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Jurisic, Drazen; Moschytz, George S.
International journal of circuit theory and applications, September 2019, 2019-09-00, 20190901, Letnik: 47, Številka: 9Journal Article
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. The effect of coupling on the overall sensitivity to component tolerances of two resonators or biquads (CO) is compared with the sensitivity of a noncoupled cascade (CA) realizing the same transfer function. Minimum sensitivity is analytically shown to be obtained when the resonators inside the coupled structure are identical. The effect of parameter variation in an optimized coupled structure of two biquads is shown to be up to 30% lower than in the equivalent cascade.
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