page_title: Distributed-element filter
section_title: Stub band-pass filters
hierarchical_section_title: Distributed-element filter / Band-pass filters / Stub band-pass filters
context_page_description: A distributed-element filter is an electronic filter in which capacitance, inductance, and resistance 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.
context_section_description: As mentioned above, stubs lend themselves to band-pass designs. General forms of these are similar to stub low-pass filters except that the main line is no longer a narrow high impedance line. Designers have many different topologies of stub filters to choose from, some of which produce identical responses. An example stub filter is shown in figure 12; it consists of a row of λ/4 short-circuit stubs coupled together by λ/4 impedance transformers. The stubs in the body of the filter are double paralleled stubs while the stubs on the end sections are only singles, an arrangement that has impedance matching advantages. The impedance transformers have the effect of transforming the row of shunt anti-resonators into a ladder of series resonators and shunt anti-resonators. A filter with similar properties can be constructed with λ/4 open-circuit stubs placed in series with the line and coupled together with λ/4 impedance transformers, although this structure is not possible in planar technologies.
  Yet another structure available is λ/2 open-circuit stubs across the line coupled with λ/4 impedance transformers. This topology has both low-pass and band-pass characteristics. Because it will pass DC, it is possible to transmit biasing voltages to active components without the need for blocking capacitors. Also, since short-circuit links are not required, no assembly operations other than the board printing are required when implemented as stripline. The disadvantages are (i) the filter will take up more board real estate than the corresponding λ/4 stub filter, since the stubs are all twice as long; (ii) the first spurious passband is at 2ω₀, as opposed to 3ω₀ for the λ/4 stub filter.
  Konishi describes a wideband 12 GHz band-pass filter, which uses 60° butterfly stubs and also has a low-pass response (short-circuit stubs are required to prevent such a response). As is often the case with distributed-element filters, the bandform into which the filter is classified largely depends on which bands are desired and which are considered to be spurious.
caption: Figure 12. Stripline stub filter composed of λ/4 short-circuit stubs