# Cone-shaped roller inductor

*Pieter-Tjerk de Boer, PA3FWM pa3fwm@amsat.org*

(This is an adapted version of part of an article that I wrote for the Dutch
amateur radio magazine *Electron*, February 2015.)

In a previous installment of this series, I wrote about variable coils. In particular, I pointed out that with a normal roller inductor, the inductance increases roughly proportionally to the number turns being active. Furthermore, I described my own switchable coil, in which turns have successively larger diameters to make the inductance increase exponentially, which is convenient for use in an antenna tuner. In a roller inductor, such an exponential increase in diameter would be mechanically problematic.

However, on the radio flea market at "De Lichtmis", I found the coil shown in this picture.
It's a roller coil with turns having increasing diameters in such a way that they together form a cone,
rather than a the cylinder as in a normal roller coil.
The nice thing about the cone shape is that a line *along* the cone is still a straight line,
despite the increasing diameter.
Therefore, it is possible to have, just like with a cylindrical coil, a contact wheel rol along an axis
along the coil, as is visible in the picture (at the right).

Because of the increasing coil diameter, the inductance of this special roller coil does not increase linearly in the number of active turns, but faster than that. Measurement showed a quadratic increase. That is to be expected. The inductance of each circular turn is approximately linear in its diameter, and the latter increases linearly with the cone-shaped coil. The total therefore increases quadratically. For practical use, such a quadratic increase already gets close to the desired exponential increase.

B.t.w., this coil is rather big: the maximum diameter is 22 cm, and the "wire" has a diameter of 7 mm, resulting in a nice Q of around 250. I guess it comes from a transmitter with way more than legal amateur power...

Although I hadn't seen such a cone-shaped roller coil before, it turns out to be an old idea, mentioned as long ago
as a 1939 patent (US patent 2163644),
from which the second picture has been copied.
In this patent, the goal was to maximize the tuning range in what was called an "all-wave set" at the time.
The patent claims this coil achieved tuning ranges from 0.5 to 3.5 MHz and from 3.5 to 19 MHz.
From 0.5 to 3.5 MHz is a factor of 7 in frequency, so a the inductance must be varied by a factor 7^{2}=49.
The patent also describes a normal cylindrical roller coil suitable for this; on that one, the distance between the
turns changes, as is also done on the cone shaped coil depicted.

A nice overview of several types of variable coils can be found on http://www.g3ynh.info/comps/Vari_L.html.