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

We show that anRCorRLdriving-point impedance functionZ(s)maps the closed right-half s plane onto a region in theZplane which is covered by the closed circular disk with the straight line segment joiningZ(0)andZ(\infty)as a diameter; and which covers the open circular disk with center atZ(u)and radius|{1/2}uZ'(u)|, and the straight line segmentZ = Z(u) + jtuZ'(u),-1 < t < 1, for any real positive numberu.