This calculator takes as input:
the maximum and minimum frequencies [fmax & fmin] of your desired tuning range,
the reactance [Xmid] you want the tuned circuit to have in order for it to match with whatever it is connected to,
the coil's diameter [d]. Make this as large as you can comfortably accommodate while leaving adequate 'breathing' space around it. This will ensure that it has the highest possible Q [quality] factor.
Enter new values on the 4 input lines — those 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. The default values shown initially are for a Long Wave Amateur Band coil.
The calculator displays the following 12 outputs:
The formulae used by the calculator are:
|mid-frequency||fmid||= (fmax + fmin) ÷ 2;|
|radius of coil||r||= d ÷ 2|
|coil circumference||c||= d × π|
|angular frequency||ω||= 2π × fmid|
|inductance of coil||L||= Xmid ÷ ω|
|mid-frequency capacitance||Cmid||= 1 ÷ (ω × Xmid)|
|number of turns on coil||n||= √(736000L ÷ r)|
|pitch [dist between turns]||p||= √(r³ ÷ 184000L)|
|minimum capacitance||Cmin||= 1 / (4πfmax² × L)|
|maximum capacitance||Cmax||= 1 / (4πfmin² × L)|
|Reactance of Cmin at fmax||XCmax||= 1 / (2πfmax × Cmin)|
|Reactance of L at fmax||XLmax||= 2πfmax × L|
|Reactance of Cmax at fmin||XCmin||= 1 / (2πfmin × Cmax)|
|Reactance of L at fmin||XLmin||= 2πfmin × L|
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, Pich, of a coil is the distance between successive turns.
The number of turns, Trns, 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 = 184000P² × L
r = ³√(184000 × p² × L)
Now knowing the value of r, calculate the number of turns required:
L = n² × r ÷ 736000
n² = L × 736000 ÷ r
n = √(736000 × L ÷ 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)