Good Morning all,

I want to calculate the mutual impedance of two parallel dipole.

The first hypothesis is to assume that the dipole 2 is in open circuit, nothing difficult here I knew how to do it enter image description here

Hypothesis 2 is to assume that dipole 2 is short circuited or loaded with some impedance

Are there equations for hypothesis 2, or is there a parameter to add or modify on Baker's equations?

thank you

  • 1
    $\begingroup$ Welcome! and keep asking good questions. $\endgroup$
    – tomnexus
    Sep 10, 2020 at 17:47
  • $\begingroup$ Please, tell us where you found the graph that appears in your question. $\endgroup$
    – Brian K1LI
    Sep 10, 2020 at 23:07
  • 1
    $\begingroup$ @BrianK1LI It's in Balanis, Antenna Theory, Analysis and Design, 2nd ed, p419. Apart from using NEC, there are closed-form solutions for trivial cases (parallel and collinear), for feedpoints at the current maxima, for half-wave dipoles with sinusoidal current. The equations are large, I could re-type them if you really can't find them. $\endgroup$
    – tomnexus
    Sep 11, 2020 at 4:58
  • 2
    $\begingroup$ @BrianK1LI : I got the graph by integrating baker's equations : Digital computation of the mutual impedance between thin dipoles ( ieeexplore.ieee.org/document/1137835), and there are multiple configurations $\endgroup$
    – Tarik L
    Sep 11, 2020 at 8:24

1 Answer 1


I think if you're worried about the load on the other dipole, you need to go back and look at how Z parameters work.

$Z_{21}$ doesn't assume anything about the impedance on the two dipoles. It's just one of the impedance parameter term - $Z_{21}$ is the voltage developed on dipole 2 due to a current in dipole 1. It's not the final voltage or current present on dipole 2, for that you need to know other things.
I can't find the equations online, they're in any good electromagnetics book, I can't find mine either.

To calculate the input impedance on port 1, you need to consider the impedance on port 2, whether that's a short or an open.

So if you know $Z_{11}$ (self-impedance of the dipole alone), $Z_{21}$ (mutual impedance from the equation, same as $Z_{12}$ in a passive system), and $Z_{22}$ (self-impedance of dipole 2) and choose $Z_L$, then

Zin equation from wikipedia

This is how you can calculate the currents on a yagi antenna, for example, without resorting to numerical methods. Wikipedia Yagi Antenna actually has a nice section about this, now that I scratch a bit.

  • $\begingroup$ thanks a lot @tomnexus, that helped me alot $\endgroup$
    – Tarik L
    Sep 11, 2020 at 7:55

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