Waveguide filter

A waveguide filter is an electronic filter constructed with waveguide technology. Waveguides are hollow metal conduits inside which an electromagnetic wave may be transmitted. Filters are devices used to allow signals at some frequencies to pass, while others are rejected. Filters are a basic component of electronic engineering designs and have numerous applications. These include selection of signals and limitation of noise. Waveguide filters are most useful in the microwave band of frequencies, where they are a convenient size and have low loss. Examples of microwave filter use are found in satellite communications, telephone networks, and television broadcasting.
Waveguide filters were developed during World War II to meet the needs of radar and electronic countermeasures, but afterwards soon found civilian applications such as use in microwave links. Much of post-war development was concerned with reducing the bulk and weight of these filters, first by using new analysis techniques that led to elimination of unnecessary components, then by innovations such as dual-mode cavities and novel materials such as ceramic resonators.
A particular feature of waveguide filter design concerns the mode of transmission. Systems based on pairs of conducting wires and similar technologies have only one mode of transmission. In waveguide systems, any number of modes are possible. This can be both a disadvantage, as spurious modes frequently cause problems, and an advantage, as a dual-mode design can be much smaller than the equivalent waveguide single mode design. The chief advantages of waveguide filters over other technologies are their ability to handle high power and their low loss. The chief disadvantages are their bulk and cost when compared with technologies such as microstrip filters.
There is a wide array of different types of waveguide filters. Many of them consist of a chain of coupled resonators of some kind that can be modelled as a ladder network of LC circuits. One of the most common types consists of a number of coupled resonant cavities. Even within this type, there are many subtypes, mostly differentiated by the means of coupling. These coupling types include apertures, irises, and posts. Other waveguide filter types include dielectric resonator filters, insert filters, finline filters, corrugated-waveguide filters, and stub filters. A number of waveguide components have filter theory applied to their design, but their purpose is something other than to filter signals. Such devices include impedance matching components, directional couplers, and diplexers. These devices frequently take on the form of a filter, at least in part.

Scope

The common meaning of waveguide, when the term is used unqualified, is the hollow metal kind, but other waveguide technologies are possible. The scope of this article is limited to the metal-conduit type. The [|post-wall waveguide] structure is something of a variant, but is related enough to include in this article—the wave is mostly surrounded by conducting material. It is possible to construct waveguides out of dielectric rods, the most well known example being optical fibres. This subject is outside the scope of the article with the exception that dielectric rod resonators are sometimes used inside hollow metal waveguides. Transmission line technologies such as conducting wires and microstrip can be thought of as waveguides, but are not commonly called such and are also outside the scope of this article.

Basic concepts

Filters

In electronics, filters are used to allow signals of a certain band of frequencies to pass while blocking others. They are a basic building block of electronic systems and have a great many applications. Amongst the uses of waveguide filters are the construction of duplexers, diplexers, and multiplexers; selectivity and noise limitation in receivers; and harmonic distortion suppression in transmitters.

Waveguides

s are metal conduits used to confine and direct radio signals. They are usually made of brass, but aluminium and copper are also used. Most commonly they are rectangular, but other cross-sections such as circular or elliptical are possible. A waveguide filter is a filter composed of waveguide components. It has much the same range of applications as other filter technologies in electronics and radio engineering but is very different mechanically and in principle of operation.
The technology used for constructing filters is chosen to a large extent by the frequency of operation that is expected, although there is a large amount of overlap. Low frequency applications such as audio electronics use filters composed of discrete capacitors and inductors. Somewhere in the very high frequency band, designers switch to using components made of pieces of transmission line. These kinds of designs are called distributed element filters. Filters made from discrete components are sometimes called lumped element filters to distinguish them. At still higher frequencies, the microwave bands, the design switches to waveguide filters, or sometimes a combination of waveguides and transmission lines.
Waveguide filters have much more in common with transmission line filters than lumped element filters; they do not contain any discrete capacitors or inductors. However, the waveguide design may frequently be equivalent to a lumped element design. Indeed, the design of waveguide filters frequently starts from a lumped element design and then converts the elements of that design into waveguide components.

Modes

One of the most important differences in the operation of waveguide filters compared to transmission line designs concerns the mode of transmission of the electromagnetic wave carrying the signal. In a transmission line, the wave is associated with electric currents on a pair of conductors. The conductors constrain the currents to be parallel to the line, and consequently both the magnetic and electric components of the electromagnetic field are perpendicular to the direction of travel of the wave. This transverse mode is designated TEM. On the other hand, there are infinitely many modes that any completely hollow waveguide can support, but the TEM mode is not one of them. Waveguide modes are designated either TE or TM, followed by a pair of suffixes identifying the precise mode.
This multiplicity of modes can cause problems in waveguide filters when spurious modes are generated. Designs are usually based on a single mode and frequently incorporate features to suppress the unwanted modes. On the other hand, advantage can be had from choosing the right mode for the application, and even sometimes making use of more than one mode at once. Where only a single mode is in use, the waveguide can be modelled like a conducting transmission line and results from transmission line theory can be applied.

