Targets frequency response

[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.

[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]

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]

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]

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]

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]

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]

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]

Polar Graph of Voltage Trasfer

Voltage Trasfer of an Eddy current as Polar Graph
When Network Analyzer is inversed (flipped horizontally), instead hybride H-parameters, it represents G-parameters (inversed hybride parameters). Therefore, two readings on the Network analyzer's skin should be changed:
- The inscription "H-Parameters" should be "G-parametrers" and
- Inscription on button pressed H12 must be G21. Parameter G21 is nondimesional forward voltage transfer. This is inversion of H21 - the nondimesional forward current transfer parameter.
Home work

:-( for those who hate to work, but like to watch) -:
1. In time domain, the Voltage transfer by an eddy current loop is scaled derivative of its Transfer admittance. Compare the polar graph of Transfer admittance (shown in posting #116) with the polar graph of Voltage transfer shown here. Explain how differentiation in time domain amended complex spectral response in frequency domain.


2. In analyzing the transfer admittance, we parted frequency spectrum of the LF region and HF region as the boundary between them is the Cutoff frequency of target. Do the same analysis and Voltage transfer. Check with Network Analyzer that once differentiation signal in time domain amended Cutoff frequency.

3. The timeconstant of conductive ground depends on TX coil diameter. In frequency domain that means we can increase or decrease the width of LF region for ground signal. Analyze how we can use it?
NOTE: When we change TX coil diameter, the timeconstant (cutoff frequency) of conductive target remains unchanged only if its eddy diameter is smaller than TX coil diameter.

[mikebg]

Network for voltage transfer of an eddy current loop

Network for voltage transfer of an eddy current loop

As is known in the study of transistor amplifiers, the hybrid parameter H12 represents reverse voltage transfer. In common emiter network this is the parameter Hre. Since in principle both ports of two port network are equivalent (not defined input and output), we can flip horizontally Network Analyzer to make parameter H12 forward voltage transfer parameter G21. For a detailed explanation of G21, search WEB for "Two-port network" and read "Inverse hybrid parameters (g-parameters)" .