Analysis of information sources in references of the Wikipedia article "Characteristic impedance" in English language version.
If we imagine the line as broken up into small lengths Δℓ, each length will look like one section of the L-C ladder with a series inductance ΔL and a shunt capacitance ΔC. We can then use our results for the ladder filter. If we take the limit as Δℓ goes to zero, we have a good description of the transmission line. Notice that as Δℓ is made smaller and smaller, both ΔL and ΔC decrease, but in the same proportion, so that the ratio ΔL/ΔC remains constant. So if we take the limit of Eq. (22.28) as ΔL and ΔC go to zero, we find that the characteristic impedance z0 is a pure resistance whose magnitude is √ΔL/ΔC. We can also write the ratio ΔL/ΔC as L0/C0, where L0 and C0 are the inductance and capacitance of a unit length of the line; then we have √L0/C0.
