Real inductor modeling: Which option best represents a practical equivalent circuit for an inductor including its dominant parasitics?

Introduction / Context:
No physical inductor is ideal. Winding resistance and interwinding capacitance alter behavior at both low and high frequencies. A suitable equivalent circuit helps predict resonances, Q factor, and losses—critical in filters, RF chokes, and switch-mode power supplies.

Given Data / Assumptions:

• Winding resistance (R_s) is in series with the inductance (L).
• Parasitic self-capacitance (C_p) appears effectively in parallel with the winding.
• We focus on the simplest widely used small-signal model.

Concept / Approach:
A common small-signal model is L in series with R_s, representing copper loss, with a shunt (parallel) capacitance C_p modeling self-capacitance between turns or layers. This topology exhibits a self-resonant frequency where the inductive reactance and capacitive reactance cancel, beyond which the inductor can appear capacitive. Such a model matches measured impedance-versus-frequency curves for practical components.

Step-by-Step Solution:

Verification / Alternative check:
Impedance analyzers reveal a peak and phase crossover at the self-resonant frequency, predicted by the R_s–L series branch shunted by C_p.

Why Other Options Are Wrong:

• Series L–R–C: Places capacitance in series, not representative of interwinding capacitance.
• L in parallel with (R–C series): Not the standard dominant-parasitic model.
• Only inductance: Ignores real-world losses and capacitance.

Common Pitfalls:
Neglecting C_p at high frequency, leading to incorrect assumptions that inductors stay inductive across all frequencies.

Final Answer:
A capacitance in parallel with the series combination of a resistance and an inductance