inductor losses and parasitic effects

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@@ -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
+<inductor-losses-and-parasitic-effects>
+
+====== Physical mechanism
+<inductor-losses-and-parasitic-effect-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
+<inductor-losses-and-parasitic-effects-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
+<inductor-losses-and-parasitic-effects-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],
+) <table-inductor-losses-and-parasitic-effects-typical-magnitude>
+
+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 <inductor-losses-and-parasitic-effects-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 <inductor-losses-and-parasitic-effects-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-losses-and-parasitic-effects-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 <error-compensation-strategies>
 
 == Advanced compensation topologies <advanced-compensation-topologies>