Changing signs of coupling coefficients

Sometimes it may become necessary to change the sign of one or more couplings in a synthesized filter.
A couple of examples are investigated in the following.
Example 1:

The first example is a 6-pole filter with the coupling matrix shown below.

It is seen that all mainline couplings (S-1-2-3-4-5-6-L) are positive - i.e. inductive. The CMS tool gives as default positive main line couplings.
If this filter is going to be used in an application with a DC voltage on the source pin - 'S' - the inductive coupling between this terminal and resonator 1 is a problem, since the inductive coupling may short-circuit the voltage if implemented as a tapped connection in e.g. a combline filter (below left). A more convenient coupling method would be the capacitive coupling disc shown below right.

In CMS the coupling matrix may be edited by selecting the "Plot Using Coupling Matrix" radio button (see below).
When this is done the entries in the coupling matrix may be changed by right clicking the mouse on the coupling, which one want to change. The coupling coefficients may be zeroed and have their values or signs changed.
When the changes are done the influence on the filter characteristics can be inspected by selecting the "Update" button.

Changing the signs of the coupling Mij in the coupling matrix can be done by multiplying -1 to all the entries in row and column i, or row and column j. The sign is therefore not changed, but merely "shifted" to other couplings in the matrix.

In CMS this operation is done automatically by selecting the "Change Sign" option when right clicking on a coupling.

In the actual example the sign is changed for the input coupling, which leads to the coupling matrix shown below.
One can verify that the sign change does not affect the filter characteristics by pressing the "Update" button.

In the present example the sign change has not had any effect on other couplings since the input coupling only couples to resonator 1, but in the next example this is not the case.

Example 2:

A folded 6-pole filter with coupling matrix and topology as shown below is investigated.
We now want to change sign on all main line couplings.

The best way to do this is to start backwards i.e. from Load towards Source:
First change sign on the coupling (6,L), this has the side effect of also changing sign on the coupling (5,6).
Then change sign on the coupling (4,5), this has the side effect of also changing sign on the coupling (3,4), etc, etc.

The sign change sequence for the main line couplings is illustrated below:

The resulting coupling matrix and topology diagram is shown below:

It is noted that changing signs of the main line couplings has led to sign change for two out of four cross-couplings.