Dr, Foerster Codebreaker: Your Guide to the Complex Permeability Plane

In Eddy Current Testing (ECT), understanding how your test frequency relates to your specimen’s properties is crucial. Figure 1—the Complex Permeability Plane—condenses this relationship into a single, powerful curve. Here’s how to read it, and how to use it to select the right frequency for detecting surface vs. subsurface flaws.

Figure 1

What Figure 1 Shows

• Axes:

  • Vertical (Real μeff): The magnitude of the material’s effective permeability—how strongly it “lets through” the alternating magnetic field.

  • Horizontal (Imag μeff): The phase-lag component introduced by eddy-current losses—how much the induced currents “fight back” against the excitation field.

• Curve Points: Marked at frequency‐ratio values f/ fg = 1, 5, 10, … up to very high multiples. Fg is the limit frequency, where eddy-current shielding becomes significant .

The Frequency Ratio f / fg

The limit frequency fg ties your test setup (material, size) to a baseline: 

• μrel= material’s relative permeability

• σ = conductivity (m/Ω·mm²)

• d = specimen diameter (cm).

Your frequency ratio f / fg tells you where you fall on the curve:

• Low f / fg (near 1): μeff. ≈1 (top of curve). Eddy currents are weak—fields penetrate deeply.

• High f / fg (10 – 50 or more): μeff. →0 (bottom). Strong shielding—currents stay near surface.

Practical Takeaways from Figure 1

1. Surface‐Crack Detection

   • Choose high f / fg (e.g., 10–50) so μeff. drops and eddy currents concentrate at the surface.

2. Subsurface Flaw Finding

   • Opt for low f / fg (≈1–5) to let currents penetrate deeper.

3. Material Characterization

   • Track how the real and imaginary components shift with f / fg to separate conductivity vs. permeability effects.

   
   

By plotting your specific f / fg on Figure 1, you immediately see whether your setup is tuned for shallow or deep inspection—and how much signal loss to expect from eddy‐current shielding .

How Dr. Foerster Used Figure 1 in His Workflow

1. Calculate f / fg: Use your material’s σ, μrel., and specimen diameter in the fg formula.

2. Pick Test Frequency f: Factor in your equipment’s capabilities and the type of defect you’re targeting.

3. Locate f / fg on the Curve: Read off real vs. imag μeff. to anticipate signal amplitude (real) and phase shift (imag).

4. Adjust Probe & Settings: Optimize lift-off, probe type, and gain based on the expected μeff. values.

5.   How Do We Use Figure 1 Today?

Well, we don’t really use it directly, but because Dr. Foerster figured this all out for us, we know that:

·         High test frequencies concentrate dense eddy currents at the material surface next to the coil, and are best for surface-breaking crack detection

·         Low test frequencies have more penetrating power, and are better for detecting sub-surface discontinuities

·         The separation angle (think F90) will vary as the test frequency is raised or lowered, which can be used to distinguish between the variables encountered during an eddy current test.

Enjoying the Dr. Foerster Codebreaker series?  Drop a comment below and learn more about Dr. Foerster’s foundational contributions to modern-day  eddy current testing at eddycurrent.com!