Introduction

 

Within the Experimenting with magnetic components challenge I am conducting experiments to develop an intelligent coin discriminator using inductive sensitivity.

 

Cover

 

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 distance-dependent 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.

 

 

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.

 

Euro coins and magnets

 

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.

Analog Discovery 2 Impedance Analyzer

 

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 through-hole power inductor with ferrite core made with enameled copper.

https://www.avnet.com/shop/emea/products/bourns/rlb1112v4-102j-3074457345642083414/

 

I have not found the reference in the farnell store but I did find another Bourns inductor of the same series the RLB1112V4 RLB1112V4

RLB1112V4 Series 400 Volt Radial Inductor RLB1112V4 Series 400 Volt Radial Inductor

Datasheet: https://www.bourns.com/docs/Product-Datasheets/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.

 

 

RLB1112V4 Series 400 Volt Radial Inductor. Impedance measurement

 

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

 

MeasureDescriptionNo Coin1 cent2 cent5 cent10 cent20 cent50 cent1 EUR2 EUR
LsSeries Inductance952.5 uH1.025 mH1.014 mH1.033 mH949.3 uH946.6 uH943 uH961.9 uH969 uH
|Z|Impedance5.985 Ω6.44 Ω6.37 Ω6.494 Ω5.965 Ω5.948 Ω5.925 Ω6.044 Ω6.089 Ω
RsSeries Resistance-100.1865 mΩ23.62 mΩ54.77 mΩ100.4 mΩ29.15 mΩ94.34 mΩ85.78 mΩ42.77 mΩ69.8 mΩ
XsSeries Reactance5.985 Ω6.44 Ω6.369 Ω6.493 Ω5.965 Ω5.948 Ω5.925 Ω6.044 Ω6.089 Ω
Input Phase0.3432 °0.3693 °0.3653 °0.3723 °0.3421 °0.3411 °0.3398 °0.3466 °0.3492 °
θPhase90.96 °89.79 °89.51 °89.11 °89.72 °89.09 °89.17 °89.59 °89.34 °
DDissipation0.01674090.00366730.00859840.01545720.00488660.01586170.01447850.00707750.0114639
QQuality59.73392272.6792116.300564.69492204.639463.0450269.06788141.292887.23011

 

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.

RLB1112V4 Series 400 Volt Radial Inductor Phase vs Impedance 1 kHz

 

  • @ 252 kHz / 1V / 21 ºC / Averaging 500ms / 1 mm separation

 

MeasureDescriptionNo coin1 cent2 cent5 cent10 cent20 cent50 cent1 EUR2 EUR
LsSeries Inductance1.01 mH900.5 uH883 uH879.1 uH894.1 uH882.4 uH881.2 uH887.6 uH882.2 uH
|Z|Impedance1.6 kΩ1.427 kΩ1.399 kΩ1.393 kΩ1.417 kΩ1.398 kΩ1.396 kΩ1.406 kΩ1.398 kΩ
RsSeries Resistance35.4 Ω60.47 Ω59.27 Ω59.29 Ω47.6 Ω46.76 Ω46.9 Ω53.32 Ω52.43 Ω
XsSeries Reactance1.6 kΩ1.426 kΩ1.398 kΩ1.392 kΩ1.416 kΩ1.397 kΩ1.395 kΩ1.405 kΩ1.397 kΩ
Input Phase59.98 °56.06 °55.51 °55.38 °56.19 °55.83 °55.78 °55.82 °55.67 °
θPhase88.73 °87.57 °87.57 °87.56 °88.07 °88.08 °88.07 °87.83 °87.85 °
DDissipation0.02213450.04240640.04239020.04259790.03362170.03346740.03361360.03793990.0375315
QQuality45.1783223.5813423.5903323.4753229.7427129.8798429.7498226.3574526.64426

 

Coin discrimination based on phase and impedance change.

 

Coin Discrimination  @ 252 kHz / 1V / 21 ºC / Averaging 500ms

 

In this case the discrimination of the coins becomes somewhat more difficult than at the 1 kHz frequency.

 

RLB1112V4 Series 400 Volt Radial Inductor Phase vs Impedance 252 kHz

 

 

  • @ 1.1 MHz / 1V / 21 ºC / Averaging 500ms / 1 mm separation

 

MeasureDescriptionNo coin1 cent2 cent5 cent10 cent20 cent50 cent1 EUR2 EUR
LsSeries Inductance2.506 mH1.881 mH1.829 mH1.791 mH1.807 mH1.794 mH1.765 mH1.793 mH1.777 mH
|Z|Impedance17.41 kΩ13.06 kΩ12.7 kΩ12.44 kΩ12.55 kΩ12.46 kΩ12.25 kΩ12.46 kΩ12.34 kΩ
RsSeries Resistance1.749 kΩ1.312 kΩ1.252 kΩ1.212 kΩ1.243 kΩ1.216 kΩ1.186 kΩ1.267 kΩ1.235 kΩ
XsSeries Reactance17.32 kΩ13 kΩ12.64 kΩ12.38 kΩ12.49 kΩ12.4 kΩ12.2 kΩ12.39 kΩ12.28 kΩ
Input Phase97.64 °96.6 °96.59 °96.56 °96.51 °96.55 °96.53 °96.32 °96.37 °
θPhase84.23 °84.24 °84.34 °84.41 °84.32 °84.4 °84.45 °84.16 °84.26 °
DDissipation0.100970.1009570.09904680.09794820.09952560.0980870.09720520.10219690.1005858
QQuality9.9039319.90520410.0962310.2094810.0476610.1950310.287529.7850359.941766

 

Coin discrimination based on phase and impedance change.

