Design and analysis of low‐sensitivity all‐pole low‐pass switched capacitor filters

Abstract

AbstractAll‐pole switched capacitor filters (SCFs) having a zero worst‐case sensitivity of amplitude response in their passband are proposed, together with their approximate and exact design methods. In the approximate design method, a normalized doubly terminated LC ladder filter which satisfies given specification is used for an analog reference filter. the LDI s‐a transformation is applied to the equations representing this circuit. Stable equations representing the approximated circuit are obtained by replacing the terminal resistances with frequency‐ dependent cosine‐function resistances. the design is carried out based on these equations. In the exact design method, a doubly terminated unit‐element filter which satisfies specifications is used as a reference filter. From its lumped‐element equivalent circuit using two kinds of complex‐frequency variables, equations in the same form as those of the foredescribed approximated circuit are obtained. the SCFs are designed based on these equations.In this paper, first, a general Circuitstructure in which the minimum worst‐case sensitivity of amplitude response in the passband can be zero is shown. Based on this, formulas of the approximate and exact designs of an all‐pole low‐pass SCF circuit are given. As an example, the design of a third‐order all‐pole low‐pass SCF is shown. the proposed SCF is compared with a typical conventional SCF, and excellence of the former, such as a low element sensitivity, is demonstrated.