Input Section - Topology Matrix

The topology matrix describes which couplings the filter designer will allow in a filter, and which he will not allow. In this way the filter designer can define the "shape" - or topology - of the physical filter. 

For example - wheater input and output connectors are placed in the same end - or opposite - is defined by the topology matrix (see examples below).

Boxes where couplings are allowed must be 'Checked'. Empty boxes correspond to zero coupling between involved elements.
If a topology is entered, which can not fulfill the wanted filter characteristic, the error indicator 'lights' red. In that case the topology should be changed e.g. by adding more couplings. 
The coupling matrix must always be symmetrical about the diagonal (S,S)->(L,L). This is automatically enforsed in the SW.

The matrix synthesizer tries to make an identical match of the desired characteristic. If e.g. two transmission zeroes are specified the synthesis will only be characterized as 'successful' if a topology is specified which generates exactly two zeroes. A three zeroes characteristic would be characterized as a 'failure' even though the rejection performance might even be better.

The best is of course to specify a topology which is known to be able to match the desired characteristic.
If this is not possible - one approach is to start out with few couplings and add couplings until the synthesis turns out successfully.
Another approach is the opposite: To start out with a topology with a relatively high number of allowed couplings and then try to reduce the number. With the latter approach it is often seen that the synthesizer 'switches off' couplings which are not necessary. 

Topology Matrix Examples:
Fully canonical folded form Quadruplet and triplet in series

Parallel topology

Another topology

Some background:

The folded form is used as default in this software but even though this form is an often used topology in real microwave filters other forms may be more practical for a given application.
The folded form can be modified by applying a series of "plane rotations" to the folded coupling matrix whereby other filter configurations may be obtained.

A general  and very flexible method for this purpose has been presented by Atia [3]. Here the wanted topology is described by a "topology matrix" which is a NxN matrix of zeroes and ones, depending on whether the corresponding element in the final coupling matrix has to be reduced to zero or not. With the topology matrix as input, successive plane rotations are applied to the coupling matrix. The angle of rotation is determined so as to minimize the elements that are affected by the plane rotation and that have to be reduced to zero. 
The reduction procedure continues until all elements that have to be reduced to zero become smaller than a prescribed error. Any topology can - in principle - be realized by the method. If, however, the desired filter characteristic is not realizable with the wanted topology, the method will not converge and another - and more suitable - topology must be defined, e.g. with additional non-zero entries in the topology matrix.

More information may also be found in [4]

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