confusion about peak vs average power in short pulse currents

Discussion in 'General Electronics Chat' started by gojirasan, Dec 17, 2011.

1. gojirasan Thread Starter New Member

Dec 17, 2011
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I am thinking about purchasing a device that requires an input of 7500 amps at 240 volts or about 1.8 MW of power, but only for a short pulse of about 3 microseconds each second. I think the duty cycle should be .000003s / 1s = .000003 or .0003%. Assuming an ideal switching time of zero that would mean the device is only drawing 1.8 MW .0003% of the time and the rest of the time it would be drawing no power at all (aside from core losses in the transformer). So the average power should be 1800000 W * 0.000003 = 5.4 W. That's kind of hard to believe. Does that mean I don't need a thick copper cable or lots of thick copper cables in parallel even though I would be drawing (or trying to draw) 7500 amps in short bursts?

0000 AWG wire has a resistance of about half a milliohm every 10 feet. So a single 0000 AWG 10 foot long primary transformer winding that connects directly to the breaker box would drop about 7500 * .0005 = 3.75 volts resulting in 3.75^2 / .0005 = 28.1 kW power dissipation but only for .0003% of the time. If you consider the duty cycle of 0.000003 then you only end up with about 84 mW of average power dissipation in the primary winding with such thick wire.

I don't think 84 mW is going to be melting any copper, but what about the 28 kW pulses? It seems to become a question of how long it takes for copper (or magnet wire varnish) to actually melt. I don't know for sure but I'm guessing more than 3 microseconds.

Although converting peak power to average power through duty cycle calculations does seem to allow ohm's law to work its magic, it seems pretty non-intuitive to me. How can I possibly draw so much current from such a relatively small (less than 1/2" thick) wire at such a relatively low voltage? It just doesn't seem right. Can you just completely ignore such high peak currents and design solely based on average values? In this case the peak current would be 7500 amps, but the average current would only be 22.5 mA. So would I just design based on a 22.5 mA current even though there is never really any 22.5 mA current? It's either 7500 amps or almost zero or in some transitional state between the two. Admittedly most of the time there is almost no current at all in the wire. If anyone could help clarify this stuff for me I would be very grateful.

Dec 26, 2010
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I can only imagine this level of pulsed current (7500A for 3μs) being sourced from something like the kind of capacitor bank normally used with things like large pulsed lasers. Trying to do this directly from a domestic AC supply would impose a huge overload on the system: apart from anything else, the effects of parasitic resistance and inductance in series with the supply would result in the voltage collapsing as soon as the load was applied. (You may make your connections as heavy as you like, but the power company will have dimensioned their cables, transformers, etc. according to the normal expected load. )

The connection between a pulsed power source and its load would normally be very substantial, but not merely to minimise resistance, but to minimise inductance, which can become significant even in straight wires when dealing with large rates of change of current.
In some more demanding applications the interconnection uses flat copper bus-bars sandwiched each side of an insulator, so as to minimise the enclosed loop area.

As a matter of interest, what is your application?

Last edited: Dec 17, 2011
3. gojirasan Thread Starter New Member

Dec 17, 2011
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Interesting. I wasn't thinking of it really as sourcing the pulse directly from the power company. I just figured what happens on the secondary side of the transformer is mirrored on the primary side. Although I was concerned that the power company couldn't supply 7500 amps period. Or nearly 2 MW for that matter.

I guess if you can smooth out the pulses with a large capacitor bank so that the power supply transformer never sees the pulse then I really would be just looking at the average power and current. The idea of a capacitor bank occurred to me, but I wasn't sure how long a pulse you could generate. Capacitor discharges always seem nearly instantaneous to me, but I guess 3 μS isn't all that long. The voltage on the secondary side of the (primary) mains transformer would be at 30 kV. So I was also concerned about finding a high value capacitor with that kind of voltage capacity. I just checked with Mouser and the highest value capacitor they have rated at 30kV is a 4700 pF ceramic disc capacitor. That's not a whole lot of capacitance. I guess it's time for me to start researching capacitor banks and sourcing high voltage capacitors.

