cost (1/3 the cost of PVDF units), but Other applications include mobile hard also improved reliability. GAEP has rock mining (shock wave generation) delivered more than 200,000 such systems, flashlamp drivers used in food capacitors to defibrillator manufacturers processing and xerography, and laser worldwide. rangefinders. Electric gun testbeds built in the Summary last few years have often utilized metallized electrode capacitors. The capacitor banks in these systems Metallized electrode capacitors typically store 10-50 MJ at 15-24 kV and offer many advantages over foil deliver pulses of several milliseconds capacitors in low average power duration. The higher energy density of applications. Higher energy density, metallized capacitors has allowed longer life, and higher reliability are a smaller facilities to be used to house the few of the benefits of this technology. capacitor banks, at significant overall General Atomics Energy Products is cost savings. GAEP has supplied over supplying large numbers of these 52 MJ of metallized energy storage capacitors for medical defibrillator, capacitors for this particular application. electric gun, and other pulse discharge and DC applications. We invite you to Metallized energy storage inquire how GAEP's metallized capacitor banks are also being utilized electrode capacitors can benefit your in Inertial Confinement Fusion (ICF) application. experiments such as those being

References [1] D.G. Shaw, S.W. Cichanowski, A. Yializis, "A Changing Capacitor 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. (English translation available through GAEP).

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

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