Bilinear Integrator Research Articles

Novel switched-capacitor integrator for high-frequency applications

A discrete integrator for switched-capacitor (SC) filter applications is developed. The proposed integrator is generated from an optimal linear combination of the lossless discrete integrator (LDI) and the bilinear discrete integrator, and therefore it is called the composite discrete integrator (CDI). This integrator is ideal for high-frequency applications because it doubles the normal folding frequency and minimises high-frequency discrete integrator errors. Several SC realisations of the CDI are given. SC circuits for emulating general first- and second-order analogue filter sections based on the CDI are also given.

SC bilinear integrators

A different way to develop bilinear integrators is presented. It relies on the inverse recharging technique used in voltage inverter switch (VIS) circuits. Three new circuits, one inverting and two noninverting integrators developed by this technique, are presented. All circuits are parasitic-free without compensation. In two of them, there is no need for component matching to realize the bilinear z-transformation. Consequently the circuits are suitable for integration. The inverting integrator is compared to six known similar circuits.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Representation of operators by bilinear integrals

Representation of operators by bilinear integrals

Fully differential bilinear integrator for SC filters

A fully differential bilinear SC integrator, which can be used for SC filter realisations, is proposed. It is parasitic-insensitive and particularly useful in SC filters simulating analogue ladder networks. The design of these filters is different from the commonly used ones, and leads to filters with better sensitivity properties than earlier versions. Realisation of a third-order highpass filter, bilinearly transformed from the continuous-time to the discrete-time domain, is shown as an example.

Use of bilinear integrator in design of fully differential biquads

The design of a bilinear integrator in fully differential form introduces new possibilities in the design of biquad circuits. The new circuits presented here have no simple non-differential counterparts, are stray-insensitive, have small sensitivities and require capacitor values in acceptable limits.

Noninverting parasitic-compensated bilinear SC integrator with only one amplifier

A noninverting parasitic-compensated bilinear integrator is presented. For the realisation of the circuit, only one amplifier is needed. A fifth-order lowpass filter, designed using the bilinear transformation and realised with this integrator at the input, is also discussed.

ON A THEOREM OF A.A. LYAPUNOV

Abstract In this note we obtain some extensions and an approximation of the Lyapunov convexity theorem by means of the bilinear integration of a set-valued function. The integration is performed successively with respect to a non-atomic, a direct sum and a Darboux vector measure. The necessary counterexamples are provided.

Bottom-plate stray-insensitive bilinear switched-capacitor integrators

Switched-capacitor bilinear integrators are introduced which enable the exact design of leapfrog filters. The resulting networks are completely insensitive to the stray capacitances of the bottom plates.

Mean Value Theorem for the m-Integral of Dinculeanu

The classical mean value theorem asserts that if f is a real, bounded, Riemann integrable function defined on a finite real interval a≤t≤b, then , where infa≤t≤bf(t)≤y0supa≤t≤bf(t). The extensions of Choquet [3], Price [15], and of this paper generalize the fact that y0 belongs to the closure of the convex hull of f([a, b]). The version of Choquet ([3, p. 38]) applies to a continuous function on a compact interval with values in a Banach space; that of Price ([15, p. 24]) applies to a bilinear integral of a special type containing the Birkhoff integral [2]. The m-integral of Dinculeanu [6] (specialization of Bartle's *- integral [1]) leaves intact the Lebesgue dominated convergence theorem and is strong enough to support an extended development. The paper is organized as follows: the object of §2 is to express the integral of a bounded m-integrable function as a limit of Riemann sums; §3 gives Price's generalization of "convex hull" [15]; the theorem of the paper is established in §4; §5 gives applications to vector differentiation which, for continuously differentiable functions, contain results of Dieudonné [5] and McLeod [13].

Bilinear integrals of polyharmonic functions and of analytic functions.

Bilinear integrals of polyharmonic functions and of analytic functions.

Fast algorithms for simulation of neuronal dynamics based on the bilinear dendritic integration rule

Fast algorithms for simulation of neuronal dynamics based on the bilinear dendritic integration rule