Understanding Electrical Impedance for Calibrating Sensors

[Xavii0]

i am a 3rd year Mech batch doing my dissertation on developing an inductive sensor to determine wear in brake discs. As you know it works by inducing eddy currents into the disc and the are monitored by measuring the impedance of the coil. i am really struggling with understanding the impedance part of it. I have a device called miniVNA pro which measures the impedance & frequency and gives the output to a laptop/computer when the sensor is connected to it. Before testing the sensor on brake discs i need to calibrate it(change number of turns on the coil, change the diameter, thickness etc) by testing it on other metal specimens like steel/aluminium etc. This is where my problem lies, I need to know how to work out impedance for these metals so that i can compare it with my tested values. Is there a table online with these values or do i have to work it out using a formula? Can you help me with this please?

 

[sophiecentaur]

Hi and welcome to PF
Just to get things right: it is not the metal that has the Impedance, it will be the coil (sorry if you meant this in the first place). The property of the metal that affects the coil's impedance is the Permeability. This is often taken as a Real quantity. The Inductance of an inductor with a largish core is proportional to the Permeability of the core. If you know the inductance at a particular frequency with a particular core material than you should be able to scale the inductance when using a different core material by scaling according to the two permeabilities.
That simple statement ignores the possibility of the cores having a loss component, which can apply at high frequencies. Data on materials is probably available.

 

[Xavii0]

thank you so much for the reply
yeah sorry that's what i meant. I was really struggling with understanding the impedance part of it but now after reading your reply it makes a lot of sense. but just to make it more clear, say I am measuring the thickness of a steel plate with my inductive sensor and i got a value of 10 ohms impedance. I need to compare this to a known impedance value in order to calibrate the sensor, my knowledge on how to do this is not much at all. Correct me if am wrong but from what i know I can use the frequency and the plate dimensions to work out impedance. plus the formula i found is below

Z=R+jwL
using the j operator, and w to represent angular frequency,
Z = R + jwL - 1/jwC
When |Xc| and |Xl|, Z = R

You can just add impedance in series- R value for resistors, jwL for inductors,1/(jwC) for capacitors, and don't forget phase. (Where w is frequency, C is capacitance, L is inductance, R is resistance, and j is the imaginary number sqrt(-1)

To draw a phase diagram, plot R as + horizontal, Xl as + vertical, and Xc as - vertical. Z is the resultant.

This occurs when wL = 1/wC. The frequency in radians/sec then becomes w = (LC)^-1/2 ... in other words, the square root of 1/LC. At resonance, these terms cancel out and you are left with a purely real impedance = resistance of the circuit which has a phase angle of 0.

and can you tell me how to do this which is what you said " If you know the inductance at a particular frequency with a particular core material than you should be able to scale the inductance when using a different core material by scaling according to the two permeabilities"

 

[Xavii0]

Do you know how to work out the inductance of a metal plate/sheet ?

 

[sophiecentaur]

The inductance of the sheet will be incredibly low and it surely can't be what you want. You will be measuring / detecting the Reluctance of the magnetic circuit (the magnetic path through the coil and metal sheet) - which will be what affects the Inductance of your Coil. The coil impedance that you measure will probably not be 10Ω (that would be just Resistive).
As I have no idea of the actual set up you are using, I would think in terms of using sheets of known thicknesses and looking at the Impedances for each sheet (i.e. just a blind calibration). This could be plotted on a graph (perhaps 3D, if necessary) and then using the results from the test piece, see where it fits on the graph. I'm a bit in the dark about what you are actually doing. Can you produce a circuit diagram or even just a sketch of the physical layout?

 

[sophiecentaur]

Do you know how to work out the inductance of a metal plate/sheet ?

I'm not sure of what that means as a concept. Inductance is the property of a circuit element and it applies across two terminals (i.e. how it is connected into a circuit or how it is 'fed'). Inductance per unit length is a concept used in transmission line theory and Permeability has the Units of Inductance per metre.
More specific information is need about your question, I think.

 

[Xavii0]

Please read page 1 and 2 in the attachments. My first part of testing is to calibrate an inductive sensor like shown in page 2. The calibrating part is where testing it on metal sheets and measuring the change in the impedance of the coil comes in etc, after doing this i will test it on brake discs to measure its thickness.

this is the object connected to the sensor: http://miniradiosolutions.com/minivnapro which gives the output impedance and frequency in a graph format.

 

[sophiecentaur]

I am beginning to see what you need now. You are looking at how the Inductance of the Coil changes and not the brake disc.
That reference seems to make it clear how much better your proposed method is than others - I would probably agree with that.
I still suggest that a heuristic approach could give equally useful results. A number of discs of known thickness would give you points on a graph of thickness / Impedance. A new disc would produce a different impedance that would lie on the graph and you could interpolate to find the thickness of the disc. The graph would probably not be a simple 2 axis graph but that wouldn't be a problem. You don't actually care what the absolute value of the inductance is - because there may be other factors in the construction of the sensor. All that matters is to match the 'electrical' numbers to the measured dimensions via the graph / lookup table that your calibrated discs will give you. It is essential, in any case, to use the same disc materials for calibrations and measurements.
There exist methods for doing the interpolation.

 

[Xavii0]

All that matters is to match the 'electrical' numbers to the measured dimensions via the graph / lookup table that your calibrated discs will give you. It is essential, in any case, to use the same disc materials for calibrations and measurements.
There exist methods for doing the interpolation.

can you please elaborate on that, as in explain in detail exactly what i need to do to calibrate my sensor?

 

[sophiecentaur]

OK. Say you have three discs, two of known dimension and one unknown.
Using easy numbers and assuming that the Impedance is Real.
Disc 1 thickness, t1 =15mm Impedance Z1= 100
Disc 2 t2 = 20mm Z2 = 120
Disc 3 t3=? Z3 = 110

You can either draw a graph of t against Z, plot the known (t,Z) points and draw a line through them. Then draw a vertical line through Z3. The t value where it crosses the diagonal line will be the interpolated value for t3. That assumes a linear relationship between t and Z and is the simplest form of interpolation. If you plot (t,Z) points over a wide a range of thicknesses then you can see how linear the relationship is.
To work it out without a graph, you can use the linear interpolation formula
t3 = t1 + (t2-t1)(Z3-Z1)/(Z2-Z1)
I really don't think you can work out the Z's from any simple basic formula because they will depend on so many factors. It isn't cheating to treat the problem this way.
The above is just a basic principle to show you what I mean and would need to be expanded if the Z phase changes appreciably over the range of t values or if you don't get a straight line graph. In that case it can also be modified to give a result with higher order interpolation. Your processor could handle all that very easily as long as you can code it.