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# Frequency-following RF power supply

## Frequency-following RF power supply

(OP)
I need to drive about 100 watts of RF power @ 1 MHz into a moderately resonant load (estimate Q ~ 100 - 300) whose center frequency or "desired" resonant frequency drifts.  I want to (or have to) let it drift and change my drive frequency to match.  Else I won't get power to couple.

I am at prototype stage but looking for a cheap, manufacturable solution ultimately.  For now, in the lab, I have a linear RF amplifier and a Class E amplifier with enough "looseness" in its LC tanks that I can drive it over the required frequency range.  The question is, how to tell either of these amps what frequency to put out, and automatically follow what the load wants to do?  Is there standard circuitry out there for that?

### RE: Frequency-following RF power supply

There are several approaches to this, but a Q of 100 to 300 is  getting rather large. And as you suggest, the actual true power delivered to the load is going to vary hugely if the system tuning or drive frequency changes even slightly off the resonant peak.

One approach is to measure the relative phases of the voltage and the current at the load, and then to steer the driving frequency to maintain exact phase coincidence.
The phase change will be very rapid around resonance with such a high Q, and the system should remain in tight phase lock.

Another much simpler and more practical way to do this, (which is really very similar), might be to use the self resonance characteristics of the load as the frequency determining element of a powerful oscillator.
In other words, the whole system then becomes an oscillator, the oscillation frequency determined by the load resonance.

All oscillators work this way, where both the phase and amplitude create maximum total feedback around an amplifier.

You just need to couple energy back directly from the load into your power amplifier input, and include some type of automatic gain control system in the loop to set the oscillation amplitude, and hence control final output power.

I have used this method successfully myself, to drive drifting and unstable high Q resonant loads such as RF induction heaters, and ultrasonic transducers very repeatably to significant power levels.

With a bit of care and some experimentation, it can be very effective at coupling and controlling high frequency power into really nasty uncooperative resonant loads.

### RE: Frequency-following RF power supply

Try to find a suitable induction heating power supply. These supplies always track the resonance frequency. Main Problem may be that the smallest power rating you can get is about 1 kW. But even such a supply will be significantly less expensive than a 100 W linear amplifier.

### RE: Frequency-following RF power supply

(OP)
Thanks for encouraging suggestions!

Now that I think back, I recall a project going on a place of former employment, though I was not involved directly, where engineers were driving a gaseous plasma load in vacuum using an RF inductive coil.  Of course, the impedance/reactance of this plasma load changes if you vary the pressure, pumping speed, gas flow or look at it cross-eyed.  Originally, the method they used was to have an automatic matching network (with gigantic high-voltage variable capacitors) which measured reflected power via VSWR meter and minimized it by some sort of algorithm to vary the capacitors.  But then they found that they could get by with a crudely-matching fixed match network and use a variable-frequency RF supply, and tune to the load by varying frequency.  There was a manufacturer of RF plasma power supplies who specialized/invented this, but I cannot remember the company name.  Ring a bell?

### RE: Frequency-following RF power supply

Sounds like what's done with RF laser tubes (not the active matching, the RF driving of a plasma).  Universal Laser Systems and Synrad come to mind as manufacturers of such systems, for what it's worth.

Dan - Owner
http://www.Hi-TecDesigns.com

### RE: Frequency-following RF power supply

This sounds very similar to automatic antenna tuners, where a wildly varying reactive antenna impedance must be matched to a  fixed output impedance transmitter at various exact spot frequencies.

Motor driven capacitors and roller inductors are driven to a point that provides a resistive load of the correct impedance to the transmitter for optimum power transfer.

There are various commercial antenna tuners on the market that will do this. And radio amateurs have been building both manual and autotune antenna couplers for decades.

Both amateur and commercial antenna couplers mostly cover the HF radio communications band, which is from around 1.5Mhz to 30Mhz, and may struggle to reach 1Mhz. But the design concepts are sound.

The amateurs have published design details and ideas for building these, and practical suggestions for writing some software to make it all go is fairly readily available.

If that is the solution you adopt, there is plenty of information available on how to build your own.

