# Yagi Antenna - Elements Length

I am currently modeling a yagi antenna using Matlab and after I optimized the antenna, it gave me a director length shorter than the exciter itself (even if the optimization gave me a good gain).

From what I have read and learned from textbooks, the directors of a yagi Antenna should always be shorter than the dipole in order to help direct the EM waves forward in a specific direction, and hence, increase the directivity.

In fact, when I even tried to reduce the length of the director to a dimension shorter than the dipole, it gave me a lower dBi (9.17dBi instead of 13dBi).

Why does DirectorLength > DipoleLength gives better gain (dBi)? Shouldn't it be the opposite instead?

Properties of the antenna simulated with Matlab:

• Howdy, welcome to ham.se! – Tyler Stone Sep 7 at 4:32
• Did you mean to write it gave you a director longer? – Phil Frost - W8II Sep 7 at 20:18

## 3 Answers

I suspect your results are an artifact of your optimization methodology.

I simulated the design described in the link with NEC2 using the EZNEC front-end. For reference, EZNEC calculates the gain as 13.03-dBi in free space with 2-mm diameter elements (the link doesn't specify element diameter). I believe this is close enough to your model's gain of 13.6-dBi for the purpose of answering your question.

EZNEC calculates the driving-point impedance of your model's driven element as 40-j99 $$\Omega$$, which is not a good match to the 50-$$\Omega$$ transmission lines in common use. Increasing the length of the driven element by about 14% - thus, making it longer than the directors - improves the match by changing the input impedance to 59+j6 $$\Omega$$ while maintaining the 13.03-dBi forward gain.

Interestingly, the driven element is now longer than the reflector, which is also not usual. The radiation pattern of your design show many side-lobes:

I suspect that "cleaning up" the pattern will result in a design with elements whose lengths obey the customary relationships seen in the hundreds of antennas described in the literature.

There are many properties of an antenna that could be optimized:

• Maximum gain
• Beam width
• Front-to-back ratio
• Feedpoint impedance
• SWR bandwidth
• Robustness to manufacturing variation

Typical designs aim for "pretty good" in all of these parameters. Optimizing for one parameter exclusively will typically come at the detriment of others, and result in unusual designs.

The driven element length is chosen to give the right impedance for your matching network. There's no rule about it being longer or shorter than anything.

The directors(s) are always shorter than the reflector(s) because their self impedance, combined with their spacing, is important in establishing the correct currents on each element.
(of course I mean simple thin free dipoles, if they're loaded or bent etc then their physical length doesn't reflect their electrical length any more)

The impedance of a resonant driven element is usually lower than 50 Ohms, so there are various tricks to match it. One of them would be a parallel capacitor, for that you would need to lengthen the driven element to make it inductive. Another would be a parallel inductor, though I've never seen this in practice, that would require a shorter driven element. But it is entirely your choice, depending on what impedance you want to see. Any length within reason is going to be ok.