Build a horn antenna for 10.525 GHz

I want to build a Horn antenna to increase directivity of HB100 sensor and I studied principles on an Antenna's book. I started from a void rectangular waveguide.

Since the frequency is 10.525 GHz, the greater side of the waveguide is

$$L = \frac{c}{f_{cutoff}\cdot2\cdot20\,\text{mm}} = 14.28\,\text{mm}\text.$$

It's a very small waveguide, so I ask it's possible to use a smaller cutoff frequency to make a greater waveguide? Dimensions must be about of HB100 board, 40 mm × 46.5 mm.

Second question, to match intrinsic waveguide's impedance with charateristic impedance of air is necessary to increase gradually the dimensions of the waveguide, making it like a pyramid. But, how can I determmine the minimum length that of the horn?

HB100 mechanical drawing:

Dimensions: 40 mm × 46.5 mm

Given the distribution of the antenna patches, the opening of the waveguide needs to be approximately the size of the HB100.

What do you think about a guide of 28mm x 10mm? Fundamental mode is at 5.35 GHz and first higher mode is at 10.7 GHz, that permit a singlemode propagation. The problem is to connect at HB100 a so small waveguide. I thought to connect the guide centered on the arrays, is a good solution? Distance between two elements of array is exact 28mm.

Like this:

• What documents have you found on the internet to help you? – Andy aka May 25 '18 at 18:12
• It might be easier and possibly higher gain to use a parabolic reflector with the HB100 at the focus. Google "parabolic antenna booster". The solid ones for drones should work and are cheap. – crj11 May 25 '18 at 18:14
• Horn antenna calculator – Andy aka May 25 '18 at 18:16
• I wonder if you might be able use the wave guide from a Universal LNB as used in Europe as a base. They operate down to 10.7GHz, so at least close to the frequency of your radar. You'd remove all of the electronics, and use just the waveguide and the housing. As a bonus, you can mount it on a satellite dish and get some gain. And, probably a visit from your local equivalent of the American FCC. :) – JRE May 25 '18 at 18:18
• I studied from "Antennas, typical applications" for the Horn antenna. About waveguides I used my notes of a electromagnetic fields course in my university, I study information engineering. This is part of a first level thesis, so I can't use a prebuild antenna, I have to build one from myself. I calculated the cutoff frequency from the formula that I posted at the initial post, this formula comes by the condition that propagation costant of e.m. wave must be real to have not attenuation of the wave. Sorry, but I'am new in electromagnetics and my knowledged comes only from this exam. – Fabio May 25 '18 at 18:49