### RE: Frequency-following RF power supply

(OP)
Warpspeed,

Thank you so much for your posts.  I did research the RF inductive heater power supply arena as you (and electricuwe) said, and I saw that frequency following is indeed available.  I was just about to ask you some details of your idea to "use the self resonance characteristics of the load as the frequency determining element of a powerful oscillator".  Then your idea to use an antenna tuner came in.  Hmmm.  Now I will research that.  However, with antenna tuners I think will still be the transmitter that is determining the frequency.  So I really like your initial idea better, to let the load determine the frequency.

At first I thought you were suggesting to put the load somehow in the LC of an oscillator (like Colpitts or Wein), so I studied oscillator theory a bit. To get a stable oscillator, you have to meet the Barkhausen citerion of forward plant gain A and feedback gain and phase "beta" such that A * beta = -1 (minus sign for 180° out of phase).  This might not be easy with a shifty LC load, AND now I see that you were probably suggesting something else anyway.

I think you are suggesting to sample the load frequency and feed it back into the input of the linear RF power amp (let's stay with linear amp for conceptual simplicity, for now).  If I did this with an op amp chain, I could also control the amplitude of the input to the amp, which for a fixed gain of the RF power amp would effectively control the amplitude on the load side.  Is that close to what you're suggesting?

### RE: Frequency-following RF power supply

The antenna tuner idea is, as you suggest is a good solution where the driving frequency absolutely must remain fixed at a spot frequency. But it would be a far more complex solution to implement in a practical way.

In this application, as with induction heating, and ultrasonic transducer driving, slewing the drive frequency to match the load will be far simpler and much easier to implement.

The idea here is that at resonance, the tuned output tank voltage and current will be in exact phase, and also the circulating energy in the tuned tank will reach a definite peak amplitude at exact resonance.

If you feed back a sample of the circulating tank energy, the circuit will self oscillate wherever the loop gain is highest, and the total energy will continue to build up in increasing amplitude until something either self limits (saturates) or something self destructs.

Both are practical, but one may suit you better depending on what hardware you have, the power level, and personal preference.

The analog way would probably involve a commercial linear "brick" power amplifier suitably impedance matched into a tuned tank circuit.

How to suitably couple the RF into your plasma load either with an "E" field or "H" field, (or possibly both), is way beyond my expertise.  But a suitable resonant tank with suitable Q will be required regardless of how it is driven.

Just realize that 100 watts with a tuned Q of 300, is 30,000 circulating volt/amps, so either the tank voltage or tank current, or both, are going to be respectably large.
The tank tuning capacitor will need to be up to the job.
Either a ceramic transmitter "door knob" cap, or an induction heating tank capacitor would do it.

Your tank components, and how you match your "brick amplifier" into it depends on the impedance of your plasma load and tank L/C ratio. But I am sure you already know all of this.

The tank losses need to be kept low, having a 100+ watt loss in a 30Kw tank is not unlikely, you then may need 200 driving watts, not 100 driving watts.  So do not specify any higher tank Q than is absolutely necessary to couple power into the plasma load. Tank Q's of 5 to 20 are much more normal for radio transmitters and induction heaters.

Anyhow, you want to arrange for maximum feedback amplitude at resonance, and either tapping off the voltage peak, or the current peak from the tank should not present any problem with 30 circulating Kilowatts.

Now what is needed is a variable gain linear amplifier with a wide dynamic range.
Maybe at 1Mhz an analog multiplier?
The feedback voltage goes through the variable gain amplifier stage back into the input of your brick power amp.

Wide band circuit noise will be sufficient to tickle your tank into ringing. And the variable gain amplifier will initially be at full maximum gain, and the oscillation amplitude will rapidly build up over a few cycles.

What is needed is something to measure the RF amplitude, and control the loop gain, such that the system oscillates at whatever power output you require, adjustable over a very wide dynamic range.

Basically that involves an RF rectifier to measure RF amplitude, a dc control voltage from a potentiometer, and an integrating error amplifier to ramp the variable gain stage up and down in gain.

It will oscillate away merrily, and you can control the power level precisely with your potentiometer.

The digital approach involves a voltage controlled oscillator switching some MOSFETs that drive current through your resonant tank on each half cycle.

This too will shock your tank into ringing, and a sample of the ringing tank energy is used to phase lock the voltage controlled oscillator to the tank resonant frequency.

To start up reliably, the voltage controlled oscillator needs to be reasonably close to the expected tank resonant frequency, at least within a 2:1 range either way.
It will quickly pull into lock, and away you go..

Tank oscillation amplitude still needs to be controlled, and that can be done by pulse width modulating the drive to the tank.

