Solid state tesla coils - general notes

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7. Impedance matching

To get maximum power transfer from the SMPS driver to the TC secondary, the driver output impedance must be matched to the TC secondary impedance. These are matched when both impedances are equal. A matched condition also implies that you are then running your SMPS driver at the max power it can handle - cranked up to max - and you are putting maximum power into the TC secondary and streamers.

Of course, the SMPS driver output impedance may be lower than the driven TC secondary. This would mean that you are running the SMPS at lower/"safer" power levels, i.e. below the absolute maximum rating. That's generally considered a good engineering practice (though, for SSTCs, design for long term reliability can usually be ignored ;-).

When using a ferrite core step-up transformer to step up the mains voltage and feed this into the secondary base, the transformer turns ratio between secondary and primary can be used to match the SMPS and TC secondary impedances: the base impedance of the TC secondary,
Z_sec (the exact value to be measured), will be reflected to the transformer primary side as an impedance equal to:

Z_sec_reflected = Z_sec * (N_pri/N_sec)^2

and now your remaining task is to match Z_sec_reflected to the SMPS output impedance. This is easily "matched" by making sure that the SMPS can handle this low impedance load Z_sec_reflected without blowing up, i.e. can supply the power P_pri drawn by the primary of the transformer and delivered to the TC. This power is equal to

P_pri = (V_pri)^2 / Z_sec_reflected

(where V_pri is the voltage applied accross the primary. Assuming 230VAC mains, it is 350VDC for a full-bridge and 160VDC for a half-bridge)

With this info, you can build the transformer. This isn't as simple as it may sound, and requires a lot of experimenting. A good introduction and an almost step-by-step guide for designing your own transformer is available as a TI tech seminar paper, "Power Transformer Design".

It may be easier to do this design backwards - first, measure the base impedance of your TC secondary. Then come up with some realistic output power you'd like. Say, 1000W. In order for 1000W to be delivered into the secondary base impedance, the step-up transformer must have an output voltage of

V_sec = SQRT ( Z_sec * P_sec )

This leads to a turns ratio

N_sec/N_pri = V_sec/V_pri
N_sec = N_pri * (V_sec/V_pri)

(where V_pri is the voltage applied accross the primary. Assuming 230VAC mains, it is 350VDC for a full-bridge and 160VDC for a half-bridge)

After you find a ferrite core that can handle the desired 1000 Watts at the TC resonant frequency, without too high heating losses, you can use the formulas from the "Power Transformer Design" paper to calculate the minimum number of primary turns. After that, use the above formula to get the number of turns required on the secondary winding.

The hopefully clearest way to state all this is that you design the transformer turns ratio for a given output voltage. The initial base impedance of the TC secondary is somewhat constant, so that the initial power draw will be P = U_xfmr_sec^2 / Z_tc_sec.

Because the base impedance can only increase from this value (due to streamer loading as well as detuning) this power is also the maximum power drawn. With a specific transformer turns ratio you get out the desired voltage and thus can set the max power.


The same ideas apply to the direct TC primary coil drive method. In this case it is the turns ratio between the air-core primary coil and the TC secondary, as well as the coupling between these two coils, which will determine the magnitude of the TC secondary impedance that is seen by the driver circuit.
When increasing the number of pri turns, the impedance seen at the primary side increases, approaching the impedance of the secondary, thus reducing power draw. Decreasing the pri turns count also decreases the impedance seen by the driver, so power draw increases. Using tighter coupling has a similar effect like decreasing the pri turns count.

Once again, "impedance matching" isn't anything else than choosing the pri turns and coupling (well, you want maximum coupling, for sure) in such a way that the power draw doesn't exceed the maximum power your bridge SMPS (mosfet and diodes) can handle.

In a sense, this "impedance matching" isn't really one of the ordinary impedance matchings, because the impedance of the SMPS primary side is the impedance of the live mains supply, so the output impedance of the driver is always lower than the "matched" impedance. Then again, shutting down the mosfets when overcurrent conditions occur does simulates a higher average output impedance. Also, pulse width modulation, if it is used, would simulate a higher instantaneous output impedance. But PWM isn't a good idea for SSTCs...