I recently stumbled upon the “Wonder wand tunable counterpoise” and thought to build it at my own.
After a few hours of research I couldn’t find any article or video of a circuit or a picture of the open device.

Maybe there is only a varaible extension coil in it.

In my opinion, ‘tunable counterpoise’ is an oxymoron and confirms what I wrote elsewhere [links below] that nowadays the terms counterpoise and radial have become synonymous. A pity. In their original meanings, both provide an artificial ground plane but do it differently.

I’ve been doing some research on this very topic recently, in connection with a project I’m working on. From my understanding, radials are added to a (GP) antenna in order to provide “the other half” of the antenna when the GP is only 1/4 or 5/8 lambda long. In other words, the radials - typically around 1/4 lambda long - form an integral part of the antenna.

A counterpoise, on the other hand, provides a means of transforming the impedance of an antenna at the feed-point to as close to purely resistive as possible. For instance, a 1/2 lambda vertical has a feedpoint impedance of between 1500 and 3000 ohms resistive or more, and a reactance which varies with the length of the counterpoise. Many designers and builders have found by trial and error that, for 1/2-wave verticals and generally for EFHW antennas, a counterpoise of ~ 1/20 lambda provides the closest approximation to a non-reactive impedance as is practical. This can be seen in this chart which plots impedance against counterpoise length for a 1/2-wave vertical antenna (values derived empirically using a NEC v4.2 engine):

where the dashed “Optimum” line at x=0.05 (1/20 lambda) shows where the red curve (“Impedance, Reactive”) most closely approximates a zero reactance, i.e. a counterpoise of this length presents a nearly purely resistive impedance at the feed-point, while at the same time minimizing the resistive component. The counterpoise could consist of either:

a separate length of wire 1/20 lambda long, or

a section of the coax, choked at 1/20 lambda from the feed-point.