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In Need of a Little Help in Designing a Versatile High Voltage Power Supply

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Bjørn

Sun Sept 13 2009, 11:07PM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

1. Have a realistic plan.
2. Have a clear plan.
3. Never change your plan, if it is not working, scrap it and make a new one.
4. Never ask anyone to do your work for you, ask them to help you figure it out for yourself.

If you follow these strictly you can get help on this forum to build just about anything. If not people will get annoyed and it will all disintegrate into chaos.

You can find the basis of a function generator with some discussion here:

Steve Conner

Mon Sept 14 2009, 09:04AM

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

Robert Francis wrote ...

If those 3 components will not work together in that fashion, what's wrong with it, will a transformer not work well transforming a waveform from a power amplifier? Neon sign transformers used to power Tesla coils are usually 10-15 kV.

This is a good question, so I'm going to answer it. Even if you don't understand the answer, others might find it interesting.

As I said earlier, any waveform can be decomposed by Fourier analysis into a steady DC component plus a series of AC components. For instance, a square wave oscillating between 0 and 10V at 100Hz can be made by adding the following together:

5 volts of DC
A sine wave of frequency 100Hz and amplitude (20/pi) volts
A sine wave of frequency 300Hz and amplitude (20/(3*pi)) volts
A sine wave of frequency 500Hz and amplitude (20/(5*pi)) volts
And so on ad infinitum. This is called a Fourier series, and the individual parts of it are called Fourier components. Try it with a graphing calculator and the following formula from Wolfram's Mathworld.

Now, if you want to feed this waveform through a transformer, then the transformer must pass all of the components equally if it isn't to distort the waveform. This is very difficult to do. In particular:

No transformer will pass the DC component, so the output voltage will have an average value of zero, and your amplifier will be destroyed if it tries to force a DC component through. Another way of stating this is that a transformer is made of inductors, and inductors appear as short circuits to DC: the average voltage measured across an inductor must always be zero.

A Tesla transformer has only a very narrow bandwidth: because it operates by resonance, the transformation only works for frequencies near the resonant frequency. Therefore, the Fourier components will not all be stepped up equally, and hence the output waveform will look nothing like the one you put in. (It'll look like bursts of ringing at the Tesla coil's resonant frequency, no matter what waveform you put in.)

Leakage inductance and self-capacitance of the transformer will attenuate the high-frequency components, distorting the waveform. An extreme example of this is a NST, which has very high leakage inductance, put there intentionally to ballast the neon tube. It would attenuate the harmonics heavily, and the resulting output voltage, if we put our 100Hz square wave in, would just look like a 100Hz sine wave.

However, all transformers have a certain amount of leakage inductance and self-capacitance that can't be got rid of, and the higher the ouput voltage you want, the worse it gets.

Overcoming these limitations is what hvguy (and I

) would charge you six figures for...

Proud Mary

Mon Sept 14 2009, 12:41PM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

Robert, I have responded to your private message in clear, here, because it is for me to encourage or discourage privacy.

You're obviously interested in our stuff, so why not give yourself a chance and forget this unfortunate business? Give yourself a break and come back with something else. Trust me, you'll feel much better if you settle down and just become one of the guys.

I'm going out now for some bacon and eggs and a pot of tea, and won't be pleased to see further traffic in this thread later.

Robert Francis

Tue Sept 15 2009, 09:05PM

Registered Member #2355 Joined: Thu Sept 10 2009, 09:12PM
Location:
Posts: 71

I apologize if I have gotten off on the wrong foot with you Harry or anyone else, that was not my intention.

I realize now that I am quite ignorant about this subject despite months of reading. It is easy to read and yet remain ignorant because of lingering unanswered questions or misunderstandings that don't get clarified.

Just to be absolutely clear:
A positive voltage, whether pulsed square wave, sine wave, triangle wave, etc cannot be fed into a 10:1 turns ratio transformer (have its voltage multiplied by 10) and remain positive?

The output of any transformer will always have an average voltage of zero?

Steve Conner

Wed Sept 16 2009, 02:23PM

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

Yup, you got it.

Robert Francis

Wed Sept 16 2009, 03:22PM

Registered Member #2355 Joined: Thu Sept 10 2009, 09:12PM
Location:
Posts: 71

Damn, it only finally sunk in about what you were saying about pulse transformers needing a diode.

That Butler Winding page on Pulse Transformers has 1 schematic out of the 3 showing a diode and the word diode wasn't present in the page at all.

It even says:

Pulse transformers, being typically unipolar (D.C.) applications, require the primary switch to be opened ( thereby removing the voltage source ) before saturation occurs, whereas A.C. applications reversed the applied voltage before saturation occurs. Unipolar applications require that sufficient time be allowed to pass to re-set the core before starting the next pulse. This time permits the magnetic field to collapse ( reset ).

