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Finn Hammer

Mon Jun 15 2009, 08:30AM

Registered Member #205 Joined: Sat Feb 18 2006, 11:59AM
Location: SkÃ¸rping, Denmark
Posts: 741

All,

I am trying to attract the attention of someone with better grasp of math, than myself.

The "Predikter" DRSSTC driver relies on accurate current transformers, and I base my understanding of current transformers on this paper, written by Patrick A. Cattermole:

To get easy access to usable transformers, I have made this excel:

Key inputs to the design are transformer sensitivity, and burden resistor reflected into the circuit being measured.
I find it a bit awkward to enter the reflected burden resistor to get the desired real coil/burden data. And I care little what is reflected into the primary circuit.

My question to the matematician is this:

Would it be possible to substitute this latter input with either the real burden resistor or the transformer turns count.

Maby there is another easy way to design current transformers?.

Cheers, Finn hammer

EDIT:

Looking at the numbers, it struck me that there is a fixed relationship between turns count (Ns), and burden resistor (Rt) as follows:

1/S = Ns/Rt

so that for a 1V/A transformer, the ratio btwn. turns and burden is 1:1
for a 0.1V/A tranny, the ratio is 10:1
A 0.01 has a 100:1 ratio
and a 0.002 demands the 500:1 ratio

This makes the choice of turns vs. burden resistor very easy.

I guess the race against imaginary math wizzards made this post superflous.

Cheers, Finnn Hammer

Steve Conner

Mon Jun 15 2009, 11:07AM

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

Hi Finn,

For the DRSSTC current transformers I've made (including the ones I sent you) I just assumed them to be ideal transformers, and calculated their sensitivity according to: Volts per amp = Burden resistor/no of turns. So my DRSSTC CTs had 33 turns and an 0.33 ohm burden, to give an output of 1 volt per 100 amps.

There are four sources of error that I know of, and my designs have always aimed at making them negligible rather than compensating for them.

1. Self-capacitance and leakage inductance give the CT a self-resonant frequency. If this is too close to the operating frequency, it can cause phase shift and amplitude errors. I minimized this by keeping the turn count down and using a very small burden resistor. But I worry when I see people with 1000:1 cascaded CTs hooked with long wires to the unspecified burden of a Steve Ward-style circuit.

2. Leakage inductance also represents an error in the reading, because it's flux that doesn't link the secondary. With a high permeability ferrite core, the error should be considerably less than 1%, so I ignored it.

3. Magnetic saturation can cause the CT to underread at high currents. Saturation has nothing directly to do with the current, it is caused by the EMF developed across the burden resistor, plus the IR drop in the winding. So again my strategy of using a low burden resistor helped. You calculate it by the same volt-second method as for a GDT or whatever.

4. Magnetic pickup from currents that the CT shouldn't respond to because they don't thread the core. This is a major worry when the CT is located close to your primary coil, the MMF from it being a good deal greater than the one you're trying to measure. It can be mitigated by winding two layers, one forward one backward, to cancel out the "single turn effect". However, this increases self-capacitance, lowering the self-resonant frequency. The Faraday cages that I put all my CTs in probably help too.

Finn Hammer

Mon Jun 15 2009, 11:22AM

Registered Member #205 Joined: Sat Feb 18 2006, 11:59AM
Location: SkÃ¸rping, Denmark
Posts: 741

Wow,

With my edit in mind, that was a close race!

Cheers, Finn Hammer

GeordieBoy

Mon Jun 15 2009, 01:25PM

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

There is one additional source of error in CT measured currents. That is the magnetising current of the CT itself. If you image the CT as a conventional transformer, a small portion of the voltage developed across its burden causes current flow in the secondary inductance of the transformer itself. This magnetising current is current that should be flowing in the burden resistor but instead gets pinched by the magnetising inductance of the CT. In SMPSUs it causes "CT droop" and results in "under-reading" of sensed currents towards the end of long current pulses. The way to keep this problem under control is to make sure that there are enough turns on the CT secondary for the operating frequency and to keep the burden resistance as small as possible. If you keep the burden resistance really small, then almost no voltage is developed across the secondary, and therefore very little magnetising current can be robbed by the secondary inductance.

The ideal CT arrangement is actually terminated into a short-circuit. Most people substitute an arbitarily low resistance here with little detrimental effect, but it is possible to terminate a CT into the virtual earth of an op-amp and sense the current with no voltage across the CT secondary. This minimises many of the undesirable effects Steve Conner mentioned.

When sensing continuous AC signals I'd imagine that the magnetising inductance influences the lower bandwidth limit, and the leakage inductance influences the upper bandwidth limit for the CT.

