Smart Coin Sorter by Inductive Sensing. #01 How Coins Change Coil Impedance.
Posted by javagoza in Experimenting with Magnetic Components on Oct 12, 2021 5:31:26 PMIntroduction
Within the Experimenting with magnetic components challenge I am conducting experiments to develop an intelligent coin discriminator using inductive sensitivity.
In this first experiment I want to see how the proximity of different euro coins affects the impedance of an inductor that is generating an alternating magnetic field. It is assumed that when a metallic coin approaches a variable magnetic field, currents are induced in the coin, called eddy currents. The eddy currents induced inside the coin will modify the electrical impedance of the inductor which will result in variations of the amplitude and phase of the signal. This mechanism looks like a transformer, where the coil is the primary core and the eddy current is the secondary core. The inductive coupling between both cores depends on the distance and the shape. Therefore, the resistance and inductance of the secondary core (eddy current), is shown as a distancedependent resistive and an inductive component on the primary side (the coil).
Mostly amplitude variations are related to the coin conductivity whereas frequency variations relate to its magnetic permeability. In the absence of variations in distance and angle of position of the coin, the two parameters can help us to discriminate the type of metallic material in front of the coil.
The system will be composed of a simple coil that will perform the excitation and measurement functions. I will study the dependence of the resistance and inductance of the coil with the distance between the coil and the coin.

EXPERIMENTS
 #E01 Impedance measurements for inductor RLB1112V4 Series 400 Volt Radial Inductor. Coins @ 1mm
 #E02 Impedance measurements for inductor RLB1112V4 Series 400 Volt Radial Inductor. Coins @ 5mm
 #E03 Impedance measurements for LC tank with inductor RLB1112V4 and several Capacitors
 #E04 Coin discrimination with LC Tank L=1mH C=56nF @ Resonant Freq
 Conclusion
The euro coin series
For the different experiments I will observe the response of the system to the proximity of the different currencies of the complete series of euro coins.
The euro coin series comprises eight different denominations: 1, 2, 5, 10, 20 and 50 cent, €1 and €2. The euro coins have a common side and a national side. The national side indicates the issuing country.
Magnetics properties
 €1 and €2 coins: Their inner part is slightly magnetic. The outer part has no magnetic properties.
 10, 20 and 50 cent coins: They have no magnetic properties.
 1, 2 and 5 cent coins: They are highly magnetic.
Impedance measurement. Analog Discovery 2 Impedance Analyzer
During the experiments I will use the Analog Discovery 2 Impedance Analyzer AdapterAnalog Discovery 2 Impedance Analyzer Adapter adapter for impedance measurement. The Impedance Analyzer Adapter helps you measure complex electrical impedance as a function of the test frequency. The impedance analyzer takes sensitive measurements of both current and voltage are applied to the device under test (DUT) while the measurement frequency is varied.
Schematics: https://digilent.com/reference/_media/reference/instrumentation/analog_discovery_impedance_analyzer_sch.pdf
Inductor RLB1112V4 Series 400 Volt Radial Inductor
In these first experiments I use an unshielded bourns radial inductor. The RLB1112V4 Series 400 Volt Radial Inductor.
It is a radial lead throughhole power inductor with ferrite core made with enameled copper.
https://www.avnet.com/shop/emea/products/bourns/rlb1112v4102j3074457345642083414/
I have not found the reference in the farnell store but I did find another Bourns inductor of the same series the RLB1112V4 RLB1112V4
Datasheet: https://www.bourns.com/docs/ProductDatasheets/rlb1112v4.pdf
Features
 400 VDC rated
 Shrink tubing protected winding
 Fixed lead spacing
 RoHS compliant
Applications
 DC/DC converters
 Power supplies
EXPERIMENTS
#E01 Impedance measurements for inductor RLB1112V4 Series 400 Volt Radial Inductor. Coins @ 1mm
In this experiment I measure the change in the impedance of the inductor in the presence of the euro series coins placed horizontally on the coil at a distance of 1 mm.
