Horn antenna

This post describes a methodology for the design of a pyramidal horn antenna. Following posts build on it and provide more details. A pyramidal horn is a popular antenna that has very little loss and is used commonly in antenna systems.  The structure of the pyramidal horn is shown in FIGURE 1.0 below.

Pyramidal horn structure

The design of a horn like this begins with a specification. Usually the following parameters are given:

Gain (in dBi)

a (inches or cm) (usually the horn is fed from a waveguide)

b (inches or cm) (usually the horn is fed from a waveguide)

frequency (Hz)

The problem is to find A and B, and other dimensions shown below. Once we have these dimensions, we can find other parameters of the antenna.

The usual procedure is to solve an equation to get a key parameter using the given specifications. This methodology will be outlined in this post and access to the equation solver will be provided. Subsequent posts will add more detail so that an engineer will be able to get a first cut design of the horn and fabricate it.

After the required key value is obtained through solving the equation the following steps are used to find the Horn parameters.


λ is the wavelength of the signal in cm. le is found from the solution of the equation.

Calculate B from this equation.

From B, λ, le and G calculate A. The equation to be used is:

G = (½)(4π/λ2)(AB)

Now we have A and B.

lh is found from the following equation:

A = sqrt(3λlh)

Calculate RH and RE from the following equation:

RE = (B -b)(sqrt[(le/B)2 – ¼)])

Since we are dealing with a pyramidal horn RE =RH

Use the following equation for R1:

lh2 = R12 + (A/2)2

Use the following equation to calculate R2:

le2 = R22 + (B/2)2

The equation to be solved is:
The quantity σ has to be solved for.
σ =le/λ . This equation is best solved numerically with a starting value of σ = G/2π√6. The Python program that was written to do this is available on request at spg@signalpro.biz or spg327@gmail.com

Ref: This blog is partially based on “Antenna Theory and Design, by Warren L. Stutzman and Gary A. Thiele. The book was published by John Wiley and Sons, 1981.
Ref: The Python program was written by Anuj Tripathi, University of Arizona, Tucson, Arizona.