Reactance And Impedance Explained For Board Design

Resistance, capacitance and inductance are the three properties that describe how a circuit responds to a signal, and impedance is the term that combines them. On a board the distinction matters because a component that looks like a small capacitance on a schematic becomes a significant impedance at high frequency, and a track that looks like a short becomes an inductor.

This article explains the quantities, how they combine, and where each of them appears in practical board design.

The reason the subject is worth revisiting is that most of the surprising behaviour in a fast digital design comes from an impedance that was not considered rather than from a component that failed.

Resistance And Reactance

Resistance dissipates energy and is independent of frequency. A current through a resistor produces a voltage in phase with it, and the energy leaves the circuit as heat. Reactance stores energy and depends on frequency, and the voltage across a reactive element is ninety degrees out of phase with the current.

A capacitor has a reactance that falls as frequency rises, because a changing voltage can push more current through it. An inductor has a reactance that rises with frequency, because a changing current induces a voltage that opposes the change. The two are opposite in sign in the impedance expression, which is why they can cancel.

Impedance Is The Combination

Impedance is a complex quantity whose real part is resistance and whose imaginary part is the difference between inductive and capacitive reactance. Its magnitude is what a measurement reports, and its phase says whether the circuit looks capacitive or inductive at that frequency. Both matter when matching a source to a load.

At a specific frequency, a given capacitance and inductance can be chosen to cancel each other, which is the basis of resonant circuits and of many matching networks. Below and above that frequency the cancellation fails and the impedance changes rapidly, which is why resonant structures are inherently narrowband.

Parasitic Elements On A Board

Every trace has inductance, roughly one nanohenry per millimetre of length for a typical geometry, and every pair of conductors has capacitance. A via is a small inductance in series and a small capacitance to the planes it passes. A long narrow trace to a capacitor adds enough inductance to make the capacitor useless above a certain frequency.

These parasitic elements are not defects; they are the physics of the structure. Good board design consists largely of arranging the geometry so that the parasitic elements are small enough to be irrelevant, or deliberately large enough to be useful. The inductance of a trace carrying current is also what determines the voltage drop during a switching transient.

The impedance of a capacitor is often quoted as if the component were ideal, and the deviation is instructive. A real capacitor has an equivalent series resistance that sets a floor on its impedance, and an equivalent series inductance from its construction and its mounting that makes the impedance rise again above a self resonant frequency. Two capacitors with the same nominal value can therefore behave very differently, and the one with the shorter internal path is usually the better choice at high frequency.

Where Frequency Enters

The rule of thumb is that a structure behaves as a lumped element while its physical size is a small fraction of the wavelength. As the frequency rises, the same structure becomes a distributed one, and describing it as a capacitance or an inductance stops being useful.

A trace that is short compared with the wavelength of the highest frequency component in a signal can be treated as a node. A trace that is a significant fraction of the wavelength must be treated as a transmission line with a propagation delay, and the characteristic impedance concept replaces the lumped model.

Reactance And Crosstalk

Coupling between two traces is described by mutual capacitance and mutual inductance, and the contribution of each depends on the geometry and on the impedances of the circuits involved. In a low impedance circuit, the capacitive coupling dominates; in a high impedance circuit, the inductive coupling does.

This explains why the same spacing can be adequate for one net and inadequate for another. It also explains why return path continuity is so important: a shared return path creates a mutual inductance that couples two signals together regardless of how they are spaced on the signal layer. The spacing rules used to control crosstalk capture the common case rather than every case.

Transmission line behaviour is not a special case reserved for radio work. Any trace whose length is a significant fraction of the wavelength of the fastest edge on it has a characteristic impedance, and the signal arriving at the far end depends on how that impedance compares with the source and the load. The concept applies to a clock line on a microcontroller board exactly as it applies to an antenna feed, and the difference is only the frequency at which it starts to matter.

Practical Consequences

Four consequences follow from the physics and are worth keeping in mind. Decoupling capacitors must be connected with short low inductance paths, or their reactance at the frequency of interest is dominated by their mounting rather than their value. Ground connections must be short, because their inductive reactance is what raises the potential of a ground point during a fast transient.

Wide traces are preferred for power not only because their resistance is lower but because their inductance is lower, which reduces the voltage spike when the current changes. And any structure that is resonant, including a plane pair or a stub, will have a frequency at which its impedance is very different from what a static calculation would suggest.

Impedance In Measurement

An instrument measures impedance as a magnitude and a phase, or as a real and imaginary part. Reading a single magnitude figure without the phase can be misleading, because a small resistance and a large reactance produce very different circuits that may have the same magnitude at one frequency.

This is why a component’s impedance is normally shown as a curve across frequency rather than as a single number. A capacitor that is an excellent decoupling element at ten megahertz may be an inductor at a hundred megahertz, and the curve is the only way to know where the transition occurs.

It is worth connecting the theory to a measurement that can be made on a bench. Measuring the impedance of a decoupling network with a probe across the supply pins shows directly whether the network performs as intended, and the result usually differs from the calculation because the calculation assumed ideal connections. The measurement is the honest version of the model.

FAQ

Is impedance the same as resistance? Only in a purely resistive circuit. In any circuit with capacitance or inductance, impedance is a complex quantity and its magnitude varies with frequency.

Why does a via matter at high frequency? Because it has inductance and capacitance that depend on its geometry, and because the unused portion of its barrel forms a resonant stub. Both effects scale with frequency and become significant when the edge rate is fast.

Can a capacitor be replaced by a larger one with the same result? Only below the frequency where the mounting inductance dominates. Above that point, additional capacitance does not reduce the impedance, and the answer is to reduce the inductance instead.