I have used Lego to make a construction that allows to position the coin and keep it fixed during the experiment at the desired distance.
Impedance (symbol Z) is a measure of the overall opposition of a circuit to current, how much the circuit impedes the flow of charge. It's like resistance, but it also takes into account the effects of capacitance and inductance. Impedance is measured in ohms (ohms).
The effects of capacitance and inductance vary with the frequency of current passing through the circuit and this means that impedance varies with frequency. However the effect of resistance is constant regardless of frequency.
The capacitance and inductance cause a phase shift between the current and voltage which means that the resistance and reactance cannot be simply added up to give impedance. The Phase Shift is how far the function is shifted horizontally from the usual position. In our case it means that the current and voltage are out of step with each other.
As a reference, I study the response at the same frequencies that have been used in the inductor data sheet to indicate its electrical characteristics.
From the RLB1112V4 Series 400 Volt Radial Inductor datasheet
 @ 1 kHz / 1V / 21 ºC / Averaging 500ms / 1 mm separation
Measure  Description  No Coin  1 cent  2 cent  5 cent  10 cent  20 cent  50 cent  1 EUR  2 EUR 

Ls  Series Inductance  952.5 uH  1.025 mH  1.014 mH  1.033 mH  949.3 uH  946.6 uH  943 uH  961.9 uH  969 uH 
Z  Impedance  5.985 Ω  6.44 Ω  6.37 Ω  6.494 Ω  5.965 Ω  5.948 Ω  5.925 Ω  6.044 Ω  6.089 Ω 
Rs  Series Resistance  100.1865 mΩ  23.62 mΩ  54.77 mΩ  100.4 mΩ  29.15 mΩ  94.34 mΩ  85.78 mΩ  42.77 mΩ  69.8 mΩ 
Xs  Series Reactance  5.985 Ω  6.44 Ω  6.369 Ω  6.493 Ω  5.965 Ω  5.948 Ω  5.925 Ω  6.044 Ω  6.089 Ω 
∠  Input Phase  0.3432 °  0.3693 °  0.3653 °  0.3723 °  0.3421 °  0.3411 °  0.3398 °  0.3466 °  0.3492 ° 
θ  Phase  90.96 °  89.79 °  89.51 °  89.11 °  89.72 °  89.09 °  89.17 °  89.59 °  89.34 ° 
D  Dissipation  0.0167409  0.0036673  0.0085984  0.0154572  0.0048866  0.0158617  0.0144785  0.0070775  0.0114639 
Q  Quality  59.73392  272.6792  116.3005  64.69492  204.6394  63.04502  69.06788  141.2928  87.23011 
Reactance (symbol X) is a measure of the opposition of capacitance and inductance to current. Reactance varies with the frequency of the electrical signal. Reactance is measured in ohms (ohm).
Inductive reactance, XL is small at low frequencies and large at high frequencies. For steady DC (frequency zero), XL is zero (no opposition), which means that inductors pass DC but block high frequency AC.
Capacitive reactance (Xc) is large at low frequencies and small at high frequencies. For steady DC which is zero frequency (f = 0Hz), Xc is infinite (total opposition), which means that capacitors pass AC but block DC.
Coin discrimination based on phase and impedance change.
