# Modeling phase delay in high frequency resonantly coupled inductors

I am interested in simulating resonant wireless power transfer circuits similar to the ones developed by MIT and others. So far, I have been able to successfully create a basic simulation model of a set of resonantly coupled inductors with a k of 0.1 or less. However, I'm interested in exploring the behavior of the system at high frequencies where the distance between coils becomes a significant fraction of the transmission wavelength.

When I say significant, I mean within a quarter wavelength, as I am still interested in near-field coupling. However, even within this regime, I am interested in exploring the effects that the propagation/phase delay of the field from the receiver has on the transmitter.

Is there any way to model the effects of delayed phase of two resonantly coupled inductors in LTSpice? I imagine it would be something like a wireless transmission line but I have no idea how I would even start to model this. Again, the phase delay range I'm interested in is only 10-20 degrees max from the source. Any pointers in the right direction greatly appreciated!

Also, as a reference, here's a paper I've been reviewing that discusses the subject a bit more.

http://www.physics.princeton.edu/~mcdonald/examples/wireless.pdf

Thank you, Jason O

• If you're using an 'inductor' model, then there are no delay controls to adjust. So you'll need to go 'transmission line'. Unfortunately, a pair of remote but still coupled inductors aren't any textbook type of transmission line where you can just extract the parameters by inspection, you'll need to put the shapes into an antenna analysis program and extract some parameters for modelling that way. Are you really going to be using field coupled inductors at a frequency where their separation is significant in wavelength terms? – Neil_UK May 30 at 5:03
• Yes, I am interested in deliberately creating these conditions to study the loading effects of the receiver on the transmitter as the phase delay is increased. But rather than resorting to emperical methods, I was hoping that I could do some basic modeling of the system first to gain an intuitive understanding of how the various circuit parameters affect each other. Now, if the only way to do this is using an antenna analysis program to generate the parameters, what would you suggest as a starting point? I'm not familiar with any specialized RF analysis tools. – Jason O May 31 at 2:52
• Unfortunately, I'm not familiar with using those tools myself, I've only seen others use HFSS and Momentum, and be happy that I'm not! Here is where to start looking. You'll notice it's almost all commercial. Good luck. – Neil_UK May 31 at 4:59