Bad Ground

[mikebg]

Magnetic viscosity in frequency domain.


The experts of ex (R)EMI group think that is not correct to use frequency domain for analysis of nonlinear systems with hysteresis and viscosity effects. Despite this, I will use frequency of TX excitation for visual analysis of these effects because the frequency is involved in a web explanation:

http://peswiki.com/index.php/Magnetic_Viscosity

"I was taught it's different than hysteresis. Magnetic viscosity is frequency related. It's simply magnetic lag. The electron spins in the material don't change instantly when the applied field changes.
Okay, for a fixed field strength, it takes time for the field density to catch up, so to speak; hence, "viscosity". Whereas, hysteresis relates to varying applied field strength."

Using time domain, I will make an explanation of magnetic viscosity in frequency domain. The figure below shows partial hysteresis cycle formed by classic Pulse induction - the coil current decays starting from value Im. In the figure is noted an instant value – the point 1 which moves fast in direction from Im to zero as shows the arrow. If there is no magnetic viscosity, the induction B of point 2 will correspond to current of point 1. When the substance has magnetic viscosity, the induction corresponds to point 3 because appears lag or delay of the response. The point 3 moves to value Br as shown with arrow when point 1 moves to zero. If point 1 moves faster, the delay or lag of point 3 increases.

Now let we involve the conception for unidirectional sine induction and imagine that coil current oscillates between points Im and 0. We can make a real experiment because exsist function generators, which can add DC component to output wave. What happens when we increase frequency of oscillations? The point 1 moves faster and the lag of point 3 increases. In frequency domain that means the phase lag of induction B relative to excitation H increases.
However what happens with area of hysteresis loop when we increase frequency? I think it will decrease.

[mikebg]

However what happens with area of hysteresis loop when we increase frequency? I think it will decrease.

Partial hysteresis cycles at increased frequency.

[Tinkerer]

Partial hysteresis cycles at increased frequency.

What frequencies do we talk about? 100Hz? 10kHz? 50kHz? Sine wave?

How does this refer to impulse?

Tinkerer

[mikebg]

What frequencies do we talk about? 100Hz? 10kHz? 50kHz? Sine wave?

How does this refer to impulse?

Tinkerer

Tinkerer, I nave not an idea at what frequency the real Oz ground starts to fall the magnetic viscosity signal. My artificial substance, which I use for testing as bad ground, is described in post # 16. It starts to fall GND signal with 3 dB/oct at 1730 kHz. The frequencies above 1730 kHz are too high for metal detecting. I hope the magnetic viscosity effect of Oz ground will start to fall at much lower frequency.

I can not describe nothing with your term "impulse" because for me it is an irreal mathematical abstraction. At analog signal processing, the impulse function has infinitely high amplitude and infinitesimal duration, but has unit surface. However if we know frequency response of a linear and time invariant system, we can calculate its impulse response.

For bad ground this is impossible becase we can not use superposition; the properties depend of operating point and history. Note how large DC bias has the waveform of TX current for frequency test. It is described in post # 31, but here is its visual representation:

[Tepco]

I'm not sure i made proper measurements (or interpret results correctly), but "bad ground" substances described in post #16 may not be adequate equivalent. Actually, it is hard to reach "saturation" level, or any nonlinearity on B/H curve whit field straight produced by even most powerful MD in bad ground. This will act as a ferrite core whit large air gap, ferromagnetic particles separated by air or other substances, requiring enormous field straights to saturate. (Even in normal sintered ferrite energy is not stored in material itself, but in gap between grains, see focus.ti.com/lit/ml/slup109/slup109.pdf for example). So it is maybe better to address bad ground issue from standpoint of influence to balanced coil system (or coil parameter change, for monocoil), and then there are many more variables, but not B/H nonlinearity, just B/H loop losses. So hysteresis losses, but in linear system. Even then, this is just minor issue, part of the problem, at least for PI machines. Major issue is still the fact that moving coil over magnetized material will induce EMF, and bad ground may or may not be weakly magnetized, until detector pulse itself magnetize it strongly. Then you have trouble to distinguish this EMF from one generated by target. All ML trickery, multipulse, multiperiod, dual voltage etc. is in essence designed to attack this problem.
Btw. peswiki is not known to be reliable reference source.