 @ 252 kHz / 1V / 21 ºC / Averaging 500ms / 1 mm separation
Measure  Description  No coin  1 cent  2 cent  5 cent  10 cent  20 cent  50 cent  1 EUR  2 EUR 

Ls  Series Inductance  1.01 mH  900.5 uH  883 uH  879.1 uH  894.1 uH  882.4 uH  881.2 uH  887.6 uH  882.2 uH 
Z  Impedance  1.6 kΩ  1.427 kΩ  1.399 kΩ  1.393 kΩ  1.417 kΩ  1.398 kΩ  1.396 kΩ  1.406 kΩ  1.398 kΩ 
Rs  Series Resistance  35.4 Ω  60.47 Ω  59.27 Ω  59.29 Ω  47.6 Ω  46.76 Ω  46.9 Ω  53.32 Ω  52.43 Ω 
Xs  Series Reactance  1.6 kΩ  1.426 kΩ  1.398 kΩ  1.392 kΩ  1.416 kΩ  1.397 kΩ  1.395 kΩ  1.405 kΩ  1.397 kΩ 
∠  Input Phase  59.98 °  56.06 °  55.51 °  55.38 °  56.19 °  55.83 °  55.78 °  55.82 °  55.67 ° 
θ  Phase  88.73 °  87.57 °  87.57 °  87.56 °  88.07 °  88.08 °  88.07 °  87.83 °  87.85 ° 
D  Dissipation  0.0221345  0.0424064  0.0423902  0.0425979  0.0336217  0.0334674  0.0336136  0.0379399  0.0375315 
Q  Quality  45.17832  23.58134  23.59033  23.47532  29.74271  29.87984  29.74982  26.35745  26.64426 
Coin discrimination based on phase and impedance change.
In this case the discrimination of the coins becomes somewhat more difficult than at the 1 kHz frequency.
 @ 1.1 MHz / 1V / 21 ºC / Averaging 500ms / 1 mm separation
Measure  Description  No coin  1 cent  2 cent  5 cent  10 cent  20 cent  50 cent  1 EUR  2 EUR 

Ls  Series Inductance  2.506 mH  1.881 mH  1.829 mH  1.791 mH  1.807 mH  1.794 mH  1.765 mH  1.793 mH  1.777 mH 
Z  Impedance  17.41 kΩ  13.06 kΩ  12.7 kΩ  12.44 kΩ  12.55 kΩ  12.46 kΩ  12.25 kΩ  12.46 kΩ  12.34 kΩ 
Rs  Series Resistance  1.749 kΩ  1.312 kΩ  1.252 kΩ  1.212 kΩ  1.243 kΩ  1.216 kΩ  1.186 kΩ  1.267 kΩ  1.235 kΩ 
Xs  Series Reactance  17.32 kΩ  13 kΩ  12.64 kΩ  12.38 kΩ  12.49 kΩ  12.4 kΩ  12.2 kΩ  12.39 kΩ  12.28 kΩ 
∠  Input Phase  97.64 °  96.6 °  96.59 °  96.56 °  96.51 °  96.55 °  96.53 °  96.32 °  96.37 ° 
θ  Phase  84.23 °  84.24 °  84.34 °  84.41 °  84.32 °  84.4 °  84.45 °  84.16 °  84.26 ° 
D  Dissipation  0.10097  0.100957  0.0990468  0.0979482  0.0995256  0.098087  0.0972052  0.1021969  0.1005858 
Q  Quality  9.903931  9.905204  10.09623  10.20948  10.04766  10.19503  10.28752  9.785035  9.941766 
Coin discrimination based on phase and impedance change.
This is near the self resonant frequency for the RLB111V4
How does the proximity of the coin affect the selfresonant frequency?
 Impedance and phase in the neighborhood of the self resonant frequency for the RLB111V4 SRF(MHz) 1.397 MHz @ 20ºC
 Shift of the selfresonant frequency when approaching a 1 cent euro coin. SRF shifts from 1.397 MHz to 1.4857 MHz
 Shift of the selfresonant frequency when approaching a 2 cent euro coin. SRF shifts from 1.397 MHz to 1.448 MHz
 Shift of the SRF for the entire series of euro coins. Impedance and phase in the neighborhood of the self resonant frequency for the RLB111V4.
#E02 Impedance measurements for inductor RLB1112V4 Series 400 Volt Radial Inductor. Coins @ 5mm
For the second experiment I increase the distance of the coins to 5 mm
Again I take measurements, looking mainly at the characteristics that allow me to discriminate the coins.
