When seeding a new coupling matrix the default topology is of folded canonical type. This topology is frequently used to realize the most common structures like the edge coupled microstrip and combline quarter wave resonator filters. However it is often a desire to find other topologies that can support an arbitrary placement of resonators and cross-couplings to implement the response in practice. It may also be beneficial when it comes to manufacturing tolerances to try a different topology.
With Couplings Designer the user has the ability to transform from one topology to another by simply specifying which couplings to be included and let the built-in topology transformer apply a series of matrix rotation until the desired topology has been found. A rotated coupling matrix produces an identical response as the initial one but if the angle of rotation is right it is possible to eliminate unwanted couplings. A rotation will however add new couplings to the matrix. Analytical algorithms has been developed to calculate the angles of rotations that eliminates unwanted couplings and produce a number of useful topologies but an analytical method to obtain an arbitrary topology has not been found. Couplings Designer uses optimization to find these unknowns, or angles. Depending on the complexity the drawback is that this method is computation-intense. The convergence of this method also depends on the initial coupling matrix.
Modifying the topology
When you tap “Topology” from the “Matrix” view a new coupling matrix is shown with green and red labels. The green labels are the couplings that are included in the current topology. However Couplings Designer does not restrict the designer to just these couplings when tapping “Done”, these labels are only used by the topology transformer. A red label indicates that the coupling is not part of the topology but still affects the response since it’s not zero. Realizing such a topology without including all couplings would yield errors. It is easy to toggle couplings to take part of or be eliminated from the topology, just tap it.
Residues and zeroing
The topology transformer, or optimizer, will run as long as there is a chance of convergence and until the goal has been reached. The goal is to produce a coupling matrix where all unwanted couplings has been reduces to a minimum where it’s safe to completely zero them without affecting the response. The maximum remaining coupling to be reduced is called the residue and the “safe” value is hardcoded to 0.00001 (normalized coupling). If the transformation is successful the residues are still there but no longer visible to the user. It is therefore recommended if the user is confident that these residues will not affect the response that one zeros them by tapping “Zero”.
To undo any transformation and return to the initial coupling matrix, just tap the refresh symbol in the bottom-left corner.
It is not unusual for the transformer to fail. If that’s the case try tapping “Transform” again. This is due to the optimization algorithm being dependent on the initial coupling matrix. If the transformation does not converge it will produce a bunch of unwanted couplings. Even if the new coupling matrix tends to look chaotic it might be more successful at converging.
A common error is also that the new topology simply can not support the response. If the initial response has a transmission zero the new topology has to support it with appropriate cross-couplings for instance.
Couplings Designer has support for the most commonly used topologies using the built-in presets. These are, folded, arrow, extended box and Cul-de-sac, some of which are only available at certain filter orders. Please remember to include cross-couplings to support your transmission zeros, otherwise the transformer will not converge.
Leaving the topology editor
When you tap “Done” your new coupling matrix will be available to you for further editing, tuning and optimization. The new matrix will also come pre-configured with all couplings marked as taking part of optimization and Monte Carlo analysis. Remember that this operation is not undoable.
Back to the Couplings Designer documentation.