catalyst:
Well, skin depth might be part of the answer, but I also wonder if it doesn't have something to do also with how the current density is distributed across the width of the transmission line.
Did you look at the current density generated by Sonnet Lite at the different frequencies? If you notice the current density at 0.1 MHz (100 kHz), you see (even with the low resolution of 2 cells across each trace width) that the current is more or less evenly distributed across the entire line width, except at the corners.
Then, look at the current density at one of the higher frequencies (like 2.5 or 5 MHz). You can see how the current is starting to exhibit the "current crowding" effect, where more current seems to flow on one edge of the winding trace than another. It appears to me that most of the current spends most of its time on an inside edge (see the first 3 windings or so).
Now, considering these two effects, think about the "average" path length taken by the total current at each frequency. At the lower frequency (0.1 MHz), the "average distance" traveled by the current through the inductor seems to be a little bit longer than the "average distance" traveled by the current at a higher frequency. I might postulate that the apparent longer distance traveled by the current at the lower frequency could look like a larger inductance if you view the behavior from the port.
The current crowding effect is interesting. How quickly it happens (with respect to rising frequency) for an open transmission line usually depends on the loss of the metal, skin depth loss, and to some degree the self inductance per unit length of the transmission line itself. There are a few interesting references out there that explain why this happens in microstrip. Here is one from the Sonnet Software web site:
https://www.sonnetsoftware.com/support/downloads/techdocs/MTTmagMetalLoss1.zip
Other references they cite on this effect are:
A. R. Djordjevic, and T. K. Sarkar, “Closed form formulas for frequency-dependent resistance and inductance per unit length of microstrip and strip transmission lines,” IEEE Tran. Microwave Theory Tech., vol. MTT-42, No. 2, Feb. 1994, pp. 241-248.
F. Schnieder, and W. Heinrich, “Model of thin-film microstrip line for circuit design,” IEEE Tran. Microwave Theory Tech., vol. MTT-49, No. 1, Jan. 2001, pp. 104-110.
In essence, this is what they say:
At really low frequencies, the skin dept is very deep, much deeper than the metal thickness. At these frequencies, the matel appears to be electrically very thin. The edge singularity (as they call it) doesn't show up and loss is constant with frequency. Pure resistive loss effects dominate where the current goes, and we know from basic theory that the electrons will spread out as much as possible to minimize loss. Therefore, the current is nearly uniform across the transmission line.
When the frequency goes up to where your metal thickness is about 2 skin depths thick or less, then what happens is that the inductive reactance per unit length of the transmission line becomes comparable to, or greater than the resistance per unit length. As the reactance begins to dominate, the electrons begin to move to the edges of the transmission line. Apparently the forces that cause this are greater than the desire to stay uniformly distributed.
The interesting thing about spiral inductors is that they frequency have winding-to-winding interactions. The interaction between multiple turns apparently influences the field behavior so that the current is "crowded" to one side of the trace or the other, thereby changing the effective path length for the current.
This crowding effect is also something that I think has a major effect on inductor Q. If you think of the metal as a resistor, you can see that forcing more current through a smaller part of the metal would effectively raise the equivalent series resistance of the inductor. If you could find a smart way to counteract the way that current wants to flow on one edge of the inductor trace or the other, you would probably unlock a secret to raising the Q of your inductor.
I hope that some of this is useful or helpful.
--Max