Basic Assumption of the Impedance

Pollaczek s and Carson s formulas were derived under the assumption that 

It should be noted that most formulas of capacitance and inductance of conductors given in textbooks are based on the aforesaid condition. It is easily confirmed that any capacitance formula gives an erroneously large value when the radius reaches the height. Correspondingly, the inductance of an infinite conductor becomes larger than that of a real finite conductor [6,7]. Furthermore, the formulas neglect displacement currents, that is. 

For example, the applicable range of a frequency in the case of and e=So is given by 

Even in the case of = 100 Q-m, a transient of 10 ns time region cannot be simulated by Pollaczek s and Carson s impedance [8-11], It should be noted that most of the frequency-dependent line models are not applicable to the aforesaid cases, because those models are based on Pollaczek s and Carson s impedances. 

Under conditions where Equations 7.1 and 7.2 are not satisfied, only Kikuchi s and Wedepohl s impedance formulas are applicable at present [8-10]. This requires a far advanced numerical integration than that applied to Pollaczek s formula. 

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