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TCAC Air Coils Inductors, Spring Coils

Winding Formula & Q Factor

Single layer air coil winding formula Methods and Increasing Q Factor

The following single layer air coil formula is most accurate when the coil length is greater than 0.67r

and the frequency is less than 10 MHz. As the frequency goes above 10MHz, the formula becomes less

accurate, because parasitics dominate the circuit. In all cases, the length is 4 times the radius.

Formula in Inch Units: L = r2N2 / (9r + 10A); N = (L(9r + 10A) / r2)1/2

Formula in Metric Units: L = 0.394r2N2 / (9r + 10A); N = (L(9r + 10A) / 0.394r2)1/2

Where:

● L = inductance (in microhenries).

● r = radius of coil (in inches or cm).

● N = number of turns.

● A = length of winding (in inches or cm).

The Q or Quality Factor of an inductor is the ratio of its inductive reactance XL to its series resistance

RS. The larger the ratio, the better the inductor.

Formula: Q = XL / RS, Where:

● XT = 2πƒL. where ƒ = Frequency (Hz); L = Inductance in Henries.

● RS is determined by multiplying the length of the wire used to wind the coil by the D.C. resistance

per unit length for the wire gage used.

● Q changes dramatically as a function of frequency.

● At lower frequencies, Q is very good because only the D.C. resistance of the windings has an effect

which is very low.

● As frequency goes up, Q will increase up to about the point where the skin effect and the combined

distributed capacitances begin to dominate.

● From then on, Q falls rapidly and becomes 0 at the self resonance frequency of the coil.

Increasing Q of Inductors:

● Spread the windings. Air gaps between the windings decrease the distributed capacitances.

● Use a ferrite core or powdered iron to wind the coil on. This will increase the permeability of the

space around the core.

● Decrease the series resistance of the windings by increasing the wire gage used. Larger wire has a

lower resistance per unit length.

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Version 2010

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TCUT20183P Datasheet(PDF) 72 Page - Token Electronics Industry Co., Ltd.