To set the scene, the TV at my mum’s house was reported to drop out due to a weak signal, apparently worse during bad weather. There was a two way 6dB amplified splitter, so I upgraded to a 16dB amplified splitter. Not good enough. The aerial was on the roof, having replaced the original aerial an indeterminate number of years ago. The aerial socket, when removed, showed two other coax cables which had been cut. The original aerial wire to the loft space was chased into the breeze block wall but I couldn’t find where it ran using an ordinary metal/pipe/wire finder. Just going straight up from the socket to the loft, and removing the loft board didn’t reveal the cut end.
I googled wire tracers, but they seem to be when you touch the cable to identify it. I needed something with more range to locate the original wire in the walls and under the loft boards.
The idea was to quickly build up something with stuff that was to hand. I tried a quick experiment using a signal generator onto a coax cable outer, using a paint stripper as a capacitive sensor into a scope. Looked easily possible, so I knocked up the circuit below, based on running the source at 3kHz. This seemed to give a loud and easily detectable sound from the headphones, as seen by just powering the headphones directly from the signal generator.
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On the bench it oscillated at around 40kHz when the headphones were plugged in. I tried two 1nF caps across the 33K feedback resistor with no success. But since that was inaudible I just let it go and carried on.

The sensor is conductive adhesive copper tape on the bottom of a piece of wood, and wrapped around the ends to both stop it peeling and to give an easy connection point. The tape on the top edge (as shown in the picture) is the ground reference ( to be touched and held by the operator).
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The left side tape is the sensor. The middle area is the ground reference, which sits under the board as a grounded shield. The battery box was left over from an LED lighting strip (which would never have worked from battery power anyway). It hangs over the edge of the wooden block to allow access to the on/off switch on the underside of the battery compartment.
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The “insulator” under the circuit board is a piece of cardboard from an A4 writing pad. I covered it with a single layer of black electrical tape to make it look as if I had thought about insulation, at least a little. The big capacitor is 2µ2 and had been in a damp shed for 40 years. The bit of wood holding the circuit board was stuck on with quick-setting epoxy, and had a groove cut in it with a saw to hold the circuit board edge.
The picture shows alkaline batteries, but high drain batteries are not required. The current drawn was 7 mA with no tone, and 8 mA with, so the battery life should be fine with cheaper batteries.
The two blue blobs are the 1nF capacitors which were supposed to be across the 33K feedback resistor. Maybe if they had been fitted in the correct place they might have actually prevented the 40kHz oscillation!

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I went back to mum’s house, armed with a signal generator, cables and the tracer. It didn’t make any sense. I apparently traced the aerial feed to the next door TV, and the feed to the next door TV to the external aerial feed. It took a while to sink in that my idea of how the cables were wired up was now how they actually were. The TV aerial socket had been rewired to be the connection to the other room. What I took to be the feed to the other room was in fact the aerial feed. How it ever worked was a mystery since the aerial was connected to the amplifier output!
Anyway, the tracer did its job, the wires were plugged in correctly and it all worked. The old 6dB splitter could not be used as it had insufficient bandwidth, and therefore lost one of the digital multiplex channels. All working.

But how could I leave this circuit oscillating?

It is an insult to my engineering skill! That is the subject of the next post …
[EDIT]: added current consumption data