Inductive reactance – Circular loop with N lambda standing wave

[Sandgroper]

Has anyone come across, or may be able to point me in the direction of a method for evaluating the inductive reactance of a circular loop when the wavelength of the applied signal is significantly less than the conductor length of the loop - and more particularly when;

A. The driven wavelength is an even whole multiple of the loop diameter, and
B. The loop forms part of a ‘long’ leg in a parallel resonant circuit carrying a standing wave?

Inductive reactance is well understood to be a vector function of dPhi/dt and can be readily calculated and observed for parallel conductors, single loop and multi loop coils through to odd shaped coils thanks to Msrs Wheeler et. al. etc. Common to all approaches I have come across is that the applied wavelength is significantly less than the conductor length of the coil (Actually the wavelength << conductor length is implicit in the formulas). The literature suggests that as the geometry of a coil increases the inductance, and hence the inductive reactance approach infinity - this to me seems to be predicated on the assumption that the wavelength of the applied signal is significantly less than the guided path.

I can not find a generic or fundamental method of calculating inductance/reactance for cases where the wavelength is significantly shorter than the loop/coil/conductor/guide length.

Any help will be greatly appreciated.

 

[marcusl]

The concept of inductance is no longer valid because the loop cannot be considered as a single "lumped element" or device. You need to solve for wave propagation on and around the loop, which is usually done using an electromagnetics modeling code such as HFSS or FEKO. Circuit parameters such as inductance or capacitance are replaced by transmission and reflection coefficients, scattering parameters, etc. This is why microwave electronics is so much more complicated than low-frequency electronics.