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Summary: IEEE TRANSACTIONS ON ADVANCED PACKAGING, VOL. 26, NO. 2, MAY 2003 165
Causal Characteristic Impedance of Planar
Transmission Lines
Dylan F. Williams, Fellow, IEEE, Bradley K. Alpert, Uwe Arz, Member, IEEE, David K. Walker, Member, IEEE,
and Hartmut Grabinski
Abstract--We compute power-voltage, power-current, and
causal definitions of the characteristic impedance of microstrip
and coplanar-waveguide transmission lines on insulating and
conducting silicon substrates, and compare to measurement.
Index Terms--Causal, characteristic impedance, circuit theory,
coplanar waveguide, microstrip.
I. INTRODUCTION
WE COMPUTE the traditional power-voltage and power-
current definitions of the characteristic impedance [1],
[2] of planar transmission lines on insulating and conductive
silicon substrates with the full-wave method of [3] and com-
pare them to the causal minimum-phase definition proposed in
[4]. Where possible we compare computed values of the causal
impedance to measurement. In all cases we find good agree-
ment. The microstrip simulations have been reported in confer-
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