Carson’s formulas

Because Carson s formula caimot deal with conductors of different lengths, three approaches to determine an effective length x are investigated (a) x = shorter length X2, (b) arithmetic mean distance x = (x + X2)/2, and (c) geometrical mean distance x = Xj K can... 

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

The result agrees well with that in Tablel.l, which is calculated by the accurate Carson s formula using EMTP Cable Constants (see Section 1.8, Table 1.19 (b) [5,24]). 

Eq in Equation 1.23), and he further derived a series expansion of the infinite integral in Equation 1.21. The details of Carson s expansion formula are explained in many publications, for example. Reference 11. 

Therefore, it is not possible to discuss wave propagation on a finite line by Pollaczek s, Carson s, or Sunde s formulas in Equation 1.241. 

Table 1.11 shows measured and calculated results of the surge impedance of a horizontal conductor. It is clear that the proposed formula shows more accuracy than Carson s. The accuracy of the proposed formula increases as x/h decreases, corresponding to the characteristic of the inductance. A similar observation has been made in different measurements in Reference 44. 

Pollaczek s and Carson s impedances are for a horizontal conductor. In reality, there are a number of nonhorizontal conductors, such as vertical and inclined ones. Although many papers have been published on the impedance of vertical conductors such as transmission towers, it is still not clear if the proposed formulas are correct. The empirical formula in Reference 12 is almost identical to an anal5 cal formula [13], which agrees quite well with the measured results. However, the anal5 cal formula requires further investigation to confirm if the derivation is correct. 

In fhe 1920s, fhere was no compufer, and fhus if was impossible to use Pollaczek s impedance. Carson derived fhe same formula as fhe Pollaczek s one neglecfing fhe earfh permiffivify, fhaf is, e = eo in Equation 1.23, and furfher he derived a series expansion of fhe infinite integral in Equafion 1.21. The defail of Carson s expansion formula is explained in many publications, for example. Ref. [10]. 

There were no computers in the 1920s thus, it was impossible to use Pollaczek s impedance [8]. Carson derived the same formula as Pollaczek, neglecting the earth permittivity (i.e., =... 

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