Cutoff

Another feature peculiar to waveguide filters is that there is a definite frequency, the cutoff frequency, below which no transmission can take place. This means that in theory low-pass filters cannot be made in waveguides. However, designers frequently take a lumped element low-pass filter design and convert it to a waveguide implementation. The filter is consequently low-pass by design and may be considered a low-pass filter for all practical purposes if the cutoff frequency is below any frequency of interest to the application. The waveguide cutoff frequency is a function of transmission mode, so at a given frequency, the waveguide may be usable in some modes but not others. Likewise, the guide wavelength and characteristic impedance of the guide at a given frequency also depend on mode.

Dominant mode

The mode with the lowest cutoff frequency of all the modes is called the dominant mode. Between cutoff and the next highest mode, this is the only mode it is possible to transmit, which is why it is described as dominant. Any spurious modes generated are rapidly attenuated along the length of the guide and soon disappear. Practical filter designs are frequently made to operate in the dominant mode.
In rectangular waveguide, the TE₁₀ mode is the dominant mode. There is a band of frequencies between the dominant mode cutoff and the next highest mode cutoff in which the waveguide can be operated without any possibility of generating spurious modes. The next highest cutoff modes are TE₂₀, at exactly twice the TE₁₀ mode, and TE₀₁ which is also twice TE₁₀ if the waveguide used has the commonly used aspect ratio of 2:1. The lowest cutoff TM mode is TM₁₁ which is times the dominant mode in 2:1 waveguide. Thus, there is an octave over which the dominant mode is free of spurious modes, although operating too close to cutoff is usually avoided because of phase distortion.
In circular waveguide, the dominant mode is TE₁₁ and is shown in figure 2. The next highest mode is TM₀₁. The range over which the dominant mode is guaranteed to be spurious-mode free is less than that in rectangular waveguide; the ratio of highest to lowest frequency is approximately 1.3 in circular waveguide, compared to 2.0 in rectangular guide.

Evanescent modes

s are modes below the cutoff frequency. They cannot propagate down the waveguide for any distance, dying away exponentially. However, they are important in the functioning of certain filter components such as irises and posts, described later, because energy is stored in the evanescent wave fields.

Advantages and disadvantages

Like transmission line filters, waveguide filters always have multiple passbands, replicas of the lumped element prototype. In most designs, only the lowest frequency passband is useful and the rest are considered unwanted spurious artefacts. This is an intrinsic property of the technology and cannot be designed out, although design can have some control over the frequency position of the spurious bands. Consequently, in any given filter design, there is an upper frequency beyond which the filter will fail to carry out its function. For this reason, true low-pass and high-pass filters cannot exist in waveguide. At some high frequency there will be a spurious passband or stopband interrupting the intended function of the filter. But, similar to the situation with waveguide cutoff frequency, the filter can be designed so that the edge of the first spurious band is well above any frequency of interest.
The range of frequencies over which waveguide filters are useful is largely determined by the waveguide size needed. At lower frequencies the waveguide needs to be impractically large in order to keep the cutoff frequency below the operational frequency. On the other hand, filters whose operating frequencies are so high that the wavelengths are sub-millimetre cannot be manufactured with normal machine shop processes. At frequencies this high, fibre-optic technology starts to become an option.
Waveguides are a low-loss medium. Losses in waveguides mostly come from ohmic dissipation caused by currents induced in the waveguide walls. Rectangular waveguide has lower loss than circular waveguide and is usually the preferred format, but the TE₀₁ circular mode is very low loss and has applications in long-distance communications. Losses can be reduced by polishing the internal surfaces of the waveguide walls. In some applications which require rigorous filtering, the walls are plated with a thin layer of gold or silver to improve surface conductivity. An example of such requirements is satellite applications which require low loss, high selectivity, and linear group delay from their filters.
One of the main advantages of waveguide filters over TEM mode technologies is the quality of their resonators. Resonator quality is characterised by a parameter called Q factor, or just Q. The Q of waveguide resonators is in the thousands, orders of magnitude higher than TEM mode resonators. The resistance of conductors, especially in wound inductors, limits the Q of TEM resonators. This improved Q leads to better performing filters in waveguides, with greater stop band rejection. The limitation to Q in waveguides comes mostly from the ohmic losses in the walls described earlier, but silver plating the internal walls can more than double Q.
Waveguides have good power handling capability, which leads to filter applications in radar. Despite the performance advantages of waveguide filters, microstrip is often the preferred technology due to its low cost. This is especially true for consumer items and the lower microwave frequencies. Microstrip circuits can be manufactured by cheap printed circuit technology, and when integrated on the same printed board as other circuit blocks they incur little additional cost.