I would have figured that because the transformer can only output AC that even in a pulse transformer the voltage would reverse in the transformer preventing saturation.

Is what they are saying a result of the diode somehow reflecting the negative voltage back while letting the positive voltage go through and somehow this prevents the core from desaturating so the primary has to be pulsed?

Or is it a result of putting DC into a transformer, that AC will be outputted anyway but by inputting DC instead of AC the core doesn't go negative and desaturate?

Is it just wrong?

Wikipedia also has a relevant blurb on their transformer page:

The time-derivative term in Faraday's Law shows that the flux in the core is the integral of the applied voltage. Hypothetically an ideal transformer would work with direct-current excitation, with the core flux increasing linearly with time. In practice, the flux would rise to the point where magnetic saturation of the core occurs, causing a huge increase in the magnetizing current and overheating the transformer. All practical transformers must therefore operate with alternating (or pulsed) current.

That seems to imply a pulsed DC current will work.

Thanks

klugesmith

Wed Sept 16 2009, 07:10PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

At the risk of adding to the confusion:
There are circuits called "Flybacks" that use coupled inductors arguably called transformers.
These normally -do- have substantial DC components in the primary and secondary currents (not voltages),
directed such that their magnetizing effects cancel. They enable DC:DC converters with reduced parts count, at the cost of less efficient use of core and winding volume and weight.
Have you read the HV WIKI page about transformers?
- - - -
Robert, I'm going to suggest that you lay some blocks for a solid foundation before
attempting to design any pulse transformers. This goes beyond levels normally taught in high school.

1. Have a good QUANTITATIVE understanding of passive electric circuit fundamentals:
voltage, current, resistance, capacitance, inductance. Extra points for resonance.

2. Understand frequency-domain analysis as people here have mentioned. At least: how any
repeating pulse waveform can be represented as the sum of various frequencies (including DC)
each with unique amplitude and phase.

3. Learn the fundamentals of electromagnetism, enough to do quantitative homework problems:
* magnetic field caused by electric current. You can skip learning the signs (right hand / left hand rules).
* magnetization of ferromagnetic materials, including saturation
* Voltage induced by magnetic flux changes.
* A representative problem at the halfway point would be to calculate the inductance of a coil with specified core dimensions and permeability.
* Farther along, you can understand and compute the voltage at which a power transfomer will saturate, as a function of frequency.

After you pass the quiz, it won't be silly to talk about high voltage issues.

Have fun.
Rich

Dr. Slack

Wed Sept 16 2009, 08:02PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

When people have a good understanding of transformers, they will often throw terms like AC and DC around, without being too precise, expecting their audience to know that they are talking loosely, and hoping their audience really know what's going on. Even when it's clear that the audience doesn't have a good understanding, sometimes they still do it. Then when terms like "pulsed DC" start cropping up, ugh!

This may or may not help, but give it a go.

a) A transformer's two windings are linked togther by magnetic flux.

b) The units of flux is Volt.Seconds, which is another way of writing Weber (the units for total flux), or Tesla*core area

c) Any core material will have a maximum flux it can support. Saturation limits it in the case of iron, ferrite etc; the maximum practical current before the windings melt limits it in the case of air, vacuum etc.

Just sit with the maximum volt.seconds for a moment, to absorb the implications.

Consider an example

If you have a volt per turn on your windings, and keep it constant for 10mS, then the flux will increase to 10mWeber, or 10mVolt.Seconds.

If you now drop the voltage to zero, the flux will stay the same (we're neglecting losses here).

If later on you increase the voltage to 1 volt for 10mS again, the flux will be 20mV.S at the end of that time(if it's below the core's maximum flux).

I haven't talked about AC or DC, and as you see I don't need to. The action of the traansformer is purely described in the waveforms, the voltages and times.

You could look at the scenario above and say that two 10mS pulses of DC (ugh!) had been put through the transformer, and you'd be right.

From here we could do one of several things.

1) Let's now put -2v in for 10mS, the additional -20mV.S will bring the core flux back to zero. That's called "resetting the core" in some jurisdictions.

2) Or from the same core history of 20mV.S flux, let's put another pulse of 1v in for 10mS, but let's assume the core saturates at 25mV.S. As the flux rises to 25mV.S, everything happened as before. But now, the flux doesn't rise any more. If it was the applied voltage that caused the flux to change, then it was the changing flux that allowed there to be a voltage across the terminals. As the flux has stopped rising, the terminal votlage goes to zero. With the applied voltage still present, something goes bang (neglecting losses). In reality, the windings will have some resistance, the power supply will have an output impedance, and together these will limit the current; whether something goes bang or not, the secondary voltage has fallen to zero, so it's stopped working as a transformer.

