## High Current Measurements – Isolation, Day 10

I go through my collection of current transformers. Regular ratio transformers, hall effect sensors, shunts, Pearson and Ion Physics current monitors and how to make …

# SSTC design guide

Published: July 15, 2019. Updated March 19, 2020.

This article is to point out some of the design decisions and calculations that is different from a DRSSTC, so this article will not contain a description of all parts used in a SSTC. The following topics are covered by the DRSSTC design guide as the guidance and best practices is the same.

As an example in this guide, I will use the dimensions and properties of my Kaizer SSTC 2 Tesla coil. It is a full-bridge IRFP460 running at 250 kHz, making up to 47 cm sparks, see all construction details on the link.

## Primary peak current calculation

To do an easy primary current calculation, to know if the MOSFETs can drive the load, it can be simplified by ignoring primary resistance and DC blocking capacitors reactance as they are very small factors.

First calculate the primary coil inductance for your helical or spiral primary coil. Use one of the two links for the online calculator.

Next step is to calculate the primary coil reactance. f is frequency in Hertz and L is inductance in Henry. Values are written in kHz and uH for ease of reading. The 8 turn helical coil with a diameter of 115 mm, with 1.78 mm wire and 2 mm spacing has a inductance of 10.16 uH.

$X_{L}=2 \cdot \pi \cdot f \cdot L$

$X_{L}=2 \cdot \pi \cdot 250 kHz \cdot 10.16 uH = 15.95 \Omega$

The peak current for the peak-to-peak square wave voltage envelope can now be calculated using Ohm’s law. I supplied my coil from full-wave rectified 230 VAC, which multiplied with square root (2) for the peak voltage is about 320 VDC.

$\text{Primary peak current} = \frac{Voltage}{Resistance X_{L}}$

$\text{Primary peak current} = \frac{320 VDC}{15.95 \Omega}=20 A_{peak}$

Conclusion on primary peak current. We now have a basic measure for how much current we are trying to push through our MOSFETs and primary coil. The MOSFETs should as a minimum be able to withstand this, with a safety margin added on top. Voltage rating should have around 33% head room, so if you are feeding the inverter 320VDC, a 600V MOSFET is to prefer.

## Primary Geometry and Coupling

There is generally four shapes of primary coils.

• Flat spiral coil (Used in SGTC and DRSSTC)
• Helical coil (Used in VTTC, SSTC and DRSSTC)
• Cone coil (Used in SGTC, DRSSTC)
• Half-circle coil (Used in QCWDRSSTC)

A SSTC will almost always use a helical coil with a high and tight coupling to the secondary coil. Due to the relatively low primary circuit current it is necessary to have a primary geometry that gives a high coupling to get a good energy transfer.

In my SSTC constructions I have often used regular machine tool wire wound directly around the base of the secondary coil, with nothing more than 2-10 mm of insulating material in-between and also to make it able to adjust coupling by moving it up or down. The insulation needs to extend further than the primary coil to avoid flash over damages, as I have experienced.

## DC Blocking Capacitor

The DC blocking capacitor is named after its purpose, to block any DC component of a signal to enter the transformer being driven by a half- or full-bridge. A DC offset current may cause an unbalance of the transformer that initiates a runaway process that ends up with the transformer saturated and the large current drawn in this mode will damage both transformer and MOSFETs. [1]

The DC blocking capacitor can either be in series with the primary coil for a full-bridge or in series with the primary coil for a half-bridge that connects to ground. For a half-bridge it can also be two capacitors forming a voltage splitter with a midpoint where the primary coil connects to, this voltage splitter can also be used in a voltage double configuration. The most important factor is that it is a very low ESR capacitor, in order to minimize the switching losses across it. Generally this means that the same type of MKP capacitors used in a MMC is suitable for DC blocking capacitors, given the capacitance is suitable. Below the DC blocking capacitor is the blue RIFA sitting in series with the black wires going out to the primary coil connectors.

There is two factors to calculate for the DC blocking capacitor. The capacitor reactance ratio to the inverter output impedance and the resonant frequency of the primary coil L and DC blocking capacitor C is much lower than the resonant frequency of the secondary coil circuit.

First we can calculate the DC blocking capacitors reactance. f is frequency in Hertz and C is capacitance in Farad. Values are written in kHz and uF for ease of reading. I used two 0.68uF X2 MKP capacitors in parallel.

$X_{L}=\frac{1}{2 \cdot \pi \cdot f \cdot C}$

$X_{L}=\frac{1}{2 \cdot \pi \cdot 250 kHz \cdot 1.36 uF}=0.468\Omega$

So now we can check the resonant frequency against the Tesla coil secondary circuit frequency. f is frequency in Hertz, L is inductance in H and C is capacitance in Farad. Values are written in kHz, uH and uF for ease of reading.