So without a capacitor bank you don't think it would work? I guess I was sort of expecting to just start right in on the square wave pulse generator circuit etc after the rectified and smoothed transformer output. To make matters worse, although I'm living in the US right now, the final location of the device would be in a third world country which may not have the same level of electrical distribution capacity as first world countries. In the US for instance I could probably get 400 volt 3 phase power (although it isn't always easy), but I have no idea if that will be available where this will be located eventually. Could I avoid a large capacitor bank if I used my own generator?

The device is a 1 MW magnetron requiring 60 amps and 30 kV at its anode and the project is basically a kind of communications transmitter.

Dec 26, 2010
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This may be more complex than you imagine it to be. What you are describing sounds very much like a RADAR transmitter, and you might do well to look into the design of existing radar systems rather than trying to make it all up for yourself.

The use of an energy storage element, probably a capacitor, will be indispensable. Otherwise, all the power supply components and the mains supply itself would have to be rated for ridiculously high peak currents. Without energy storage, you would also have to time your transmission pulses so that they coincided with peaks of the AC waveform. Finally, the huge transient currents drawn from the mains would cause terrible electromagnetic interference, both within your premises and further afield.

Edit: Another way of looking at this is that the smoothing equipment has to be dimensioned to supply sufficient pulsed current without the voltage dropping off too much.

Last edited: Dec 17, 2011
5. jimkeith Active Member

Oct 26, 2011
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Generators have such a high source resistance, that this is not a good idea.
The type of energy storage capacitor(s) you need will not be available from Mouser or other similar distributors--perhaps surplus...

In my experience (observation only), such radar power sources were generated by oil-filled capacitor banks in the order of 5 to 10kV, hard switched by vacuum tubes into the primary of a large, very special, tightly coupled, step-up, pulse transformer. Other means of switching such as gas-discharge tubes may be workable, but the pulse shape is likely to suffer. I am definitely not up on modern techniques.

Don't mean to pooh-pooh your ideas, but this ain't going to be easy, very portable, or cheap.

Here is a cap to look at:
http://www.ebay.com/itm/Maxwell-318...853?pt=LH_DefaultDomain_0&hash=item4aa7847995

Last edited: Dec 17, 2011
6. crutschow Expert

Mar 14, 2008
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Yup, you are describing a old radar transmitter built with a magnetron. Find out how they were built and you will have your answer.

7. gojirasan Thread Starter New Member

Dec 17, 2011
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Thanks guys. All very helpful stuff. You are right that a radar system is precisely what this is. Except for having to worry about the return signal of course.

I've looked into the capacitor problem further. About the best I can do for a relatively cheap price is about 1 nF 15kV in a ceramic disc. So I was thinking I would just put a couple in series to get 30kV. Single 30kV caps are outrageously expensive even in small values. As has been pointed out it is possible to go much higher in capacitance than this, but the costs skyrocket.

Having read some more radar information it seems that something called a pulse forming network is what contains the capacitors. What is interesting about it is that it is just a kind of 'ladder' circuit consisting of a series of pi low pass filters which attempts to simulate a very long transmission line. The pulse width is proportional to the square of the product of L and C.

I'm not quite clear on whether this pulse forming network solves the supply problem in the way that a traditional capacitor bank would. I suppose that as long as I have some kind of capacitor bank between the mains transformer and the magnetron the transient behavior from the POV of the transformer will be determined by the time it takes to charge the capacitors. The only question is whether there is enough capacitance to supply 60 amps for a full 3 μS. Would raising the inductance in the pi network have the same effect as raising the capacitance in terms of the length of time it can supply a high current? It seems like all the charge in that 60 amps of current has to come from the capacitors, but could some also be stored in the magnetic field of the inductors?

