Input Section - Coupling Matrix

The coupling matrix may also serve as an input device.

By selecting the "Plot Using Coupling Matrix" button, editing of couplings in the coupling matrix becomes possible.
An entry in the coupling matrix may be edited/changed in two different ways:

  1. By right-clicking with the mouse on the coupling to be changed. 
  2. By using the 'slider' bar (to the right of the coupling matrix), which will operate stepless on the coupling to be changed.

    Changing couplings by: Right-click functions on coupling matrix:
  • Select coefficient for Monte-Carlo analysis
  • Zeroing of coupling values
  • Clear cell and Edit new value
  • Sign change (i.e. the sign is "shifted" to other couplings in the matrix - see sec. 13.5 in [4])

The influence of the change on the S-parameter characteristics can be inspected by clicking the "Update" button.
Changing the sign of an entry in the coupling matrix has no influence on the filter characteristic.

         Changing couplings by: Using the 'slider':

  • Click on the coupling which you want to modify and 'drag' the 'slider' up or down in order change the coupling value.
  • The plot is updated instantly. If the plot updating is not performed smoothly it may be a good idea to lower the number of points.
  • Use the 'Esc' button to cancel a change.

Editing of coupling coefficients is convenient for:

  • zeroing of very weak couplings in order to see if they can be omitted in a physical filter
  • change of coupling signs
  • investigation of other N+2 coupling matrices e.g. in the literature
  • analysis of where unintended couplings may arise from in a physical filter
  • sensitivity analysis of critical couplings (Monte-Carlo) or topologies


A filter with two symmetrically positioned notches is designed. The synthesized characteristic is shown below:

It is well known that such a characteristic can be implemented by a single negative x-coupling bypassing two resonators. In the present case this coupling is found between resonator 2 and 5 in the coupling matrix above.

It is, however, noted that the synthesizer has actually added an extra coupling between resonator 3 and 5 (selected by mouse "right-click" in the shown example above).
This coupling is more than 20 times weaker than the other x-coupling.

If this coupling is zeroed, the characteristic below is obtained:

It is seen that zeroing of the weak coupling has almost no influence on the filter characteristic, and this coupling can therefore be omitted if the filter is going to be manufactured. 

The characteristic can therefore be implemented by use of a single negative x-coupling which bypasses two resonators.

The reason that the synthesizer has found it necessary to include this extra small coupling originates from limited numerical accuracy in the calculations and algorithms, which lie behind the synthesis.
Zeroing of the mentioned coupling could also be achieved by adjustment of one of the notch frequencies by a very small amount, thereby moving the characteristic slightly away from perfect symmetry.
In aperture coupled combline filters the above symmetrical characteristic are often found difficult to obtain. Very often it turns out that the upper notch ends up lying closer to the pass band than the lower notch does.
It can be verified by insertion of weak positive couplings that this asymmetry may originate from unintended coupling between resonators 3 and 5 and/or between 2 and 4.


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