Some Mapping Properties of RC and RL Driving-Point Impedance Functions

Thomas S. Huang

doi:10.1109/TCT.1965.1082412

Some Mapping Properties of RC and RL Driving-Point Impedance Functions

Thomas S. Huang

Research output: Contribution to journal › Article › peer-review

Abstract

We show that an RC or RL driving-point impedance function Z(s) maps the closed right-half s plane onto a region in the Z plane which is covered hy the closed circular disk with the straight line segment joining Z(0) and Z(∞) as a diameter; and which covers the open circular disk with center at Z(u) and radius [formula omitted], and the straight line segment Z = Z(u) + jtuZ'(u), – 1 < t < 1, for any real positive number u.

Original language	English (US)
Pages (from-to)	257-259
Number of pages	3
Journal	IEEE Transactions on Circuit Theory
Volume	12
Issue number	2
DOIs	https://doi.org/10.1109/TCT.1965.1082412
State	Published - Jun 1965
Externally published	Yes

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General Engineering

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10.1109/TCT.1965.1082412

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AB - We show that an RC or RL driving-point impedance function Z(s) maps the closed right-half s plane onto a region in the Z plane which is covered hy the closed circular disk with the straight line segment joining Z(0) and Z(∞) as a diameter; and which covers the open circular disk with center at Z(u) and radius [formula omitted], and the straight line segment Z = Z(u) + jtuZ'(u), – 1 < t < 1, for any real positive number u.

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Some Mapping Properties of RC and RL Driving-Point Impedance Functions

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