F6DRO waveguide propagation modes

Guided propagation and parasitic modes by Dom F6DRO
Manufacturer characteristics of a rectangular waveguide (example WR28):
What do these characteristics mean?

26.5 GHz, it is the low cut-off frequency of the guide for the propagation mode 
which gives us which is TE10 (Transverse Electric) mode.
 
In this mode, the distribution of the electric field between the 2 short sides b 
of the guide is the next:
 
 

The propagation in the guide along the axis is carried out by reflection
between these two small sides (in green):

To keep it simple, there is a condition on the angle θ so that propagation can take place (if
theta = 0, there is no more possible propagation, extreme condition). This condition defines the
cutoff wavelength of the so-called λC waveguide in this mode TE10.
For the type of propagation TE10 that we use, after calculation:
λC = 2a (with a = long side of the guide).
For the WR28 in our example:
λC = 2x7,112 = 14.224mm or 21.077 GHz for the corresponding frequency. This corresponds
although at 21.077 GHz announced by the manufacturer.

Let's take a closer look by simulating the WR28 guide in its range
recommended frequencies.

We see in Figure 1 that the guide actually behaves like a high-pass filter with a
very abrupt cutoff frequency at the calculated cutoff frequency.

Figure 2, here is a closer look at what is happening near the cutoff frequency. We see that the
minimum frequency recommended by the manufacturer, which is 26.5 GHz is that from
which the latter considers that the attenuation s21 is sufficiently low. For us amateurs, especially
for short guide lengths, the WR28 guide can be used at 24 GHz. For the
manufacturer the rule is 1.25Fc.
We therefore justified the two data: 21.77 GHz and 26.5 GHz.
What about 40 GHz data?
If we examine the s21 of a WR28 guide section up to 50 GHz (or higher), we see nothing
abnormal appear. See figure 3

So why does the manufacturer limit the frequency to 40 GHz?
To understand this, we must return to the basics of guided propagation:
It turns out that if the dimensions of the guide allow it, there may be other modes of
propagation in this guide; for example :

Above a TE2 mode. This propagation mode has its own cut-off wavelength.
After calculation it corresponds to the frequency of 42.154 GHz.
This means that any frequency present at the entrance to the guide> at 42.154 GHz is likely to
propagate in TE1 mode but also in TE2 mode and, in this case, the phenomena in the guide
are no longer the same.
Let us be clear, for TE2 to spread, it must be created; so in principle the WR28 is
usable at 47 GHz but beware, any obstacle in the guide can create TE2 mode and bring
panic in the system.
As proof: Figure 4 shows the transmission of a 47 GHz signal in a WR28 guide.

We see that the distribution of the fields is as expected (maximum of the electric field in
the axis every λg / 2 and that the losses are minimal).
But we also see that if we create it, TE2 mode can propagate.

What happens in the guide becomes complex to understand and our classic transition in
end of guide, supposed to recover from TE1 is in difficulty. See figure 5.
To sum up: the guide will be able to transport 47 GHz (in the case of the WR28) and in most
cases will be fine. However, beware if you place discontinuities in the guide.
A practical case:
Recently a friend asked me to calculate an adapter block for an Eutelsat cone
(see Hyper n 238) in order to use it at 32 GHz by connecting it to the WR28. The exit guide
of the horn is a circular guide with a diameter of 11.9 mm.
Confident in the possibilities, I embarked on a series of simulations and calculations.
And there, surprise, it did not go as planned!

The S11 (see figure 6) shows completely abnormal mood swings and any attempt
optimization is doomed to fail.
If we examine the distribution of field E in the circular guide we see that there is a problem.
See figure 7.

The E field bellies are not regularly spaced and we are facing a
parasitic mode problem. The relationships in the circular guides are different but the
fashion phenomena are the same.
The 11.4 mm guide allows the propagation of a parasitic mode and the wedge, which is an obstacle, the
sets off.
If the diameter of the guide is reduced to 10 mm, the multi-moding disappears.

 

Figure 8 shows that s21 returns to normal; the same is true for the distribution of
fields. See figure 9.

To conclude, we can say that the guides can possibly be used above the
recommended frequency range but be careful.
 

References
https://melusine.eu.org/syracuse/immae/mp/physique-chimie/electromagnetisme/19.pdf
https://www.microwave-link.com/microwave/wr28/