Notes:
RF Toroid Calculator was developed to help users predict the RF characteristics of a toroid-wound inductor.

Inputs via the slider widgets:

• ⌀a : Conductor diameter slider changes AWG from 0-40.
• N : Number of turns or windings.
• f : The frequency of interest (MHz) for some of the calculations.
• Vrms : The RMS voltage applied to the inductor (Volts).

Characteristics on the left are independent of frequency, while the characteristics on the right are dependent on the selected frequency.

Each of the graphic representations attempt to keep the relative geometry correct, without exceeding the drawing boundary. The coil diameter relative to the conductor diameter are representative.

Calculated dimensions:

• ⌀o : Outer loop diameter (inches)
• ⌀i : Inner loop diameter (inches) - corresponds to the diameter of the winding former.
• c : Distance between windings, measured from the conductor centers (inches).
• ℓ : Length of the coil (inches). Equal to c x N.

Calculated parameters:

• L : Inductance is calculated using Nagaoka's equation incorporating his coefficient.
• C : Capacitance is calculated using Knight's 2016 paper on self-resonance and self-capacitance of solenoid coils.
• Rdc : DC resistance is calculated using conductor length divided by the conductor cross-sectional area, assuming a copper conductor.
• SRF : Self-resonant frequency (MHz) for the unloaded coil. Currently using a lumped reactances model. (Looking into modifying the model to use the conductor length and velocity factor as described by Knight (2016).
• Xₗ : Inductive reactance at the given frequency. (Ω)
• |Z| : Impedance at the given frequency. (Ω)
• δ : Skin depth due to skin effect (μm)
• Rac : AC resistance is calculated using the skin effect and proximity resistance from empirical data collected by Medhurst using the spacing ratio, and length-to-diameter ratio.
• Q : Quality factor of device, based on reactance (X) ÷ resistance (Rac) at the given frequency.