X vs R

[Sergey_P]

error in your theory

Correctly: J=p*E the density of the eddy currents
Yeah, I did not consider the magnetic polarizability in the conductor and relaxation time constant of the electric charges (t=(e*e0)/p) (to simplify )

I'm not sure about the correctness of the linear model LR ( http://www.support17.com/component/c...html?task=view )

[mikebg]

R and X signals

I have outlined a lot of questions about R and X signals, made a list roll and even started to put URLs where you can find answers. However this will take me time. Better you to find answers and to put URLs in the list roll. I think you can add questions.
Here is the list roll with my questions:

• What dimension has forward transfer function T21 of sensing system for metal detectors?
• What means “mutual inductance”? What is coefficient of coupling?
• What synonimes of X and R signals uses SPICE?

http://www.geotech1.com/forums/showt...782#post101782

• How are oriented Im and Re axes of complex plane?

http://www.geotech1.com/forums/showt...595#post101595

• How are numbered the quadrants of comlex plane? What is direction of positive angles.
• How are expressed R and X signals in polar coordinates?

http://www.geotech1.com/forums/showt...669#post101669

• When we can call the complex plane - “impedance plane”?
• When was born the Frequency domain? Who is the father of frequency domain?

http://en.wikipedia.org/wiki/Joseph_Fourier

• When was given name of Time domain?

http://en.wikipedia.org/wiki/Frequency_domain

• To what domain belong terms “reactance”, "admittance" and "impedance"?
• What means AIR signal?
• What formula is used as forward transfer function of search head for AIR signal

a) in time domain? and b) in frequency domain?

• To what domain belong terms: “phase angle”, “skin effect” and “Q factor” ?
• What response is more informative for a system: "Impulse response", "Step response", "Step-down response" or "Frequency response"?
• What is the difference between “timeconstant” and “cutoff frequency”?
• What is the difference between “Q factor of a coil” and “design timeconstant of a coil”?
• What nicknames are used instead “two-port network”?
• Why Lenz’s rule is not a law? (In UK and US is used term "Lenz's law")
• What common name is used for capacitance C and inductance L in time domain? In frequency domain?
• What is the difference between “mutual inductance” and “self-inductance”?
• When we design a two-port network without to use a NETWORK ANALYZER?
• What is the number of transfer functions anlyzed by a NETWORK ANALYZER?
• What signal generates search head without target when it is placed on the ground?
• Why AIR signal has phase lead relative to TX current?
• Why permeability generates signal with phase lead relative to TX current?
• How seems the signal from an iron object in complex plane?
• (dot means "put your questions" :-)

I will start with the answer of first question using the attached image. The block represents sensing system of a metal detector. Notation T(f) means transfer functions in frequency domain (the network is described by a 2 by 2 square matrix of complex numbers). Please read in Wikipedia for Z-parameters, Y-parameters, H-parameters and G-parameters,
http://en.wikipedia.org/wiki/Two-port_network

The forward transfer function is mentioned in a lesson attached in the post:
http://www.geotech1.com/forums/showt...0563#post70563

Inside the black box are connected in series 5 stages: TX coil, ground, target, ground and RX coil.

[Humanise]

http://www.md4u.ru/download/file.php?id=14187
(RU)

Sergey,
Could you please explain to me in simple terms (hopefully without using complex as in based on square root of negative one) the terms GEB and GB as you are using in a conversation with Alex Zorg on the md4u.ru website at: (with translation to english)

http://www.microsofttranslator.com/b...a%26start%3D25

or in Russian which I can't read

http://www.md4u.ru/viewtopic.php?f=1...D0%BA&start=25

I would also like to get a user's reference to all the other items shown on his display as shown in a picture near the bottom of the page. In particular the following:

f0
Sens
Static
Diff2
Auto
Reset
R
VCO
Umax/U0
VDI
Us
Un

Also, your interpretation of what is being graphed on the left.



I'm running a later version of that same program. The only thing that has been changed on the display is 'auto' has been changed to 'auto comp'.

If anybody else can give opinions on what each of these mean, I would appreciate it.

Many thanks and Happy New Year

Ken

[mikebg]

COMPLEX PLANE

If someone has downloaded the file
"NI_Multisim_Analog_Devices_Edition_10_0_1.exe ", he can see the NETWORK ANALYZER. It represents complex plane as shown below with axes Re (real) and Im (imaginery). However there are publications where the axes are denoted as I (inphase) instead Re axis and Q (quadrature) instead Im axis. Other notation is R (resistive) instead Re axis and X (reactive) instead Im axis.

