Topology investigation & Monte-Carlo Analysis.


When a filter designer has 'tailored' a set of filter characteristics in CMS, which fulfill his or her demands, the question arises:   Which filter topology to use?

At this stage the designer has settled on filter order, bandwidth, number of transmission zeroes and their positions. 

Even though the found S-parameter characteristics can be realized through a multitude of different filter topologies,
they are not all equally good choices.

The Monte Carlo function in CMS is an excellent tool for comparing the feasibility of different filter topologies, which will be demonstrated in the following.

In the examples below the exact same filter characteristics are implemented through 3 different topologies.

The starting point for the investigation is the 8-pole filter displayed below. It has two transmission zeroes placed in the lower stop-band:

Topology 1 - the folded form
With the Topology Matrix, preset to the folded form as shown below (left), the coupling matrix pictured below (right) is obtained. It is seen that the characteristic can be obtained with x-couplings between Res-3,6 and Res-4,6.

By selecting the radio button: 
-the Monte Carlo window shown to the right appears. 

It is here possible to subject, either a single coupling, or all couplings, to a variation within the specified percentage range. 

The effect of the variation can be observed in the plot window where the different perturbed characteristics are plotted on top of each other.

The number of curves are specified in the "Sweeps" field.

To evaluate a topology, the Monte-Carlo function is a very convenient tool for sensitivity analysis. In the present case where the overall topology is of interest, "All" coupling coefficients are chosen. The sensitivity analysis could equally well be performed on a single coupling in order to check out the influence of that one coupling on the characteristics.
Single couplings can be chosen directly from the coupling matrix by "right-click" of the mouse.

The result from the above Monte-Carlo set-up is shown below:

It is seen that the folded topology is moderately sensitive around the transmission zeroes and that return loss has decreased up to 8 dB in-band.

Topology 2 - two triplets in series
The next topology example is two triplets in series as shown below.

The Monte-Carlo analysis on this topology is as pictured below. The same Monte-Carlo variation was used as for the folded topology example above.

Topology 3 - The Cul de Sac topology
The Cul-de-Sac topology set-up is shown below together with the Monte-Carlo analysis. Same variation as before.

By comparing the sensitivity analysis for the three topologies it is seen that they behave quite differently.

The Cul de Sac topology is by far the most sensitive, which indicates that - in practice - this topology probably will be difficult to tune-in and control over changing ambient temperatures.

The cascaded triplet topology is by far the most stable and seems the best choice - if the choice is free. 
Normally mechanical constraints like occupied space and connector positions limit the available topologies.

The bottom line of all this is, however, that the Monte-Carlo function in CMS is well suited for comparing feasibility of different possible topologies.