Dusting off my old EE knowledge, and reading on the web (I went to OSU and we all used the Kraus book -- but mine is locked up somewhere in a basement with the Art of Electronics), I came up with the following.
My main references were:
- Microchip AN678
- http://www.circuits.dk/calculator_multi_layer_aircore.htm, and
- Practical Electronics for Inventors which was the closest thing I could come to the Art of Electronics on the Kindle.
The question I was trying to answer was: "If I just build a bigger coil, how much distance can I get?"
First, I used http://sagemath.org to solve for the magnetic (B) field as a function of coil radius (a), distance(r), turns (n), and current (I). This gave me:
The values I observed for the actual coil as a maximum read distance were:
Name Value Units
I 0.0369927705564946 Amps
n 71 turns
a 0.06 m
u (4.00000000000000e-7)*pi Henry/meter
So, I have a B-field of 3.74583992365717e-6. I'm going to take that as the required B-field.
Graphing the above equation for different values of coil radius, gives this graph:
If you believe this, it basically says that increasing the radius of the coil will increase the B field a tiny bit. But not enough for my needs. Note that as you increase the radius, you need to wind more turns to maintain the required inductance for the ID-3LA. This is good from the standpoint of generating a B-field, but bad from a cost standpoint.
So, my belief is that to significantly increase the distance, I'm going to need more current or more inductance. Here's a graph with some options:
So can I design a circuit with 10 * the current (or close) and a radius of 0.25? Or maybe more current and more inductance? I'll have to look into it.
If anyone comes across this and sees an error (which wouldn't surprise me), please let me know.
(For more detail, I've attached a pdf of the sage calculations here.)