Amazing Eddy Currents

Apply Them to Thin Metal Thickness Measurement

Eddy currents are swirling electrical currents created when a magnetic field is moved over a conducting metal, or the metal is moved through a magnetic field. George writes about his experiments using eddy currents to determine the layer thickness of copper on PCBs and aluminum and copper foils. He also describes a simple eddy current apparatus that he built using a PC, a single resistor, and a USB sound card to measure thickness.

Over the years, many different techniques and devices have been used in these various applications. In this study I will focus on the ideas related to finding the thickness of a thin metal sheet or plate. Research has shown that there may be a direct way to achieve this goal. These efforts have led to the method employed here, which uses experimental data to determine how the terminal impedance of an eddy current (EC) sensor is related to a physical property of the material—in this case, the thickness of thin films. Here I focus on copper layer thickness on printed circuit boards (PCBs) and aluminum foil.

EC sensors can be very simple or complex depending on the job to be done. For this project, single coil EC sensors were constructed. It was also found that low-cost, off-the-shelf devices could be easily repurposed for use as sensors.

Finally, I’ll describe a straightforward circuit employing a PC with a USB sound card to find metal thickness. Amazingly, the simple eddy current apparatus described here has enough accuracy to measure copper PCB thickness.

This project started innocently enough with an exchange of academic papers. A friend sent me a copy of some work done in the field of eddy current measurements [1], specifically related to the measurement of thin metal sheets. For curiosity more than anything else, I wondered if this work would apply to copper printed circuit board (PCB) material. Over the years, my lab has accumulated a large amount of raw copper PCBs used to produce printed circuit boards for various projects. As is well known, PCB material comes in a variety of copper thicknesses. Since the sources for this material are frequently lost or unknown, I sometimes resort to trial and error when etching a board. It would be nice to have a simple way to classify this material, as it cannot be done easily by visual inspection.

Several years ago, spurred on by the possibility of using simplified methods and low-cost measuring circuits, several experiments were undertaken to investigate eddy current methods for thickness determination. In the course of that work, several simple EC sensors and techniques were devised. These results, including building a phase meter circuit, were reported by Steber [2]. Admittedly, the phase circuit was a bit touchy, but it was accurate. In this paper I expand on that work by enlarging the number of possible off the shelf EC sensors and utilizing a PC with a USB sound card system to do the measuring task. Before I proceed too far, however, it is advisable to give some background in the field of eddy current measurements.

EDDY CURRENT CONCEPTS

At the heart of an EC measuring device is a magnetizing coil with an alternating current in its winding. When the coil is placed near a metallic object, the variable field induces into the object a distribution of eddy currents. Figure 1 shows a simple example of such eddy current fields. The amplitude and phase of these induced currents depends on many parameters, such as object material, geometry, magnetizing coil, distance to object, exciting signal amplitude and frequency. In turn, these eddy currents generate their own magnetic field that depends on the object geometry and its electrical and magnetic properties.

Stated generally, the resulting eddy current magnetic field contains, in principle, all the characteristics of the object. However, determining the object properties from this field is mathematically difficult, and has been solved only for simple geometries. Even for these cases, the solutions are complicated, and numerical simulation methods must often be employed. An excellent article by Heinzle [3], provides a general introduction to the subject, including a complete mathematical treatment. In spite of these complexities, eddy current testing has evolved into a well-developed technology for inspection of thin metals, with many applications in the aerospace, manufacturing, and service sectors.

To narrow down the subject a bit, we’ll discuss here only the specific application of eddy currents for determining the thickness of thin copper or aluminum foils. It should be mentioned, however, that other methods exist for accomplishing this goal. For example, expensive 4-point micro-resistance measuring equipment, such as the CM95or CMI165 [4], can be used for the job in many cases. However, our focus here will be mainly on eddy current methods using impedance techniques.

Considerable precision for this task can usually be obtained by using complex impedance instrumentation working at various frequencies. The simplified procedure is as follows. First, the impedance of a magnetizing coil in free space, with an AC current in its windings, is measured and saved. Next, the coil is placed on the metallic plate of interest, and the impedance is measured again. The difference between the two impedance measurements contains considerable information about the plate thickness and other factors. Of significant interest are the frequency and the real and imaginary parts of the impedance.

In what follows I will look at the characteristics of these impedance measurements and see how they relate to metallic thickness. The homemade sensors that were constructed, as well as inexpensive, off-the-shelf inductors that were used as sensors will be discussed. And finally, an apparatus for measuring metallic thickness using a PC with a USB sound card and a simple circuit will be presented. But first, we’ll look at some background material related to eddy current testing.

