Distributed-element circuit

Distributed-Element Circuits: A New Frontier in Electrical Engineering

Imagine a world where the traditional circuit board is replaced by lengths of transmission lines and other distributed components. This isn’t just a futuristic dream; it’s the reality of distributed-element circuits. These circuits are composed of lengths of transmission lines or other distributed components, performing functions similar to conventional circuits but at microwave frequencies.

The Basics of Distributed-Element Circuits

Conventional circuits consist of individual components manufactured separately. In contrast, distributed-element circuits are built by forming the medium itself into specific patterns. This approach offers a cheap and compact alternative for consumer products like satellite television and radar applications. These circuits use phenomena such as resonators in transmission lines to create filters, power dividers, directional couplers, and circulators.

A Historical Perspective

Distributed-element circuits were studied during the 1920s-1930s but gained importance during World War II for radar applications. The distributed-element model is used when the assumption of ‘lumped’ passive elements no longer holds, particularly at higher frequencies where electromagnetic waves travel significant distances.

Technological Scales and Applications

Distributed designs are feasible above 300 MHz and are the technology of choice at microwave frequencies. The choice between distributed and lumped element models depends on technological scales, with miniaturized circuits often using the lumped model at higher frequencies. A further simplification occurs in commensurate line circuits, where all the elements are the same length.

Key Components and Structures

A design theory for producing commensurate line circuits exists; no general theory exists for circuits consisting of arbitrary lengths of transmission lines (or any arbitrary shapes). Although an arbitrary shape can be analysed with Maxwell’s equations to determine its behaviour, finding useful structures is a matter of trial and error or guesswork.

Frequency Response and Delay

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 exhibit this periodicity. Another difference is that cascade-connected lengths of line introduce a fixed delay at all frequencies, assuming an ideal line. There is no equivalent in lumped circuits for a fixed delay, although an approximation could be constructed for a limited frequency range.

Types of Transmission Lines

Several types of transmission lines exist and can be used to construct distributed-element circuits. The oldest (and still most widely used) is a pair of conductors; its most common form is twisted pair, used for telephone lines and Internet connections. Coaxial line, a centre conductor surrounded by an insulated shielding conductor, is widely used for interconnecting units of microwave equipment and for longer-distance transmissions.

Planar Transmission Lines

The majority of modern distributed-element circuits use planar transmission lines, especially those in mass-produced consumer items. The kind known as microstrip is the most common. It can be manufactured by the same process as printed circuit boards and hence is cheap to make. It also lends itself to integration with lumped circuits on the same board.

Other Structures

Planar lines can be used in monolithic microwave integrated circuits, waveguide designs can have multiple modes but are preferred for lower loss and higher quality resonators over conducting lines, mechanical components are used in high-end radio transmitters for their high-quality resonators. Several common structures are used in distributed-element circuits including stubs, coupled lines (which can be direct or indirect), are often used in power dividers and directional couplers.

Cascaded Lines

Lumped-element filters use cascaded lines with different characteristic impedances. A single line forms a quarter-wave impedance transformer, useful for transforming networks into their dual. Alternating transformers and resonators achieve ladder topology as a distributed-element circuit.

Resonator Types

A cavity resonator is an empty space surrounded by conducting walls with apertures that couple to the rest of the circuit. Resonance occurs due to electromagnetic waves reflected back and forth from cavity walls setting up standing waves. A dielectric resonator is a piece of dielectric material exposed to electromagnetic waves in a cylindrical or disc shape. The major advantage is smaller size compared to equivalent air-filled cavities.

Helical Resonators

A helical resonator is a helix of wire in a cavity with one end unconnected and the other bonded to the cavity wall. Used for VHF and lower UHF bands, it offers unique properties that make it suitable for specific frequency ranges.

Fractals: The Future of Circuit Design

The emerging field of fractal circuits uses space-filling property to create smaller designs, especially in filters and antennas. Wide-band and multi-band designs are possible with this approach. Tapers are used for joining lines of different characteristic impedances, reducing mismatch effects. Distributed resistors may be used in attenuators and line terminations, often as meandering high-resistance material or deposited thin-film material.

Filters

Filters are widely used with distributed elements, including stubs, coupled lines, cascaded lines, interdigital filters, combline filters, hairpin filters, and fractal filters. Impedance matching is achieved with single or complex networks, depending on the application.

Directional Couplers

A directional coupler is a four-port device that couples power from one path to another. Two types of directional couplers: 1) Directional coupler with low coupling factor; 2) Power divider with high coupling factor. Hybrid couplers include 3 dB coupler (hybrid), hybrid ring or rat-race coupler.

Circulators

A three- or four-port device in a circular rotation, power flows in one direction, no power transferred to other ports. Uses include isolators and duplexers for radio systems. There are several equivalent ways to define reciprocity in circuits, one of which is using S-parameters for distributed-element circuits at microwave frequencies.

Key Figures and Developments

Distributed-element modelling was first used in electrical network analysis by Oliver Heaviside in 1881. Warren P. Mason investigated the possibility of distributed-element circuits in the 1920s, leading to key breakthroughs like the cavity magnetron introduced in 1940, which operated in the microwave band and resulted in radar equipment small enough to install in aircraft.

Conclusion

Distributed-element circuits have revolutionized the way we think about circuit design. From their humble beginnings during World War II to today’s advanced applications, these circuits continue to push the boundaries of what is possible in electronics and microwave engineering. As technology advances, so too will our understanding and utilization of distributed-element circuits.