Center-Fed Dipole : elements length for a Z=200 +/- 0j ohms

A chap asked online for dimensions of a 50MHz dipole with a feed point of 200+j0 to suit 50Ω feed line and a 1:4 coax half wave balun. The “+/- 0j” is hammy Sammy talk from an ‘Extra’.

This type of balun, properly implemented, is a good voltage balun, and it is quite suited to a highly symmetric antenna.

A good voltage balun will deliver approximately equal voltages (wrt the input ground) with approximately opposite phase, irrespective of the load impedance (including symmetry).

Where the load is symmetric, we can say a good voltage balun will deliver approximately equal currents with approximately opposite phase, irrespective of the load impedance.

It is an interesting application, and contrary to the initial responses on social media, there is a simple solution.

One solution

Let’s take a half wave dipole and lengthen it a little so the feed point admittance becomes 1/200-jB (or 200 || jX). We will build an NEC model of the thing in free space.

Above is a sweep of the dipole which is 3.14m long (we will talk about how we came to that length later), and the Smith chart prime centre is 200+j0… the target impedance.

Note here that at 45.4MHz, the feed point impedance is 72Ω.

Above, spinning up to 50.2MHz, feed point impedance expressed as a parallel equivalent is 201||j203. So, if we shunt the feed point with 203Ω of capacitive reactance (15.6pF) we have impedance close to 200+j0.

So, the length was adjusted so that Rp=200Ω with some Xp>0 at the desired frequency.

Now in case you think that Smith charts MUST have a prime centre of 50Ω…

… there is the solution wrt 50Ω.

Another solution

Now it is probably more convenient to make the dipole short and use a shunt inductive reactance… so let’s work that through.

This time on a 50Ω chart, the necessary shunt element is an inductive reactance of 119Ω which will yield a feed point impedance of about 200Ω. That could be provided by a small solenoid inductor, or a shorted transmission line stub (aka a hairpin or beta match).

Above is a Simsmith model based on the NEC model imported into element L, and a shunt inductance created by a hairpin of 3mm wire spaced 100mm (Zo=500Ω) and length 222mm.

Contrary to some expert opinions, there is a simple practical solution to the stated problem.

Setting it to work

There are many ways, but a simple one if you have an analyser that can be OSL calibrated, or a VNA (eg NanoVNA) is to calibrate it to measure the impedance or admittance at the dipole centre.

Now sweep the frequency range of interest, and adjust the dipole length until the conductance at the desired frequency is 1/200S (equivalent parallel resistance component is 200Ω). Then connect the shunt matching element and adjust it so that susceptance is zero, or the parallel reactance component of impedance is extremely high.

Connect the feed line up in the normal working configuration with the 1:4 coax half wave balun, and the impedance looking into the coax should now be close to 50+jΩ at the desired frequency.

This can provide a simple solution for a rotatable dipole with good match to 50Ω line.