Targets frequency response

[mikebg]

Voltage transfer in Mag-Ph coordinates

Voltage transfer of an eddy current loop in Mag-Ph (polar) coordinates

Amplitude and phase diagrams give some answers to homework tasks, but let's supplement it with additional tasks:
4. Draw Bode plot on the amplitude diagram.
5. Compare the new Bode plot to that of Transfer admittance in posting # 117 and explain how they change poperties in LF region and HF region.
6. Frequency domain may mislead with the phase delay of response. In the case shown, the response anticipates excitation. This is not possible because the system can not predict the future. Share the true values of phase delay on the phase diagram.
7. Make the Network Analyzer to provide Voltage transfer in Re-Im (rectangular) coordinates.

[mikebg]

Voltage transfer in Re-Im coordinates

Voltage transfer of an eddy current loop in Re-Im (rectangular) coordinates
Since the Network Analyzer is turned horizontally, I turned horizontally in its skin the markings on the keys and connecting clamps as accession wrote in red letters on their true value.
The Re and Im coordinates of spectral response are not as informative as Mag-Ph, however, they may be obtained easily as a DC signals by synchronous demodulators. For this purpose, should get reference voltage by an additional coil having enough mutual inductance with TX coil, but small enough to eddy current loop. It will be induced voltage with the same spectral composition as electromotive voltage V1. The difference will be only in scale.
With such sensors, we can construct absorption metal detector which responds only to the Re component. For this purpose, we can draw Bode plot on Re diagram and to determine at what frequency region must work the absorption detector.

[mikebg]

Transfer impedance of an eddy current loop

Transfer impedance of an eddy current loop
Let us introduce the TX current in the network analyzed . According Lenz's rule, the derivative of current induces negative electromotive voltage V1 in time domain. This means phase reverse in frequency domain.
Taking account the direction of current I2 from port P2, we must turn signal phase bargaining leads to a winding of any transformer.
It remains to introduce data for network analysis as shown in the attached figure, and to run the instrument.

[mikebg]

Polar Graph of transfer impedance

An eddy current loop in sensing network.
Marker in larger scale shows that cutoff frequency remains the same.
EMI makes a first order LP filter to act as second order HF filter.
Polar graph shows signal as a negative frequency dependent coil. This coil has positive frequency dependent resistance and negative frequency dependent inductance. Parameters-L (f) and +r(f) are analyzed more easily in Re / Im coordinates, which will make later. Let's see first in rectangular coordinates how the transfer impedance Z (f) determines the amplitude and phase of the received signal.</SPAN></SPAN>

[mikebg]

Z21 as Mag/Ph

Transfer impedance in polar coordinates
Let us draw the Bode plot of amplitude diagram and look what happens in the LF region and HF region. As shown cutoff frequency remains the same with the same frequency 1KHz and phase angle -45deg. The LF asymptote has a steep 40dB/dec = 12dB/oct, which means twice differentiation. However, in the HF region is obtained steep 20dB/dec = 6dB/oct, which is inherent in the once differentiation! This is easily explained, because in HF region the eddy current loop acts as a real integrator.
It remains to investigate howchanges with frequency the parameters of "negative" coil which imported the eddy current loop. They are seen better as Re / Im coordinates.

[mikebg]

Z21 as Re / Im


Transfer impedance in rectangular coordinates
Re coordinate means resistance.
Im coordinate means reactance (in this case inductance).
But where are they connected?
For RX coil this is induced electromotive voltage. However TX coil acts as each RX coil, even most pronounced because mutual inductance is the maximum possible (k=1). Therefore, using the term "selfinductance".
An impedance like Z21 is connected always in the TX coil when it is near a conductive environment. This complicates the operation of metal detectors because the movement of the TX coil above the ground, the ground acts as a core with a variable distance and variable properties.

[mikebg]

Moreland's effect.


In this exercise, we analyzed the spectral characteristic of a ring. It is different from the spectral characteristic of a coin made of same metal and having the same diameter. The difference is best viewed in the complex plane. Compare figures in posting #42 and posting #124. Their shapes are different in HF region. This is illustrated in the attached figure. We see that in HF region the Re component of the ring is greater than the Re component of a coin. It follows that we can construct metal detector, which indicates whether the object is open form as a bracelet or solid form.

[mikebg]

Timeconstants

Here's how Carl Moreland describes this effect in his article "Induction Basics":

“Would there be a difference between a solid round target like a coin and an open round target like a ring?
It turns out there is. A ring will give a stronger response, even though it has less surface area. That’s because it is more like a shorted loop of wire, in which the induced current flows around the loop, instead of moving in smaller surface circles as it does with a solid disc. So the extra metal in the middle of the coin actually hurts the response. It’s a fairly subtle effect, but it’s there.
You can demonstrate this for yourself, by comparing a ring and a coin to see which gives the greater response.
This does not account for possible conductivity differences, so a better test is to compare two coins, one with most of the center drilled out. I used two prezinc Lincoln cents, with a 5/8” [16mm] hole drilled through one. Both a VLF (allmetal mode) and PI detector indicated the drilled-out cent 3/4”-1” [2–2,5 cm] deeper than the solid cent. I repeated the experiment with silver Washington quarters with the same result. So, with the conductivity variable removed we see that the shape will slightly edge out the solid coin, even when the metal and diameter are identical.”

