After (nearly) overheating my computer from running LTSpice simulations, I learned that a 0.1uH inductor wouldn't cut it for my needs, but a 22nH inductor will work since I am dealing with around 433Mhz.
I have looked on ebay for some and since I don't do smd, the others I found are air core and tuneable. Just by looking at air core I feel I could make one myself.
Since 22nH is such a small number, is there an equation I can use to calculate inductance if all I used to make the inductor is a flat piece of 22awg shielded (i think steel here since the wire color is silver) wire with maybe 5mm of shielding stripped off each end?
Once I know the perfect length, I will then make a U shape out of it and hook it onto the circuit board through-hole style.
I understand I can make one from a circuit board itself but I want to go against that option because if I need to change the inductor value later, its much cheaper for me to replace the wire with one of different size than to replace an entire circuit board.
Hello there,
For a square shaped loop missing one side (the feed side) the total inductance is the self inductance minus the mutual inductances and this comes out to:
I=4*L*asinh(L/p)-4*sqrt(L^2+p^2)-2*asinh(1)*L+2^(3/2)*L-2*L+4*p+1/2
where p is the radius of the wire, L is the length of one side of the square, and I is the inductance in nanoHenries.
All length dimensions in centimeters.
Since the radius of a 22 AWG wire is 0.03226 if we substitute that in for p and solve for L when I=22 we get something close to 1.6cm
This is the open circuit inductance so the closed circuit inductance will be somewhat less because of the unknown extra mutual inductances of the rest of the circuit but that gives us a starting point.
The shape is 1.6cm up from the board, across 1.6cm, and down 1.6cm, forming a square with one open side (the bottom side).
The construction is fed from both ends, with the joining wires or traces meeting the square loop at right angles.
That formula is a direct result of the application of the Biot Savart Law so in theory it is exact, however as mentioned circuit conditions change it a little, as is usual for small inductances. This has to be dealt with in an application specific manner based on the physical layout.
For information about Biot Savart as well as a solution see my article on that topic right here on ETO.