Distributed-element circuit
Circuits using transmission lines to replace lumped components at microwave frequencies.
Distributed-element circuits are built from lengths of transmission lines or other components that are spread out, rather than from discrete parts. They can do the same jobs as ordinary circuits made with capacitors, inductors, and transformers. Their main use is at microwave frequencies, where standard components are hard or impossible to make. A key benefit is that they can be manufactured cheaply as printed circuit boards for consumer goods like satellite TV equipment. They are also made in coaxial and waveguide forms for radar, satellite communication, and microwave links.
In conventional circuits, individual components are made separately and then connected by a conducting medium. In distributed-element circuits, the conducting medium itself is shaped into specific patterns. A common trick is that a length of transmission line can act as a resonator. Components that do this include stubs, coupled lines, and cascaded lines. These are used to build filters, power dividers, directional couplers, and circulators.
Research on distributed-element circuits began in the 1920s and 1930s, but they only became important during World War II, when they were used in radar. After the war, their use was limited to military, space, and broadcast infrastructure, but improvements in materials science soon led to wider applications. Today they appear in household items such as satellite dishes and mobile phones.
Distributed-element circuits are designed using the distributed-element model, which is an alternative to the lumped-element model. In the lumped model, resistance, capacitance, and inductance are assumed to be concentrated at a single point in a resistor, capacitor, or inductor. The distributed model is used when that assumption no longer holds, because these properties are spread out in space. The assumption breaks down when electromagnetic waves take a noticeable time to travel from one terminal of a component to the other—"noticeable" meaning enough time for a significant phase change. How much phase change depends on the wave's frequency (and inversely on its wavelength). A common rule of thumb among engineers is to switch from the lumped to the distributed model when distances exceed one-tenth of a wavelength (a 36° phase change).
- Frequency range
- above 300 MHz
- Changeover frequency range
- 100–300 MHz
- Rule of thumb threshold
- one-tenth of a wavelength (36° phase change)
- Failure point
- one-quarter wavelength (90° phase change)
- Earliest study period
- 1920s and 1930s
- Wartime use
- World War II radar
Lore & Background
Distributed-element circuits were studied during the 1920s and 1930s but did not become important until World War II, when they were used in radar. After the war their use was limited to military, space, and broadcasting infrastructure, but improvements in materials science in the field soon led to broader applications. They can now be found in domestic products such as satellite dishes and mobile phones.
The distributed-element model is used when the lumped-element model assumption breaks down—when there is significant time for electromagnetic waves to travel from one terminal of a component to the other, causing a noticeable phase change. A common rule of thumb among engineers is to change from the lumped to the distributed model when distances involved are more than one-tenth of a wavelength. The lumped model completely fails at one-quarter wavelength, with not only the value but the nature of the component not being as predicted.
A phenomenon commonly used in distributed-element circuits is that a length of transmission line can be made to behave as a resonator. Distributed-element components which do this include stubs, coupled lines, and cascaded lines. Circuits built from these components include filters, power dividers, directional couplers, and circulators.
Reader's Guide
Distributed-element circuits are cheap and easy to manufacture in some formats, but take up more space than lumped-element circuits. This is problematic in mobile devices, especially hand-held ones, where space is at a premium. If the operating frequencies are not too high, the designer may miniaturise components rather than switching to distributed elements. However, parasitic elements and resistive losses in lumped components are greater with increasing frequency as a proportion of the nominal value of the lumped-element impedance. In some cases, designers may choose a distributed-element design even if lumped components are available at that frequency to benefit from improved quality. Distributed-element designs tend to have greater power-handling capability; with a lumped component, all the energy passed by a circuit is concentrated in a small volume.
The overwhelming majority of distributed-element circuits are composed of lengths of transmission line. Such an element is entirely characterised by its length and characteristic impedance. A further simplification occurs in commensurate line circuits, where all the elements are the same length. With commensurate circuits, a lumped circuit design prototype consisting of capacitors and inductors can be directly converted into a distributed circuit with a one-to-one correspondence between the elements of each circuit. An important difference between distributed-element circuits and lumped-element circuits is that the frequency response of a distributed circuit periodically repeats; the equivalent lumped circuit does not. Another difference is that cascade-connected lengths of line introduce a fixed delay at all frequencies, for which there is no equivalent in lumped circuits.
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