Complex permeability: how a ferrite passes 50 Hz and absorbs MHz noise

The Denka® Platinum Plate is made of a Ni-Zn ferrite / sintered ceramic composite (grade DT400L). Its behaviour follows from one equation:

$$\mu (\omega )={\mu }^{\prime }(\omega )-j{\mu }^{\prime \prime }(\omega )$$

Qualitative illustration of how the storage (μ′) and loss (μ″) components behave across frequency — not measured DT400L data.

Storage vs loss

• μ′ (real part) stores magnetic energy. At 50/60 Hz it dominates while μ″ is negligible, so the added series reactance $\omega L$ is negligible and fundamental power passes essentially unaffected.
• μ″ (imaginary part) dissipates energy. Across 150 kHz – 30 MHz it rises, so the plate behaves as a frequency-dependent resistance, converting HF magnetic-field energy into heat.

How much power is absorbed?

$$P_{\text{absorbed}}=\pi f{\mu }_0{\mu }^{\prime \prime }(f)H_{\text{peak}}^2{V}_{\text{plate}},H=\frac{I}{2\pi r}$$

Two consequences follow:

1. Absorption scales with $H^2$, and $H$ falls with distance $r$ — so plates are clipped directly against the phase conductors.
2. HF noise currents are small compared with load current, so absorbed power is small — self-heating stays at or below 0.4 °C.

References

1. Physics & mathematical formulation
2. Unified product specification
3. Bertotti, 1988 — power losses in soft ferromagnetic materials