On Transfer Functions Realizable with Active Electronic Components

Abstract : In this work, we characterize transfer functions that can be realized with standard electronic components in linearized form, e.g. those commonly used in the design of analog amplifiers (including transmission lines) in the small signal regime. We define the stability of such transfer functions in connection with scattering theory, i.e. in terms of bounded reflected power against every sufficiently large load. In the simplest model for active elements, we show that unstable transfer functions exist which have no pole in the right half-plane. Then, we introduce more realistic transfer functions for active elements which are passive at very high frequencies, and we show that they have finitely many poles in the right half-plane. Finally, in contrast to the ideal transfer functions studied before, the stability of such "realistic" transfer functions is characterized by the absence of poles in the open right half-plane and the positivity of the real part of the residues of the poles located on the imaginary axis. This report is written in a way which is suitable to the non-specialist, and every notion is defined and analyzed from first principles.
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[Research Report] RR-8659, Inria Sophia Antipolis; INRIA. 2014, pp.36
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Laurent Baratchart, Sylvain Chevillard, Fabien Seyfert. On Transfer Functions Realizable with Active Electronic Components. [Research Report] RR-8659, Inria Sophia Antipolis; INRIA. 2014, pp.36. 〈hal-01098616〉

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