PHASE METHODS

At first glance it might not appear possible that simply putting a coil above a metallic plate, as shown in Figure 1, can provide thickness information. Yet, eddy current techniques are used, for example, to measure the thickness of a hot sheet in a rolling mill, and metal thinning of an aircraft fuselage due to corrosion. Many different types of sensors are used in these applications. The impedance plane (R vs. jX) is often used to display thickness variations and subsurface defects.

Many ways of looking at the impedance data have been considered over the years. A major simplification has been proposed by Pinotti and Puppin [1] for measuring thickness by concentrating on the phase only. They have devised a simple lock-in method using inexpensive CMOS integrated circuits. To accomplish this goal, they introduced a pickup coil in addition to the field coil. This arrangement is shown in Figure 2. Excitation is provided by a sine wave signal generator. Amplifier A1 provides the reference signal proportional to the current in the field coil. Amplifier A2 is a high-gain amplifier providing the pickup coil signal.

Using a pickup coil enables more direct measurement of the eddy current field, and permits measurement of the phase difference between the free space field (reference field) and the field with the metallic plate. An interesting result is achieved by this arrangement. As the frequency is swept, there will be a peak in the phase difference field. The location of this peak phase, in frequency, corresponds to the thickness of the plate. Results obtained by this arrangement reportedly produced peak phase differences on the order of 80°. So, it should be easy to determine metal thickness by looking for the phase peak versus frequency scan.

Although this method is appealing and may work well, it does involve building a precise two-coil probe and lock-in circuit. Could similar results be obtained with a single coil? Considering this possibility, I decided to experiment with a single coil configuration and see if there was another way to get the thickness information. This brings us to the concept of phase signature.

MULTI-FREQUENCY PHASE SIGNATURE

In eddy current testing, differential signals are often employed. For example, the difference in the complex sensor impedance given as ∆Z = Z – Za is used, where Z is the sensor impedance and Za is the impedance in free space. A multi-frequency phase signature is found by measuring the phase angle of ∆Z at a number of frequencies. Here, the ∆Z phase angle is obtained as ø = arctan [Im(∆Z)/Re(∆Z)], where Re and Im are the real and imaginary parts.

An example of a phase signature of an inductive EC sensor in the presence of a nonmagnetic metal plate is shown in Figure 3. Here, we see that the imaginary part decreases with frequency, indicating that the magnetic flux is reflected more at higher frequencies. The real part is related to the heat loss in the conducting plate.

Yin and others [5], made use of this concept by comparing it to mathematically modeled air-core and ferrite-core coils above a metallic plate. It was also successfully applied to estimate plate thickness. This was done in two steps. First, the phase signature was obtained. Then it was compared, in the least squares sense, with pre-calculated phase signatures obtained from values on the material datasheet. Relative errors on the order of 2% were realized. This method, while successful, does require considerable modeling, simulation experience, and complex impedance measurements using a vector impedance analyzer (VIA).

In my previous work [2], a specially constructed VIA based on an impedance bridge described earlier [6] was used to make the complex measurements. Its use in obtaining data is described later. However, that instrument is out of the realm for most experimenters. Therefore, in that work, a relatively simple phase meter was designed using integrated circuits that could be used for finding the differential phase of the EC sensor at different frequencies. It performed well but required several separate instruments and a calibration procedure. In the present paper, I will show a less complicated technique that uses only a PC with a low-cost USB sound card to make the measurements. But before I get to that, let’s review the types of EC sensors that were used in this work.

EDDY CURRENT SENSORS

I decided to experiment with air-core coils, ferrite-core coils, and off-the-shelf inductors. Three of the sensors used are shown in Figure 4.

Although the coils are shown on their sides for clarity, during operation, the flat, circular end should make contact with the metallic material being studied.

Air-core coils are the easiest to make. However, experiments showed that they were not as sensitive or as compact as ferrite core sensors in this application. Hence, extensive tests with air-core coils were not continued. Proceeding only with ferrite cores, several EC sensors varying in diameter from 8 to 10mm were constructed. They were made using 30 to 80 turns, and had inductances of 40 to >150µH.

Some commercial ferrite-core inductors from Murata and Coilcraft were also obtained and tested. Most surprisingly, they performed as well as or better than the handmade versions. Various values in the range of 150µH to 1,000µH were tested. Results of this testing will be shown later.

