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Formal Expression of Sensitivity and Energy Relationship in the Context of the Coupling Matrix

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4 Author(s)

Precise formulas to express the formal relationship between the time average stored energy in the resonators of a low-pass filter network and the sensitivity of the reflection S -parameter with respect to the coupling matrix terms are demonstrated in this paper, considering the normalized frequency axis. These relationships are found in the modern context of the N+2 coupling matrix, and for both diagonal and general nondiagonal coupling elements of the matrix. The results are valid for any type of coupling topology represented by the N+2 coupling matrix. Different examples are included as validation. Furthermore, important implications and applications derived from the new relationships are highlighted.

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IEEE Transactions on Microwave Theory and Techniques  (Volume:60 ,  Issue: 11 )