Six-Pole Bandpassfilter with Single Cross-Coupling

Tuning of coupled-resonator filter is performed in this article by using the group delay response of the input reflection coefficient of sequentially tuned resonators containing all the information necessary to design and tune filters. To achieve high out-of-band rejection losses a single transmission zero is introduced producing a pair of finite frequency poles.  CST MICROWAVE STUDIO® (CST MWS) is used to optimize and/or tune the bandpass filter resonse in a complete model by applying the new, fast MOR-Frequency Domain Solver. To speed-up the tuning process the entire model is split up into several sections and recombined in CST DESIGN STUDIO™ (CST DS) to get the overall filter response

The example presented here is a 6-pole folded combline bandpassfilter with a center frequency = 1793 MHz, a bandwidth = 170 MHz, a return loss of VSWR= 1.2 (equivalent to -21dB) and an out-of-band rejection for frequencies > 1920 MHz of less than -30dB. The u-shape type was chosen to create a quadrupole section by introducing a pair of transmission zeros. Although the filter geometry looks quite simple, it is a very challenging tuning task since the posts are positioned in an open waveguide environment without any irises to confine the cavities. Also the tuning of the individual posts is performed by simply changing their lengths hereby varying their capacitances against the waveguide's walls.

The tuning process for the simple Chebychev response was started with the cross-coupling by optimizing the group-delay response of sequentially tuned resonators. The process is very well described in [1] and [2]. The procedure can be automated within CST MWS using PostProcessingTemplates allowing to compose complex goals for the optimizer.  The beauty of this method is the limited number of varying parameters at each tuning stage: the coupling bandwidth and the resonance frequency.

Since the geometry is symmetric, only the first 3 resonators need to be tuned. The only additional missing parameter to be tuned is the coupling bandwidth between resonators 3 and 4. Overall there are seven free parameters to completely describe und tune the filter: the distance of the input coupling disk towards the first resonator, the distances between second and third resonators, the distance between resonator 3 and 4 and the resonator's lenghts. As the group-delay response is getting quite difficult to interprete, another method was chosen instead: Two discrete ports were positioned above the two resonators and the coupling distance was determined by the two adjacent peaks of the transmission parameter. The final geometry is shown in Figure 1.

Instead of performing the optimization with the complete filter, the model was split up into several sub-sections. wWaveguide ports considering a sufficiently large number of modes are assigned at the intersections . CST MWS is used to compute the required S-parameters. Since the number of meshcells of the submodels is small compared to a complete model the runtimes are extremely short, thus the meshdensity can be increased to achieve higher accuracy. Since frequencies below cutoff are considered it is advisable to use the Frequency Domain solver within CST MWS: here the Model order Reduction solver (MOR) was used. Figure 3 illustrates this procedure: Only four submodels are required to describe the complete filter.

The sub-models are loaded into CST DS and linked together. The local sub-model parameters can be accessed and assigned to a global CST DS parameter. These parameters can be used in an optimization process. CST DS uses an interpolation scheme in order to avoid numerous recomputations of S-parameters for individual setups required by the optimizer.

In a next step, the length of the capacitive cross-coupling stub is enlarged to increase the coupling bandwidth for a quadruplet type behaviour described in [3] and [4].

Finally, the cross-coupling is further increased, resulting in a symmetric location of the transmission zeros above and below the passband. The next two figures show the geometry and the respective S-parameters.

References:

[1] John B. Ness: "A Unified Approach to the Design, Measurement, and Tuning of Coupled-Resonator Filters", IEEE Trans. on MW Theor. and Tech., Vol 46, No 4, April 1998

[2] Peter Martin, John B. Ness: "Coupling Bandwidth and Reflected Group Delay Characterization of MW Bandpass Filters", Applied MW&Wireless, Vol 11, No 5.

[3] Raph Levy: "Filters with Single Transmission Zeros at Real or Imaginary Frequencies", IEEE Trans. on MW Theor. and Techn., Vol. MTT-24, No 4, April 1976

[4] Ralph Levy, Peter Petre: "Design of CT and CQ Filters Using Approximation and Optimization", IEEE Trans. on MW Theor. and Techn., Vol 49, No. 12, Dec. 2001

Appendix:

A bandpass filter can simply be described by low-pass prototype LC elements and by coupling coefficients of the inverter coupled filter. Approximation techniques can be used to get good initial values of the lumped elements [4] to find an optimal overall performance in a consecutive optimization loop. The cross-couplings requires slight changes of the theoretical Chebychev values resulting in very small geometrical modifications. A The next figure shows the equivalent network including also a cross-coupling admittance inverter with a negative C across the nodes 2 and 5.