 

RLB1112V4 Series 400 Volt Radial Inductor Phase vs Impedance 1_1 MHz

This is near the self resonant frequency for the RLB111V4

 

How does the proximity of the coin affect the self-resonant frequency?

 

  • Impedance and phase in the neighborhood of the self resonant frequency for the RLB111V4 SRF(MHz) 1.397 MHz @ 20ºC
  • Shift of the self-resonant frequency when approaching a 1 cent euro coin. SRF shifts from 1.397 MHz to 1.4857 MHz
  • Shift of the self-resonant 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.

 

RLB1112V4 Series 400 Volt Radial Inductor Phase Resonance.png

 

 

#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

 

MeasureDescriptionNo Coin1 cent2 cent5 cent10 cent20 cent50 cent1 EUR2 EUR
LsSeries Inductance953.3 uH963.4 uH964.5 uH965.9 uH950.4 uH950.7 uH949.7 uH952.5 uH954 uH
|Z|Impedance5.99 Ω6.053 Ω6.06 Ω6.069 Ω5.972 Ω5.974 Ω5.967 Ω5.985 Ω5.994 Ω
RsSeries 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
XsSeries Reactance5.99 Ω6.053 Ω6.06 Ω6.069 Ω5.972 Ω5.974 Ω5.967 Ω5.984 Ω5.994 Ω
Input Phase0.3435 °0.3472 °0.3476 °0.3481 °0.3425 °0.3426 °0.3422 °0.3432 °0.3438 °
θPhase90.93 °90.5 °90.66 °90.48 °90.71 °90.63 °90.52 °90.74 °90.59 °
DDissipation0.01630480.00879280.01144440.00839470.01233320.01105920.00910270.01298820.0103385
QQuality61.33151113.729587.3788119.12381.0816590.42268109.856976.9931896.72555

 

 

RLB1112V4 Series 400 Volt Radial Inductor Phase Impedance Discrimination 1 kHz 5mm

 

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.

 

RLB1112V4 Series 400 Volt Radial Inductor Phase Impedance Discrimination 1 kHz

 

 

 

#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

 

Polyester film capacitors

 

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

 

Testing LC Tank

 

Impedance response to the frequency of the different LC tanks.

 

RLB1112V4 Series 400 Volt Radial Inductor Phase LC TANK impedance

RLB1112V4 Series 400 Volt Radial Inductor Phase LC TANK phase

 

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.

 

 

CapacitorResonant FrequencyTheoretical calculation (L= 1mH)
SRF1.38 MHz
1nF162.5 kHz

159.15 kHz

2.2 nF110.06 kHz

107.3 kHz

3.9 nF81.70 kHz

80.59 kHz

5.6 nF66.98 kHz67.26 kHz
33 nF27.40 kHz27.71 kHz
68 nF18.41 kHz19.3 kHz
220 nF10.707 kHz10.73 kHz
1000 nF4.91 kHz5.03 kHz

 

Resonant Frequency LC Tank

 

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.

RLB1112V4 Series 400 Volt Radial Inductor LC 220 nF tank

 

 

#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

 

 

 

LC Tank L1mH C56nF

 

Theoretical Resonant Frequency L= 1mH C= 56nF 21.27kHz. Measured =

 

 Impedance Frequency response LC tank 56 nF 1mH

 

Impedance measurement of the system

 

  • @ 21.32 kHz / 1V / 20 ºC / Averaging 500ms / 1 mm separation

 

MeasureDescriptionNo coin1 cent2 cent5 cent10 cent20 cent50 cent1 EUR2 EUR
LsSeries Inductance124.8 uH4.055 mH3.576 mH3.178 mH6.958 mH8.907 mH8.725 mH9.109 mH8.837 mH
|Z|Impedance4.872 kΩ1.383 kΩ1.028 kΩ923.1 Ω1.049 kΩ1.362 kΩ1.315 kΩ1.511 kΩ1.461 kΩ
RsSeries Resistance4.872 kΩ1.273 kΩ910 Ω819.8 Ω488.4 Ω663.8 Ω609.6 Ω896.9 Ω862.7 Ω
XsSeries Reactance16.72 Ω541.3 Ω477.4 Ω424.2 Ω928.7 Ω1.189 kΩ1.165 kΩ1.216 kΩ1.18 kΩ
Input Phase0.4368 °13.59 °14.21 °13.28 °32.15 °35.76 °36.1 °32.88 °32.56 °
θPhase0.1967 °23.03 °27.68 °27.36 °62.26 °60.83 °62.37 °53.59 °53.82 °
DDissipation291.30532.3522581.9062651.9328090.52592480.55829650.52340080.73766070.7313722
QQuality0.00343280.42512340.52458610.51738171.9014131.7911631.9105821.3556371.367293

 

Coin discrimination based on phase and impedance change.

 

Coin Discrimination LC Tank 1mH 56nF

 

 

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.