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How do you determine component values for Class-E operation?

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Sigurthr

Fri May 31 2013, 05:52AM

Registered Member #4463 Joined: Wed Apr 18 2012, 08:08AM
Location: MI's Upper Peninsula
Posts: 597

Hello everyone!

I've been thinking of doing a -small- SSTC for a change (I normally make multi-kW monsters) that uses a simple monolithic fixed frequency oscillator and single ended drive. I would like to attempt Class-E operation for higher efficiency. I have built a class-E resonant flyback driver that uses feedback to determine the operational frequency, but I did not really choose the Drain-Source capacitor, I just used one I had handy, and it happened to work very well. This time I would like to properly design a class-E amplifier and I don't really know where to begin. I found several books which detail it well in easily understood terms (even if some of the math is out of my normal range) but they are all super expensive (>$90).

I would be eternally grateful if someone could detail the process of determining the component values for a very basic Class-E amplifier.

How do I mathematically determine the values for the Drain-Source shunt capacitor and de-Qing (primary tank dampening) resistor? I know that you can adjust the primary tank Q by adjusting coupling but I think fine tuning the coupling via a resistor and using fixed coupling might be a bit easier if it doesn't eat too much power. I tend to have a hard time with the physical construction aspect of things.

I am planning on using a 1MHz oscillator similar to:

and running the entire coil on 12V from a battery or wall-wart.

Any suggestions?

Edit: went back and re-read Richie Burnett's page on Class-E and figured a few things out better. Even he has "????" marked as the value for the shunt capacitor though!

WaveRider

Fri May 31 2013, 10:14AM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Hi Sigurthr!

I will take this opportunity to plug a short article I wrote a couple of years ago on finding the component values for Class-E output networks. The analysis is simplified (in that I do not consider the input network), but it should get you started in choosing component values. Look for the design equations in boxes throughout the text and check out the design example at the end of the article.

Also, a question: what do you mean "de-Qing resistor"? If you want an efficient power amplifier, you will never put a de-Qing resistor in the output network.

Cheers!
Bill

Steve Conner

Fri May 31 2013, 10:15AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Ultimately the shunt capacitor value will depend on the streamer loading. We have no mathematical model for streamer loading, so you adjust it by trial and error. Richie gives instructions for doing this.

Edit... Simulpost with WaveRider, what he said

WaveRider

Fri May 31 2013, 10:27AM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Indeed, Steve. This is a problem with Class-E and tesla coils. The loading is non-linear and randomly time varying. The trick is two-fold: 1) trying to get arc ignition (where there is little dissipation, high voltages, bad amplifier-load match) without burning out your mosfets from overvoltage or overcurrent and 2) have a decent match, on average, during running...so you get a good meaty arc. Trial and error is indeed the only way to get good results.

HV Enthusiast

Fri May 31 2013, 01:23PM

Registered Member #15 Joined: Thu Feb 02 2006, 01:11PM
Location:
Posts: 3068

There used to be a very good document on Class-E tuning that showed a whole bunch of example waveforms and exactly what needed to be changed in the circuit to bring it into tune. I'll have to find it.

Another resource is the following:

But Richie's is a great resource on Class-E theory.

Scott Fusare

Sat Jun 01 2013, 12:07PM

Registered Member #531 Joined: Sat Feb 17 2007, 10:51AM
Location: Burlington, Vermont
Posts: 125

Jim Tonne's "Class E" software works great -

I have built several small (<20W) class E amps using it and they came out spot on.

Sigurthr

Sun Jun 02 2013, 05:28AM

Registered Member #4463 Joined: Wed Apr 18 2012, 08:08AM
Location: MI's Upper Peninsula
Posts: 597

That software looks marvelous, thank you!!

Also thank you to everyone for replying.

What I meant about the de-Qing resistor was the load resistance shown in most class E amps that prevents the damped oscillation from going into the negative causing the body diode to conduct. I think in TCs we rely on coupling factor and streamer/corona loading to accomplish this.

Steve Conner

Sun Jun 02 2013, 09:41AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Yes, that "de-Qing resistor" is the load itself. The Class-E design software will probably assume a 50 ohm load, or allow you to enter the load resistance you want to design for. Then in service, you're supposed to use an antenna matching unit to present the amp with its design load resistance.

