From f9da3edb5ce385b61f856b4dfa019146b6d975dc Mon Sep 17 00:00:00 2001 From: Denis Chevalier Date: Mon, 10 Aug 2026 00:00:30 +0200 Subject: inductor losses and parasitic effects --- module-design.typ | 119 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 119 insertions(+) (limited to 'module-design.typ') diff --git a/module-design.typ b/module-design.typ index 2e21425..c9bb128 100644 --- a/module-design.typ +++ b/module-design.typ @@ -1894,6 +1894,125 @@ Mitigation requires strict physical layout controls: - Enforcing minimum trace clearance constraints between low-level signal traces and high-voltage/power rails. +===== Inductor losses and parasitic effects + + +====== Physical mechanism + + +Inductors, when used in analog circuits (filters, RF chokes, DC-DC converters, +etc.), introduce several non-ideal error mechanisms: +/ DC resistance ($upright("DCR")$): Finite copper wire resistance cause IR + voltage drops and thermal power dissipation, +/ Core losses: Ferromagnetic cores exhibit hysteresis and eddy current losses, + acting as a frequency-dependent parallel resistance, +/ Parasitic capacitance: Winding-to-winding and winding-to-core capacitance + creates self-resonance ($omega_0$), above which the inductor behaves as a + capacitor, +/ Core saturation: Ferromagnetic cores have finite permeability that decreases + at high flux densities $B$, causing inductance $L$ to drop with high currents, +/ Core noise: Barkhausen noise from discrete domain-wall motion in magnetic +materials introduces non-Gaussian voltage fluctuations. + +====== Mathematical model + + +The complex impedance of a real inductor is modeled as: + +$ + Z_L (f) = R_upright("DC") + R_"core" (f) + j omega L dot 1/(1 - (omega/omega_0)^2) +$ + +Where $R_upright("DC")$ is DC winding resistance, $R_"core" (f)$ is +frequency-dependent core loss, and $omega_0 = 1/sqrt(upright("LC")_"parasitic")$ +is the self-resonant frequency. + +Core hysteresis/eddy loss power density is governed by the Steinmetz equation: + +$ P_"core" = k dot f^alpha dot B^beta $ + +Where $alpha approx 1.3 - 1.8$ and $beta approx 2-2.5$ for typical ferrite +materials. + +====== Typical magnitude + + +#figure( + table( + columns: 5, + table.header([Inductor type], [$upright("DCR")$], [Core loss ($qty(10, "kHz")$)], [Self-resonance], [Notes]), + [Air core], + [High ($qtyrange(1, 100, "ohm", delimiter: "\"to\"")$)], + [None], + [High ($gt qty(100, "MHz")$)], + [No saturation, no core noise], + + [Ferrite bead], + [$qtyrange(0.1, 1, "ohm", delimiter: "\"to\"")$], + [Very high], + [$qtyrange(10, 100, "MHz", delimiter: "\"to\"")$], + [Designed for loss (filtering)], + + [Ferrite inductor], + [$qtyrange(0.1, 10, "ohm", delimiter: "\"to\"")$], + [Moderate], + [$qtyrange(1, 50, "MHz", delimiter: "\"to\"")$], + [General purpose], + + [Powdered iron], + [$qtyrange(0.5, 5, "ohm", delimiter: "\"to\"")$], + [Low], + [$qtyrange(1, 10, "MHz", delimiter: "\"to\"")$], + [DC bias tolerant], + + [Laminated steel], + [$qtyrange(0.1, 1, "ohm", delimiter: "\"to\"")$], + [Low at audio rate], + [$qtyrange(0.01, 1, "MHz", delimiter: "\"to\"")$], + [Audio transformers], + ), + caption: [Inductor losses and parasitic effects typical magnitudes], +) + +For a $qty(10, "mH")$ ferrite signal-path inductor with +$qty(5, "ohm") upright("DCR")$ carrying a $qty(1, "mA")$ signal current: + +$ V_"drop" = qty(5, "ohm") times qty(1, "mA") = qty(5, "mV") (qty(250, "ppm")) $ + +This single $upright("DCR")$ term exceeds out $qty(200, "uV")$ systematic +error budget by a factor of $25$. + +====== Where it enters + +- Passive $upright("RLC")$ anti-aliasing and reconstructive filters, +- Front-panel input RF rejection chokes, +- LC power supply rail decoupling networks, +- Isolation transformers and baluns in external Interface Modules per + @reference-implementation. // TODO update ref when writen + +====== Scaling law + +DC resistance voltage drop scales linearly with signal current $I$ and +$upright("DCR")$. Core losses scale non-linearly with frequency($f^alpha$) and +flux density ($B^beta$). Parasitic impedance peak scales inversely with +winding capacitance $C_"parasitic"$. + +====== Compensation strategy + + +Inductor $upright("DCR")$ drop and core non-linearities cannot be actively +feedback-compensated across frequency without introducing complex phase lead/lag +instability. Mitigation relies on topological avoidance: +- Prohibiting inductors within active precision computing loops; implementing + active RC filter topologies (Sallen-Key, Multiple Feedback) instead of + passive RLC filters, +- Restricting ferrite beads exclusively to power supply rails and input RF + filtering paths where high-frequency attenuation is desired, +- Utilizing air-core inductors where precision inductance is mandatory to + eliminate core saturation and Barkhausen noise, +- Isolating magnetic components away from high impedance summing nodes to +prevent inductive coupling. + == Error compensation strategies == Advanced compensation topologies -- cgit