BTW, I am well aware that this is an ambitious project and I am in fact way over my head with it. This is a long term project and I plan to do a lot of learning along the way. I would be quite satisfied if I could have the project finished in 5 years. I'm watching MIT course videos in EE and physics and calculus. I'm reading Horowitz and Hill and some books on communication electronics. I'm planning to buy specialized books on microwave electronics and radar, but I don't quite have enough calculus yet for most of those books. I took several years of calculus 20 years ago, but I never used it and haven't remembered any of it. I'm planning to go back to university eventually as well. I never finished my EE major 20 years ago which may be just as well since I seem to have forgotten pretty much everything I learned. Probably not for 1-2 years though. Until then I'll be without the help of an instructor.

8. crutschow Expert

Mar 14, 2008
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The purpose of the pulse forming network is to generate a controlled pulse width. If you just discharge a capacitor directly into the magnetron, the width of the pulse will be uncontrolled and arbitrarily determined by stray impedances in the circuit. Since you mention 3μs, then I assume you would need some form of pulse network to establish this pulse width.

This network is only partially related to the capacitor supply or the amount of energy stored. How much capacitance it takes to store the required energy depends upon what the starting and stopping voltages are when delivering the 60A 3μs pulse. If the voltage went to zero, then the required capacitance equals (3μs * 60A)/30,000V = 6nF, but that is a best case scenario. It somewhat depends upon how well the pulse forming network transforms the capacitance energy into the proper current and voltage pulse energy.

9. BillB3857 Senior Member

Feb 28, 2009
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In the APS-20 radar system (lower radome of plane in my avitar), we had a hi-voltage power supply feeding the Pulse Forming Network. The output of the PFN was switched to the magnetron by a very large thyratron (gas filled tube) Once it fired, current to the magnetron continued until the voltage dropped below that needed to maintain ionization. The PFN storage capacity determined the transmitted pulse width. The radar system had two different pulse rate options. For the higher frequency option, a small motor drove as switch which shorted out a part of the PFN to shorten the pulse width by reducing the amount of stored energy. Wow, subjects like this bring back a lot of memories.

10. gojirasan Thread Starter New Member

Dec 17, 2011
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Because the duty cycle is so short I have to assume that the voltage would have plenty of time to go to zero, possibly helped by the thyratron switch cutting off at a certain voltage threshold. I wonder if that voltage threshold might have an effect on the squareness of the pulse waveform. This might be an additional advantage of using a hydrogen thyratron which is supposed to have ultrafast switching times. Those puppies are not cheap though.

Edit: What am I talking about? If the thyratron cuts off before the capacitor discharges fully that would in fact prevent the PFN voltage from reaching zero volts. Assuming that there is no other discharge path except through the thyratron. I was confused thinking of the input to the pulse transformer instead of the output of the PFN. Because the thyratron cuts off the current so suddenly it would certainly seem to affect the squareness of the pulse seen at the pulse transformer primary winding. So does that increase the value of capacitance necessary? I'm going to have to find that equation.

When you talk about 'how well' the PFN changes C and V into pulse energy are you at least partially referring to the squareness of the pulse?

Thanks so much for that 6 nF result. I'm currently searching in The Art of Electronics for that apparently simple equation you used to get the capacitance. It must be some really basic capacitive transient equation that I've forgotten over the years and is no doubt on this site as well.

6 nF is certainly no problem. I can easily get up to 8-10 nF without significant added complexity or cost. For a bit of a fudge factor I guess. I'm assuming that it won't harm anything to have more capacitance than I really need. It seems like I could just make up for it with lower inductance values to keep the pulse width at or just under 3 μs. Actually the pulse width doesn't have to be exactly 3 μs. It just can't be over 3.5 μs, and I'd prefer if it were not under 2.5 μs. I would however like to get as perfect a square wave as I can. Something I'm looking into with respect to the PFN design.

Interesting system. I wonder if you could accomplish some kind of pulse width modulation by selectively shorting out sections of the PFN. My current plan for modulation is to use a kind of negative pulse width modulation by varying the time between pulses. That is varying the off time instead of the on time by controlling the thyratron trigger timing with programmable logic.

