Distributed element filter

A distributed element filter is an electronic filter in which capacitance, inductance and resistance (the elements of the circuit) are not localised in discrete capacitors, inductors and resistors as they are in conventional filters. Its purpose is to allow a range of signal frequencies to pass, but to block others. Conventional filters are constructed from inductors and capacitors, and the circuits so built are described by the lumped element model, which considers each element to be 'lumped together' at one place. That model is conceptually simple, but it becomes increasingly unreliable as the frequency of the signal increases, or equivalently as the wavelength decreases. The distributed element model applies at all frequencies, and is used in transmission line theory; many distributed element components are made of short lengths of transmission line. In the distributed view of circuits, the elements are distributed along the length of conductors and are inextricably mixed together. The filter design is usually concerned only with inductance and capacitance, but because of this mixing of elements they cannot be treated as separate 'lumped' capacitors and inductors. There is no precise frequency above which distributed element filters must be used but they are especially associated with the microwave band (wavelength less than one metre). A distributed element filter is an electronic filter in which capacitance, inductance and resistance (the elements of the circuit) are not localised in discrete capacitors, inductors and resistors as they are in conventional filters. Its purpose is to allow a range of signal frequencies to pass, but to block others. Conventional filters are constructed from inductors and capacitors, and the circuits so built are described by the lumped element model, which considers each element to be 'lumped together' at one place. That model is conceptually simple, but it becomes increasingly unreliable as the frequency of the signal increases, or equivalently as the wavelength decreases. The distributed element model applies at all frequencies, and is used in transmission line theory; many distributed element components are made of short lengths of transmission line. In the distributed view of circuits, the elements are distributed along the length of conductors and are inextricably mixed together. The filter design is usually concerned only with inductance and capacitance, but because of this mixing of elements they cannot be treated as separate 'lumped' capacitors and inductors. There is no precise frequency above which distributed element filters must be used but they are especially associated with the microwave band (wavelength less than one metre). Distributed element filters are used in many of the same applications as lumped element filters, such as selectivity of radio channel, bandlimiting of noise and multiplexing of many signals into one channel. Distributed element filters may be constructed to have any of the bandforms possible with lumped elements (low-pass, band-pass, etc.) with the exception of high-pass, which is usually only approximated. All filter classes used in lumped element designs (Butterworth, Chebyshev, etc.) can be implemented using a distributed element approach. There are many component forms used to construct distributed element filters, but all have the common property of causing a discontinuity on the transmission line. These discontinuities present a reactive impedance to a wavefront travelling down the line, and these reactances can be chosen by design to serve as approximations for lumped inductors, capacitors or resonators, as required by the filter. The development of distributed element filters was spurred on by the military need for radar and electronic counter measures during World War II. Lumped element analogue filters had long before been developed but these new military systems operated at microwave frequencies and new filter designs were required. When the war ended, the technology found applications in the microwave links used by telephone companies and other organisations with large fixed-communication networks, such as television broadcasters. Nowadays the technology can be found in several mass-produced consumer items, such as the converters (figure 1 shows an example) used with satellite television dishes. Distributed element filters are mostly used at frequencies above the VHF (Very High Frequency) band (30 to 300 MHz). At these frequencies, the physical length of passive components is a significant fraction of the wavelength of the operating frequency, and it becomes difficult to use the conventional lumped element model. The exact point at which distributed element modelling becomes necessary depends on the particular design under consideration. A common rule of thumb is to apply distributed element modelling when component dimensions are larger than 0.1λ. The increasing miniaturisation of electronics has meant that circuit designs are becoming ever smaller compared to λ. The frequencies beyond which a distributed element approach to filter design becomes necessary are becoming ever higher as a result of these advances. On the other hand, antenna structure dimensions are usually comparable to λ in all frequency bands and require the distributed element model. The most noticeable difference in behaviour between a distributed element filter and its lumped-element approximation is that the former will have multiple passband replicas of the lumped-element prototype passband, because transmission line transfer characteristics repeat at harmonic intervals. These spurious passbands are undesirable in most cases. For clarity of presentation, the diagrams in this article are drawn with the components implemented in stripline format. This does not imply an industry preference, although planar transmission line formats (that is, formats where conductors consist of flat strips) are popular because they can be implemented using established printed circuit board manufacturing techniques. The structures shown can also be implemented using microstrip or buried stripline techniques (with suitable adjustments to dimensions) and can be adapted to coaxial cables, twin leads and waveguides, although some structures are more suitable for some implementations than others. The open wire implementations, for instance, of a number of structures are shown in the second column of figure 3 and open wire equivalents can be found for most other stripline structures. Planar transmission lines are also used in integrated circuit designs. Development of distributed element filters began in the years before World War II. Warren P. Mason founded the field of distributed element circuits. A major paper on the subject was published by Mason and Sykes in 1937. Mason had filed a patent much earlier, in 1927, and that patent may contain the first published electrical design which moves away from a lumped element analysis. Mason and Sykes' work was focused on the formats of coaxial cable and balanced pairs of wires – the planar technologies were not yet in use. Much development was carried out during the war years driven by the filtering needs of radar and electronic counter-measures. A good deal of this was at the MIT Radiation Laboratory, but other laboratories in the US and the UK were also involved. Some important advances in network theory were needed before filters could be advanced beyond wartime designs. One of these was the commensurate line theory of Paul Richards. Commensurate lines are networks in which all the elements are the same length (or in some cases multiples of the unit length), although they may differ in other dimensions to give different characteristic impedances. Richards' transformation allows a lumped element design to be taken 'as is' and transformed directly into a distributed element design using a very simple transform equation.