# Mutual impedance of two parallel dipole

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

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

• Welcome! and keep asking good questions. – tomnexus Sep 10 at 17:47
• Please, tell us where you found the graph that appears in your question. – Brian K1LI Sep 10 at 23:07
• @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. – tomnexus Sep 11 at 4:58
• @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 – Tarik L Sep 11 at 8:24

## 1 Answer

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

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.

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