Competition!

[Tinkerer]

3 time constants?
I don't know how relevant this is; with such detector and coil I will hunt only for described targets.
I am not interested in any different and larger targets then what I described already.

It might be useful to build a simple, basic PI and run some tests with it, looking at the decay curve and time constants of your desired targets.
Then you have a much better idea of what you really want.
All the targets you show, have relatively long time constants.
Silver and high carat gold usually has a long TC. Low carat gold is much more variable and often has a short TC.
A 3mm diameter lead bird shot has a very short TC. A gold nugget of similar size has a much longer TC.

If you desire a PI with the capability of detecting a TC of less that 1us, I can help you with a tested circuit, but it does not have ground balance.

[ivconic]

It might be useful to build a simple, basic PI and run some tests with it, looking at the decay curve and time constants of your desired targets.
Then you have a much better idea of what you really want.
All the targets you show, have relatively long time constants.
Silver and high carat gold usually has a long TC. Low carat gold is much more variable and often has a short TC.
A 3mm diameter lead bird shot has a very short TC. A gold nugget of similar size has a much longer TC.

If you desire a PI with the capability of detecting a TC of less that 1us, I can help you with a tested circuit, but it does not have ground balance.

I am always in mood to see new schematics, kinda type of "insanity", already have tens of GB of such documents.
But those are never enough!
So yes, post it.
At this moment I have here in my "collection" Barracuda, Pulse Star 2, probably few other simpler PI detectors.
Barracuda is nice little diy. Pulse Star 2 is "heavyweight" category, yet without GEB.
I was thinkig to figure out GEB circuit for both, also auto-zeroing circuit too.
Long story short; yes, do post what's on your mind.
Next question; describe in steps, using oscilloscope: hot to determine/measure accuratelly TC at targets?
I don't have digital one with textual values on the screen. I do have analog one, good though, brand new, bought it back in 2019. 2X20MHz.
With such oscilloscope you can see the signal fine even which those cheaper digital ones can't.
But it will need math to add to what you see on the display.
It would be good for all other layman members too; somebody to explain step by step such measurements and math.
You see flyback voltage, you see what's on RX frontend output, all in form of oscillograms.
But exact numbers you don't see on such simpler analog oscilloscopes.
You need to use simple math to figure out accurate TC.
So, one good explanation and step by step instruction is welcome here!

[Tinkerer]

Analog scope is fine.
Do you have a PI where you can connect your scope probes at the following places:
Output to TX coil, so you can see the TX ON, OFF and Flyback
TX Mosfet gate and timing signals
Input to preamp
Output of preamp
Input and output of integrator

Then we can look at the signals without target and with different targets and I will explain what to look for.

I could also set up an LTSpice simulation to look see how close the simulation compares with the real signals.

[ivconic]

I have Barracuda.
I can do that. These days though, next few days will be busy!
I will shot the pics and post here.

[Tinkerer]

I am always in mood to see new schematics, kinda type of "insanity", already have tens of GB of such documents.
But those are never enough!
So yes, post it.
At this moment I have here in my "collection" Barracuda, Pulse Star 2, probably few other simpler PI detectors.
Barracuda is nice little diy. Pulse Star 2 is "heavyweight" category, yet without GEB.
I was thinkig to figure out GEB circuit for both, also auto-zeroing circuit too.
Long story short; yes, do post what's on your mind.
Next question; describe in steps, using oscilloscope: hot to determine/measure accuratelly TC at targets?
I don't have digital one with textual values on the screen. I do have analog one, good though, brand new, bought it back in 2019. 2X20MHz.
With such oscilloscope you can see the signal fine even which those cheaper digital ones can't.
But it will need math to add to what you see on the display.
It would be good for all other layman members too; somebody to explain step by step such measurements and math.
You see flyback voltage, you see what's on RX frontend output, all in form of oscillograms.
But exact numbers you don't see on such simpler analog oscilloscopes.
You need to use simple math to figure out accurate TC.
So, one good explanation and step by step instruction is welcome here!

IVICA, I did the work for you. Here are the screenshots of some targets. I just slapped a 2 stage preamp together on a breadboard, quick and dirty.
The TX is a bipolar CCSQW, Continuous Current Square Wave
The coil is a DD coil, about 38cm diameter
The cycle is about 100us, that is about 10,000 Flybacks per second, 5000 positive and 5000 negative
The cursor shows the beginning of sampling at about 4.5us
Yellow trace is the TX Flyback
These are static or non motion tests

You can see that the Eddy currents decay faster or slower than the blue trace which is a US 5 cent, also called a NICKEL. The Nickel has a TC of about 10us. We use it often as reference.
The white trace is the NO Target reference.
Targets on picture 1
Red= 1 Gram gold bar
Green= very small gold ring, 0.35Grams
Blue= US Nickel

Picture 2
White trace=No target
Blue=Nickel
Red=a coin about the same size as the Nickel, made out of lead
Green, tiny high conductive coin from Netherlands Antillen
Turquoise= 26mm diameter silver coin

The pictures are not very good, first try, if there is enough interest, I will try to make better ones.
Since this is a DD coil, many iron targets give a positive response, opposed to the negative response you see with colored metals, at the same place under the coil.