Posted on 01 June 2019

Ceramic Capacitors for Very High Voltage and High Energy Storage

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 Electrical Parameters Involved in the Design

Today a large range of dielectric materials is available for manufacturing ceramic capacitors from NP0 dielectrics with low permittivity and very low D.F, to X7R or even Z5U materials with higher permittivity, and an unfortunately high D.F . However few materials are in fact acceptable for very high voltage or high energy discharge applications.

By Patrick Hardy, Applications engineer, AVX, TPC Division, Dijon, France


The correct design and use of very high voltage ceramic capacitors requires knowledge of the critical parameters involved in electric charge storage. Besides the permittivity (εr) and the dissipation factor (D.F) measured with low rms voltage (currently < 5Vrms) the other factors that play a key role in the operating life and reliability of high voltage ceramic capacitors are:

¤ the nature (and real electrical properties) of the dielectric materials used
¤ the density of active power (losses) generated vs. dielectric permittivity and D.F factors
¤ the energy storage density, the working and breakdown electric field strength of the selected ceramic materials
¤ the electrostatic force and piezo/electrostriction properties of the dielectric
¤ the influence of the dv/dt across a device submitted to charge/discharge


Paraelectric & Ferroelectric materials

NP0 dielectrics are paraelectric materials (working temperature range is above Curie temperature).

These materials exhibit low permittivity between ~30 and ~100.

Dielectric materials

The linear relationship between polarisation (D) and electric field (E) leads to a very stable permittivity vs. electric field applied.

In contrast, ferroelectric materials exhibit a permittivity which is strongly influenced by the electric field applied. Under ac, hysteresis can become widespread leading to greater dielectric losses, especially at low frequency (< 10kHz) and may give rise to mechanical deformations/vibrations due to their Piezo properties. Barium Titanate (BaTiO3) is the most popular ferroelectric semi stable material. It exhibits high permittivity ~1700 ⇒ ~4000 (strongly decreasing under DC bias) and D.F typically: 200 x 10-4 ⇒ ~800 x 10-4.

This dielectric material shows marked Piezo/electrostriction property, limiting its more widespread use, with high voltage, high energy storage and very fast pulse applications.

Conversely, Strontium Titanate materials exhibit medium, but quite stable permittivity versus electric field applied, together with very low D.F (often close to NP0 with D.F typically < 10 x 10-4) and because they are not ferroelectric, these dielectric materials do not suffer from piezo/electrostriction behaviour.

Dielectric properties vs. dielectric nature of the material and vs. DC field applied

The density of active power (or dielectric losses) vs. DF & εr

The following equation describes the density of dielectric losses:

Equation 1

Wa = dielectric losses (Watt/cm3)
E = V/t = electric field (V/cm)
V = Voltage (V)
t = dielectric thickness (cm)
F = frequency (Hertz)
tg δ = DF (1 x 10-4)

This equation can be re-arranged as:

Equation 2

b factor shows the importance of the working field ratio (hence working voltage) with regard to rated voltage, and how any over voltage, test voltage, or surges must be taken into account and “handled” with care.

Equation 3

⇒  “manufacturer parameters” (referenced to the dielectric properties of the selected material).

c factor, focuses on the importance of selecting the right dielectric material for a given high voltage application, especially with very high dv/dt voltage applied (large dv/dt is equivalent to a high frequency signal). This requires knowledge of how permittivity and DF behave in relation to frequency, sometimes up to 10 MHz.


The density of energy stored is the most critical electrical parameter:

Equation 4

J = density of energy (Joule/cm3 )
E = electric field (V/cm)

Importance of factor “c” versus different dielectric materials

Thus, the total energy stored in a capacitor is:

Equation 5

But with ferroelectric materials, εr is strongly influenced by the electric field E applied, thus: εr = dD /dE

and the energy stored is:

Equation 6

(D = electric displacement or electric induction.)

Permittivity of ferroelectric materials, strongly decreases, as the electric field increases , as does the energy stored. The density of energy stored in a given dielectric material is limited by the electric breakdown field (Ebk) (see Figures 1, 2, and 3).

Permittivity vs electrical field

Breakdown voltage & breakdown electric field vs. thickness

Breakdown voltage is a parameter which is largely influenced by the dielectric thickness, as illustrated in Figure 2. This figure shows that the breakdown voltage increases with dielectric thickness whatever the dielectric type. Nevertheless, with low permittivity materials, the influence of thickness is greater.

Breakdown voltage vs thickness (kV-mm)

The most interesting parameter is not the breakdown voltage but rather the electric breakdown field (Ebk) and remarkably the breakdown field decreases when dielectric thickness increases! Figure 3 shows that for a given insulating material the highest “electric field breakdown values” are obtained with the thinnest dielectrics and low permittivity materials. This behaviour is very common among all dielectric materials. This analysis shows that it is preferable to design a high voltage ceramic device, with several thin dielectric elements stacked up, rather than manufacturing a single piece of much thicker dielectric.