The axes divide complex plane in four quadrants named as shown in image.
A point placed in complex plane represents the value of a function at given frequency. There are a slider and two keys for movement of marker (change of frequency). Here a triangle marker is used instead point . The position of point M in complex plane can be expressed in rectangle coordinates (Re, Im) or in polar coordinates (magnitude and phase). The phase angle is measured relative to Re axis.

The pont M placed in 1st quadrant has positive Re coordinate and positive Im coordinate or its argument (phase angle) is between 0 and 90 deg. The position of point M is expressed as Re + jIm. For the given example, the marker M at freqency 5024Hz is in position 0.38 + j0.44. To express marker position in magnitude and phase, you should press a small key with triangle symbol on it.

[Humanise]

It represents complex plane as shown below with axes Re (real) and Im (imaginery). However there are publications where the axes are denoted as I (inphase) instead Re axis and Q (quadrature) instead Im axis. Other notation is R (resistive) instead Re axis and X (reactive) instead Im axis.

Mike,
I think that your phasor/vector description is the correct description of what the fat green green line is in the display of the above metal detector program written by Alex Zorg. Thank you for your description. It cemented into my mind what I was heading towards.
What I don't know yet is what is represented by the thin yellow line that goes across in the above picture at a slight angle to the X axis.

By the way, the X axis can also be thought of as the Sin Wave component of each wave and the Y axis as the Cos component. Alternatively, they can be just described as the X component and the Y components. For me, it is too many years since I studied complex maths (use of imaginary numbers) without ever having used them for me to feel comfortable with them although I feel OK with phasors/vectors but I just don't think of them as using imaginary numbers.

I'm slowing trying to take the maths I have learned relating to metal detectors and then document it in ways that don't require the use of imaginary numbers. Some of my descriptions are probably a lot longer because of it, but I think that a large number of people who like myself don't use imaginary numbers in ordinary day to day work, will find my descriptions easier to understand.

Happy New Year
Ken

[mikebg]

I'm slowing trying to take the maths I have learned relating to metal detectors and then document it in ways that don't require the use of imaginary numbers. Some of my descriptions are probably a lot longer because of it, but I think that a large number of people who like myself don't use imaginary numbers in ordinary day to day work, will find my descriptions easier to understand.

HAPPY NEW YEAR!
Hi Ken, please give a link where to read your descriptions!

Years ago, Bruce ^ C (an Australian participant in this forum with nickname B ^ C) just like you changed terms. He renamed used by me term for transfer function "frequency response" with "frequency of the target response signal".
http://www.geotech1.com/forums/showt...1389#post71389

Now you are the next Australian who change the used by me term. My term "transfer function" was changed with your term "imaginary numbers". Nowhere in my posts I use such a term, but soon will use it to explain the AIR signal.

I'm talking about a spectrum characteristic inherent to the system "Coil & Target". For easier analysis is used frequency domain. The system is presented as two-port network which parameters H, Y, Z or G are complex functions with real and imaginary part. Your term "imaginary number" means a point in the complex plane, which lies on the Im axis. The complex transfer function is a line in complex plane and each point on this line represents different frequency:
http://www.geotech1.com/forums/showt...595#post101595

My avatar is Australian actor Paul Hogan because I love Australians. So, especially for you, I change the order of my posts pulling forward the SPICE of a complex function, which consists of only "imaginary numbers". This is the AIR signal.

[Humanise]

HAPPY NEW YEAR!

Years ago, Bruce ^ C (an Australian participant in this forum with nickname B ^ C) just like you changed terms.

I'm in Melbourne which is generally a lot cooler. Here it is 41 degrees Centigrade (106 degrees Fahrenheit) today. In the outback of Western Australia where he was prospecting, the temperatures are generally more extreme. You have to be a Crocodile Dundee type to survive. I got the impression that when he was prospecting he was so far outback that it wasn't realistic to be on the Internet. Hopefully when he comes back to civilization he will come back to the forum.
While we are both in Australia, the distance between where he is and me is greater than the distance between Russia and USA.

Oh, by the way, another name for the two axis are calling them the 'Inphase' axis and the 'Quadrature' axis. This seems to be used in some University type Metal Detector Research Papers.

Regards
Ken

[mikebg]

Oh, by the way, another name for the two axis are calling them the 'Inphase' axis and the 'Quadrature' axis. This seems to be used in some University type Metal Detector Research Papers.

