Passive Rational Function Fitting of a Driving-Point Impedance from Its Real Part

An important consequence of the passivity of a network driving-point impedance, Z(s), is that knowledge of its resistive part along the imaginary axis of the complex-frequency plane ( s = alpha + jomega plane) suffices for the determination of Z(s) everywhere on the complex plane. By exploiting this property we show that a passive rational function fit of the driving-point impedance of a passive network, valid over a desirable frequency bandwidth, 0 les omega les omega
_BW
, can be readily obtained from the sampled values of its real part over a range of frequencies 0 les omega les omega
_S
, where omega
_BW
les omega
_S
. The fitting algorithm proposed for this purpose is computationally simpler than related, commonly used, rational fitting processes