PI holes

[Qiaozhi]

One GB newbie question: the 1/t ground response is opposite or same polarity as a conductive target? Thanks!

If you're talking about a PI detector with a mono coil, then all targets (including ground) have the same polarity. The coil current decay time can only increase in the presence of a target that supports eddy currents. It will never decrease.

[Teleno]

Thansks Qiaozhi. Any suggestions on how to model ground response in LTspice? Any readily available material suitable for experimenting with GB in the lab?

[Davor]

You'll find my attempt on modelling viscous ground - if that's what you seek. You'll find it here: Target models for simulation
Viscous ground is what is referred to as "ground" in PI world. There are two other effects that are short lived in PI and usually dissipate before you start sampling, permeability and conductivity.

[Teleno]

Yes Davor, I was referring to viscosity.

As I understood from the papers I've read, the demagnetization (down-pulse response) of one single magnetic domain with one single tau is M0*exp(-t/tau), where M0 is the initial magnetization proportional to the top coil current I. in other words. k*I*exp(-t/tau). Thus the current I effectively "charges" the magnetic domain. When integrating over a continuous range of tau's you get the 1/t equivalent that is so popular.

In a conducting target the "charging" is not caused by I, but by dI/dt. The form is k*dI/dt*exp(-t/tau). The Rx voltage is one time derivative of I more than the ground response.

Now if you model ground response using inductors you're one time derivative further than where you want to be. This wouldn't be of much concern if dI/dt is constant (the coil discharge is linear and you're not comparing responses between different fly-back voltages), but if not then you get wrong results.

I was thinking along controlled sources where you can define the coupling with the best math model available to you.

In the Laplace domain the transform of the first derivative of k*I*exp(-t/tau) is k*I*(s/(s+1/tau) - 1). The integral over a range of tau's would be the ground response.

[Qiaozhi]

Thansks Qiaozhi. Any suggestions on how to model ground response in LTspice? Any readily available material suitable for experimenting with GB in the lab?

As Davor said - you can use his model for viscous ground in a simulation.
In the lab you'll need a grid of ferrite cores. The cores should all be the same type, otherwise your emulated ground will be non-homogeneous.

[Teleno]

In the lab you'll need a grid of ferrite cores. The cores should all be the same type, otherwise your emulated ground will be non-homogeneous.

It is my understanding that real ground contains a range of grain sizes with a range of tau's, but ferrite cores are basically one grain size and one tau. I would then expect an exponential decay rather than 1/t as in real ground.

[Davor]

You can also replace di/dt with simple e because L is ~ constant. It also turns your focus where it matters - your coil as a probe. There is also a great deal of averaging in terms of domains being small, and a coil being large.

WM6 uses expanded clay aggregate instead of ferrite cores.

[Teleno]

Regarding modeling, LTspice has controlled sources that take a Laplace transform in their definition. It would suffice to insert such a controlled voltage source in the coil circuit, one that depends on the I in the coil and the transform.

Problem is L{1/t} is not defined. But 1/t is just an approximation of the integral -exp(-t/tau)/tau between tau = t1 and tau =t2, where t2>t1, so you can use a finite sum of exponentials with a range of tau's like Davor did.

Syntax: Gxxx n+ n- nc+ nc- Laplace=<func(s)> + [window=<time>] [nfft=<number>] [mtol=<number>]

Would look something like: G1 n+ n- nc+ nc- V = i(L1)*1e-2 Laplace=(s/(s+1/1e-6)+s/(s+1/1e-5)+s/(s+1/1e-4)+s/(s+1/1e-3)-4)/4
but using more tau's.

That said, I haven't tried this yet

[Qiaozhi]

It is my understanding that real ground contains a range of grain sizes with a range of tau's, but ferrite cores are basically one grain size and one tau. I would then expect an exponential decay rather than 1/t as in real ground.

The obvious "best solution" is to get a largish sample of the soil of interest. PI detectors tend to ignore mild to medium ground anyway, due to the way they work. However, highly mineralized soils (the sort that sticks to a magnet) are a different matter. You'll probably just have to do the experiments to see what works, and what doesn't.

[Teleno]

A screenshot of my Laplace soil model and a log-log plot of the signal at the coil:



Should add more tau's for better log linearity.

[Davor]

Maybe not.
What I see in your model is that there is a little offset which is easily remedied by removing it from a plot, say, V(N003,Vdd)-0.005
Also to confirm the 1/t behaviour, you should put log time scale as well. If it runs linear from 10us to 1s you're on.

My model is a little too perfect, as it is reported that 1/t works as advertised only up to 100kHz or so, and for any practical purposes you'd need to go down to 1Hz, not more. I added a few taus too many upwards from 100kHz.

I used Laplace in LTspice before to play with some all pass filters. Their only problem is that you can't do much more than by using common components. 1/t is one example of a function that wouldn't come peacefully, and the only sound way of doing it is by combining several taus, as you noticed.

I also use voltage and current sources for some clever models, say vari-L. It is handy for testing a circuit with a coil in varying permeability conditions. I even tried to model viscous ground that way by applying equations with powers, but the problem came in form of infinite values at zero time which is not what happens in nature. It served its purpose for a time, but it was not that good.

The model I came up with uses lumped elements, and is easy to build and tune. Using Laplace functions of s should lead you in a same direction, yet in a bit cryptive way for a less seasoned engineer.

[Teleno]

According to this paper ground response is A*(1/t - /(t+T)), where A is a constant and T is the pulse width.

On chapter 3.3 the authors tell target from ground by calculating the "A" that minimizes the error between the viscosity model and the received signal. A larger misfit is a target, the opposite is ground.

Now, when T -> 0 so does the ground response. The shortest T for your intended target is therefore the best choice. Constant current TX will be necessary for short pulses for targets such as small gold.

[Davor]

If you pay a close attention to Figure 3.2: Effect of pulse length on the ferrite decay, you'll see precisely why you need long constant charge pulse to achieve perfect ground balance. Most probably this effect is responsible for different values (other than 1/t) for ground response reported in various sources. This effect is also seen in my spice model of viscous soil.

[Teleno]

Long pulses maximize ground effect. Is this desirable?

It follows from fig. 3.2 that for early sampling the deviation from 1/t is minimal, so it's predictable by an estimate of "A".

The log-uniform distribution of taus (see 2.1.3) means most of them are packed on the smaller tau values, so cutting off the larger taus has almost no effect at early time.

I believe the "other than 1/t" responses are caused by the real pulse shape differing from the ideal rectangular current pulse the 1/t approximation is extracted from. Eq. 3.29 on page 18 taskes into account all of these factors.

[Qiaozhi]

The bottom line is in the conclusions:
"While the differential measurements trialed in this SEED did not result in an appreciable improvement
in soil compensation techniques, the study did considerably improve the UXO community's understanding
of magnetic soils."

By the way, something went wrong when you posted the soil model equation.

The soil model is defined as:
which demonstrates the effect that different TX on-times have on the response.