3) Or again from the same starting point, put in -1v for 40mS. At the end of that, the core will be carrying -20mV.S of flux. You could describe the total history as two half-cycles of AC (with the first half cycle a bit strange). But the core is now swinging between a positive and a negative flux.

From a more mathematical viewpoint, if the flux is volt.seconds, then the flux represents the time integral of the applied voltage. As the flux is bounded by saturation, this means the time integral of the applied voltage must be bounded.

If you look at a conventional AC waveform, you will see that its time integral is bounded, and depending on the moment of switch-on, is bounded to be within +/- the area under a half cycle. This actually gives rise to a very important problem in AC transformers, as the maximum flux permitted in most transformers is +/- half the area under a half cycle. This is the cause of the thud sound, and fuse-blowing, when a mains transformer is switched on. If it's switched on at the voltage zero crossing, the core saturates. Fortunately, winding resistance and thermal capacity in small transformers, and explicit soft-start and protection circuits in big ones, let it ride through the high-current event undamaged, while voltage across the winding resistance gradually reduces the average flux to zero.

If you look at a conventional DC waveform, you will see that its time integral is unbounded, so it won't go through a transformer.

These last two observations are why most people are happy to throw DC and AC terms about when talking about transformers, though you see they are neither necessary, nor sufficient, just lazy approximations.

So, if you can come up with a waveform that has a voltage time integral bounded by less than the saturation flux of your intended transformer, it will pass that waveform relatively undistorted.

Whoa, you said "relatively", what gives?

Oh, yes. Practical transformers are much more complicated than a mere volt.second integrator. Made with real copper wire, they have resistance, capacitance from turn to turn and winding to winding, less than 100% coupling from primary to secondary, core losses of various types, and the need to insulate turn from turn and winding from winding and core. All these mean that real transformers only operate over a small range of frequencies, and that high voltage transformers have to be big. Getting a real transformer to do what you want is some people's day job, and why they will charge you 6 figures for it.

Robert Francis

Fri Sept 18 2009, 07:16PM

Registered Member #2355 Joined: Thu Sept 10 2009, 09:12PM
Location:
Posts: 71

So putting pulsed DC into a transformer can work, that's what I originally thought.

I've been crunching some numbers using the formula:

Ac = (V x dt x 10^8)/(dB x Np x Sf)

where dt is the maximum time duration of the pulse, Ac is the coreâ€™s cross-sectional area and Sf is the core stacking factor ratio. Units are gausses, turns, square centimeters, volts and seconds.

It looks like the duty cycle of the pulse would have to be about 1% and the core about 12" in diameter for V = 1MV, f = 2MHz.

The biggest problem I have had is in finding the maximum flux density of air and/or epoxy. It looks like ferrite and iron have a rating of 500 gauss at 100 kHz and 150 gauss at 1 MHz.

Does anyone know offhand the maximum flux density of air for an air core?

Even with this info the cost of the transformer would get up there in price. 12" PVC pipe is not cheap. If I was to make a laminated core that would also add a lot of cost to the transformer.

I had another idea, scrapping waveform, frequency and duty cycle adjustment, and voltage adjustment and going with a cockcroft walton generator.

These are known to get into megavolt territory.

A couple problems though:
Can I deliberately induce a very large ripple? I am looking for voltage pulses but a marx generator with the spark gaps and resistors is not what I am looking for. I came across this equation for the ripple in a cockcroft walton generator:
(4n^3 + 3n^2 - n) = (Vdrop * 6fC)/Iload

n stands for the number of stages, f is frequency (according to the hvwiki this is the frequency of the supplied AC. How does one determine the frequency of the ripple), C is capacitance.

I calculated that to get a 1MV output voltage, 1MV Vdrop, 2MHz frequency, .0018 Iload, I would need 100 stages and 10 kV capacitors of about 600 pF.

Would this work where the output of the generator under load would oscillate between about 0 - 1MV at a frequency of about 2MHz?

And further, what exactly is voltage sag and are there any equations for it?

P.S. Thanks Klugesmith for the suggested homework, its been almost 10 years since college physics class and I haven't needed to do this kind of work since. Thanks Dr. Slack for the primer on transformers.

Proud Mary

Fri Sept 18 2009, 07:40PM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

Hello Robert,

here is a Cockcroft & Walton generator producing a mere 750kV, rather less than is required in your plan. As you can see, it's the kind of endeavour involving entire design teams, structural engineers, welders, concrete construction engineers and what have you - the kind of thing usually paid for out of national budgets.

All the best,

Harry

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