Mutal inductance between air-coils

Hi,
I want to calculate mutual inductnace between aircoils.
Can anyone help?

Regards,
N.Narayanan

N.Narayanan said:

Hi,
I want to calculate mutual inductnace between aircoils.
Can anyone help?

Regards,
N.Narayanan

Click to expand...

Mutual inductance is a function of self inductance of each coil and mechanical/magnetically distance between the coils (because coupling factor k is a function of magneticallly distance only ).Therefore there is only way to define is to measure the self inductances of the coils and then measure these coils again when the others are magnetically approached.
Another solution is to simulate within 3D EM simulator.

If you have access to the IEEE papers, there are many articles on this topic, many related to coaxial coils. However you can be interested in these articles

https://jpier.org/PIER/pier91/18.09021907.pdf
https://www.coe.ufrj.br/~acmq/tesla/maxwell.pdf

Manual calculation is difficult to (almost) imposssible. An EM solver can be helpful.

If you can measure inductance with reasonable accuracy, you could use:

Lshort/Lopen = 1-k^2. k = coupling coefficient

Lopen is inductance of primary coil when secondary coil is open circuited
Lshort is inductance of primary coil when secondary coil is short circuited.

When you know both Lprim, Lsec and k, you can calculate M.

In case of small k, Lshort/Lopen is almost 1. You can measure the inductance by making it part of a resonator. When you know the shift in resonance frequency, you also know Lshort/Lopen.

If the distance between the coils is large with respect to their size (so you can use approximate formulas), you can use hand calculation.

Hi WimRFP and everyone, can you help me?

I have a helical coil with open end and short end as showed below.

For helical coil, we need to take into account the stray capacitance of coil.

So, how can I have the value of L and C, separately, using HFSS

@nvt088: This is a bigger challenge as it seems that you are using the coil as a resonator in half wave center fed dipole mode.
The current is no longer uniform in the coils, hence simple low frequency determination of inductive coupling coefficient no longer holds. There may also be a capacitive coupling component between the two coils.

I'm sorry but I don't have a simple to apply procedure for this case. Finding equivalent series and parallel resonant equivalent circuits is possible with a wide enough sweep, but addding the magnetic and capacitive coupling may be the difficult part.

nvt088 said:

Hi WimRFP and everyone, can you help me?

I have a helical coil with open end and short end as showed below.

For helical coil, we need to take into account the stray capacitance of coil.

So, how can I have the value of L and C, separately, using HFSS

View attachment 104556

Click to expand...

You do a fundamental mistake.
A Transmission Line can not be regarded being as a helical coil or similar device.Hence, your coil will NOT change the phase PI.Because there isn't ONE single Transmission Line, there are many magnetically/capacitively coupled Transmission Lines and thus there are many unknown modes.
Your theory wouldn't work..

Hi WimRFP, Bigboss and everyone

The function of these coils is resonator in wireless power transfer system at 13.56 MHz.

These coils are self-resonance, so they have self-capacitance and self-inductance. In some books, they models helical coils as transmission line, and I don't agree at this point.

To perform Wireless Power Transfer system using Helical coil, I need to its calculate L and C

Is there any idea?

Many thanks

I can imagine the transmission line approach as your structure will also show resonance behavior at higher frequencies, similar to shorted or open transmission lines. Like the LCR series circuit, it is an approximation.

I would just run a sweep around the lowest real impedance (series resonant behavior). Based on the impedance and -3 dB impedance bandwidth, you can calculate the equivalent LCR series circuit. Just using Q = Fcenter/(-3 dB BW), and Q = w*Ls/Rs w = Omega (2*pi*f).

You may also need a parallel capacitor (in parallel with the LCR series circuit) to model the behavior above the first series resonance.

If you want to excite the helical structure with a square wave, you may run into severe problems as the square wave has harmonics that may excite higher resonance modes that are not in the LCR model, but can be modelled with a transmission line model. To find these, you need to know the impedance behavior (EM simulation or measurement) at odd harmonics of the center frequency.