Calculating and displaying the far-field radiation pattern of a parabolic antenna using Julia. The case of why Julia must be a part of the engineering syllabus...

To calculate the far-field radiation pattern of a parabolic antenna, we model the aperture as a circular disk. In the far-field (Fraunhofer region), the radiation pattern is essentially the Fourier Transform of the aperture's field distribution. For a uniform circular aperture, this results in the Airy Pattern.

Parabolic Antenna Pattern in Julia

This implementation uses SpecialFunctions.jl for the Bessel function calculations and Plots.jl for visualization.

The Physics

The normalized electric field pattern $E(\theta)$ for a circular aperture of diameter $D$ is:

$$E(\theta) = \left| \frac{2 J_1(k a \sin \theta)}{k a \sin \theta} \right|$$

Where:

• $a = D/2$ (Aperture radius)

• $k = 2\pi / \lambda$ (Wavenumber)

• $J_1$ is the first-order Bessel function of the first kind.

The Julia code...

using SpecialFunctions

using Plots

# --- Parameters ---

f = 10e9 # Frequency (10 GHz)

c = 3e8 # Speed of light (m/s)

D = 1.0 # Diameter of the dish (m)

λ = c / f # Wavelength

k = 2π / λ # Wavenumber

a = D / 2 # Radius

# --- Pattern Calculation ---

# We calculate θ from -10 to 10 degrees to see the main lobe and side lobes

theta_deg = range(-10, 10, length=1000)

theta_rad = deg2rad.(theta_deg)

function calculate_pattern(θ)

if θ == 0

return 1.0 # Limit of 2*J1(x)/x as x -> 0 is 1

end

u = k * a * sin(θ)

return abs(2 * besselj1(u) / u)

end

# Calculate field and convert to Power in Decibels (dB)

E_field = [calculate_pattern(t) for t in theta_rad]

Power_dB = 20 .* log10.(E_field)

# Ensure we don't plot -Infinity for zeros

Power_dB = clamp.(Power_dB, -60, 0)

# --- Plotting ---

p = plot(theta_deg, Power_dB,

title="Far-Field Radiation Pattern (Parabolic Antenna)",

xlabel="Angle θ (degrees)",

ylabel="Relative Power (dB)",

label="Uniform Circular Aperture",

lw=2,

grid=true,

ylim=(-60, 5))

display(p)

wait()

And the output looks like the following...

The Case for Julia in the Engineering Syllabus

Julia isn't just "another language"; it is a paradigm shift specifically optimized for the technical mind. Here is why it belongs in the modern engineering curriculum:

I. Solving the "Two-Language Problem"

Traditionally, engineers are forced to learn two worlds:

1. Python/MATLAB for rapid prototyping and intuition.

2. C++/Fortran for the heavy-duty performance required in CFD, structural analysis, or real-time control systems.

Julia bridges this gap. It provides the high-level syntax of Python with the execution speed of C. Teaching Julia allows students to spend more time on engineering logic and less time on memory management or rewriting code for production.

II. Mathematical Syntax as a First-Class Citizen

In Julia, the code looks like the textbook. You can use Unicode characters ($\pi$, $\lambda$, $\theta$) directly. For a student, the cognitive load of translating a formula from a paper to a script is significantly reduced.

Example: In Python, you write math.sqrt(math.pi). In Julia, you can literally write √π.

III. Multiple Dispatch: The Engineer's OOP

Standard Object-Oriented Programming (OOP) is often a poor fit for mathematics. Math is naturally polymorphic—the way you multiply a scalar by a vector is different from a matrix by a vector, yet the operation "multiply" is conceptually the same.

Julia's Multiple Dispatch handles this naturally. It allows engineers to write generic code that works across different data types (complex numbers, dual numbers for automatic differentiation, etc.) without the architectural "boilerplate" of classic Java or C++.

IV. The SciML Ecosystem

The future of engineering is Scientific Machine Learning. Tools like DifferentialEquations.jl and ModelingToolkit.jl allow students to perform acausal modeling—defining the physics (ODEs/PDEs) and letting the compiler handle the optimization and solving. This moves the syllabus focus from "how to write an Euler solver" to "how to model a complex physical system."

Conclusion

Every engineering graduate should leave university fluent in a language that lets them think in math and run at machine speed. Julia is that language. It is not “just another tool” — it is the future of technical computing, and the sooner it enters the core syllabus (alongside Python/Matlab), the more competitive our engineers will be.