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How to make a susceptometer

How to make a magnetic susceptometer using a lock in amplifier

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In the 70s, susceptometers with large working volumes were built to study ferrites and superconductors. These devices seem not to be available nowadays, and if you need a custom susceptometer for a project, they tend to be very expensive - so why not build your own instead? With this project, we show how this may be done. feel free to comment or contribute; we're looking for feedback from experts on this one.

This project is an AC Susceptometer designed to characterize the magnetic properties of materials from ~1KHz - ~1MHz. The core of the device is a custom coil assembly featuring a large outer driving solenoid (76 mm diameter, 54 turns) and a differential inner pickup pair (45 mm diameter, 86 turns each).

We drive the outer coil with a function generator to create an oscillating magnetic field (20uT RMS at low frequencies). The pickup coils are wound in opposition so that, in free space, the induced voltages theoretically cancel out. We use a Lock-in Amplifier (LIA) referenced to the drive signal to demodulate the output, allowing us to extract signals buried in noise.

The measurement relies on Faraday’s Law of Induction. When a sample is placed inside one of the pickup coils, its magnetic susceptibility chi modifies the local magnetic flux, breaking the symmetry of the coil pair. This imbalance induces a net voltage. By analyzing the signal components in-phase X and out-of-phase Y with the drive, we can determine the complex susceptibility of the material. The in-phase component corresponds to the real susceptibility X', indicating magnetization, while the quadrature component X'' relates to energy dissipation. This allows us to observe magnetic phase transitions and loss mechanisms that DC measurements might miss. 

We are able to get qualitative measurements but we are unable to verify the quantitative accuracy of most measurements due to the lack of calibration samples within an order of magnitude of most of our ferrite samples. Additional corrections prevent us from precisely comparing samples of different geometries. 

Results:

We measured the susceptibility of 6 samples:

  1. Dy2O3 Powder
  2. Fe2O3 Powder
  3. Ferrofluid
  4. Ferrites
    1. Barium Hexaferrite
    2. Type 77 Ferrite
    3. Type 78 Ferrite

The signal from our Dysprosium Oxide (Dy2O3) calibration standard is extremely weak—hovering at just a few microvolts below 10 kHz, which is barely indistinguishable from our 6 uV noise floor. It also appears to be inaccurate to compare samples of different volumes. We compared the Dy2O3 powder against an Iron Oxide (Fe2O3) sample with 5x the volume. Based on standard molar susceptibility values, density, and volume, the Fe2O3 signal should be roughly one-third the strength of the Dy2O3. However, experimental data shows the Fe2O3 magnitude is 5x stronger—a ~15x deviation from prediction. The results for the samples are below:

Material

Dysprsium

Fe2O3

BaM

Ferrofluid

77 Ferrite

78 ferrite

Volume (cm^3)

3.534

18.65

5

18.65

8.96

10.77

Weight (g)

7.7264

28.1353

98.69

Susceptibility (cm^3/mol)

89,600·10−6

3586.0x10−6

volume susceptibility

0.00186

0.00063

2.5

2000

2300

Relative Signal Strength (Permeability * volume) compared to Dy2O3

1

0.34042

1,347

1,077,584

1,239,222

Measured relative signal strength at 10KHz

1

5

280

1,300

2,700

6,000

The ordering is accurate except for the iron oxide which is inaccurate likely due to the volume correction error.

The baseline is also quite large, 6 uV, this may be due to poor common ground noise from our outlet, em radiation noise or other sources. At higher frequencies the parasitic capacitance between the driving and pickup coils becomes significant, this limits the frequency range of the device.

centerpieces - CenteringPiece.step

Pieces to be 3D printed that centered our smaller coil within the larger driving coil, If you use the same tube print these otherwise modify for your dimensions.

step - 8.55 kB - 01/20/2026 at 21:55

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  • 1
    Step 1

    Bill of materials:

    1. Lock In amplifier
    2. Function Generator
    3. Oscilloscope (Optional)
    4. 50 Ω BNC resistor (Must be a coaxial resistor)
    5. BNC Cables
    6. Plastic tubes Large and Small
    7. 26 AWG enameled cable
    8. 12 AWG cable

    Tools

    1. Wire stripping tools
    2. Soldering ability
    3. 3D printing or woodworking ability
    4. LCR meter
    1. Construct the driving coil: Wrap your insulated 12 AWG wire around the larger driving coil and tape it securely, we used 54 turns. The driving coil should be at least 5*longer than each of your individual pickup coils.
    2. Construct the pickup coils: Wrap the enameled 12 AWG wire enough turns that the length is at least similar to the diameter, for us this was 86 turns for a length of 38 mm. Then have a gap of at least this distance between the two pickup coils and begin your second pickup coil, this one needs to have opposite chirality to the first. Scrape the enamel between the two coils and on either end of the coil. Add turns until the inductances of the two coils match.
    3. Connect your BNC cables: You want the cables to be coaxial as close as you can to the coils to prevent external pickup. Cut a BNC coax cable and strip the end so only the center conductor is showing. Solder that to the end of your pickup coil. Strip the insulation from a section of the BNC where it will line up with the other end of the pickup col. Solder the outer GND conductor at that location as well. Repeat for the driving coil. Make sure your BNC is long enough to comfortably reach your equipment.
    4. Connect the components like the schematic above, see image above as well. Most LIA’s have their own function generator and you can use that instead of the Oscilloscopes function generator. The oscilloscope is also optional, its purpose is to measure the current through the coil. The 50 Ω resistor allows the current to be more constant and stable, at low frequencies the impedance of the driving coil is very small and the current will likely be limited by the current output of the function generator and will not be able to supply the voltage it is set to. 
    5. Apply settings for you instruments:
      1. LIA
        1. Single ended input and output
        2. Reference to external and select the port you connected to function gen
        3. Typical Low pass is BW 3 dB of 100 Hz
      2. Function generator
        1. Max voltage that does not exceed power limits of your resistor
        2. Impedance to high Z
        3. For calibration I used 5 KHz but checked the response at multiple frequencies.
    6. Centering Coil: 3D print at least 4 of the spacers included in the files or print your own to match the dimensions of your tube. While applying the oscillating voltage to your driving coil at 5 KHz (higher frequency stronger signal but if too high parasitics will add error), move the center coil back and forth until the in phase component of the signal is as close to zero as possible.
    7. Verification: With the pickup coil fixed, slide a sample through the center of the device taking measurements along the way. It should look like the image below. If one of the humps is greater than the other you need to adjust your pickup coils to have the same inductance. 3D printing a sample holder to get it centered in the pickup will help your measurements especially at higher frequencies.
    8. Record data: Place your sample at the location that maximizes the signal strength and record the signal magnitude and phase. Recording the STD Deviation of these values can also give you a sense for the error.

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