[Tinkerer]

Tinkerer, I nave not an idea at what frequency the real Oz ground starts to fall the magnetic viscosity signal. My artificial substance, which I use for testing as bad ground, is described in post # 16. It starts to fall GND signal with 3 dB/oct at 1730 kHz. The frequencies above 1730 kHz are too high for metal detecting. I hope the magnetic viscosity effect of Oz ground will start to fall at much lower frequency.

I can not describe nothing with your term "impulse" because for me it is an irreal mathematical abstraction. At analog signal processing, the impulse function has infinitely high amplitude and infinitesimal duration, but has unit surface. However if we know frequency response of a linear and time invariant system, we can calculate its impulse response.

For bad ground this is impossible becase we can not use superposition; the properties depend of operating point and history. Note how large DC bias has the waveform of TX current for frequency test. It is described in post # 31, but here is its visual representation:

Hi Mikebg,

sine wave frequency of 100kHz has been used for finding very small nuggets in shallow ground, but the depth penetration has been very low.

For deep soil penetration the frequencies used are usually below 10kHz.

Pulse Induction detectors use a step function or an impulse function. At best this is a half sine wave. How can we compare this with the sine wave?
The eddy currents in the target (and the soil) are generated by the di/dt. This applies for the sine wave as well as for a step or an impulse. The same lead or lag happens, but how do we compare the di/dt of a sine wave and it's effects, with the di/dt of the step or impulse?

Tinkerer

[mikebg]

Hi Tinkerer,
Different authors measured different frequencies of maximal magnetic loss tangent for the same substance. Chart below is taken from paper
"Magnetic Relaxation and the Electromagnetic Response Parameter" by G.R.Olhoeft and D.W.Strangway
Note that the loss tangent of polycrystalline magnetite falls with 6 dB/oct after the maximum. I measured that at my artificial substance it falls with 3 dB/oct. The magnetic viscosity of my substance is far from reality.

[Tinkerer]

Hi Tinkerer,
Different authors measured different frequencies of maximal magnetic loss tangent for the same substance. Chart below is taken from paper
"Magnetic Relaxation and the Electromagnetic Response Parameter" by G.R.Olhoeft and D.W.Strangway
Note that the loss tangent of polycrystalline magnetite falls with 6 dB/oct after the maximum. I measured that at my artificial substance it falls with 3 dB/oct. The magnetic viscosity of my substance is far from reality.

Hi Mikebg,

now you really got me lost. Above you work with 1.73MHz and now you are down to very low frequencies again?

Tinkerer

[mikebg]

Magnetic viscosity and Lissajous oval

"A pure phase shift affects the eccentricity of the Lissajous oval. Analysis of the oval allows phase shift from an LTI system to be measured."
Source:
http://www.enotes.com/topic/Lissajous_curve

How this relates to bad ground with magnetic viscosity?
First, the ferromagnetic properties make the system nonlinear.
Second, the magnetic viscosity makes the system time variant.
Third, the Fourier transform is not applicable to a system that is not LTI system, so we can not talk about the phase shift.

However, look at the oval in posting #32 and the figure of Lissajous below. We can measure the diameters of the ellipse on the oscope and calculate the phase difference between TX current and the GND signal induced in the RX coil.

[Sergey_P]

Ej=-dФ/dt =-((w*X*V*N*Nr*S*C*Im)/2R)*cos(wt)
Er=((w^2*Ω*V*N*Nr*S*C*Im*мю)/2R)*sin(wt)
http://md4u.ru/forum/viewtopic.php?f=77&t=4788&start=75

[mikebg]

Hi Sergey, you are welcome in this forum.
Your formulas relate to LTI (Linear Time Invariant - "линейная и инвариантная во времени") system.
Unfortunately, the bad ground forms with target very nonlinear time variable system. If you try to analyze such system with frequency functions, you should express the generation of harmonics without to use superposition and describe the role of operating point on the system properties.
I think, we should make a lot of tests and measurements according the block diagram of the system which shows signal flow. To find the optimal method for signal processing, we should know how signals are generated and what role plays the bad ground in the block diagram of the system. Let we make a drawing of the block diagram.

