page_title: Waffle-iron filter
section_title: Design
hierarchical_section_title: Waffle-iron filter / Design
caption_attribution_description: Various types of wffle-iron filter teeth. A: square teeth, B: rounded teeth, C: circular teeth with TE0n mode suppression wires.
context_page_description: A waffle-iron filter is a type of waveguide filter used at microwave frequencies for signal filtering. It is a variation of the corrugated-waveguide filter but with longitudinal slots cut through the corrugations resulting in an internal structure that has the appearance of a waffle-iron.
  Waffle-iron filters are particularly suitable where both a wide passband, and a wide stopband free of spurious transmission modes, are required. They also have a high power-handling capability. Applications include suppressing the harmonic output of transmitters and the design of wide-band diplexers. They are also used in industrial microwave manufacturing processes to prevent the escape of microwave radiation from the microwave chamber. Filters with an analogous design are now appearing in photonics, but, due to the higher frequency, at a much smaller scale. This small size allows them to be incorporated into integrated circuits.
  Design techniques for waffle-iron filters include image-parameter methods, network synthesis methods and numerical analysis methods.
context_section_description: 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.
  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.
  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.  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.
  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.
  Synthesis methods allow better control of the precise filter response.  A common response function used by filter designers is the Chebyshev filter which trades steepness of the transition band for passband ripple.  However the Chebyshev response is not always the best choice for waffle-iron filters.  Low-pass waveguide filters do not pass frequencies all the way down to zero because of the waveguide cutoff effect.  A better choice 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.
  Another design approach, particularly suitable for CAD because it is a numerical method, is to decompose the filter into a number of finite elements.  These elements are a large number of simple steps and ridges.  A number of methods are available to analyse the individual elements.  The mode matching technique expands the field equations of the element into a series of eigenfunctions and then for each mode matches the field at the interface between elements.  The Galerkin method expands the field equations into polynomial functions such as Gegenbauer polynomials or Chebyshev polynomials.  These methods can be mixed according to what is convenient
caption: Waffle-iron filter teeth types.  Bottom rows only are shown.  A: square teeth. B: rounded teeth. C: circular teeth with TE0n mode suppression wires.
exif: {}