 @ 1 kHz / 1V / 21 ºC / Averaging 500ms / 5 mm separation
Measure  Description  No Coin  1 cent  2 cent  5 cent  10 cent  20 cent  50 cent  1 EUR  2 EUR 

Ls  Series Inductance  953.3 uH  963.4 uH  964.5 uH  965.9 uH  950.4 uH  950.7 uH  949.7 uH  952.5 uH  954 uH 
Z  Impedance  5.99 Ω  6.053 Ω  6.06 Ω  6.069 Ω  5.972 Ω  5.974 Ω  5.967 Ω  5.985 Ω  5.994 Ω 
Rs  Series Resistance  97.6593 mΩ  53.2237 mΩ  69.3522 mΩ  50.9471 mΩ  73.649 mΩ  66.0638 mΩ  54.3151 mΩ  77.7273 mΩ  61.9693 mΩ 
Xs  Series Reactance  5.99 Ω  6.053 Ω  6.06 Ω  6.069 Ω  5.972 Ω  5.974 Ω  5.967 Ω  5.984 Ω  5.994 Ω 
∠  Input Phase  0.3435 °  0.3472 °  0.3476 °  0.3481 °  0.3425 °  0.3426 °  0.3422 °  0.3432 °  0.3438 ° 
θ  Phase  90.93 °  90.5 °  90.66 °  90.48 °  90.71 °  90.63 °  90.52 °  90.74 °  90.59 ° 
D  Dissipation  0.0163048  0.0087928  0.0114444  0.0083947  0.0123332  0.0110592  0.0091027  0.0129882  0.0103385 
Q  Quality  61.33151  113.7295  87.3788  119.123  81.08165  90.42268  109.8569  76.99318  96.72555 
And I compare with the one obtained for 1mm of separation. It is clear that the distance affects the impedance quite a lot and that the coin discriminator should limit both the angular position and the distance to the inductor.
#E03 Impedance measurements for LC tank with inductor RLB1112V4 and several Capacitors
Generating an alternating magnetic field with just the coil consumes a large amount of energy. This consumption can be reduced by adding a parallel capacitor, turning the circuit into a resonator. In this way, power consumption is reduced to inductor losses and eddy currents only.
Introduction to LC Tanks
In the two previous experiments I have made impedance measurements with just the inductor and a series resistor to be able to measure the circulating current. In this experiment I am going to use different configurations with capacitors parallel to the coil.
This is named a parallel LC circuit, also called a resonant circuit, tank circuit, or tuned circuit. It is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together.
If an inductor is connected across a charged capacitor, the voltage across the capacitor will conduct a current through the inductor, creating a magnetic field around it. The voltage across the capacitor drops to zero as the current flow consumes the load. At this point, the energy stored in the coil's magnetic field induces a voltage across the coil, because the inductors oppose current changes. This induced voltage causes a current to begin to recharge the capacitor with a voltage of opposite polarity to its original charge.
The EMF driving the current is caused by a decrease in the magnetic field, so the energy required to charge the capacitor is drawn from the magnetic field. When the magnetic field has completely dissipated, the current will stop and the charge will be stored back in the capacitor, with the opposite polarity as before. Then the cycle will start again, with the current flowing in the opposite direction through the inductor.
There is a resonance effect when an LC circuit is driven from an external source at an angular frequency ω0 at which the inductive and capacitive reactances are equal in magnitude. The frequency at which this equality holds for the particular circuit is called the resonant frequency. The resonant frequency of the LC circuit is
where L is the inductance in henries, and C is the capacitance in farads. The angular frequency ω0 has units of radians per second.
I carry out different tests with a series of capacitors and study the frequency response of the different LC tanks, keeping the inductor fixed.
Components used in the experiment
Series of capacitors used in the experiment: 1 nF, 2.2 nF, 3.9 nF, 5.6 nF, 33 nF, 68 nF, 220 nF and 1000 nF
For the experiment I put the coil and the capacitor to be tested on the impedance analyzer board.
