# Inductive Properties of Electric Circuits

Characterizing the inductive properties of the power and ground interconnect is essential in determining the impedance characteristics of a power distribution system. Several of the following chapters are dedicated to the inductive properties of on-chip power distribution networks. The objective of this chapter is to introduce the concepts used in these chapters to describe the inductive characteristics of complex interconnect structures.

The magnetic properties of circuits are typically introduced using circuits with inductive coils. The inductive characteristics of such circuits are dominated by the self and mutual inductances of these coils. The inductance of a coil is well described by the classical definition of inductance based on the magnetic flux through a current loop. The situation is more complex in circuits with no coils where no part of the circuit is inductively dominant and the circuit elements are strongly inductively coupled. The magnetic properties in this case are determined by the physical structure of the entire circuit, resulting in complex inductive behavior. The loop inductance formulation is inconvenient to represent the inductive characteristics of these circuits. The objective of this chapter is to describe various ways to represent a circuit inductance, highlighting specific assumptions. Intuitive interpretations are offered to develop a deeper understanding of the limitations and interrelations of these approaches. The variation of inductance with frequency and the relationship between the absolute inductance and the inductive behavior are also discussed in this chapter.

## Keywords

Current Loop Mutual Inductance Current Path Current Density Distribution Circuit Analysis## Preview

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