Either approach works.

The analog way will be more suitable for relatively low power levels, with a linear power amplifier, and 100 watts is not a lot. It will be much simpler to get going, and potentially have fewer design issues to think about.

For several Kw, or tens or hundreds of Kw of RF power, a switching amplifier is going to be the method of choice hands down every time.

### RE: Frequency-following RF power supply

(OP)
Warpspeed, Thanks for the detailed explanation.

Analog: Can you point to sources for "brick" amplifiers in the 1 MHz, 200 watt range?

Digital: You mention "Tank oscillation amplitude still needs to be controlled, and that can be done by pulse width modulating the drive to the tank."  That's great, and I think we could do this, but luckily we also can control the DC voltage that the MOSFETs switch in to drive the tank, and of course, that controls the amplitude of oscillation, too.  At least, we can do that in the lab.  But in production, to save cost, PWM of a raw DC supply would be better.  Thanks for mentioning it.

### RE: Frequency-following RF power supply

The best way to do the PWM for something like this, is to use a buck regulator running off a direct rectified mains supply.

A suitably large dc feed choke then supplies a constant current into the tank via a chopper bridge to steer this current.

The reason for doing it like that, is that a current source can stand an indefinite short circuit, or the wild transient reactive loads that the tank may have under startup, or fault conditions if the whole thing goes out of frequency lock. A constant current is exactly that, and far more short circuit friendly.

A voltage fed circuit, such as hard switching the DC rail with an H bridge, will go *bang* if the tank suddenly shows a large capacitive reactance. Massive current spikes can wipe out your semiconductor switches in an instant.

Using a current fed chopper instead of a hard switched voltage chopper to drive your tank at 1Mhz will save many tears, save the lives of many innocent semiconductors, and be vastly more reliable once this goes into production.

First design your tank to couple into your load. That needs some thought as to tank geometry and L/C ratio. Then work backwards from there.

The tank circuit, and coupling sufficient power into the load is the key to the whole problem.

### RE: Frequency-following RF power supply

(OP)
Warpspeed,  Absolutely good idea, to put an inductor in series to make the raw DC supply a constant-current-seeking source.  I like to think I or my eectrical guys (I am a materials scientist) would have thought of that.  In the past I recall EEs I have worked with worrying about a huge forward voltage developing across the inductor in case of a sudden open circuit, which could exceed the off-state voltage stand-off of the MOSFETs.  They would put a diode clamp (zener with resistor?) or maybe a snubber across the inductor.  But you don't have to teach me that - either our EEs will know or I can look it up.

You are right.  The core challenge is to design a resonant LC tank that includes the load as part of the L and C AND making sure that, at the (drifting) resonant frequency of the load, the gain (probably Q, too) of the overall LC tank maximizes.  The L & C of the load need to dominate the overall tank, but not by too much - just enough to determine the preferred frequency.  I need to measure or calculate what the L and C of this load are near resonance, to be able to come up with topology of tank and other component L and C values.  Maybe we can back this out of some test run data we already have.  Maybe this is one thing people use network impedance analyzers for?

I STILL HAVEN'T GIVEN UP ON THE ANALOG APPROACH THOUGH.  You mentioned a commercial linear "brick" power amplifier.  Any manufacturer you can think of for me to look at?

Thanks again!

### RE: Frequency-following RF power supply

With a parallel resonant tank, the impedance will always be maximum at resonance.
Off resonance the impedance will be minuscule.
You never need to think about driving an open circuit load, unless something physically falls off.
And as you have suggested, protective voltage clamping diodes would be fairly easy to implement across the energy storage choke.

Your current steering chopper needs no dead time, in fact some  degree of conduction overlap would be a good idea. That too greatly simplifies things.

If the current is steered into the tank on the correct half cycle, it adds to the tank energy.  If it tries to add current on the wrong half cycle, or around the zero crossing, no harm is done to the driver. It just drags down the circulating energy, until proper phase lock is restored.

This makes the system very bullet proof. What is required are series diodes connected to the drains of each current steering MOSFET, so that the internal drain source diode does can never conduct.  That way the chopper always appears as an open circuit to the tank.

The chopper can drive current through the tank, but the tank cannot drive current backwards and destroy your chopper bridge.

