Do reflector and director widths (wire size) affect Quagi bandwidth?

A 2m Quad antenna made from 1/2" tubing will have a larger bandwidth than the same Quad built with 14 AWG wire.
Would the respective bandwidths be maintained if both Quad loops were made into Quagis by adding, say, a reflector and five directors (on a boom) that were all 14 AWG wire. Or, would the 1/2" tubing Quagi need 1/2 tube elements, or even just the reflector, to keep its larger bandwidth?

So, yes, the Yagi-Uda part of a Quagi has a limited bandwidth, too.

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Let's assume the reflector has exactly length $\frac12 \lambda$.

The idea of the reflector (labeled $R$ above) in the Yagi-Uda design is that it gets excited by the actual driven element (labeled $A$). Due to the half-period delay in emission of the energy stored that way, plus the $2\cdot \frac14\lambda$ distance, the wave hits $A$ with a total delay of one full period – that way, they interfere constructively at $A$.

So from this, you can already see that spacing between the driven element $A$ and the reflector $R$ is critical to operation. Things get a little more complicated, though:

Now, that's nice and all, and it already gives us some directional gain, because left of $R$, $A$'s emissions and $R$'s emissions are $\frac34\lambda$ "out of phase", whereas at $A$, they're in-phase.

However, making $R$ exactly half a wavelength long isn't commonly done for various reasons (you can build a good Yagi-Uda with that, but you need to be very careful in alignment and stuff, and your driven element's efficiency will be sub-optimal), especially when considering that we commonly see Yagi antennas where $R$ is a bit longer than $A$.

Essentially, what you'd do is make the driven element a half-wavelength dipole, and make the reflector a bit longer. Thus, the reflector becomes an element that is essentially a inductive parasitic to the driven elements – and inductive reactance means that the current in the reflector lags behind the voltage the field from the driven element causes, leading to additional delay in the emitted field. Thus, you can arrange the distances and element sizings in a way so that there's constructive interference in the far field in front of the antenna, and basically destructive interference behind. The sizing of directors give you enough design freedom to theoretically repeat that as often as you like to increase your gain – for a single wavelength.

Now, the more broadband your antenna needs to be, the less exact the Yagi-Uda calculations for the nominal wavelength apply. Thus, the more you move away from your nominal frequency, the less gain your antenna has; you'll also notice that the mismatch increases.

Now, I'm not experienced with Quagis at all. But to me, the whole point of using a frame=loop=quad antenna in place of the driven dipole and the shorted reflector dipole is exactly that: to increase antenna selectivity and thus, gain, in exchange for reducing bandwidth.

So I'm relatively certain that the idea of increasing a Yagi-Uda design's bandwidth and using a quad in place of driven element and a rectangle/ring in place of a reflector don't work well together.

All in all, the Quagi, to me, looks a bit like a Frankentenna. It probably works pretty well for a single use case, but isn't quite as versatile as a simple Yagi. The design history indicates it was more found by accident then by analysis or simulation – which is fine, many antenna designs are happy accidents – for a very specific frequency and purpose and thus, I'd say:

In the year 2016, unless someone comes up with a well-done model and simulation of the Quagi, I'd say you can probably find easier ways to build a broadband directional antenna for the same frequency range then improving the bandwidth of the driven element, then the reflector, then the directors, then the spacing of the directors, then reiterate, and match the antenna impedance, ... of a Quagi. In other words, the moment your Quagi has the same bandwidth as that of a simple Yagi with the same directors, it also has lost its advantages over that Yagi – you could have built a classical Yagi-Uda design straight away.

If you're after bandwidth while maintaining more than 10dBi of gain: Look at the well-known and -understood logarithmic-periodic ("logper") antenna type. Instead of driving one dipole, you drive a set of dipoles, each "optimal" for a different frequency¹. That means that unlike the Yagi, every element in a Logper antenna is driven. However, you of course arrange the elements such that you get the same directivity effects as in the Yagi.

I'd really love to see something like a Quagi (or any other combination of well-known, proven-to-work-well-for-their-purpose antenna types) as some antenna model that I could e.g. use in OpenEMS or another electromagnetic simulation tool –

¹ It actually gets a little more complicated than that – you can't just go and parallely drive a set of dipoles and hope for great bandwidth. The logper is actually more of a design derived from antennas that have the property of self-complementarity, which is the reason for it being broadband. (self-complementary means that if you draw the antenna, then take the negative, then rotate/shift it, and overlay the original and the negative, you get the whole plane without overlap or "holes")

However, if you look at those, they typically can't have incredible one-sided gain – so someone took a square pattern and "flattened" it to achieve Yagi-style directivity. If you want to get the rough idea, have a look at the wikipedia article.

• Thanks for the ideas. Let's say a Yagi is the end goal. One built with a DE of 1/2" tubing will have more bandwidth than one with a DE using 14AWG wire (I've heard). Does the one with 1/2" tubing DE need to also have a 1/2" tubing reflector and/or 1/2" tubing directors to maintain its wider bandwidth? Would a 1/2" DE lose its advantage if 14AWG wire was used for REF and directors? – Mein Tenah Nov 24 '16 at 23:06
• It won't matter. The rest of your antenna isn't getting broader, so making a broader driven element is in vain. – Marcus Müller Nov 24 '16 at 23:07
• Is 'getting broader' the same as increasing conductor diameter? I thought that, generally, increasing DE conductor diameter increased bandwidth. I have found a few references to increasing the diameter of the elements (plural) so I'll go with that. I have a little 4/0, 0, and 4 AWG and a lot of 12 and 14 AWG (just wired my house) and I'd like to use it efficiently while experimenting with a couple antenna types for home and travel. Overall design is the big deal but the little things add up...so I'm learning.Thanks. – Mein Tenah Nov 25 '16 at 0:13
• "getting broader" was meant to say "getting able to cover a broader amount ouf spectrum" – Marcus Müller Nov 25 '16 at 9:19
• I'd really try to simulate your antenna! OpenEMS is getting very mature; the only thing it lacks is a proper 3D modeler. You have to "handcode" the locations of your copper cylinders yourself etc. But that's actually cool here, because it allows you to use the diameter as something you can parameterize! – Marcus Müller Nov 25 '16 at 9:25