Last edited: Dec 17, 2011
11. BillB3857 Senior Member

Feb 28, 2009
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The Pulse Repetition Rate (PRR), in search radar determines the maximum search range. By controlling the PRR, the average power is also controlled while maintaining a fixed pulse width powering the magnetron. Basically, it is a PWM system where the repetition frequency is changed rather than the pulse width.

12. crutschow Expert

Mar 14, 2008
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The capacitance equation is C = Q/V where C is in farads and Q is charge in coulombs. Since Q = I * t then for a constant current, substituting give C = (I*t)/V.

Dec 26, 2010
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But note that as the capacitor voltage drops during discharge, this may be too optimistic.

The energy E stored in a capacitor is given by E = 0.5*C*V$^{2}$ , so C=2E/V$^{2}$, if Vcan fall to zero.

If only a partial discharge can occur, from say V1 to V2, the capacitor has to increase by a factor V1$^{2}$/(V1$^{2}$-V2$^{2}$)

How much difference this would make will depend how far the capacitor can be discharged: in practice the characteristics of the magnetron may make it unproductive or even impossible to discharge below some limit.

To make things extra difficult, some capacitors, particularly ceramic, show a noticeable variation of capacitance with voltage.

@gojirasan: You really would be better to have such relationships clearly in mind before planning to build such a transmitter. In my opinion, building such a thing at home would be an extremely ambitious project for a fully qualified and experienced electrical engineer.

What is your motive for embarking on such a difficult, costly, and even potentially hazardous project?

14. bountyhunter Well-Known Member

Sep 7, 2009
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It's impossible to draw huge peak currents out of thewall because the inductance in the lines will limit it. I actually designed a power supply used in a TWT (travelling wave tube) burst transmitter which did exactly what you are talking about: put out a huge burst of bradband EM radiation for brief pulses. It was in electronic warfare countermeasures which would "blind" incoming missiles and cause them to lose their radar lock with such a bright pulse of energy.

To deliver these energy pulses we had a 3kV source charging up a metallized poly capacitor about the size of a brick.

Feb 28, 2009
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16. gojirasan Thread Starter New Member

Dec 17, 2011
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I just noticed this note from an HY3202 Thyratron data sheet:

Although the current stops when the gas deionizes, getting the gas to deionize doesn't seem that easy with these devices. Maybe that's why they are considered 'latch' devices. Turn on behavior can be induced with a well defined pulse (or double pulse) at the grid but turn off behavior requires patience. In fact it appears this may require some additional circuit complexity. I have to make sure that the anode voltage stays at zero or slightly negative for a full 0.1 ms. If the anode goes even a little bit positive again during this period the thing won't turn off at all.

If true I'm not sure if this is good or bad. It may mean the capacitors don't need to be as large, but it also seems to mean that I don't get as much benefit from the lightning fast switching times of a hydrogen thyratron in increasing pulse squareness. At first I was frustrated looking for specs on the breakdown or deionization voltage which I assumed would be at least a few thousand volts as with other gas discharge devices, but it looks like there aren't any such specs because the deionization voltage is actually 0.

Nevertheless I think I am going to try to get the capacitance as high as possible in the network. It looks like it won't do any harm, but could help a lot. At least I can try to increase the capacitance to around 20 nF by spending a bit more money on more of the comparatively cheap ceramic caps.

I'm not sure I understand how I would use your energy equation in this application.

Well that's what I'm trying to do. As I said I'm expecting this project to take quite a long time as I learn while I build out various sub-circuits. I'm hoping by the time I'm finished with the entire project to maybe have a BSEE or equivalent 4 year degree. As for experience, you get that by actually doing stuff. Stuff like this. I agree that it is very ambitious, and I am even expecting to quite possibly fail, but I have to at least try.

