Inversion of some or all of the resonators in an evanescent-mode bandpass structure allows for achieving wide bandwidth filters, with some transmission zeroes located at DC, some at infinity. Close spacing, as occurs when bandwidth is large, implies higher-order mode coupling and thus accurate design requires consideration of these modes. The resulting filters still display the small size, low loss and wide stopbands common to evanescent mode structures in general. Resonator inversion is equivalent to replacing the magnetic wall equivalent between conventional evanescent resonators with an electric wall, which allows for some degree of net capacitive coupling. Resonator inversion applied to evanescent mode filters results in networks with similar upper and lower stopband slopes, bandwidths of up to 80% and stopbands extending up to 20 times the filter center frequency. As has been shown [1], [2], the method can be applied to cases in which the resonators are a mixture of dielectric resonator, waveguide, etc. In a conventional evanescent mode filter with all resonators pointing in the same direction, the internal coupling is essentially magnetic (inductive) and thus the filter stopband is what is termed "semi-lowpass". Series equivalent inductors comprise the main coupling, and so the upper stopband slope is steeper than the lower.
Fig. 1 illustrates the effect of obstacle direction, for the case in which the obstacles are reactively loaded on their ends. If the illustrated field quantities oppose, the net coupling between obstacles tends to become capacitive. The proportion of coupling which is capacitive is dependent upon the diameters of the obstacles. If two adjacent opposing obstacles are of a diameter of less than 15% of the waveguide cutoff dimension, the magnetic wall between the obstacles is effectively thin and the coupling is essentially capacitive. As the diameter of the obstacles increases, the field variation over the surfaces of the obstacles becomes important, and the magnetic wall effectively "thickens". This results in some inductive coupling, as the net magnetic fields do not cancel. If the fields do not oppose, the net coupling is inductive, with the same comments applying as before. It is possible to mix the inverted/non-inverted resonators within the same filter and thus achieve almost symmetrical stopband slopes.
Figure 1
Fig. 2 illustrates the physical interconnection for an inverted design, in the case where the resonating capacitance consists of a variable and a fixed component, with the fixed element implemented as a capacitive substrate.
In this case, the main coupling between inverted lines is essentially capacitive, and the lower stopband slope of the filter is emphasized, at the expense of the upper slope. Evanescent mode bandpass filters operate on the principle of capacitively-resonating the shunt elements of a simple inductive pi single-mode representation of below cutoff waveguide. The inductive elements are generally of high unloaded Q, with a value related to the distance below the cutoff frequency of what would be the dominant propagating mode in an unperturbed cross-section of waveguide shaped like the filter interior. Taking into account the higher order mode coupling enables extension of this design approach from bandwidths of 1% to at least 80%. Modification of the design, as presented in [1], enables the design technology developed conventional evanescent designs to be applied to the inverted case. The net result is availability of filters achieving specified stopband levels on both sides of the passband, with fewer elements and with less size and loss. Fig. 3 is a photograph of an inverted design, in which elements 4 and 8 have been inverted, thus displaying capacitive coupling from element 4 to elements 3 and 5 and from 8 to both 7 and 9, with the remaining elements essentially inductively coupled. The filter response is almost symmetrical.
In conclusion, it is now possible to achieve smaller, less lossy filters that do not have to be overdesigned to achieve the required stopband levels in the case where one slope specification is much greater than the other. The design approach described in this note allows for almost symmetrical responses and thus more optimum filters.
1. R. V. Snyder, "Inverted Resonator Evanescent Mode Filters", IEEE MTT-S Symposium Proceedings, San Francisco Symposium, 1996
2. R. V. Snyder, "Embedded-Resonator Filters", Proceedings of the ESA-ESTEC, Conference on Filter CAD, ESA, The Netherlands, Nov. 6-8, 1995.
3. R. V. Snyder, "New Application of Evanescent Mode Waveguide for Filter Design", IEEE Transactions: On Microwave Theory and Techniques, December, 1977