$Frequency=\frac{1}{2\cdot\pi\cdot\sqrt{L\cdot C}}$

$Frequency=\frac{1}{2\cdot\pi\cdot\sqrt{ 10.16 uH \cdot 1.36 uF}} = 42.8 kHz$

Being 5 times lower than the resonant frequency, there is no risk at the primary LC circuit resulting in a DRSSTC condition which would destroy the MOSFETs.

The reactance of the two capacitors was 0.468 Ω and the inverter output impedance should be higher than this.

$\text{Inverter output impedance}=\frac{\text{Voltage output}}{\text{Current output}}$

$\text{Inverter output impedance}=\frac{320 VDC}{20 A}=16\Omega$

It is worth noting that the inverter output impedance should be almost identical to the primary coil reactance as the pure Ohm resistance of the primary coil is very small.

The DC blocking capacitor reactance is 32 times smaller than the inverter output impedance and the design requirement is fulfilled. A lower capacitance would result in even smaller losses in the DC blocking capacitor.

Conclusion on DC blocking capacitors is that they should behave like a dead short at the resonant frequency of the Tesla coil or inverter. So anything below 2 Ω reactance should be considered to work.

## Gate Drive Current

Many different driving methods are used for SSTC’s and their half- or full-bridge of MOSFETs / IGBTs. Unlike the DRSSTC universal drivers, there is a wide variety of gate drive ICs, transistors or other implemented in different SSTC driver circuits.

It is important that there is enough current and fast enough rise time when driving the gates of the MOSFET/IGBT that switching losses are minimized as much as possible.

Use the MOSFET / IGBT Gate Drive Calculator to estimate the required peak current needed and RMS power consumption for the power supply design.

## References

[1] Alexander Gertsman, Sam Ben-Yaakov, “Zeroing Transformer’s DC Current in Resonant Converters with No Series Capacitors”, Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, 2010.

# MMC calculator

MMC tank design calculator for SGTC, VTTC, DRSSTC and QCWDRSSTC Tesla coils. Results are guidelines to designing a MMC and should always be double checked in your final design! Most importantly is that voltage rating is the DC voltage rating, from experience this can used for good quality capacitors, AC voltage rating with frequency derating would be much lower.

Capacitor specifications are taken from data sheets at 100 kHz and some values for peak current, rms current, ESR and dv/dt are estimates from similar capacitors and graph read outs.

Inputs are in green. Outputs are in red. Formulas used can be seen below the calculator.

 Basic MMC configuration – List of good MMC capacitors Capacitance uF Aerovox RBPS20591KR6G CDE 942C20P15K-F CDE 940C20P1K-F EFD SP 2550-2 Kemet R76UR3150SE30K Panasonic ECWH16333 Panasonic ECWH16473 Panasonic ECWH16563 TPC CMPPX4K0K0405 WIMA FKP1O131007C00 WIMA FKP1T031007E00 WIMA FKP1R032207F00 Voltage rating VDC Capacitors in series Strings in parallel Price per capacitor Results MMC voltage rating VDC MMC capacitance uF Total capacitors Total MMC price Advanced options MMC capacitor parameters Peak current rating A RMS current rating A dV/dt rating V/uS ESR rating mΩ Find correct ESR ratingfor your resonant frequency specificdissipation factor ºC/W Tesla coil parameters – Examples are small, medium and large Frequency kHz Small – Kaizer DRSSTC 2 Medium – Kaizer DRSSTC 1 Large – Kaizer DRSSTC 3 Primary inductance uH Primary peak current A On time uS BPS BPS Advanced results Primary impedance Ohm MMC Xc(reactance) Ohm MMC Zc(impedance) Ohm Energy(single cap) Joule Power dissipation(single cap) Watt Temperature rise(single cap) ºC 0-5 very good, 5-10 good10-15 not good, 15+ bad Actual values MMC rating Peak voltage MMC VDC VDC RMS current MMC A A dV/dt for MMC V/uS V/uS Peak current for MMC A A

Theory used

MMC voltage rating: MMC voltage rating = DC voltage rating * capacitors in series.

MMC capacitance: MMC capacitance = (single capacitor capacitance * amount of capacitors in parallel) / amount of capacitors in a string.

Primary impedance: Zprimary = SQRT(Lp / Cp).

MMC Xc, reactance: Xc = 1 / (2 * PI * F * C). F is frequency in Hertz. C is capacitance in Farad.

MMC Zc, impedance: Zc = SQRT(ESR^2 + Xc^2). ESR is the combined ESR for the MMC. Xc is the MMC reactanse from above.

Peal voltage MMC: DC peak voltage over MMC = Zc * primary peak current

RMS current MMC: Irms = 0.5 * primary peak current * SQRT(on time * bangs per second). Steve McConner.

dV/dt MMC sees: Actual dV/dt in V/uS the MMC sees = (2 * Pi * V) / F. V is peak DC voltage over MMC and F is frequency in Hertz.

dV/dt rating MMC: dV/dt rating in V/uS = Primary peak current / MMC capacitance.

Peak current for MMC: Peak rating = capacitor peak rating * amount of capacitor strings in parallel.