Breakdown electrical field vs thickness

ELECTROSTATIC FORCES EXERTED ON A CERAMIC CAPACITOR vs. dielectric material and vs. electric field applied

Due to the electric field applied to the dielectric material, a stress is exerted on the ceramic device such as:

Equation 7
S = surface
t = dielectric thickness
V = voltage
E = electric field
J = density of energy

The electrostatic force exerted is proportional to the density of energy stored and the surface area of the capacitor electrodes. Bearing in mind that it is very common to apply 30kVdc on a ~ 10mm thick dielectric layer, the corresponding electric field is: E = 3 x 106 V/m, and this field (depending on the permittivity of the dielectric material) may induce electrostatic force F > 10kN so ~ 1 Ton.

When a large percentage of reversal voltage is applied to a capacitor, the very high electrostatic compressive stress is suddenly cancelled. However ceramic materials are not able to withstand such large mechanical stress modifications due to their microstructure, and are definitely not able to reorganise their structure at these speeds. Such sudden electromechanical stresses, can lead to fracture and hence electrical breakdown very quickly. That’s why, high reversal voltage is one of the worst case application conditions, especially when the percentage of reversal voltage is high (> 20%) and/or the dv/dt rise time very short. Consequently, fine grain dielectric microstructures, and non ferroelectric material give better performances.


NP0 materials are not affected by this phenomenon. Strontium Titanate materials show very little sensitivity to piezo/electrostriction, but ferroelectric materials can be cause for concern.

Piezo/electrostriction is caused by a crystal lattice displacement induced by polarisation under an applied dc/ac field. This displacement leads to a sudden variation of the dielectric’s mechanical dimensions. In addition, fast rise times (dv/dt) of the signal can increase the destructive effect.

This effect can be described by the following equation:

Equation 8

M33 = electrostriction constant
t = thickness
E = electric field

Once again the electric field applied plays a key role in the behaviour and reliability of high voltage ceramic capacitors.

COMMENTS ABOUT THE INFLUENCE OF A LARGE dv/dt applied to a ceramic capacitor

The following equation:  Ipeak = C . dv/dt  (1V/µs ⇒ 1A/µF)

shows that a large dv/dt may lead to a very high peak current flowing into the capacitor. This current will in turn lead to a temperature rise of the device, generated by:

a - the electrodes and terminals losses: P = ESR . I 2
b - the dielectric material losses: P = DF. U . I

In most laser applications, typical peak current is beyond: 30kA. Knowing that, when the temperature increases, insulating resistance decreases, leading most of the time to a sharp increase in the D.F and subsequent thermal avalanche and total destruction of the device.

This analysis shows that for applications such as “high energy laser pulses” where millions or even billions of very large dv/dt will be applied to the capacitor, the designer should take special care of the thermal aspect of the device, and try to minimise the thermal resistance of the capacitor, and therefore, the temperature rise: delta T = P . Rth.


Corona discharges are localised discharges (concerning a very small volume of the dielectric) triggered by the electric field applied to the dielectric. If the energy dissipated by these discharges is small enough, they are not considered as damaging to the capacitor. Nevertheless, a parasitic “white noise” is generated which “pollutes the signal”. However, beyond a certain level of energy dissipated by these discharges, a thermal avalanche may be triggered leading to the total destruction of the component.

These discharges only appear inside the insulating materials used (dielectric materials ad coating or potting materials) when an ac electric field is applied across the capacitor. These discharges are localised in voids, cracks, and defects of the dielectric or coating, and on the dielectric surface, just at the edges of the electrodes, where the electric field gradient is highest.

As a rule of thumb: the higher the electric field applied, the worse the Corona discharge level (and rate) and so the higher the temperature rise. Most of the time these discharges show a large “voltage hysteresis” which means that for any device we may find an “inception voltage Ui” where one can “turn on” this discharge regime, by simply increasing the rms voltage applied, and an “extinction voltage Uex” whereby decreasing the voltage applied, all discharges will turn off. Generally: Ui >> Uex.

Typical partial discharge level vs. Urms


In order to reach a highly reliable operating level the manufacturer should carefully choose the best dielectric material, keeping in mind the real working conditions of the application.

The customer should carefully select the right type of capacitor and be careful to moderate the electric field applied during operation by taking into consideration, working, and test voltage requirements, and any over voltage, transient regime, or reversal voltage across the capacitor.

After many years of experience with both AC and DC high voltage applications, it appears clear that Strontium Titanate dielectrics demonstrate superior behaviour on heavy duty applications (energy storage, laser pulses, and Marx generators) compared to Barium Titanate materials.

To design a reliable high voltage capacitor, one must pay special attention to the true electrical properties of the chosen dielectric material under real life operating conditions, and definitely “forget” the characteristics obtained under standard measurement conditions (most of the time < 5Vrms) which cannot describe the real behaviour of the component in application.



1) Bartnikas and Mc Mahon : Engineering dielectrics V1.
2) Aguet and Ianoz : Haute tension.
3) Fournié : Les isolants en électrotechnique, concepts et théories.
4) Gallagher and Pearmain : High voltage.
5) Kuffel and Zaengl : High voltage engineering.



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