Mainly to do something truly interesting before I die. I was tired of reading various science fiction novels that presented these interesting worlds full of techno-wonders and then put the book down and realize how little genuine excitement there is in my life. I struggled to come up with something, anything, even moderately worthy of a science fiction story that I had at least some chance of doing in my own life. This project is what I came up with. I guess you could say it's my dream. Which is another reason why I so appreciate the help you guys are giving me. I can't overstate how much I appreciate it.

17. shortbus AAC Fanatic!

Sep 30, 2009
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Can I take out a life insurance policy on you?

Dec 26, 2010
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You also need to think of the safety of anyone who gets near this thing. A magnetron like that can kill or maim. This is not simply a question of high voltages: microwave radiation is dangerous.

Your statement about not understanding the relevance of the stored energy in a capacitor surprises me. If for instance you want 1MW of power for 3μs, it should be clear that this is 3 joules of energy. This gives you a bottom limit for the stored energy in the capacitors: more will be needed in practice.

Whether or not this approach will be better than working out the capacitance required to deliver a certain charge for a certain voltage drop may depend on how far the capacitors will be discharged.

19. gojirasan Thread Starter New Member

Dec 17, 2011
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Thanks for the warning. I'll keep that in mind. During testing I'll always aim the waveguide or horn antenna at the sky and stay at least 6 feet away, and I'm considering the idea of wearing some kind of metal mesh suit like a wearable faraday cage or just building a shark cage sized faraday cage in the back yard. Something like a box with the sides made of aluminium screen. In actual use the parabolic dish will always be aimed at the sky. Never at building structures or people.

Ah. I think I get it now. For the moment I've settled on the idea of 17 nF for the PFN. So if E=1/2CV^2 then for .000000017 Farads and 30000 Volts E = 7.65 Joules. But at 15000 volts E is only 1.91 Joules. So I guess that means that if the voltage only drops to 15kV before the discharge is stopped nearly 2 Joules of energy would not be used. So I would really only have 5.65 Joules of energy available per pulse.

If I were to substitute a neon tube for the hydrogen thyratron something like 2900 V might be a realistic deionization voltage. In which case 7.58 Joules or about 99% of the available energy would be used in each pulse. I think neon tends to require more voltage to ionize than most gas discharge tubes. So for most realistic gas discharge tube scenarios whether the capacitor discharges to zero doesn't appear to make much difference. That result seems strange. Perhaps it's because the stored energy is proportional to the square of the voltage? I guess the E to V curve would be some kind of parabola. I'm interpreting E as potential energy stored in the capacitor. Maybe that interpretation is not correct.

In any case it does now appear that the PFN will be discharged all the way to 0 volts and will have to stay that way for at least 0.1 ms if I want the thyratron switch to turn off. Although the question does remain of how useful the lower voltage part of the discharge curve actually is to the magnetron. I'm guessing not particularly useful. And it appears that most of the energy in the pulse is used up at the start of the discharge when the voltage is still high.

One thing that still bothers me. The current discharged from a capacitor is normally some kind of curve, is it not? But the whole point of the pulse forming network is to try to make that discharge curve sqaure-ish and, well, pulse-like. I would really like to be able to plot I, V, and E with respect to time and make sure that I stays close to 60 amps throughout the 3 μs period. I guess some kind of π filter or π filter network equation which represents those values with respect to time would do it. Or maybe just a SPICE simulation.

I'd like to see the voltage and current drop nearly straight down with respect to time. According to the above analysis it would seem that a thyratron that turned off by itself above 0 volts would be of some benefit for that desirable sharp dropoff. I wonder if a spark gap switch would be more useful than a thyratron in this case. Or maybe a spark gap in series with a thyratron. I found this in an abstract here. As usual I would have to purchase it in order to read it. As a species we have stopped sharing scientific knowledge. Now we keep it to ourselves and try to sell it. Well, except in this forum of course.

20. BillB3857 Senior Member

Feb 28, 2009
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You are right about the normal discharge curve of a capacitor being a curve BUT, in a PFN, the inductors compensate for that and the result is a fairly sharp pulse. Google "Pulse Forming Network" and you will get a lot of information. Several hits have Youtube examples of home built units.