# Page 1, Cylindrical, Single-Layer, Air-Core Coils of Various Proportions

Author: R.J.Edwards G4FGQ © 13th May 2003
This program assists with the design of single-layer coils having a wide range of proportions, including single-turn loops, close-wound solenoidal forms, coarse helices of thin wire, and ranging in size from miniature coils in VHF receivers to large coils used in high-power radio transmitters, antenna tuners, and RF traps.

*Program Output data*: Coil inductance, reactance,
self-capacitance, self-resonant frequency, loss resistance, Q, capacitance
needed to tune to a test frequency, resonant impedance at a test frequency,
and power dissipated for a given RF voltage across the coil.

*The program has facilities to sweep these input data
values*: Coil length, diameter, number of turns, wire diameter-to-pitch
ratio, and frequency over wide ranges using pairs of adjacent up/down
numerical keys. Refer to the menu near bottom of data screen.

"Ratio" refers to ratio of bare wire diameter to the coil winding pitch. If turns touch, the ratio equals 1, but to allow for the thickness of wire insulation the ratio is automatically restricted to 0.97 of maximum. For close-wound turns just enter 1.

Important

- Coil Diameter = diameter of the former on which the wire is wound.
- Coil Length = distance between the wire centres at the ends of the coil.

Coil Q is officially defined as the ratio (Inductive reactance)/(Series loss resistance). That is the value computed by this program. However, it is impossible to achieve that value of working Q in a practical circuit due to other losses. Imperfections in associated components such as capacitors, tubes and transistors increase the effective circuit resistance.

The resulting circuit Q of a coil with Q = Q1 in resonance with a capacitor of Q = Q2 is given by Q1*Q2/(Q1+Q2). This causes Q meters to underestimate the true Q of high Q coils at the higher radio frequencies. In fact, all direct methods of measurement reduce the effective Q of the item under test. Fortunately, high values of Q seldom need to be known with an accuracy better than approximate.

Two values of Q are computed depending on the type of circuit in which a coil may be used. The higher value applies when the tuning capacitor is connected directly in parallel with the coil as in a tank circuit or rejector circuit, such as an antenna trap. The coil's self- and external-capacitances are then in parallel.

The lower value of Q applies when the tuning capacitor is connected in series with the coil and another part of a series-resonant circuit. The coil's self-capacitance in shunt with the coil causes both the effective-inductance and loss-resistance to increase. As the operating frequency nears the coil's self-resonant frequency the circuit Q rapidly falls, for example, in frequency filters.

*Note*: Ordinary Q meters measure Q with the coil in a series-resonant circuit.

The computed self-resonant frequency is the value with the coil isolated, i.e., not within several coil-diameters plus a coil-length of any other material, either conducting or insulating. Coil wiring, components and other materials in the immediate vicinity will reduce resonant frequency by an indeterminate amount.

Page 1 | Page 2

Search other ham radio sites with Ham Radio Search