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Minimum sensitivity coupled resonators and biquads
Author(s) -
Jurisic Drazen,
Moschytz George S.
Publication year - 2019
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2683
Subject(s) - resonator , sensitivity (control systems) , transfer function , cascade , pole–zero plot , coupling (piping) , loop (graph theory) , band pass filter , control theory (sociology) , topology (electrical circuits) , coupling coefficient of resonators , equivalent circuit , physics , electronic circuit , feedback loop , engineering , electronic engineering , mathematics , computer science , voltage , electrical engineering , optics , control (management) , artificial intelligence , mechanical engineering , computer security , combinatorics , chemical engineering , quantum mechanics
Summary The effect of coupling on the overall sensitivity to component tolerances of two second‐order resonators is compared with the sensitivity of a non‐coupled cascade of two second‐order resonators. Coupled resonators consist of two second‐order resonators “coupled” within a negative feedback loop. The resulting overall fourth‐order transfer function of the two circuits, coupled and non‐coupled, is identical. The “cascaded” poles, ie, the poles of the two cascaded resonators, are therefore identical to the poles of the coupled circuit, the coupled poles. The poles within the negative‐feedback loop, the “open‐loop” poles, will be different. We assume that the manufacturing technology used to realize the open‐loop poles of the coupled circuit is the same as that of the cascaded, non‐coupled circuit. The open‐loop poles will therefore be subject to the same component tolerances as those of the cascaded non‐coupled circuit. Our analysis leads to the optimum location in the s‐plane with regard to minimum sensitivity, for the open‐loop poles of the coupled circuit. Since resonators are essentially the equivalent of second‐order bandpass filters, the results obtained are applied to coupled second‐order active‐RC filters, or biquads, for which insensitivity to component tolerances is critical. The examples given pertain to the coupling of biquads.