CALIBRATION SAMPLES

Copper samples in the thickness range expected for single-sided copper PCB material are needed for testing. Sheets or foils of 0.4, 1.0, 1.25, 1.4 and 3.0mil were obtained. Various samples may be stacked for testing. For example, a 1.0mil and 1.4mil foil can be stacked to obtain a 2.4mil-thick test sample. Each sample sheet is at least 3×3”.

Copper PCB material is often specified by copper weight. Table 1 shows the relation between copper PCB weight and copper thickness in mils (thousandths of an inch) and mm (millimeters) for several popular single-sided PCBs.

Also, some common, kitchen-type, aluminum foil was cut into small 3×3” rectangular sheets. According to the manufacturer, each sheet is 0.9799mil (23.62µm) thick. Foil sheets can be stacked to obtain various thicknesses for test purposes. Since copper and aluminum have different conductivities, the results for one do not correspond to the other. Nevertheless, it is useful to have aluminum material for testing.

OBTAINING IMPEDANCE DATA FROM EC SENSORS

As discussed earlier, the phase signature depends on finding the difference in the complex sensor impedance, as given by ∆Z = Z – Za, where Z is the impedance over a nonmagnetic metal plate and Za is the impedance in free space. The complex parts, Im(∆Z) and Re(∆Z)], are used to determine the phase angle. In this work, a VIA is used to collect this impedance data for various EC sensors on different thicknesses of material. Thus, it’s possible to find out how the phase changes with the thickness parameter over frequency.

My VIA arrangement is shown in Figure 5. It works this way. An experimental, single-coil ferrite EC sensor, which is firmly placed on the test material, is connected to the VIA inputs. Data on the phase and other impedance parameters is obtained for specific material thicknesses, over a frequency range of 1kHz to 20kHz. This data is then plotted to see if a relationship can be found, like that shown in the typical phase signature.

My strongest interest at this point was in checking how the EC sensor phase would change with thickness, and seeing if it was anything like that observed by Pinotti and Puppin [1]. To this end, various EC sensors were built and tested. It was found that those devices having less than 100µH did not produce large enough or consistent phase variations to be reliable at large material thicknesses. This is probably because this method relies on the ratio of Im(Z) to Re(Z) (of the sensor) to find phase. This ratio is strongly influenced by Re(Z), which is a small quantity for a coil, and is hard to measure consistently. It is expected that phase measurement accuracy will improve as Im(Z) gets larger, corresponding to a bigger inductance.

One of the larger EC sensors constructed—a 60-turn coil wound with 28 AWG wire on an 8mm diameter ferrite rod—proved interesting. It measured about 125µH with a resistance of about 0.35Ω measured at 5kHz. Figure 6 shows the phase response over material thicknesses of 0mil to 3.0mil.

With no copper present (0mil curve) the phase tends toward 90° as expected for an inductor. There is an interesting region around 5kHz, with all the curves in this region separated nicely in phase. That is, there is a phase difference between the copper foils without the curves crossing. In the region from the 0.4mil foil to the 3mil foil, there is a substantial phase difference. Hence, a sensitive phase measuring instrument set to 5 or 6kHz should be able to distinguish between the copper foils based on phase alone.

We also know from the phase signature shown earlier (Figure 3), that Im(Z) decreases when metal is placed in front of the EC sensor. This would imply a reduction in inductance with increased material thickness. That is exactly what we see in Figure 7 for this sensor. The separation in inductances at 10kHz, with material thickness, is large enough to be used for discrimination of copper foil thickness based on inductance alone. An inductance meter operating at 10kHz with 1-2% accuracy should be able to do the job quite well.

These results led me to investigate commercial ferrite inductors. Several types of Murata and Coilcraft 10mm diameter inductors were obtained and tested. Extensive testing was done on a 330µH Murata (19R334C) and a 470µH Coilcraft (RFC1010B) ferrite inductor.

Figure 8 shows the inductance values versus frequency for the 330µH Murata inductor. There is enough spread at 10kHz to make this a viable way to find copper thickness. A calibration curve based on inductance versus thickness is easily derived and is shown in Figure 9. Phase curve separations (not shown) for this device were small—on the order of 5°. So, phase measuring for thickness determination would be marginal.

