I'm thinking of using a single center loading coil for a short dipole as described by WB6BYU here:

http://www.eham.net/ehamforum/smf/index.php/topic,14908.msg85263.html#msg85263The idea is that a single coil serves to inductively load both of the dipole arms. The dipole is fed in the middle of the coil, so a small center portion of the loading coil functions as a shunt coil for impedance matching. An illustrative image is here:

www.freeimagehosting.net/newuploads/2x8zx.pngNow, I'm scratching my head over this question: what is the optimum form factor (length vs diameter) for this coil?

The complicating factor is that functionally, we have three inductors that are magnetically coupled. Referring to the above diagram, the left half of the coil, up to the tap for the coaxial cable center conductor, serves to load the left dipole arm. The middle of the coil, between the coaxial center conductor and the coaxial braid, serves as an impedance matching shunt coil. The right half of the coil, from the coaxial shield and rightwards, serves to load the right dipole arm. The total required inductance is at 7 MHz around 20 uH or 879 ohms of inductive reactance.

So how should we analyze this coil to determine the optimum form factor?

W8JI provides some guidelines for optimum coil form factors based, in part, upon the required reactance:

http://www.w8ji.com/loading_inductors.htmHowever, in analyzing the shortened dipole system, is the "required reactance" the reactance required by one dipole leg, or is it the reactance required by both dipole legs? For one leg we only require about 439 ohms of reactance, which is seems somewhat like a "low impedance" system (hundreds of ohms of reactance), calling for a square coil form factor. If we treat the left and right loading coil segments separately and create a square form factor coil for each, then connecting the two in series gives a longer form factor, something like 2:1 length:diameter. But it's not clear if we can treat the left and right loading coil segments separately since they are magnetically coupled.

On the other hand, if we consider both dipole legs together, we get to 879 ohms required reactance, which starts to approach a "high impedance" system (more than one thousand ohms or so of reactance), calling for a longer coil form factor.

So based on some shaky logic it would seem that a longer form factor, perhaps something approaching 2:1, might be appropriate.

Opinions? Any ideas about the optimum coil form factor in this case?