Need help matching two coils and calculations

• edlee008
edlee008
TL;DR Summary
i have a 40mm inner diameter coil and wish to match the output (mT) with a 60mm inner diameter coil ?
need help with coils and calculations

i have a 40mm inner diameter coil with 52 turns 0.4mm wire 3mm height (simple round/square type coils) and wish to match the output (mT) with a 60mm inner diameter coil still using 0.4mm wire will remain 3mm height how many turns is required ?

the actual coils will be triggered by a low frequency pulsed input (its hard to explain as the coils will be connected to a PEMF medical device)

i have used an online coil calculator and it came up with 78 turns ? to match the output mT of the smaller 52 turns 40mm coil (measured at coil center)

40mm coil 52 turns = 0.8156 mT
60mm coil 78 turns = 0.8157 mT

i made the larger coil with 78 turns and i have no way of testing the low frequency pulsed output of the coils (40mm/60mm) but have set them up as DC coils connected to 3.7v and used a teslameter on them they don't seem to match (i know they wouldn't be the same readings as the online calculator)

40mm was 2.1 Gs
60mm was 1.6 Gs

both reading taken from the center of each coil / does voltage play a part ? will one always be stronger than the other as its a larger coil that's why the magnetic field is weaker in the center ?

Welcome to PF.
If the excitation currents could be the same, you would match the ampere⋅turns to the coil area. But the coils will have different values of resistance and inductance, so will probably draw different currents.

i have tested the coils again they both seem to measure the same at the inner edge of the coils, at about 4.0mT so I'm guessing the calculations are correct and its the magnetic field shape that is affecting the output i.e. the magnetic field strength is weaker in the center of the larger coil due to the larger diameter,
(correction for all measurements above they are in mT not Gs as stated

Baluncore said:
Welcome to PF.
If the excitation currents could be the same, you would match the ampere⋅turns to the coil area. But the coils will have different values of resistance and inductance, so will probably draw different currents.
thanks for your quick reply, i am a bit rusty at all the theory involved

To adjust the inductances to be identical, I suggest placing a capacitor of 100pF across each in turn and checking its resonant frequency (which will be in the region of 1 MHz). The coils should be tested each in isolation.

tech99 said:
To adjust the inductances to be identical, I suggest placing a capacitor of 100pF across each in turn and checking its resonant frequency (which will be in the region of 1 MHz). The coils should be tested each in isolation.

tech99 said:
To adjust the inductances to be identical, ...
That is the reciprocal problem.

For the inductance to stay the same, with a greater diameter coil, you must reduce the number of turns, because inductance rises with the radius.

For the flux density to remain the same, with a greater diameter coil, you must increase the current in proportion to the coil area. You could also increase the flux density by increasing the number of turns, but that would raise the inductance dramatically.

To maintain both the inductance and the flux density, requires that you reduce the number of turns to match the inductance, then significantly increase the current to match the flux density. The current must be increased in proportion to the reduction in the number of turns, and the increase in the area of the bigger coil.

The magnetic flux density should be measured in the plane of the coil, at the centre of the coil, not at the side where the local field is wrapping around the winding.

A first guess at the changes, going from 40 mm diam with 52 turns, to a 60 mm diameter coil, while maintaining flux density and inductance, would be as follows:

Radius increases by 30/20, so inductance will rise by approximately 3/2.

To correct the inductance, (which is proportional to the square of the number of turns), reduce the number of turns to, (2/3)^2 = 4/9 = 52*4/9 = 23 turns.

The current must increase by 9/4 to compensate for the area increase, and by another 9/4, to compensate for the reduced number of turns. 9/4 * 9/4 = 81/16 = 5.

So five times the original current must flow, which will require changes to the drive circuit, the drive voltage, and possibly the gauge of wire used to wind the coil.

Tom.G
thanks for the advice i will see how to change the system,,

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