Aerial & Tuning Coil Calculator 1      Calculator 2

Maximum Capacitance, Cmax Farads
Minimum Frequency, Fmin Hertz
Coil Inductance, L Henries
Minimum Capacitance, Cmin Farads
Maximum Frequency, Fmax Hertz
Coil Pitch, P metres
Coil Radius, R metres
Coil Winding, N turns
Coil Length = Diameter, D metres
Total Wire Length, W metres

Enter new values on the lines with the light brown background. Press the carraige-return key within one of these fields to calculate the parameters on the lines with the blue background.

Dialectric Constants
MaterialMinMax
Air11
Styrofoam1·031·03
Dry Wood1·42·9
Dry Paper1·53
The default values shown initially are for a Medium Wave band aerial coil. For best results, wind coils on cylinders made of a material of low dialectric constant. However, since the cylinders will be, for the most part, hollow, the material of which a coil's cylinder is made shouldn't influence the coil's inductance significantly. For frequencies up to 1·5 MHz, wind coils with Litz Wire to minimize losses due to skin and proximity effects. Above 1.5 MHz, use enamelled copper wire.

The formulae used by the calculator are:

Coil Inductance  L= 1/(4π²Fmin² Cmax)
Maximum Frequency  Fmax= 1/(2π√(LCmin))
Coil Radius  R= ³√(184000P²L)
Coil Winding  N= √(736000L/R) turns
Coil Length=Diameter  D= 2R [known as a "square" coil]
Wire Required  W= N√((πD)²+P²)

Derivations of The Above Formulae

Reference: http://info.ee.surrey.ac.uk/Workshop/advice/coils/air_coils.html

L = 0·001 × N² × R² ÷ (228R + 254l)    l = length of coil winding.
But for best results, coil length = coil diameter, so
L = 0·001 × N² × R² ÷ (228R + 254 × 2 × R)
L = 0·001 × N² × R² ÷ (736 × R)
L = N² × R ÷ 736000

The pitch, P, of a coil is the distance between successive turns.
The number of turns, N, of a coil is its length, l, divided by its pitch, P.
But for best results, we decreed that l = 2 × R (its diameter), so
N = 2 × R ÷ P     N² = 4 × R² ÷ P²
Now substitute this in the equation for L above:

L = (4 × R² ÷ P²) × R ÷ 736000
L = 4 × R² × R ÷ (736000 × P²)
L = R³ ÷ (184000 × P²)
R³ = 184000P²L
R = ³√(184000P²L)

Now knowing the value of R, calculate the number of turns required:
L = N² × R ÷ 736000
N² = L × 736000 ÷ R
N = √(736000L/R)

The amount of wire, W, required to wind the coil is the amount of wire, T, needed for one turn times the number of turns, N. If you unwind one turn, while maintaining the pitch, its length is the diagonal of a rectangle whose sides are the circumference, C, of the coil and the pitch, P, of the coil.

C = π × D     D = 2 & R
T² = C² + P²
T = √(C² + P²)
W = N × T
W = N × √(C² + P²)


©13 September 2016 Robert John Morton