Ken, please read my posts carefully. This is explained above in the post # 19.

If you have not loaded the file
"NI_Multisim_Analog_Devices_Edition_10_0_1.exe "
to your computer, do so because we will make exercises with it.
Now let's continue to remember the lessons in the basics of electricity.

AIR signal in time and frequency domains.

When search head is lifted far from ground, it generates AIR signal. There are no target and ground inside the black box called "two-port network" or shortly "twoport" shown in post #17 . Inside the box remain only TX and RX coils.

The AIR signal is caused by mutual parameters between TX and RX loop. Using suitable shield, we can suppress action of mutual resistance Rm and mutual capacitance Cm. To suppress action of mutual inductance M we need induction balance. The attached figure illustrates the concept of mutual inductance. A part Ф2 of the whole magnetic flux Ф1 generated by TX loop, appears linked with RX loop. Mutual inductance M is the concept that the current change in one loop induces electromotive voltage in another nearby loop. Shown is what means coefficient of coupling k.

The EMV induced in RX coil is expressed in time domain and in frequency domain. Mutual inductance has sign + or minus depending on what lead of RX coil is connected to ground. Mutual inductance is positive at connection shown in circuit diagram. Sign minus is according Lenz's rule:

“Whenever a change in magnetic field occurs, an electric field is generated to oppose the change.”

Below is shown a TX current and its derivative.
What happens in frequency domain?
Instead derivative of TX current, we have multiplication by jω. Letter j means imaginery (quadrature) part, ie the frequency transfer function generating AIR signal consists only of imaginery part.
The angle frequency ω has dimension radians pro second; ω = 2πf, where f is periodic frequency masured in Hz (Hertz has dimension periods or cycles pro second). The formula shows that

The AIR signal is proportional to TX frequency.

Remains to see how NETWORK ANALYZER will show this in complex plane. The circuit diagram of search head connected to the analyzer is given in post #21.

[WM6]

Excellent mike, thank you for your efforts.

[Sergey_P]

to be continued ->
IB : Ф2 = Ф2(+)+Ф2(-) = 0 =>
=> k=M=0

[mikebg]

to be continued ->
IB : Ф2 = Ф2(+)+Ф2(-) = 0 =>
=> k=M=0

or simply Ф2 --> 0 at orthogonal and "almost orthogonal" configurations:

[mikebg]

AIR signal at positive mutual inductance

The AIR signal in complex plane

The simple two-port network shown in post #21 represents the sensing system when there is no ground and no taget.

http://www.geotech1.com/forums/showt...389#post163389

Here is the network analyzis. The analyzed parameter is Z21 (voltage induced in RX coil vs current through TX coil).
The marker is set to a frequency almost 10 KHz. The Re component of Z21 is almost zero.
You can press a key to show Z21 as Magnitude and Phase and move frequency between 200Hz and 20 KHz.

[Sergey_P]

field of the same magnitude in the target creates more current if the frequency is higher:
Ei= B*w*cos(wt+90)
for small highly conductive target - choose a high frequency…

[mikebg]

field of the same magnitude in the target creates more current if the frequency is higher:
Ei= B*w*cos(wt+90)
for small highly conductive target - choose a high frequency…

Depends on timeconstant of target:
http://www.geotech1.com/forums/showt...378#post101378

However we speek for AIR signal wich appears without target.
Let we analyze the negative mutual inductance or M<0. Here is the network connected to analyzer.

[Humanise]

Hi Ken, please give a link where to read your descriptions!

A quote from Albert Einstein is as follows:
"If you can speak of technical things only in technical terms, you do not understand them."

I'm trying to express technical things in a way that doesn't require the reader to know the technical terms or complex maths, particularly without having to understand how maths based on a number that doesn't exit (square root of negative one) can be used. As a result, the descriptions tend to be long winded. Since my objective is to convert all requirements to computer programs, having everything specified in long winded minute detail makes it easier to convert to software.

Some of the documents I have done in the past can viewed from the following links

Digital Signal Processing related to the Design of VLF Metal Detectors
http://conzerned.org/demining/dsp

Underlying maths of a Software implemented VLF Metal Detector
http://conzerned.org/demining/underlying-maths

General description of how current metal detectors work
http://conzerned.org/demining/how-metal-detectors-work

General description of the methodology used by the main metal detector types
http://conzerned.org/demining/metal-detector-types

Your documentation of phasers/vectors inspires me to try to create some simply documentation on the use of these as my next documents.