[Sergey_P]

we should make a lot of tests

– wherefore? We do not know the actual level of soil reaction to compensate for
Form - a historical response of soil ( Ej =f(X,w), Er=f(Ω,w^2) )

[Sergey_P]

The energy spectrum of the ground, G = G(B1) + G(B2) + ... sum of the spectra with different values of the field
PI is not possible to describe the energy of the signal ground
In the IB - the phase spectrum

[mikebg]

The energy spectrum of the ground, G = G(B1) + G(B2) + ... sum of the spectra with different values of the field
PI is not possible to describe the energy of the signal ground
In the IB - the phase spectrum

Sergey, in frequency domain we can sum magnitudes only if they are expressed in decibels. Designers use this method to avoid multiplication when calculate frequency response of a system with several stages.

The problem at bad ground is that signal passes twice the soil. We don't know excitation spectrum because soil excites target and we don't know how soil distorts target response transfering it to RX coil. I will explain this with two block diagrams in time domain and in frequency domain.

If you have difficulties with machine translation from Russian in English, post me the Russian text via e-mail. I will return it via e-mail in English.

[mikebg]

THE BLOCK DIAGRAM OF SENSING SYSTEM

Below are shown two block diagrams of the sensing system with target. The upper one is valid for all types sensyng sistems (linear, nonlinear, time invariant, time variable). The lower block diagram shows a LTI system which can be analyzed in frequency domain.

Description in time domain:

A time varying signal TX(t) excites with magnetic field the ground with target. We can make identification of target (block 2) if we know its impulse response h2(t). To calculate h2(t), we should know the input signal x(t) and the output signal y(t) of block 2 because we know that
y(t)=x(t)*h2(t)
where the sign * means convolution (свёртка) - an integral math operation (search the web for details). For calculation of h2(t) we should make deconvolution (обратная свёртка) - a complicated math operation.
At air test we know x(t) and y(t). The air test is specific case of measurement when h1(t)=1 and h3(t)=1.
The block diagram shows the common case (when the target is buried). Then the output of block 1 (input ground) excites the target (block 2) and output of target (signal y(t)) excites the block 3 (output ground). As result we receive a very convolved TGT signal from block 3. If we know only the TGT signal and TX signal, we can not calculate the deconvolution of h2(t).

Analyzis in frequency domain
(if the system is LTI)
A TX current containing suitable frequency spectrum excites with magnetic field the ground with target. We can make identification of target (block 2) if we know its frequency response H2(f). To calculate H2(f), we should know the input signal X(f) and the output signal Y(f) of block 2 because we know that
Y(f)=X(f).H2(f)
where the sign . (point) means multiplication. For calculation of H2(f) we should make division of two functions - a simple math operation:
H2(f)=Y(f)/X(f)
We know X(f) and Y(f) when we make air test. The air test is specific case of measurement when H1(f)=1 and H3(f)=1.
The block diagram shows the common case (when the target is buried). Then the output of block 1 excites the target (block 2) and output of target excites the block 3. As result we receive from block 3 a TGT(f) signal which is multiplication of several frequency responses. If we know the shape of frequency responses H1(f) and H3(f), we can calculate the shape of H2(f).
To know the shape of H1(f) and H3(f), we should receive a separate GND signal. A method for making this is illustraded in the lower left corner of the figure. A reference coil REF is positioned in induction balance to TX coil. Balance means AIR signal is zero, ie it receives only GND signal.
However if the ground has conductivity, H1(f) and H3(f) have different shape. We should make measurements to see if H1(f) and H3(f) differs in shape.