# Snubber capacitor selection for Tesla coils and inverters

Published on: Mar 2, 2015. Updated on: Jan 15, 2018.

This is chapter 6 of the DRSSTC design guide: Snubber capacitor

When we switch on and off very large peak currents in a DRSSTC, residual energy will be trapped in the circuit stray inductance of the switching devices and busbar, that causes a voltage transient that can be many times higher than the IGBT ratings.

Snubber capacitors should never be used to make up for a bad circuit layout. It is will very important to design a circuit with low inductance as discussed in chapter 2 on Busbar and primary circuit design.

The following oscilloscope shots show a IGBT switching on and the resulting voltage overshoot from the stray inductance. The black curve show the switching waveform without any kind of suppression and the brown curve show a switching transient that is suppressed by a capacitor.

Snubber capacitor selection

Snubber capacitors are subjected to high peak and rms currents and high dV/dt. All types of high frequency polypropylene film capacitors are suitable to be used as a snubber capacitor, there is however a magnitude of difference in internal inductance from normal capacitors with through hole leads and those made for direct mounting on IGBT terminals. [1]

Aim to use polypropylene capacitors with a voltage rating that at least matches the IGBT and have a dV/dt rating at at least 500-5000 V/μs and above.

Snubber capacitors can come in many different packages and sizes.

Calculation of snubber capacitance

A approximation of the needed snubber capacitance can be found using stray inductance LS in H, peak current Ipeak in A, allowed transient voltage peak Vtransient in V and DC bus voltage Vbus in V. [2]

$C_{snubber}=\dfrac{\mbox{L}_{S}\cdot\mbox{I}^2_{peak}}{(\mbox{V}_{transient}-\mbox{V}_{bus})^2}$

Let us of look at the same example, as used earlier, where we have some numbers from my large DRSSTC. With 564 V on the DC bus, 2000 A primary peak current, maximum allowed transient voltage of 1000 V on a 1200 V IGBT and assuming 200 nH stray inductance.

$C_{snubber}=\dfrac{\mbox{200 nH}\cdot(\mbox{2000 A})^2}{(\mbox{1000 V}-\mbox{564 V})^2}=~4\mu\mbox{F}$

There is also another estimation method that uses a rule of thumb with two assumed scenarios. Where a snubber capacitor is used alone in a circuit where a low or high inductance is expected, the following quick rules can used. [3]

A design where you expect a low inductance you can use 0.5 μF for each 100 A the IGBT is switching. That would result in 10 μF needed snubber capacitance for the above calculation.

A design where you expect a high inductance you can use 1 μF for each 100 A the IGBT is switching. That would result in 20 μF needed snubber capacitance for the above calculation.

The estimations will naturally give a higher value needed than the calculations as the estimation will have to make up for the lack of knowledge about the exact stray inductance that the snubber capacitance will have to act against.

Snubber capacitor power dissipation

The transient voltage caused by the IGBT switching a current  would normally oscillate until the energy was dissipated in the resistive part of the busbar and components circuit. The snubber capacitors forms a shorter DC loop where the oscillation dies out faster due to its low ESR. The ESR of the snubber capacitor is also the dominant resistive part in this new loop and it will be here the energy from the oscillations is dissipated.

The overall power dissipation is however very low due to the very low duty cycles used in a DRSSTC and it is not necessary to take extra precautions in regard to RMS current if IGBT snubber capacitors mounted directly on the terminals are used.

A word on physical dimensions of capacitors for either DC link or MMC

As demonstrated by El-Husseini, Venet, Rojat and Joubert in their article “Thermal Simulation for Geometric Optimization of Metallized Polypropylene Film Capacitors”, the  physical geometry of a capacitor can have an impact on capacitor temperature, power loss  and life. They demonstrated that for the same electrical stress, taller capacitors experienced higher temperature and losses than shorter capacitors.

As stated in their article, in taller capacitors, the current must travel a longer distance through the very thin metal films, thus the total I²R losses are higher compared to a short capacitor. The authors demonstrated that the total power loss in the capacitor is proportional to Equivalent Series Resistance (ESR) and to the square of the true rms current.

ESR represents the eddy current and dielectric losses, which are affected by both frequency and current. If capacitor current is elevated, power loss increases. Likewise,  power loss in a metallized film capacitor increases if the frequency of the current increases. Thus, harmonic current flowing in a metallized film capacitor, the power loss will be higher than if pure sinusoidal current were to flow. [4]

As the following equation shows, it is the RMS current flowing through a capacitor that is the most vital parameter in temperature rise and too high temperatures lowers life time dramatically.

$P_{Total}=\mbox{ESR}\cdot\mbox{I}^2_{trms}$

Cooling of capacitors by forced air can be a solution to get a longer life time. Approximately 2/3 generated heat rise moves out axial and 1/3 radial. So it is most important to cool a capacitor at its terminals as it does not radiate the heat evenly from all over its surface.

Some capacitors have a metal mounting stud in the opposite end of the terminals, these are meant for installation in heat sinks or other material that can lead the heat away. Be aware that the metal can and stud might not be isolated from the negative terminal, depends on manufacturer and capacitor type.

The thermal resistance (Rth) from case to ambient is given for still air in most datasheets, so if forced air cooling is used the thermal resistance can be de-rated. Some manufacturers supply equations to calculate a exact thermal resistance in regard to capacitor surface and forced air speed velocity.

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### References

[1] Rudy Severns. “Design of snubbers for power circuits”, cde.com

[2] Yi Zhang, Saed Sobhani, Rahul Chokhawala. “Snubber Considerations for IGBT Applications”, International Rectifier Applications Engineering 233 Kansas St., El Segundo, CA, 90245 USA.

[3] Kemet. “Film Snubber Capacitors for IGBT Modules”, SA1211. Kemet 2011.

[4] M.H. El-Husseini, Pacal Venet, Gerard Rojat and Charles Joubert, “Thermal  Simulation for Geometric Optimization of Metallized Polypropylene Film Capacitors”, IEEE Trans. Industry Appl, vol. 38, pp713-718, May/June 2002.

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