What will happen if I use a air core for 50Hz current tranformer

[chudiandeyu]

I am thinking to use the air core to make transformer to get better linearity behaviour, but I found air core often use in high frequency,so can I use air core for 50Hz? what is the difference between high frequency and low frequency?
Thank you!

 

[Bob S]

The equation relating voltage and current for a transformer primary is

V = L dI/dt, or

V∫dt = L∫dI

If you increase the period ∫dt by lowering the frequency, you will need to increase the inductance L in order to maintain the same maximum reactive input current I_max = ∫dI.

If you do not add iron, you will need to add turns to the primary. For example, if you remove iron from a 50Hz transformer, the inductance will drop by a factor of ~4000. You will therefore need to increase the number of turns by a factor of ~√4000 = 63 to compensate.

Bob S

 

[chudiandeyu]

@Bob S
Thank you for your answer
my transformer is a part of a current probe, so do you think it is reality to use air core for it?
and the 63 is 63 times the turns of the previous winding? can I decrease the secondary turns?
Thank you :)

 

[chudiandeyu]

@Bob S
What is the formula for the inductance and factor?

 

[chudiandeyu]

This is some more discrabetion of my question

I have a current transformer, it is soft iron core.
I want to change the core to air core to improve the linearity, but according to the information I checked, the output current will become very small.
I don't understand how will the output current change, it become small only because the inductance become small? And how can i calculate how small the output current will be?

The primary winding is a straight wire, and this current transformer is a part of a current probe. working in 50Hz.

 

[Bob S]

Are you talking about a current probe that is measuring a steady ac current in a single-turn transformer primary (current probe) wire? For example a N-turn secondary on a transformer toroid that has a single-turn primary carrying I(ω) = I₀sin(ωt) ? Please describe the situation in more detail. I have ordered special gapped toroids (to limit permeability) to measure 100 amp, 500 Hz signals on single-turn primary conductors. Is this what you want?

Bob S

 

[chudiandeyu]

My situation is a current probe for measuring ac current in single turn primary winding, and the current probe is a current transformer with secondary winding 500 turns, the current in primary wire is 10A and 50Hz.
So how can i calculate the current in secondary winding if i use a air core, and is it practical to use the air core?

Thanks !

 

[Bob S]

This is an interesting problem. I simulated a 1-turn-primary, 500-turn-secondary Rogowski coil wound on a toroid with permeability = 1. The toroid is the only shape that will give a high mutual coupling inductance. The dimensions of the toroid were outer radius 4 cm, inner radius 2 cm, length 4 cm. This gives a primary inductance of ~5 nanohenrys. See model in thumbnail. The simulation shows that for 10 amps rms 50 Hz input, the peak open circuit output voltage is ~ 7 volts. This is limited by the shunt input inductance. To get 0.1% accuracy, you need to keep the output voltage to less than 7 mV and the output load to less than 0.2 ohms. So the maxumum output voltage is ~ 4 mV rms at 10 amps rms input. Normally, Rogowski coil output signals go into a transimpedance amplifier. To increase the maximum recommended output load (and voltage), the shunt input inductance should be increased either by using a longer toroid, or a coil form with a limied amount of permeability. How do you plan to process the toroid output signal? I hope this helps.

Bob S

 

[Bob S]

There are current transformer toroids available that nearly exactly match your requirements. See the model TR-5025 in

http://www.toroid.com/standard_transformers/current_sensing_transformers/current_sensing.htm

It has a single turn primary, 500 turn secondary, 90 amp peak primary. The cost is probably ~$20.00 in unit qty (see bottom of page). It is not worth the effort to make your own at this price. I am not advertising this brand, but just letting you know that inexpensive ac current transformers with 1:500 turns ratio are available.

Bob S

 

[chudiandeyu]

@Bob S
Thank you for your answer i decided to use a Hall effect sensor to make the current probe:)