3 · Physics & Mathematics

Physics & Mathematical Formulation

Name: Denka® Platinum Plate
Brand: Denka®

The Denka® Platinum Plate behaves as a frequency-selective magnetic absorber. Its behaviour follows from the complex permeability of the DT400L Ni-Zn ferrite.

3.1 · Complex permeability

The permeability of a ferrite is complex and frequency-dependent. The real part μ′ stores magnetic energy; the imaginary part μ″ dissipates it.

μ (ω) = μ^{'} (ω) - j μ^{''} (ω)

(Eq. 3.1)

50 / 60 Hz

At 50/60 Hz, μ′ dominates and μ″ is negligible. The added series reactance ωL is negligible, so fundamental power passes through essentially unaffected.

150 kHz – 30 MHz

Across 150 kHz – 30 MHz, μ″ rises. The plate behaves as a frequency-dependent resistance, converting HF magnetic-field energy into heat.

3.2 · Volumetric power absorption

The power absorbed by the plate volume depends on frequency, the loss component μ″ and the square of the local magnetic field strength:

P_{absorbed} = π f μ_{0} μ^{''} (f) H_{peak}^{2} V_{plate}, μ_{0} = 4 π \times 1 0^{- 7} H/m

(Eq. 3.2)

The magnetic field of a conductor falls off with distance r, which is why plates are clipped directly against the phase conductors:

H = \frac{I}{2 π r}

(Eq. 3.3)

NOTE

Because HF noise currents are small relative to the load current, absorbed power is small — self-heating stays at or below 0.4 °C.

3.3 · Skin effect & copper skin depth

As frequency rises, current crowds to the surface of the conductor. The effective conducting area shrinks and AC resistance rises.^{[9[9] Novitskiy et al., 2020Supraharmonic losses in MV/LV cables.,10[10] Mariscotti & Mingotti, 2024Supraharmonics, cable losses and partial-discharge activity.]}

δ (f) = \frac{ρ}{π f μ _{r} μ _{0}}

(Eq. 3.4)

Frequency	Skin depth δ (Cu)
50 Hz	9.2 mm
150 kHz	0.17 mm
2 MHz	0.046 mm
30 MHz	0.012 mm

Interactive: copper skin depth

Conductor cross-section (current-carrying region highlighted)

Frequency

191 kHz

Skin depth δ

0.15 mm

ρ = 1.68×10⁻⁸ Ω·m · μr ≈ 1 · conducting area ≈ 3% of cross-section

Losses at each frequency add independently, so HF currents contribute disproportionately to total conductor loss:

P_{total} = I_{50}^{2} R_{50} + k \sum I_{k, HF}^{2} R_{k, AC}

(Eq. 3.5)

3.4 · Core losses in motors & transformers

Bertotti's loss-separation model splits core loss into hysteresis, classical eddy-current and excess components. The classical eddy-current term scales with the square of frequency — so HF content drives eddy losses up sharply:^{[14[14] Bertotti, 1988General properties of power losses in soft ferromagnetic materials. IEEE Trans. Magnetics (loss separation).,7[7] Ding & Mi, 2011Iron losses in induction motors under PWM supply (+29% under load, +86% at no load).,8[8] Yaghoobi et al., 2020Distribution transformer eddy-current losses and insulation ageing under inverter harmonics.]}

P_{core} = P_{hyst} + P_{eddy} + P_{exc}

(Eq. 3.6)

P_{eddy} = K_{e} \cdot B_{m a x}^{2} \cdot f^{2} \cdot t^{2}

(Eq. 3.7)

K_e: material constant · B_max: peak flux density · f: frequency · t: lamination thickness