In Tesla coil work it is the resistive part of the streamer load, and we don't know quite what that is. Some modelling work has been done at regular Tesla coil frequencies, but at Class-E frequencies the behaviour of the plasma seems quite different. In any case, you can adjust the loading on the amp by adjusting the coupling and/or playing with the coil's topload capacitance. These have similar effects to the loading controls on an antenna tuner.

GeordieBoy

Mon Jun 10 2013, 02:38PM

Registered Member #1232 Joined: Wed Jan 16 2008, 10:53PM
Location: Doon tha Toon!
Posts: 881

This graph summarises Class-E tuning specifically for a Class-E SSTC:

The aim is to get the local minimum in the drain-source voltage waveform to be zero right at the point where the MOSFET turns on again. Then the drain-source voltage lands smoothly at zero before turn-on. Under these conditions there is no voltage across Cds (no stored charge) and the drain current is also zero at the instant of turn-on. The flat gradient that arrises in Vds from the zero drain current affords some immunity to imperfect tuning since the drain voltage lingers in the vicinity of zero volts for some time around the ideal turn-on instant!

Zbase is the AC resistance seen at the base of the resonator. This encompases all of the losses in the resonator including the resistance, radiation, and loading of the corona at the top of the coil transormed by the 1/4 effect of the resonator itself. Increasing Zbase makes the resonant load network in the Class-E amplifier more lossy and the drain voltage oscillation is more heavily damped and doesn't swing as far down towards zero. Conversely a lower Zbase means less losses, and the drain voltage swings further back down towards zero, or even his the 0 volt line.

Cds is the total capacitance across the MOSFET channel. This encompases the dynamic Cds intrinsic to the MOSFET, the parasitic capacitance of any external wiring or heatsinking arrangements, plus any additional shunt capacitance connected from drain to source in the Class E amplifier. Increasing the drain-source shunt capacitance makes the drain voltage dip later, and more shallow. Conversely decreasing Dds causes the minimum to occur earlier and for it to be deeper.

Finally the inductance and capacitance reflected back to the drain of the MOSFET are summed up in Ls and Cs. Increasing either the reflected inductance or capacitance will lower the resonant frequency of the load network and make the dip occur later and deeper. Conversely decreasing Ls or Cs makes the dip occur earlier and shallower.

It's hard to control Zbase as it depends to a large extent on the impedance of the corona from the top of the coil, but you can influence the reflected impedance by changing the number of primary turns because this alters the effective transformer turns-ratio at the bottom of the TC. You can achieve a similar effect by altering the coupling also since this alters how many of the secondary turns the primary actually couples into!

Cds can easily be altered by fitting additional shunt capacitors across the MOSFET terminals. However, it can't be decreased below the inherent Cds of the MOSFET. This value does fall however as the supply voltage is increased!

You've got complete freedom in the choice of series indutance and capacitance seen at the drain of the MOSFET in the Class-E amplfier. Therefore by manipulating Zbase, Cds and the resonant frequency arrising from Ls & Cs you can move the point of minimum voltage in any direction you want.

In practice turn-on losses in a Class-E amplifier are proportional to Vds squared so you don't need the drain voltage to come all of the way right down to zero, you just need to get it nice and close to zero to keep the losses down and the efficiency high.

As others have said though, the typical TC is a very "dynamic" system and things like allowing the discharge to strike a grounded (or even floating) object will seriously perturb the "perfect Class-E drain waveform"

-Richie,

kiat

Thu Jun 13 2013, 08:38AM

Registered Member #2115 Joined: Fri May 08 2009, 01:17PM
Location: Singapore
Posts: 46

Is there any method to calculate the Class E values when the output is matched to a primary-coupled resonator because in this case you have on top of the reflected secondary side RLC circuit you also have the magnetizing inductance of the primary which affects the tuning.

Class E papers and calculators usually match into a RLC load without the additional magnetizing inductance so I was wondering if there is a more intelligent way than trial and error to find values when matched into a Primary fed Class E tesla coil?

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