Two Single-Layer Magnetically-Coupled SolenoidsAuthor: R.J.Edwards G4FGQ © 11th November 2001
Pairs of coupled coils appear in RF power amplifier tanks, interstage transformers, unbalanced-to-balanced Z-matching networks and receiver preselectors.
The two solenoids have a common axis. The program allows coil centres to be spaced apart at any distance along the axis. When spacing is set to zero one coil is centrally located inside the other and the coupling coefficient versus spacing is at its maximum.
It is clear when a coil or part of a coil is inside the other the diameter of the outer coil must be large enough to provide a safe clearance between the two windings. This overlapping coil condition is indicated to the program user.
If the coil lengths are L1 and L2, one coil will remain inside the other until the spacing exceeds 0.5*(L1+L2). When there is no overlap both coils may then have the same diameter and be wound adjacent to each other on the same former.
A tuning capacitance is computed for each coil. In practice only one coil or perhaps neither coil may be associated with a series or shunt capacitor.
Of greater interest to circuit designers will be the computed values of the coupling coefficient k and the mutual inductance M. These may be of use in a later calculation of bandwidth. If particular values of k and M are needed the program allows other parameters to be varied in small increments over a wide range until requirements are satisfied.
Because k and M are of use only for later calculations it is intended to incorporate the mathematical procedures herein in a more comprehensive program for for designing circuits such as unbalanced-to-balanced antenna tuners.
IMPORTANT - The program assumes both windings have spaced turns. Computed wire diameter and wire gauge allows for a winding pitch Sqrt(2) = 1.414 times wire diameter. For a given amount of copper spaced turns handle greater power and coils have higher Q. If more convenient close-wound coils are wanted multiply computed wire diameter by 1.3 which will allow for the thickness of the enamel wire insulation. Or, subtract 2.5 from AWG.
This program can be used only to design single ordinary proportioned solenoids and is accurate enough for most purposes. For greater accuracy and more detail use program solnoid3.
Run this Program from the Web or Download and Run
it from Your Computer
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