RS Microwave Technical Corner

December 1998

Quasi-Optimum Filters - A series of Articles

Part 2:  CROSS-COUPLING

Implementation of generalized cross-coupled filters [2], [3], [4], [5], [8], [9] (see Fig. 7) requires the use of both positive impedance (inductive) and negative impedance (capacitive) couplings.  The former are used for placing real-axis transmission zeros for delay equalization while the latter are used for placing real-frequency zeros, used for additional selectivity.  Inductive and capacitive irises are common in the literature and, in many cases, can be used for the aforementioned positive and negative couplings.  The iris couplings usually take the form of a simple opening between two segments of the filter.  One example is a direct opening between the input portion of the filter and the output.  This opening in essence provides a shorter path between the two terminating ports than is represented by the full traverse of all the filter elements.  Some energy “leaks” from the input directly to the output.  If the “leaking” energy is coupled in an inductive manner, the coupling is such as to reduce the net effect on attenuation of the remaining filter elements and simultaneously to reduce the total group delay variation due to the interference generated at the output termination between the leaking energy and the remainder which fully traverses the filter. In other cases, the “leaky” (or cross) couplings will be placed well within the filter, between any pair of resonant sections. In some cases, however, the values of computed coupling are such as to make impractical a simple opening between two parallel portions of the filter. The use of resonated evanescent mode sections allows implementation of both positive and negative couplings by employing the phase shift and impedance characteristics of the bandpass element represented by a short resonated section of evanescent mode waveguide.  Figure 8 illustrates the pi and tee models for ideal inverters, Figures 9 and 10 the use of odd and even mode half circuits, as used in the synthesis of symmetrical cross-coupled structures, in the state-of-the-art synthesis program FILPRO.  Cross-coupling can also be used effectively in lumped element circuits.  A good example of this is illustrated in Fig. 11, in which the result of applying asymmetric couplings is a quasi-elliptic response, comparing quite favorably toChebychev for loss/slope, or for element count and ultimate attenuation floor to an elliptic design.

                                                                                                                                               FIGURE 8

Fig. 11 presents the response of a VHF frequency range tubular-filter equivalent with asymmetric inductive cross over couplings.  Note the two low-Q notches on the upper skirt, one high Q notch on the lower skirt. Although the indicated example uses 50 ohm in/out impedance, filters of this type can be synthesized to match complex source and load impedances, within the bounds of the Fano and Bode criteria.

  FIGURE 11
 Asymmetric bandpass filter using Inductive crossover connections
 

RS Microwave has produced many such filters, with implementation in coax, dielectric resonator, waveguide, stripline and lumped element.  We will be happy to apply this exciting technique to your particular problem.

Rev 08- [figures replaced with jpg’s 12/08]