In the picture the RLB1112V4 radial inductor parallel to a 2.2 nF polyester film capacitor
Impedance response to the frequency of the different LC tanks.
As the capacitor capacity increases, the resonant frequency of the LC tank decreases.
I take data from the resonant frequencies and compare them with the theoretical resonant frequencies assuming an ideal inductance of 1 mH.
Capacitor  Resonant Frequency  Theoretical calculation (L= 1mH) 

SRF  1.38 MHz  
1nF  162.5 kHz  159.15 kHz 
2.2 nF  110.06 kHz  107.3 kHz 
3.9 nF  81.70 kHz  80.59 kHz 
5.6 nF  66.98 kHz  67.26 kHz 
33 nF  27.40 kHz  27.71 kHz 
68 nF  18.41 kHz  19.3 kHz 
220 nF  10.707 kHz  10.73 kHz 
1000 nF  4.91 kHz  5.03 kHz 
LC tank C= 220 nF / Resonant Frequency Shift bringing a coin closer to 1mm in front of the coil. For the entire series of euro coins.
Finally, I study the change in the resonant frequency when bringing coins to 1 mm of the inductor of an LC tank composed of the 1 mH inductor and a 220 nF capacitor.
#E04 Coin discrimination with LC Tank L=1mH C=56nF @ Resonant Freq
For the next experiment I build an LC tank with a 56 nF capacitor and a 1 mH parallel inductor. The theoretical resonant frequency is 21.27 kHz
Components
 RLB1112V4 Series 400 Volt Radial Inductor L = 1mH
 Polyester Film Capacitor C = 56 nF
Theoretical Resonant Frequency L= 1mH C= 56nF 21.27kHz. Measured =
Impedance measurement of the system
 @ 21.32 kHz / 1V / 20 ºC / Averaging 500ms / 1 mm separation
Measure  Description  No coin  1 cent  2 cent  5 cent  10 cent  20 cent  50 cent  1 EUR  2 EUR 

Ls  Series Inductance  124.8 uH  4.055 mH  3.576 mH  3.178 mH  6.958 mH  8.907 mH  8.725 mH  9.109 mH  8.837 mH 
Z  Impedance  4.872 kΩ  1.383 kΩ  1.028 kΩ  923.1 Ω  1.049 kΩ  1.362 kΩ  1.315 kΩ  1.511 kΩ  1.461 kΩ 
Rs  Series Resistance  4.872 kΩ  1.273 kΩ  910 Ω  819.8 Ω  488.4 Ω  663.8 Ω  609.6 Ω  896.9 Ω  862.7 Ω 
Xs  Series Reactance  16.72 Ω  541.3 Ω  477.4 Ω  424.2 Ω  928.7 Ω  1.189 kΩ  1.165 kΩ  1.216 kΩ  1.18 kΩ 
∠  Input Phase  0.4368 °  13.59 °  14.21 °  13.28 °  32.15 °  35.76 °  36.1 °  32.88 °  32.56 ° 
θ  Phase  0.1967 °  23.03 °  27.68 °  27.36 °  62.26 °  60.83 °  62.37 °  53.59 °  53.82 ° 
D  Dissipation  291.3053  2.352258  1.906265  1.932809  0.5259248  0.5582965  0.5234008  0.7376607  0.7313722 
Q  Quality  0.0034328  0.4251234  0.5245861  0.5173817  1.901413  1.791163  1.910582  1.355637  1.367293 
Coin discrimination based on phase and impedance change.
Conclusion
I have reviewed concepts that I barely remembered about electromagnetism and analog electronics and now I understand better.
I have verified that the impedance of the system varies differently when approaching different euro coins to the inductor when it is producing an alternating magnetic field and I will be able to use this differentiation to feed the classifier that will allow to discriminate the coins.
Blogs 

Smart Coin Sorter by Inductive Sensing. Introduction 
Smart Coin Sorter by Inductive Sensing. #01 How Coins Change Coil Impedance. 
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