A horn antenna is composed of a coaxial / waveguide transition which respects the WR standards of a horn, making it possible to define the gain as well as the -3 dB opening of the antenna.
There are no equations making it possible to perfectly conceive the sizing of the horn antenna (in particular for the horn part). However, the coaxial / waveguide transition part can be sizing from the following equations.
Equation (1):Cutoff frequency for the TE10 fundamental mode in a waveguide (a*b*l)
From this equation, we can determine the width a of our waveguide for the transition part. The height b being equal to a / 2.
Equation (2): Calculation of the guided wavelength
Equation (3): Calculation of the gain
Equation (4): Opening at -3 dB vertical
Equation (5): Opening at -3 dB horizontal
Equation (6): Gain as a function of efficiency and Directivity G=ηD
With η the efficiency and D the directivity
The dimensions used to produce a range of horn antenna are standardized. for example, we want to size a horn antenna operating in the Ku band.
We therefore have for the horn antenna a WR-62 waveguide (a = 15.799 mm; b = 7.899 mm) at the level of the coaxial / waveguide transition. Then, the horn has for dimensions (H = 50mm E = 40 mm). For a total antenna length of 80 mm. (Fig. 1.)
figure n ° 1: Dimensions of the horn antenna
The horn antenna access connector must be placed at a distance approximately equal to λg / 4 (here 6.3 mm taking f0 = 15.2 GHz) from the short circuit of the transition to correctly propagate the electromagnetic wave .
The length of the connector in the transition must be around b / 2 and the length of the transition must be greater than λ / 2 (for the lowest frequency, i.e. 12.4 GHz, the length must therefore be greater than 12 mm) to allow the mode to settle in the waveguide. Then, the length of the transition (22 mm) is greater than λ / 2. The design of this horn antenna sizing is shown in Fig. 2 (a).
figure n ° 2: Ku band horn antenna with a gain of 15 dB under ANSYS HFSS (a) Simulation of the reflection coefficient S11 of the Ku-band horn antenna (b)
The reflection coefficient S11 makes it possible to check whether the antenna is suitable, at least 10 dB of adaptation is required for an antenna and thus allow the maximum power to be transmitted. In this case, Fig. 2. (b), the antenna has an adaptation of at least 15 dB over the entire operating band of the antenna (12.4-18 GHz).
The simulation of the horn antenna gives the following results in terms of gain and radiation pattern in both planes at the center frequency of 15.2 GHz.
Here are all of our horn antenna solutions
Figure n ° 3: Simulation of the gain of the horn antenna in Ku band (a) and the radiation pattern of the Ku-band horn antenna in the two planes (b)