Stub (electronics)

Lore & Background

Stubs are constructed with any type of transmission line: parallel conductor line (Lecher lines), coaxial cable, stripline, waveguide, and dielectric waveguide. Their behavior is due to standing waves along their length, and their reactive properties are determined by physical length relative to the wavelength of the radio waves. Stub circuits can be designed using a Smith chart, a graphical tool that determines what length line to use to obtain a desired reactance.

A short-circuited stub is inductive or capacitive depending on whether tan(βl) is positive or negative. An open-circuited stub is capacitive or inductive depending on whether cot(βl) is positive or negative. Stubs function as resonant circuits in oscillators and distributed element filters; an open-circuit stub of length l < λ/4 has capacitive impedance at low frequency, and above that frequency the impedance is inductive. At precisely l = λ/4 the stub presents a short circuit, qualitatively the same behavior as a series resonant circuit. Unlike lumped element resonant circuits, stubs have multiple resonant frequencies: in addition to the fundamental resonant frequency f₀, they resonate at multiples of this frequency: nf₀.

Stubs can match a load impedance to the transmission line characteristic impedance. The stub is positioned a distance from the load so that the resistive part of the load impedance is made equal to the resistive part of the characteristic impedance by impedance transformer action. The length of the stub is chosen to cancel the reactive part of the presented impedance. A single stub achieves a perfect match at only one specific frequency; multiple stubs can be placed along the main transmission line to achieve wideband matching, creating a structure similar to a filter.

Reader's Guide

Stubs are significant in radio electronics because they provide a practical way to realize reactive components and resonant circuits at UHF and microwave frequencies, where lumped components are ineffective due to parasitic reactance. They are commonly used in antenna impedance matching circuits, frequency selective filters, and resonant circuits for UHF electronic oscillators and RF amplifiers. The ability to design stubs using a Smith chart makes them accessible for engineering practice. Radial stubs, which consist of a sector of a circle rather than a constant-width line, are used with planar transmission lines when a low impedance stub is required, overcoming the difficulty of a wide line junction. Filter circuits using stubs often use them in pairs, one connected to each side of the main line, forming a butterfly stub or bowtie stub. Unwanted open-circuit stubs can inadvertently be created in printed circuit board design; a λ/4-wavelength stub would completely cancel the desired signal. With higher-frequency signaling on the order of 12 Gbps (6 GHz), the length of the stub required to reach λ/4 has greatly decreased, making vias a common culprit. Since the 2020s, backdrilling is used to shorten vias so that they do not affect the intended signal frequency. The legacy of stubs includes their role in enabling compact, efficient RF circuits and their continued relevance in modern high-speed digital design.

Did You Know?

• A 200 MHz stub is 19 cm long, while a 300 MHz stub is 12.5 cm long.
• An open-circuit stub of length l < λ/4 behaves as a capacitor at low frequency.
• Stubs have multiple resonant frequencies: f₀, 3f₀, 5f₀, etc.
• Radial stubs narrow to a point at the junction to provide a well-defined connection.