The technique given at A method for estimating the impedance of a ferrite cored toroidal inductor at RF can be used for the design of common mode chokes that use toroidal ferrite cores.
A ferrite cored toroidal inductor has important characteristics that make design a challenge:
(1) is dealt with by using the correct complex permeability in calculations.
(2) has little effect at less than say one tenth of the lowest self resonance frequency, and up to about half that first self resonant frequency can be modelled reasonably well by a small equivalent shunt capacitance.
This article offers several spreadsheets for design of chokes using various ferrite mixes, all of which are potential candidates for a general purpose HF balun for use with an ATU. The spreadsheets contain examples of conventional multi-turn chokes, and the #43 sheet contains a model of a W2DU choke using 25 cores.
The spreadsheets allow specification of an equivalent shunt capacitance (Cs), which has a marked effect on the performance for most practical configurations. Typical values of Cs range from below 1pF to more than 3pF for untidy construction, metal enclosure, coax and crammed cores. Input cells are yellow, and green cells are calculated results and should not be edited.
As mention earlier, these devices are really resonators and exhibit self resonances. Up to perhaps twice the first self resonant frequency these effects can be modelled reasonably well by a small equivalent shunt capacitance.
So the first step is to carefully measure the first self resonant frequency of a prototype, carefully meaning to ensure that the test fixture is not disturbing the thing being measured. Then calibrate the model by adjusting the value of Cs in the spreadsheet to obtain the same first self resonant frequency as measured.
The calculated Zcm can be plugged into an NEC model of an antenna system (as a load element), and common mode current and power dissipation will be calculated by the model.
The spreadsheets use VBA macro functions which you must permit, and complex number functions from the Analysis ToolPak add-in that comes with Excel.
The files for various materials can be downloaded at: Zcm* files .