-Richie,

Finn Hammer

Wed Jun 17 2009, 08:37PM

Registered Member #205 Joined: Sat Feb 18 2006, 11:59AM
Location: SkÃ¸rping, Denmark
Posts: 741

Steve, Richie

Thanks for great input.
A litle concern of mine:

For "Thumper" I want to make a 0.0025V/amp transformer.
This will allow me to measure up to 6000A within the 15V input limit to the comparators.

With 25 turns on the core, a 0.1ohm burden resistor is needed.

Now to the tricky stuff:

To develop 15 volts across a 0.1 ohm resistor requires 150 amps.
I sense heat already ....
But it gets worse:
I^2*R heating is then 150*150*0.1 = 2250W
That's a big resistor, even for, say 1/100 duty cycle, it is 22.5W?

I must be missing something central, here?

Cheers, Finn Hammer

Finn Hammer

Wed Jun 17 2009, 08:47PM

Registered Member #205 Joined: Sat Feb 18 2006, 11:59AM
Location: SkÃ¸rping, Denmark
Posts: 741

Finn Hammer wrote ...

Steve, Richie

Thanks for great input.
A litle concern of mine:

For "Thumper" I want to make a 0.0025V/amp transformer.
This will allow me to measure up to 6000A within the 15V input limit to the comparators.

With 40 turns on the core, a 0.1ohm burden resistor is needed.

Now to the tricky stuff:

To develop 15 volts across a 0.1 ohm resistor requires 150 amps.
I sense heat already ....
But it gets worse:
I^2*R heating is then 150*150*0.1 = 2250W
That's a big resistor, even for, say 1/100 duty cycle, it is 22.5W?

I must be missing something central, here?

Cheers, Finn Hammer

Edit: This last post is the effect of too litle sleep, obviously. Pls. delete

klugesmith

Wed Jun 17 2009, 09:46PM

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

If there's a problem I think it is with (1) your duty cycle estimate and (2) ratio between peak and RMS values.

Please excuse some guesses since I'm not a tesla coil guy.
You are sensing current in something (TC primary?) that could peak at + - 6000 A.
Say, 4000 amps RMS during your estimated duty cycle of 1%. That would heat the
main conductor as much as a continuous 400 amps. Is that realistic?

Now with proposed 40:1 CT, the output (as you said) is up to + - 150 A peak, for
+ - 15V on burden R. Say 100 A RMS for 1% of the time. CT winding and burden
resistor will be heated as much as a continuous 10 amps; that's 10W in the burden.

If you can't reduce the primary current or duty cycle requirement, but want to reduce the
power in CT secondary circuit, just wind more turns -- make it 80:1 or 100:1.
If the burden (current shunt) is still 0.1 ohms, its power will be reduced by factor of 4 or 6.25.

Steve Conner

Thu Jun 18 2009, 10:53AM

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

Hi all

You must be careful when calculating RMS values of things that have a duty cycle, and use the square root of the duty cycle where appropriate.

A formula that I use to estimate the RMS primary current of a Tesla coil is:

Irms = 0.5*Ipk*sqrt(Ton*PRF)

(the 0.5 is a rough approximation: 1/sqrt(2) because it's a sinewave, times another 1/sqrt(2) because of the ringup envelope.)

For 5kA peak current, 150us on time and 200Hz PRF that gives us 433A RMS, therefore one of my 33:1 CTs with 0.33 ohm burden would dissipate: ((433/33)^2)*0.33 = 56 watts. This is excessive, so for a coil of this power I'd use more turns and a lower burden. Say 100 turns and 0.1 ohm which gives us 1V per 1000A and a dissipation of 1.8 watts. This also causes 5kA to work out at 5V, which is the full scale setting for the current limiter on my drivers.

GeordieBoy

Thu Jun 18 2009, 12:46PM

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

Wow, 433A RMS is a whole lot of current! I wonder what the rated life of DC bus caps is in DRSSTC applications!?!?

-Richie,

Steve Conner

Thu Jun 18 2009, 02:46PM

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

Well, 5kA implies a really big coil throwing 12 foot sparks. It would need a big bank of paralleled DC bus caps, and I imagine the size of the bank would be dictated by the RMS current.

My Mjolnir coil ran at a more modest 400A peak, 300us on-time and 100Hz PRF, giving 35A RMS, which I thought was reasonable for the large Rifa inverter-grade cap that I used. It also produced a dissipation in the CT burden of about 1W, which again wasn't a problem: I used a non-inductive power resistor.

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