Calculation of single-layer inductors in the Coil64 app

The Coil64 application allows you to calculate 4 types of single-layer winding.

1. One-layer close-winding coil;
2. One-layer coil with winding pitch and round wire;
3. One-layer coil with winding pitch and rectangular wire;
4. One-layer coil with a winding pitch, with a round wire wound on a polygonal former;

In all cases the one-layer inductance coil is calculated as the single layer RF coil with an arbitrary winding pitch. In the close-winding coil case, it's assumed that the gap between adjacent turns is equal to twice wire insulation thickness.

Note! The wire diameter with insulation cannot be less than the nominal diameter of the wire. The winding pitch cannot be less than the wire diameter with insulation.

You can see the result of the example calculation:

In the results section one can see the calculated number of turns or inductance, depending on the calculation tab. The total length filled by the winding on the former is calculated, the length of the wire required for winding, its weight in grams. DC wire resistance, coil reactance, parasitic self-capacitance, self-resonant frequency, constructive Q-factor of the coil are also calculated. In the interface tab of the application settings, you can specify what information should be shown in the output field.

The equivalent series resistance ESR corresponds to the following lumped element model of the inductance coil.The following expression is true: ESR = R_dc + R_ac Where R_ac is the AC loss in the coil at the working frequency. The calculated input data for the LTSpice app correspond to the following coil model assumed in that program:According to this circuit, the series resistance is equal to Rdc, the parallel capacitance Cp is equal to the stray self-capacitance of the coil Cs, the parallel resistance Rp determines the AC losses in the coil. The Rp is related to the Rs=ESR and Q-factor of the coil by the following conversion formulas:

It is assumed that the working frequency of the inductor is much lower than its self-resonance frequency. Otherwise, the coil cannot be considered as a lumped elements model, but as a transmission line model. At frequencies close to the self-resonance, the inductance, self-capacitance, and losses in the coil are highly dependent on frequency, and above the self-resonance, the coil cannot be considered as an inductive element in principle.
So, if you see the warning "Working frequency > 0.7 * Coil self-resonance frequency!" - this is not a some mistake. In this case, the coil is working at an unacceptable frequency near or even higher its self-resonance frequency. This means that part of the calculations loses its meaning and they are not shown, and the remaining calculations should be considered only as estimates. To correct the situation, you need to either reduce the working frequency or reduce the dimensions of the coil.

Related links:

• Agreement on the dimensions and notations;
• Single-layer air core coil winding formulas;
• Calculation of the single layer RF coil with an arbitrary winding pitch;
• Inductor with non-circular winding;
• About Q-factor of RF inductance coil;
• The self-capacitance of a single-layer air core solenoid;
• The self-resonance frequency of the solenoid;
• Parallel resonant LC circuit;
• Bandspread capacitors;
• How to calculate single layer LC-circuit coil in Coil64?