USB SOUND CARD LCR METER

It has been shown that measurements of the inductance of an EC sensor at 10kHz can be used to determine copper foil thickness. Many quality vector LCR meters can measure inductance accurately at this frequency. For example, my Tonghui TH2811D LCR meter was used to verify these measurements. Other vector LCR meters, such as the DE-5000 LCR meter (DER EE Electrical Instrument), also work well at 10kHz. So, using a commercial LCR meter can be a direct way to measure copper foils. For those without access to these instruments, I will present a different kind of LCR measuring system. It is based on an old design of mine [6] that has worked well.

This system uses an inexpensive USB sound card, a single resThis system uses an inexpensive USB sound card, a single resistor, and some PC software. LCR components can be measured at frequencies of 1kHz, 5kHz, 10kHz, and 20kHz. It works well in this application—measuring inductors at 10kHz.

Figure 10 shows my test setup, with the sound card on the left and the test rig on the right. The USB device is a compact unit, with a front speaker output and a stereo line input, and it operates at 48kHz (48,000 samples per second). Inputs and outputs use 3.5mm stereo jacks. It is important for the sound card to have a CM6206 chip inside. Older look-alike versions used a CM106 that has does not work as well. This nice audio interface device was obtained on eBay for $10.

The parts arrangement and circuit for this measuring system are shown in Figure 11. Only a single 68Ω resistor and some input and output connectors are required. Switches S1, S2, and S3 are used to perform the direct, open, and short compensation for the software. For example, the direct compensation is done when S1 is closed and S2 is open. During normal operation S1 is open, S2 is closed, and S3 is open. Jumpers could be used instead of switches. Measuring inductances at 10kHz with this circuit, in the 50µH to 1,000µH range, has proved to be accurate. In case anyone wants to experiment with this inductance testing system, Windows software will be provided on the website. More operating details are provided with the software. Figure 12 shows the computer screen.

An important thing to consider when using an eddy current device is the surface area being measured. It must be large enough to encompass most of the eddy current field lines. Typically, at least 1.5” must be allowed around the sensor.

Also important, the sensor must be in contact with the surface to reduce lift-off effects. As the sensor is moved over the copper, changes in the field will occur, due to scratches or other defects in the material. If you get close to the edge of the foil, the field will drop off drastically. Nevertheless, if used carefully, this eddy current method can be used to differentiate thin copper and aluminum material up to 3mil thick.

SUMMARY AND CONCLUSIONS

In this study, several experiments were performed using eddy current methods to measure the thickness of copper foils and single-sided copper PCB material. It was verified that phase information from the impedance data could be used to differentiate thickness.

Of the EC sensors described, the air-core coil was the least sensitive to phase, with the ferrite-based sensors being the best. Inductance was shown to be a strong discriminating indicator of metallic thickness for copper foils.

Inductance measurements of a Murata 330µH inductor showed that it could be used to determine copper thickness with proper calibration. Although not as sensitive as a homemade ferrite coil, it can easily be used for this purpose. The Coilcraft 470µH inductor could also be used. These stock inductors will need calibration of inductance versus thickness, because of the part tolerances involved.

It was shown that standard 10kHz LCR meters may be used to measure the inductance, which corresponds to the value to mils. A low-cost LCR measuring system was also described that could do the job. Having stock copper foils on hand will be helpful for calibration of these meters. Extending this method to double-sided copper PCBs would be a useful addition to this work. In this situation, one would need to investigate how the eddy currents are formed.

It was fun working with these amazing eddy currents. Hopefully you have learned something about them and perhaps you will find new uses for them in your next project. 

REFERENCES
[1] E. Pinotti and E. Puppin, “Simple Lock-In Technique for Thickness Measurement of Metallic Plates”, IEEE Transactions on Instrumentation and Measurement, vol 63, no. 2, pp 479-484, February 2014
[2] G. Steber,”Experiments With Eddy Current Methods for Thickness Measurements of Thin Metallic Materials,” QEX, No. 287, November/December 2014
[3] www.omicron-lab.com/bode-100/application-notes-know-how/articles-use-cases/eddy-current-testing.html
[4 ] www.oxford_instruments.com 
[5] W. Yin and A. Peyton, “Thickness Measurement of Metallic Plates With an Electromagnetic Sensor Using Phase Signature Analysis”, IEEE Transactions on Instrumentation and Measurement, vol 57, no. 5, pp 1803-1807, August 2008
[6] G. Steber, “An LMS Impedance Bridge”, QEX, No. 232, September/October 2005

PUBLISHED IN CIRCUIT CELLAR MAGAZINE • DECEMBER 2024 #413 – Get a PDF of the issue

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