Characteristic impedance

The appropriate impedance of a parallel-wire manual band like accompanying advance or ladder band depends on its dimensions; the bore of the affairs d and their break D. This is acquired below.

The appropriate impedance of any manual band is accustomed by

Z = \sqrt{{R + j \omega L} \over {G + j \omega C}}

where for twin-lead band the primary band constants are

R = 2 {R_s \over \pi d}

L = {\mu \over \pi} \, \operatorname{arccosh}\left({D \over d}\right)

G = {\pi \sigma \over \operatorname{arccosh}({D \over d})}

C = {\pi \epsilon \over \operatorname{arccosh}({D \over d})}

where the apparent attrition of the affairs is

R_s = \sqrt{\pi f \mu_c / \sigma_c}

and area d is the wire bore and D is the break of the affairs abstinent amid their centrelines.

Neglecting the wire attrition R and the arising conductance G, this gives

Z = \frac{Z_0}{\pi \sqrt{\epsilon_r}} \, \operatorname{arccosh}\left(\frac{D}{d}\right)3

where Z0 is the impedance of chargeless amplitude (approximately 377 Ω), εr is the able dielectric connected (which for air is 1.00054). If the break D is abundant greater than the wire bore d again this is approximately

Z \approx 276 \log_{10}\left(2\frac{D}{d}\right)4

The break bare to accomplish a accustomed appropriate impedance is therefore

D = d \cosh \left(\pi\frac{Z\sqrt{\epsilon_r}}{Z_0}\right)