Invisible dog fence

A while ago I read about invisible dog fences.
It could be a usefull project for people who own a dog (I don't).
All I want to know is how they exactly work.
I can find very little info on the net about designing one yourself.
What I know is that you have to dig in a single core wire ~5cm deep, all around the perimeter of your property.
When the dog comes too close to that wire, a receiver inside a collar will warn the dog with sound.
And then zap him if the warning did not work.
The dog has to be trained to stay clear of the wire ofcourse.
I have seen 7khz and 10khz collars on the net, but that could be the modulating frequency instead of the carrier.
I have seen DIY fence transmitters with 1Mhz crystals in them.
Seen AM and FM systems mentioned.
I have designed/build hearing aid loops, but AFAIK the field is the strongest INSIDE the loop.
These fence systems claim activation only NEAR the wire.
Throw me a bone.

Changing current flow in the fence wire makes a signal that is weak but the loop that catches it can be as big around as the collar.

Look up the Faraday-Lenz Law.

Yes, know about induction. Just looking for the best frequencies to use.
Just a constant 10khz signal, intermittend 10khz signal, 10khz signal modulated onto a higher frequency carrier, etc.
I just thought a 10khz signal would not have a sharp strong field near the wire, but a more uniform field inside the loop.
Basically confused about the "footprint" that certain frequencies have .

The higher the frequency, the stronger the signal since strength has that divided by delta-T term.

The collar chip has to know and be able to pick up the frequency. 10k is not bad for Arduino as far as being able to keep up and still output to a buzzer.

One of my nephews had one of those for his Pitbull, a very smart dog, and it worked.

The higher the frequency, the harder it is to get some current in a very big loop.
I remember hearing loop amplifiers have current feedback to equalise the current difference across the audio spectrum.
Trying to calculate the resistance of a 200meter diameter single loop (partially inground) @10khz.
I get ~125ohm, PLUS the wire resistance.
I think the sharp dip (field reversing) on top of the wire is used for detection.

This would be on-off frequency and for sure it's going to take more power in to get more out.

Try raising the voltage and switch it through a FET? Power companies use high voltage, high frequency to reduce power losses over long distances then bring those down at the pole before you get house AC. I don't think that frequency makes an intrinsic problem but maybe higher voltage is required.

All else I can say is why not run some tests?

High voltage is not an option.
This wire lies 5cm underground, and a bit of gardening shouldn't get you killed.
I think 48voltAC is the legal limit, but I can feed that at both ends of the loop out of phase.
That doubles the voltage and current in the loop.
Like driving a motor with an H-bridge.

I just thought a 10khz signal would not have a sharp strong field near the wire, but a more uniform field inside the loop.

The frequency is largely irrelevant.

Whilst most of the diagrams one can find are rather vague on the matter (being more illustrative than accurate), I would be pretty sure that the field is progressively stronger near the wire (according to an inverse - not square - relationship). This may be cancelled out when "loops" are in effect, stacked to form a solenoid which does have a more uniform internal field. You can easily test this out with a wire, a power supply and a compass.

That said, if the collar is mostly vertical, it will be crossed to the orientation of the loop until the dog approaches, with maximum coupling directly over the loop wire itself.

I think there are limits when frequency increases.
Higher voltage (not allowed) to get some power into the loop is one of them.
And with a 400meter wire, there will be phase issues if you have to feed the loop at both ends out of phase, e.g. with a simple H-bridge.

I just found this paper with facts and formulas.
"If we scan along line Z1 in Fig.1, we will get a component of very high value close to the wire, and weakest in the middle. If we scan along line Z2, we will find that now we meet a "null" in the field nearly above the wire."
I think this part explains what I was basically looking for.
The best way of detecting if the dog is near the wire.
There must be some sort of 3-D pickup coil system inside that collar, because the dog can approach the wire in two ways.
Walking in the length of the wire, and approacing the wire perpendicular.

Good article.

Well - I have to say that! It seems to confirm precisely what I said - the field is much stronger near the wire (inverse or hyperbolic proportion), and a pickup loop in a collar held vertical will be maximum directly above the wire (unless the dog is standing parallel to the wire.).