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design of ferrite core (toroid) current transformer for 50 Hz or 27 Mhz

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philipperr

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Hi,
I want to make a toroid current transformer with a large aperture so that it can fit around the arm or ankle.
The current transformer is meant to measure the induced current in the body ( arm or ankle ) caused by electromagnetic fields.
I found some ferrite toroid cores on ferroxcube.com with a large enough aperture ( see image ). The question now is how many secondary windings do i need to wind around the core to be able to measure currents in the range of 1 mA - 1 A ?
I would be most gratefull if someone could assist me with the design parameters.
toroid_core.png
 

FvM

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1 mA - 1 A
I don't believe that you consider currents above a few mA in 50 Hz frequency range. Can you imagine why? I presume you have a medical/physiological background.

- - - Updated - - -

Referring to the technical current transformer problem, a current transformer has a high-pass cut-off frequency

ωc = Rs/Ls, where Rs is the total secondary circuit resistance (winding + optional shunt), Ls the secondary inductance, AL*n²

To implement a cut-off frequency below 50 Hz, you'll need a low windings resistance and preferably no shunt at all (possible with an active I/V converter). Number of turns isn't too critical, 50 to 100 would be my first guess.

A high µr material (tape wound core) would be better suited for low frequency, but ferrite is basically feasible.

My personal favourite (light and small) would be a Rogowski coil, although it's somewhat demanding to achieve 1 mA sensitivity.

What's the meaning of 27 MHz in the question title?
 

philipperr

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Indeed, my apologies, the higher currents are for the 27 MHz design
In the 50 Hz design, i need to able to measure mA's
And I am a student in electronical engineering, but I am fairly new to the design of transformers.
I can calculate the inductance of the secundary coil ( L = A_l * N^2 ), but what inductance do i need to get a high enough sensitivity to measure mA's? what is the influence of the resistor placed between the two ends of the secondary coil? (i want to measure the voltage over it and put that into relation with the current that went through the arm/ankle)

I already did some calculations:
H*2 Pi r = N*I (law of hopkinson, with N=1 here because it's the primary coil aka the arm/ankle )
=> H= I / (2 Pi r)= 1 mA / ( 2 Pi 6,4 cm) = 0,002486796 A/m
with {inner diameter + outer diameter}/2 =2,4 cm ; (2,4 + inner radius)/2 = 6,4 cm = r ; i took the middle of the core
B= µ_0* µ_r * H = 4 Pi 10^(-7)*H=3.125 nT
(i took µ_i here for µ_r)
flux= double integral of B*dS
V= - N * d(flux)/dt


Thank you for your response

- - - Updated - - -

I want to make two transformers: one for 50 Hz and one for 27 MHz.
The original plan was to make a transformer for 1Hz - 110 Mhz, but that is clearly not possible.
I have already researched the rogowski coil, but I read that it was used for measuring A's - kA's and that the output wasn't steady at the low end side of that current range.
i have started looking at other types of cores but there aren't that many cores with the aperture that i need for an affordable price.
I am looking into tape wound cores as we speak.

thank you again, you have already been very helpfull
 

FvM

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Standard tape wound core shapes have at least larger aperture and higher AL value with similar weight. Ideally you'll want to make a light core with smaller cross section.
https://www.vacuumschmelze.com/index.php?id=306

If you have a core with specified magnetiical properties like the Ferroxcube part, you don't need to perform much calculations, except for the windings and amplifier related. Turns ratio will be suggested by the intended output current, secondary resistance and amplifier noise considerations. I stay with he suggested 50 to 100 range for the time being. A possible way to further reduce the transformer cut of frequency is a current compensation scheme with two secondary windings. Noise has to be calculated thoroughly in this case. Also a DC capable compensating transducer with hall sensor is possible.
 

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if we use a tape wound core the lower cut off frequency will easily be under 50 Hz.
But what about the sensitivity = R(shunt)/N(windings) ?
if we use an active I/V converter, then R = 0 (ideally) so the sensitivity will be also 0?

after the current transformer we want to filter the signal (to reduce noise of higher frequency components) and amplify the it with a low noise amplifier.
further, we want to measure this signal with a matlab module and do a FFT with matlab to get the amplitudes of the current running through your body for each frequency component.

I have also looked into a DC capable compensating transducer with hall sensor, but couldn't find one with large enough aperture to put around your arm or ankle
 

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With an active I/V converter, the amplifier input represents a zero shunt impedance while the sensitivity is set by the conversion resistor.

I don't expect DC current sensors with large aperture being commercially available. I just mentioned the option to build a sensor.
 

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ah ok, thank you.

If we increase the windings of the secondary to increase the voltage at its terminals, what are the consequences?
I've read that the higher cut off frequency will go down because of the leakage inductance and stray capacitance.
But is there any formula to estimate the higher cut-off frequency?
 

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If we increase the windings of the secondary to increase the voltage at its terminals, what are the consequences?
I've read that the higher cut off frequency will go down because of the leakage inductance and stray capacitance.
That sounds highly plausible.

But is there any formula to estimate the higher cut-off frequency?
I think the problem demands for an empirical measurement.

The only substantiated reason to increase the output voltage would be noise minimization, according to the amplifier noise parameter.
 

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We would like to expand the frequency range to 50Hz - 100kHz
But based on following figure vitroperm_vs_ferrite.png
I am not quite sure this will be possible with the vitroperm core.
 

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