Transmission Line Calculations

A transmission line is a conductor arrangement designed to carry high-frequency signals from one point to another with minimal loss and distortion, such as coaxial cable, two-wire line or the microstrip tracks on a circuit board. At high frequencies a cable can no longer be treated as a simple wire, because the signal travels as a wave and the line's geometry strongly affects how it behaves. Transmission-line calculators apply the relevant formulas so a designer can work out impedances, dimensions and matching figures from the physical details of the line.

The most important property of a line is its characteristic impedance, the ratio of voltage to current for a wave travelling along it, which depends on the conductor dimensions and the surrounding insulating material rather than the line's length. For a microstrip line, a flat track over a ground plane on a printed circuit board, calculators find the characteristic impedance from the track width, the board thickness and the dielectric constant of the substrate, or work backwards to find the track width needed for a target impedance such as the common fifty ohms.

When a line is not terminated in its characteristic impedance, part of the signal reflects back, and several related quantities describe the mismatch. The reflection coefficient gives the fraction of the wave reflected, the voltage standing-wave ratio (VSWR) describes the resulting pattern of peaks and troughs along the line, and the return loss and mismatch loss express the reflected and lost power in decibels. Calculators convert among these figures and relate them to the load and line impedances. Time-domain reflectometry, which sends a pulse down a line and examines the reflections, locates faults and impedance changes; virtual tools simulate this to help understand how discontinuities appear. Together these calculations let engineers design and troubleshoot the lines that carry RF and fast digital signals.

Frequently asked questions

What is characteristic impedance?

The ratio of voltage to current for a wave travelling along a transmission line, set by the line's geometry and dielectric rather than its length. Fifty ohms is a common value.

What does VSWR indicate?

The voltage standing-wave ratio measures how badly a line is mismatched to its load. A ratio of one means a perfect match with no reflected wave; higher values mean more reflection.

What is time-domain reflectometry?

A technique that sends a pulse down a line and examines the reflected signal to locate faults, breaks and impedance changes by where and how the reflections appear.