Frequency dependent target response

[Aziz]

Hi friends,

we have to revisit the skin effect and the frequency dependent target response to see what really happens. It will really open your eyes and has consequences to the detector design.

This is owed to the fact, that Paul (Moodz) has made the super early sampling (super fast damping) possible. We are talking about frequencies up to 1 Mhz and more. The skin effect can not be neglected anymore. We have to enter the next level of engineering.

Targets do not have a fixed time constants anymore. At the end of the thread we will be able to model frequency dependent target responses in LTspice.

We will have lots of questions and we will solve all the problems in this journey. And we will answer the most interesting questions I think. I have to prepare some work with very limitted spare time.

Stay tuned.. big big surprise is there

Aziz

[Aziz]

Can you imagine that a massiv target lets say a time constant TC of 300 us behaves like a target of time constant TC of 12 us at 1 Mhz?
Thin aluminum foil (12 um thicknes for instance) has almost no frequency dependency (TC const).

A lot of work to be done...
Aziz

[Carl-NC]

This effect shows up in the usual decay response plot of targets:



The decay starts out with a higher slope which implies a low TC, but then settles out to a lower slope that accurately represents the higher TC. This can actually happen with any target but is more noticeable with high TC targets. I've explained what causes this to happen but since you've been gone a while I'll give you a few minutes to read the rest of the forum before continuing.

[Tinkerer]

This effect shows up in the usual decay response plot of targets:



The decay starts out with a higher slope which implies a low TC, but then settles out to a lower slope that accurately represents the higher TC. This can actually happen with any target but is more noticeable with high TC targets. I've explained what causes this to happen but since you've been gone a while I'll give you a few minutes to read the rest of the forum before continuing.

This effect does not show up with the standard simulations.
However, with real tests using the AMX circuit, using different cycle length and relatively long TC targets I see this effect.
This seems to reduce the usefulness of my planned CHIRP TX idea.

[boilcoil]

The foil not changes parameters, because by freq of 1Mhz, the scin layer of copper wire has to be about 66um - bigger then real thickness of foil (aluminium is not so different).
Hi frequency make target looks thinner.
But time constant is fixed, this is another beer.

[Aziz]

Hi all,

I see we can learn a lot. Especially regards to high frequency PI technology.
We will model the targets resistances dependent on the frequency response. Of course a simplified model of different mutualy coupled inductances of targets.

Aziz

[Carl-NC]

The effect is due to eddy current "inertia." Suppose the target is a Big Silver Coin (BSC). Initially it has no eddy currents, then an AC magnetic field hits it and creates eddies. But those eddies don't instantaneously form in their final state, they have to "grow." Due to skin effect, eddies normally penetrate the depth of the coin with an exponential decay in strength vs depth. But eddies also tend to push themselves out to the perimeter of the coin. Both of these effects take time. At t = 0+, the eddies are evenly dispersed vs depth and radial distance; this makes the BSC look like a thin low conductor. Over time, the eddies push themselves to the surface and push themselves out to the perimeter. The time it takes this to happen is about 1 tau of the target. If you look at the decay plot I posted above it is a US quarter that has a tau of about 150us. You can also see that the inertial effect takes about 150us to settle out.

This effect does not show up with the standard simulations.

In sims we usually use a single tau parallel R-L to represent a target. To simulate the inertial effect would require a more complex model.

[Tinkerer]

The effect is due to eddy current "inertia." Suppose the target is a Big Silver Coin (BSC). Initially it has no eddy currents, then an AC magnetic field hits it and creates eddies. But those eddies don't instantaneously form in their final state, they have to "grow." Due to skin effect, eddies normally penetrate the depth of the coin with an exponential decay in strength vs depth. But eddies also tend to push themselves out to the perimeter of the coin. Both of these effects take time. At t = 0+, the eddies are evenly dispersed vs depth and radial distance; this makes the BSC look like a thin low conductor. Over time, the eddies push themselves to the surface and push themselves out to the perimeter. The time it takes this to happen is about 1 tau of the target. If you look at the decay plot I posted above it is a US quarter that has a tau of about 150us. You can also see that the inertial effect takes about 150us to settle out.



In sims we usually use a single tau parallel R-L to represent a target. To simulate the inertial effect would require a more complex model.

Adding a target with a tau of 10us and a target of 150us in the simulation, gives an approximation.

With the exceptions of thin gold/copper rings, most targets behave like 2 or several tau superimposed. A shape like a cross usually has a mixture of tau that makes it hard to detect. Often gold nuggets fall into that category.

[Aziz]

Hi Carl,

yes, it describes the eddy current process a bit. But we can not simulate it in circuit desings yet. We did use a constant TC for targets.

This is an attempt to do it. In a simplified manner of a non-trivial process of course.
I will provide the data for targets inductive models and some formulas I have found in the literature (Excel table to play with).
Everybody is invited to bring his contribution to this challenge.

Aziz

[Carl-NC]

With the exceptions of thin gold/copper rings, most targets behave like 2 or several tau superimposed. A shape like a cross usually has a mixture of tau that makes it hard to detect. Often gold nuggets fall into that category.

Those are called multi-domain targets. Simple rings and coins are almost completely single-domain, while most other targets (complex jewelry, nuggets, pull tabs, etc) are not. Each domain can have its own inertial component, and the resulting composite signal can get quite messy, though there is usually a dominant response.

[Aziz]

Hi friends,

I'm using some formulas for skin depth calculations and the frequency dependent resistance of the targets. These formulas can be found in the followings links or provided in attachment (pdf).
So you can read into the matter.

Links:
https://en.wikipedia.org/wiki/Skin_effect (english wiki)
https://de.wikipedia.org/wiki/Skin-Effekt (german wiki, R/Rdc formula is of interest)

Book (sorry, it's a german book):
Karl Küpfmüller · Wolfgang Mathis · Albrecht Reibiger
Theoretische Elektrotechnik
Eine Einführung
pages 433 - 455, particularly page 438, which is uploaded here for citation, R/Rdc formula is of interest

Aziz

[pito]

[Aziz]

Thanks pito.

You have found the same formulas in english.

But there seems missing some symbols and variables.
So not a good base for us. Anyway.

[pito]

That is a google images ( JPEG ) translation

[Aziz]

Hi friends,

I'm still at it and it is getting more and more a complex and non-trivial problem. But there is a rule of life: If you can not solve a complex problem, just break it down and make it easier.

We are really dealing with heavy complex math here and will get out the smoke of the brain and write down the complex analytical model.
(Ok, just kidding. But we will try to make it easier).
It will take time. I have to read a lot of theory. Even the proximity effect is involved in our simplification model.
First of all, we have to understand the basic concept of eddy currents and the mentioned physical effects.
We will see, how far we come and make a spice model for it.

Cheers,
Aziz