Brick amplifiers invariably consist of a large rectangular heatsink (the brick) with some type of high power amplifier module bolted directly to it underneath.  It is an expensive way to go about producing a couple of hundred watts, and it may be fairly easy to blow up during testing.

No time now, I will be late for work, but I will see what I can find around the internet later on.

Designing the tank will require some experimentation, and what you are doing is totally out of my narrow range of experience.

The only plasma I have had anything to do with exists in Xenon flash tubes for laser pumping. The impedance is very low, which suggests the magnetic H field is the key to coupling in energy, but I really know nothing about that side of it.

### RE: Frequency-following RF power supply

(OP)
Warpspeed,

Thanks again for even more useful info.

BRICK linear amplifiers: I have RFQs out for a couple, just to get an idea of price, but I think I am convinced to go with the FET-switched resonant tank, digitally.

CORRECTION:  My load is actually a piezoelectric ultrasonic transducer.  I was being a bit "coy" about defining the load and overall application.  I am new to this forum and, for all I know, some of my company's competitors search it and read it regularly.  I still will not hint at the application.  Anyway, when I was talking about a plasma load, that was back at an old job, and I wasn't even on that project.  Somehow you got the idea that plasma was my load.

### RE: Frequency-following RF power supply

Nothing really changes, except a piezo load has two closely spaced resonances, parallel and series resonance.

It is far easier to drive significant power into the transducer at the series resonant dip. Impedance will be at minimum, and drive current highest. Hence more lovely watts at a sane drive voltage.

The trick here, is to use a current transformer to tap off a sample of the actual transducer current, and use that to lock your phase locked loop.
The system will seek and then lock onto the series resonant dip.

One advantage of a piezo load is that you don't see the horribly low impedances of an LC tank circuit off resonance.
The piezo looks like an open circuit at pretty much any frequency except series resonance.  Your driver is less likely to self destruct.

Only problem I have had with driving piezo transducers to significant power levels is shattering the thing.

And I fully understand your reluctance. About thirty years ago I was sucked into a top secret project that involved ultrasound used with race horses to apply heat to damaged muscle tissue to aid healing and recovery.

There was huge secrecy and paranoia about the cloak and dagger guys stealing the idea.  That was long long ago, but some things never change, hehehehe.

### RE: Frequency-following RF power supply

(OP)
More good advice from experience - thanks.

The only thing that might make my piezo application a little special is that there are essentially two mechanical resonances in the system.  One is the obvious plate-thickness resonance of the piezo slab itself.  The other is in the acoustic medium to which the piezo is coupled.  We intend to excite that mechanical resonance in the medium.  But, both the frequency of the piezo plate resonance and the medium's resonance change a little with temperature, loading and other factors. And these two resonances' freqs can change in opposite directions.  We have/can damp the piezo a little but to make it more broadband (decrease the Q of its plate resonance) so that it's resonance always overlaps the medium's resonance somewhat.

So, what we want is the freq-following RF supply to find and track the best "compromise" resonant frequency of the system as a whole as that freq drifts.

I don't think this changes anything.  Probably RF inductive heating, other piezo applications and plasma excitation all have secondary load or system effects which change the optimum operating frequency.

### RE: Frequency-following RF power supply

So perhaps you need to extract acoustic feedback energy from the resonant medium instead of right at the transducer itself?

That way you are getting the overall coupled response, and can steer the drive frequency accordingly.

Some type of frequency independent means of measuring mechanical amplitude. A capacitor microphone, or optical interferometry come to mind...

This will give you reliable amplitude information, but not which way to steer the drive frequency. If it is possible to rock the drive frequency very slightly, that will then tell you which way to go.

I have never tried to do anything quite like that myself, just thinking out loud here.

### RE: Frequency-following RF power supply

(OP)
Hmmmm.  No, I convinced myself that the two resonances, the piezo's and the medium's, if close enough in frequency, would "compromise" to one intermediate frequency, if I put the piezo (and its "load", the medium) into an appropriate tank circuit.  You convinced me that an appropriate tank circuit would have Q << 300 (more like 10, I think) and that with good design I could get a tank circuit that would naturally resonate at whatever frequency the piezo and the medium together decided they wanted.  Then your suggested current transformer would work to sample the frequency of the tank and be used to feed back to the drive freq of the FETs.  Then I just have to worry about amplitude control, but we taalked about that and I think I can handle it.

