methods. Network synthesis is a more advanced method than image-parameter techniques but the latter can still be used where a simple repeated-pattern design is desired. Numerical methods can be used to analyse either design.
Description
The waffle-iron filter was invented by Seymour B. Cohn at
corrugated-waveguide filter. This consists of a series of ridges, or corrugations, across the width of the filter. There are corrugations inside the waveguide on both the top and bottom surfaces. The rising and descending ridges are aligned with each other but do not meet in the middle; there is a gap in between. In the waffle-iron filter there are, in addition, slots cut through the ridges down the length of the waveguide. This leaves a matrix of square islands, or teeth, on the top and bottom surfaces.[2]
Waffle-iron filters are, in essence, low-pass filters but like all waveguide devices will not transmit anything below the waveguide cutoff frequency. Waffle-iron filters are used where both a wide passband with low insertion loss, and a wide (sometimes very wide) stopband are needed. They are particularly good where suppression of spurious modes is required.[3]
Waffle-iron filters have been built with a 10 GHz wide stopband and 60 dB attenuation.[4] Even wider stopbands are possible with a relaxed attenuation specification.[5]
Operation
One of the performance issues addressed by the waffle-iron filter is that in many waveguide filters the attenuation is dependent on the
isotropic to TEM waves in all these directions. Since any TEn0 mode wave can be decomposed into two TEM mode waves travelling in different diagonal directions, all TEn0 modes are affected nearly equally.[6]
Incident signals containing TM modes above a certain frequency can generate modes which propagate along the longitudinal slots with the slots themselves acting as waveguides. The point at which this can start to happen is the frequency at which the height of the slot is greater than half the free-space wavelength of the signal. If this frequency is above the required stopband of the filter the effect is of no consequence. Otherwise, steps outside the filter are needed to suppress these modes and can be incorporated into the end-matching sections.[7]
Other design criteria will usually result in a filter which does not match the waveguides to which it is to be connected at its input and output. There are many structures that can be used for matching but a useful one here is the stepped-impedance transformer which has the added advantage of helping to suppress the unwanted slot modes.[8]
Applications
A common application of waffle-iron filters is to remove the harmonics of transmitters, such as high power radar, before applying to the antenna. Legislation in most jurisdictions requires strict limits on out-of-band transmissions since these can cause serious interference with other stations. This is an application that usually requires a very wide stopband, a characteristic of waffle-iron filters. For instance, to remove all harmonics up to the fifth it is necessary for a low-pass filter to have a stopband greater than three times the passband.[9]
The wide-band nature of waffle-iron filters finds applications in satellite communications. A satellite
earth station may have multiple diplexers connected to a multi-band antenna feeder. Each diplexer delivers a wide-band signal in a different band and it is essential that its signal does not contain out-of-band components, particularly harmonics. These can seriously interfere with, or even stop entirely, communication in another band. The diplexer must therefore have a stopband that is even wider than the passband. For this reason, as well as the other advantages of waffle-irons, these diplexers are commonly made to a waffle-iron design.[10]
Waffle-iron filters are used in industrial microwave processes. The many industrial applications of microwave energy include drying of food products and industrial films, heating, such as in polyurethane foam production, melting,
vulcanisation. In high-volume production the process is continuous necessitating openings to the microwave chamber where the product can be fed in and exit. Steps need to be taken to prevent unsafe levels of microwave radiation escaping from these apertures which are often large to accommodate the product. It is usual to line the product feed ducts with microwave absorbent material for this purpose. However, the absorbed microwaves have a heating effect and this can be severe enough to damage the absorbent material. Waffle-iron filters are a useful alternative because the product can be passed between the filter's teeth. An ideal filter will reflect all the unwanted radiation rather than absorbing it so will not suffer from overheating. This is an example of a filter being used in a choke application. In some processes both techniques are used simultaneously. The waffle-iron is placed nearest the microwave chamber to first reduce the energy to a level which will not cause the absorbent lining to overheat. The absorbent lining then removes the small residue.[11]
Design
The number of teeth, their size, and the gap between them are all design parameters that can be used to control the design of the filter. As an example, a filter with a 3:1 stopband might have five teeth across the width of the waveguide. The number of rows of teeth down the length of the waveguide primarily affects the stopband attenuation. The more rows of teeth, the better the attenuation, each row being equivalent to a
lumped element circuit filter section. A filter with ten rows of teeth has a theoretical stopband rejection of around 80 dB and one with seven rows around 60 dB.[12]
The earliest waffle-iron filters were designed with the
image parameter method of filter design. Cohn's original data for the corrugated filter could also be applied to the waffle-iron with only a small adjustment of one parameter. An alternative approach to using Cohn's empirical data, but still an image parameter design, is due to Marcuvitz who used a waveguide T-junction equivalent circuit to represent corrugations and this method was later extended by others to waffle-irons.[13]
One of the main drawbacks of the image parameter design method in this, as in other, filters is that the impedance match at the terminations is not good. This usually requires that impedance matching sections are provided at the input and output. These usually take the form of multi-section stepped impedance transformers. These add considerably to the overall length of the filter.[14] A small improvement to matching can be had by starting and ending the filter on a half-space instead of a full tooth or space. The lumped circuit equivalent of this is T-half-sections terminating the filter at either end. Starting and ending on a half-tooth instead of a half space is the equivalent of Π-half-sections.[15]
Direct synthesis avoids many of the problems of the image parameter method. Not only does it take better account of the terminal impedances but the designer has additional degrees of freedom allowing improved matching. The size and gaps of the teeth are tapered in this method of design. That is, the teeth can be different sizes according to their position in the filter, compared with an image design where all sections are identical. With this approach, the original specification for passband and stopband can be kept while simultaneously improving the impedance matching. The stepped impedance transformers can be dispensed with, or at least significantly reduced in size.[16]
Synthesis methods allow better control of the precise filter response. A common response function used by filter designers is the
Achieser-Zolotarev filter. This filter is based on Zolotarev polynomials (which include the Chebyshev polynomials as a special case) discovered by Yegor Ivanovich Zolotarev. The Zolotarev response has a stopband at low frequency, the cutoff of which can be controlled by the designer so it is not detrimental in a waveguide filter. The advantage of the Zolotarev response is that it results in a filter with a better impedance match to the connecting waveguides compared to the Chebyshev filter or image-parameter filters.[17]