Coupling matrix seeding

Seed options

When creating a new design a coupling matrix seed is automatically added to it using some hardcoded settings. A seed is useful to get you started from something not an empty matrix. It is possible however to initiate the matrix with completely custom couplings but this is a tedious operation.

In most situations you will want to generate your own seed to get access to another filter order. While in the “Matrix” tab, tap “Seed” to open up the seed generator. Choose your desired filter order and passband ripple, or return loss. You may also want to include a common loss, or unloaded quality, to all resonators. Tap “Done” to generate a new seed. You may recognize that the coupling matrix represents the Chebyshev response. This response is a good starting point for most filter designs since it allows you to easily compromise between rejection and passband ripple. If you set the return loss to a high value the response will converge towards Butterworth.

Please note that this operation will completely overwrite your current coupling matrix, analysis and topology settings. The topology generated is of folded form which is one of the most common topologies. Symmetry, optimization/Monte Carlo settings are also applied to the matrix appropriately. You may want to transform to a different topology when done.

Transmission/reflection zeros

Advanced coupling matrix seeds with prescribed zeros are easy to generate in Couplings Designer. Just tap the “Zeros…” button and add a new zero. Keep in mind however that you may only define N zeros, where N is the order of your filter. A zero at a finite frequency counts as one (1) and a symmetric pair or conjugate pair counts as two (2).

A finite frequency zero can be added to get a sharper rejection slope at one side of the response. The rejection on the other side is unfortunately reduced and the filter will be asynchronous. A symmetric pair automatically defines two finite frequency zeros located symmetrically about the center frequency of the filter based on the first zero you define. The advantage is that your filter is always guaranteed to be synchronous. A conjugate pair can be added to equalize the group-delay response.


If one is forced to use low-quality resonators, due to size/weight requirements or lossy materials, the response will suffer from severe distortion of the passband linearity. In these situations predistortion can be used to compensate for a low quality resonator. The predistorted response will mimic the response of a filter with resonators of a higher quality. This “synthetic quality factor” is called the effective quality factor. For instance, a filter incorporating resonators with a quality of 4000 but predistorted with an effective quality of 20000 will have the same linearity as a filter with resonators 5 times as good without an increase to its size. In-band insertion loss and return loss performance is sacrificed to improve the linearity but it may not be a big issue if the filter is located somewhere where high loss and poor match is tolerated.

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