But you are correct that, by sampling only the piezo, I will have no idea (without other experience or measurements) how much power is actually going into the mechanical resonance of the medium.  I think that mechanical power will be pretty linear with either the voltage or current (or the square of them) resonating in the tank, as long as the frequency of the tank is self-optimized (i.e., cureent and voltage are nearly in phase in the tank).

### RE: Frequency-following RF power supply

When you have two very close in frequency linked resonances, the coupling coefficient is vitally important.

If the coupling is very loose, then the two peaks will essentially add in the intuitively expected fashion, but total energy transfer will be lossy.

But when the coupling is made extremely tight, the two resonances can fight each other, and you then get two lower amplitude peaks, with a dip in the middle.

Optimum coupling of two resonances gives maximum energy transfer, without the dip in the middle.

### RE: Frequency-following RF power supply

(OP)
Hey, here is a piece of news.  I spoke with a technical sales manager at one of the well-known RF inductive heating companies (company name withheld in case it is against forum rules or detrimental to that company), and he said that they do NOT want to operate exactly at peak resonance.  As the load changes, the optimal frequency does drift, and their power supply does actively track it, but they avoid the dead-on resonance frequency.  He said, if they do operate at resonance, the semiconductors in their power supply go "poof".  So they scan frequency from some starting point known to be above or below the resonance, find a three frequency points where the load response (power?) is still monatonic with respect to frequency and just work there.  Evidentally, they have to periodically jump to different close-by freqs to assure that they're still on the monatonic slope on the side of the resonance peak, and move the ceter-point freq. one way or another to follow the peak as it drifts.  Or something like that.  Interesting, eh?

### RE: Frequency-following RF power supply

I have never heard that one before.
Sales managers also believers in Voodoo and snake oil.
A full moon may also be required to observe this phenomena.

In several decades of tuning radio transmitters, and other types of tuned power amplifiers. Maximum power and efficiency ALWAYS corresponds with conjugate coupling and resonance.

But that is the simple case............

Now two very closely related resonances involved with coupling significant power need the coupling coefficient to be adjustable for maximum power transfer, OR to obtain a required fairly narrow flat bandpass characteristic.

A really good example of this is tuning bass reflex loudspeaker enclosures, where cone resonance, port resonance, and box volume (coupling coefficient) are adjusted to extend acoustic coupling a half octave lower than the loudspeaker cone resonance by itself in free air is capable.

A seminal paper published by Thiel and Small totally revolutionized bass loudspeaker box design, and may not in principle be so very different to what you are trying to achieve at at other extreme end of the acoustic spectrum.

To couple acoustic power efficiently into a medium, where two very closely related resonances are involved.  I urge you to seek out the original acoustic research carried out by the Australians Thiel and Small, it may be helpful.

Another application is the Tesla coil.  Here there is a primary tuned tank circuit of high Q, and a secondary very high voltage tuned circuit tuned by stray capacitance.

To get maximum power transfer, the primary and secondary need to be neither under coupled or over coupled.  There is a sweet spot where both primary and secondary have maximum power transfer with both at resonance.

Increasing the coupling does not increase power transfer. The higher the Q, the looser the critical coupling point is.

There are many other examples of this, but two resonant systems if severely over coupled, just fight each other.

### RE: Frequency-following RF power supply

(OP)
Yes, we can adjust the Q of the piezo's self-resonance by damping and, maybe have some control over the load's resonances.  But to know what we're looking for, you are correct, I should do the the Thiele-Small analysis.  I looked at it a bit and do think it is applicable - coupling of two resonances close in freq.  What I first found was a retired engineer Art Ludwig's summary of the T-S analysis, and I copied it and uploaded it here.  Then I found a place where you can obtain the original papers.  Actually several by Small and a couple by Thiele - apparently they never co-authored, even though both were from Australia.  Here is that link:
http://jordan-usa.com/technicalpaper.html

### RE: Frequency-following RF power supply

Both were not only from Australia, but were both at Sydney university together at the same time, doing very similar post graduate work.

I cannot find my copy of the original joint paper, but I know for certain that it exists.  That paper is the basis for the "Thiel and Small" characteristics that every bass speaker manufacturer now routinely supply for each of their drivers.

Anyhow, with a bit of lateral thinking, I believe you will be  able to effectively couple acoustic power between two closely resonant media, but the coupling coefficient needs to be optimum for highest power transfer.

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