six-pole bandpassfilter with single cross-coupling

7/29/2019 Six-Pole Bandpassfilter With Single Cross-Coupling

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Six-Pole Bandpassfilter with Single Cross-Coupling

2013 CST AG - http://www.cst.com Page 1 of 12


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.


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Figure 1: Final geometry. Note, that the capacitive cross-coupling is made inactive by minimizing its length


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Figure 2: Typical Chebyshev- response after completion of the tuning process

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.


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Figure 3: Definition of the sub-models: At the common interfaces between the sub-models waveguide ports areassigned (not shown here)

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.


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Figure 4: CST MWS submodels and their connections via modes. Note the link to global CST DS parameters


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Figure 5: S-Parameter view of CST DS results

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].


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Figure 6: Enlarging the length of the stub reinforces the coupling bandwidth


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Figure 7: The transmission zeros are still in the upper stopband indicating that the coupling is too small. Shownhere is also a comparison between a complete model and a sub-model result using CST DS

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.


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Figure 8: Further enlargement of the cross coupling stub


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Figure 9: Results of the CST DS model: Two transmission zeros appear above and below passband. Adding adiagonally positioned coupling would allow a more symmetric rejection shape

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 MWWireless, 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


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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.

Figure 10: Circuit elements for inverter coupled filter structures


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Figure 11: Optimized filter response of the bandpass filter within CST DS

Figure 12: Parameter list of optimized LC lumped element values

six-pole bandpassfilter with single cross-coupling

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