Magloop Explorer equations
permeability of free space
permeability of copper and aluminum are essentially the same as free space
conductivity of copper and aluminum
if the loop shape is a circle, the area is π*r^2, if it's a polygon we calculate the area by first calculating the apothem:
radiation resistance calculation
we calculate the free-space radiation resistance (see Kraus: Antennas 2nd ed.) from the loop area and the wavelength....this is fairly accurate (said to be within 2%) for loops with a diameter < approx. 0.1λ
AC resistance calculation
we calculate skin depth from angular frequency, and the conductor's permeability and conductivity
we calculate the effective AC resistance as the wire length divided by the effective cross-sectional area of the wire (i.e. the product of the wire circumference and the skin depth) and divided by the conductivity
loop inductance calculation
we calculate the loop inductance using functions described by Grover of NBS:
sample calculation inputs
let's use aluminum for the conductor
not the best formula for this, but should err on conservative (high) side for additional cap calculation
Yes, I know this gives a different result than many calculators do. Q and VCPeak are higher, and BW is narrower. I contend that this is correct. See also Owen Duffy's discussion of this at: https://owenduffy.net/blog/?p=1682
