Schematic used

Something about the derivation of Telegrapher's equation is really bugging me. When deriving the Telgrapher's equations for a transmission line using a model as shown above, why do we only use a capacitor in parallel, and not a series capacitor? Same goes to the inductor in series: why not an inductor in parallel?

  • \$\begingroup\$ sure, can you please transfer it to there? \$\endgroup\$ Commented Oct 27, 2013 at 17:11

2 Answers 2


If you mean by "series capacitor" one that is in series with the inductor on your picture then remember that the usual telegrapher equation is trying to model a transmission line of two wires that passes dc; same answer for a shunt inductor. Now if you want to model a line that has high-pass characteristics then you get what is called TE (H) and TM (E) modes, and those do have caps in series with the inductor (TM), and shunt inductors parallel with the caps (TE); these are the higher order waveguide modes. TE, TM stand for transversal electric or magnetic, resp. (Old books call them H or E modes because the whole propagating field can be derived from the longitudinal H or E component.) These also exist in a standard transmission line of two wires but can also propagate in an empty guide, where it is obvious that dc cannot "propagate" and whatever does it must have high-pass character, after all you can see through a tube.

  • \$\begingroup\$ but [wikipedia] (en.wikipedia.org/wiki/Telegrapher%27s_equations) says " The theory applies to transmission lines of all frequencies including high-frequency transmission lines (such as telegraph wires and radio frequency conductors), audio frequency (such as telephone lines), low frequency (such as power lines) and direct current. " \$\endgroup\$ Commented Oct 27, 2013 at 3:29
  • \$\begingroup\$ The wikipedia article only talks about the simplest so-called TEM mode that has no cut-off, and it can propagate down to dc. There are other modes, in fact an infinity of them and those do have the series cap and shunt inductors in their model. Check out any book on EM waveguides on higher order modes. \$\endgroup\$
    – user31748
    Commented Oct 27, 2013 at 14:57

There can't be a capacitor in series since, if there were, a resistively terminated TL would appear as an open circuit to a DC voltage source.

There can't be an inductor in parallel since, if there were, a non-terminated TL would appear as a short-circuit to a DC voltage source.


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