This article contains incorrect explanation of the reason for this effect and irregular shapes with an illustration of the eddy currents in the coin. Clearly, these figures are taken from the cited literature. Nature does not allow in one path to flow currents in opposite directions.
Measurement of time constants in the coin and theoretical studies show that EMI sees the coin as if it is build of rings with different diameters that are inserted into one another. This is true also for the signal received by the halfspace (conductive ground). The correct shapes of eddy currents are given below.

[WM6]

Nature does not allow in one path to flow currents in opposite directions.


.

Hi mikebg

Nature does not allow currents to flow on longer path, if there exist shorter path with same conductivity too. And direction is nothing more opposite than in your sketch.

So I think Carls drawing of eddy currents on full circle (coin) surface is basically correct.

We must also take into account the frequency of origin, the origin and target orientation in space, non-ferro-ferro, loss of currents on longer (eddy) circles (overcome by short current circles) and more.

[Qiaozhi]

Hi mikebg,

If your explanation was correct then the non-drilled coin would give the greater response. Also, as WM6 points out, electrical current will take the path of lowest resistance, which your example does not. Therefore Carl's explanation is the correct one.

[Aziz]

Look at the induction heater and pay attention, where it gets hot red first!
http://www.youtube.com/watch?v=I_gFJ71Kp8M
http://www.youtube.com/watch?v=XVCmiWKRrkI
http://www.youtube.com/watch?v=jLNaVV9l18k
http://www.youtube.com/watch?v=RcIaYIYtc74

Aziz

[mikebg]

Timeconstants

To WM6:
Eddy currents are driven by EMV (electromotive voltages) induced in loops.
Experiments and theory show that relations between cutoff frequencies of eddy loops are 1:9:25:49 etc. (timeconstants are inversely proportional).
The attached figure illustrates what I mean with words:
"Nature does not allow in one path to flow currents in opposite directions".

[mikebg]

To Qiaozhi:
The response is derivative of eddy current. Therefore, the eddy currents that flow in larger diameters and subside more quickly, produce a stronger signal. We have quickly subside currents in the ring because the greatest resistance. Coin generates a weak signal because the energy is dissipated more slowly.
Indeed, at pulse induction, the coin accumulates more energy than the ring because it has a larger volume of metal. If a PI machine integrates the signal from a coin, integral (adopted energy) will be higher than the integrated signal from a drilled coin.

[mikebg]

Let us rediscover eddy currents!

After rediscovering the sensing network in frequency domain, the REMI group started to rediscover eddy currents in time domain. This means the instrument will be differential calculus. A Bulgarian saying: "Crazy is never tired." Let us see how the crazy designers will rediscover time constants in a coin and running tracks of eddy currents.
For me (as spokesman of REMI group) is very difficult to explain with English terms what mathematical operations are made and what formulas mean. Hopefully Google Translator able to do my job.

STEP DOWN RESPONSE OF A COIN
Q: What happens inside a coin at pulse induction?
A: According Lenz's rule, the conductor opposites to change of magnetic field inside its volume.
Q: How?
A: With many eddy currents.
Q: Why not with only one eddy current?
A: An eddy current can not reconstruct the magnetic field shape in coin volume at "switch off" moment. The reconstruction of magnetic field with an eddy current is possible if the target is a ring or bracelet.
Q: I can not imagine visually what you should get multiple eddy currents in a coin. Can you explain this with a drawing?
A: Yes, can be drawn but only for the t=0 or moment "Switch off". What happens after this moment in the coin, can be described only by a differential equation.
Q: Can we post in the forum adrawing and differential equation? Many participants in the forum have studied differential calculus, so they can understand the equation and analysis.
A: Yes, but we have to explain how to solve it.
Q: Who of REMI group discovered how to solve this differential equation?
A: In the REMI group have not yet included mathematicians. The way to solve differential equations with two variables is proposed by Fourier in the early 19th century.
Q: Why two variables? Right in time domain the variable is time?
A: Because we need more variables to describe the change of the magnetic field at any point, the position of which is described by three coordinates. However, we will use cylindrical coordinates and uniform magnetic field to simplify the analysis and to reduce variables to two. Let we illustrate with a drawing how to obtain it.
The drawing represents a coin with diameter D placed in a uniform magnetic field H, which is perpendicular to its plane. At some instant, called "switch off" or t = 0, exciting magnetic field disappears. However, according Lenz's rule, the coin metal opposites to change of magnetic field inside its volume. At this instant, the field inside the volume remains the same, as illustrated in the diagram at right. This drawing shows the shape of H at instant t = 0. We see that H = Hm when cylinder coordinate "r" is in interval from-D/2 to +D/2. Magnetic field is zero outside the coin.

[Qiaozhi]

You seem to be talking at cross-purposes. You said, "Nature does not allow in one path to flow currents in opposite directions". In fact this is exactly what is happening in the target, but by the principle of superposition these opposing currents cancel. The result is that the current density is stronger at the surface (close to the coil) and decreases further away.

The changing flux from the TX coil induces voltage loops in the metal target, and the associated current is known as an eddy current. The modeling of eddy currents is difficult in the case of a metal detector because the target is often not homogeneous, or of regular shape and orientation. For a coin with the center removed, and lying parallel to the plane of the search coil, the effective current density (and hence the target response) is increased. There is also the added difficulty that the target is 3-dimensional, and the eddy current flow does not follow the simple paths shown in your diagram. Eddy currents are so-called because they are small (local) current loops, similar to those seen in rivers, and shown in Carl's diagram. Your own diagram shows the distribution of current density in a 2-dimensional target,