spiral inductor on pcb
The spiral inductor gets its "main" inductance from the physical properties i.e number of turns, width, spacing. But coupling between the different tracks of the spiral of cause influince each other. This is know as mutual coupling.
Very briefly: the sides having current flowing in same direction give positive mutual coupling, this is nice, this is why a spiral(which often is very small) can achieve relatively high inductance values. But the sides having current in opposite direction give rise to negative mutual inductance. As you can see, the inner turns of a spiral are very close and they contribute very little to the "main" inductance, because they are very short. But they introduce negative mutual inductance, because they are very close.
Because the inner turns contribute very little to the "main" inductance and the fact that the negative mutual inductance introduced by the inner can be larger than this, the inductance of the spiral remains almost the same.
Because you remove some of the metal from the spiral, you have lower losses and the Q goes up.
You can read an article by Greenhouse, I think its from the 60's. He introduces a calculation method for plannar spiral inductors with this mutual coupling. His apporach should be very precise, although somewhat difficult to program.
There are the classic formula by "Wheeler" and some formulas by other guys to design spirals, but they are only approximate. I found them as a good starting point and then used "that trial and error" :D.
I was not able to find any books with closed form exspressions that I could use.
But concerning your spirals, what process are you using?
What are the minimum spacing and width possible?
Puhh.....this was a long one.
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