When designing filters, a pervasive requirement is the implementation of couplings between adjacent resonators. The resonators might be cavities, dielectric pucks, L-C tank circuits, waveguide sections, coaxial stubs, resonated evanescent waveguide, printed elements, active devices, or others. In common, however, is the requirement to provide some coupling between the resonators. The coupling must provide for proper vector addition of energy between the resonators, as required by the synthesis. Frequently, such couplings are described as “inductive” or “capacitive”, a nomenclature referring to the sign of the coupling impedance type (positive for inductive, negative for capacitive). Filters that have a single path for energy transit from input to output are usually derived from circuits called “ladder networks”, because the alternating series and shunt elements have the physical form of a ladder. Such filters employ either inductive or capacitive coupling between adjacent resonators. These filters can approximate various transfer functions (e.g. Butterworth, Chebychev, Bessel, Gaussian, etc.) with monotonic attenuation characteristics. Sometimes, a better approximation of these monotonic functions is made possible if some of the inter-resonator couplings are inductive while some are capacitive. If both forms of coupling are used, the attenuation characteristics can be made more symmetrical, when comparing the attenuation slope above the passband region to that below the passband. Providing the correct impedance sign is frequently difficult, because most physical filter structures force the inter-resonator coupling to be either inductive or capacitive, but not both within the same normal configuration.
Filters that provide for more than one path for energy to move between input and output offer certain potential advantages compared to purely ladder-derived networks. It is possible to place points of higher attenuation close to a passband or to flatten the group delay characteristics of a passband region, by using appropriate couplings between non-adjacent (electrically, not physically) resonators. Depending upon the synthesis, the “appropriate” coupling might be inductive or capacitive. Mechanically folding a filter to place the input resonator next to the output resonator is relatively simple, but providing the correct coupling impedance type is again a problem for the same reasons as discussed for the monotonic slope filter types: structures tend to dictate the predominant coupling type. The recognition that a resonant circuit has an impedance that varies from capacitive to inductive leads to the solution. If the coupling between resonators is a resonant circuit, energy passing through the coupling will be phase-shifted and amplitude adjusted, depending on the resonant frequency and magnitude of the coupling. A positive phase shift will implement an inductive coupling, a negative phase shift implements a capacitive coupling. The coupling magnitude can be adjusted by simply adjusting the size of the opening between the coupled resonators. Of course, the coupling magnitude and the coupling phase are both affected by adjustment of the coupling resonant frequency. Thus, it is usually necessary to adjust both the resonant frequency and opening size to achieve the correct magnitude and phase for the coupling. An example of the technique is shown in Fig. 1.
In this example, the main filter path employs inductive coupling, as the filter is an evanescent mode structure [1], [2], [3]. The cross-couplings between non-electrically adjacent resonators are implemented using one-pole evanescent filters connecting the resonators. Adjusting the cross-section of these couplings while also adjusting the resonating capacitor provides for either coupling type (inductive or capacitive). In this example, inductive couplings will flatten passband group delay, while capacitive coupling will place pairs of transmission zeros in the stopband region, resulting in a non-monotonic attenuation skirt with the appearance of an “elliptic” response. A discussion of the technique can be found in US Patent 5,220,300 and will be fully discussed during the 1997 MTT-IMS to be held in Denver, June, 1997.
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