Main lobe forms at θ=0° (axial direction). Increasing N narrows the beam and raises gain. Element pattern × array factor = total pattern.
Theory & Key Formulas
Isotropic — uniform in all directions:
$$F(\theta) = 1$$
What is an Antenna Radiation Pattern?
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What exactly is a "radiation pattern"? Is it just a fancy polar plot?
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Basically, it's a 3D map showing how strongly an antenna transmits or receives signals in different directions. Think of it like a lighthouse beam—some directions are bright (strong signal), others are dark (weak). In this simulator, we flatten that 3D shape into a 2D polar plot for clarity. Try moving the "Number of elements" slider above from 1 to 4. See how the single bright spot becomes sharper?
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Wait, really? So adding more antenna elements changes the shape? What's that "Array Factor" in the formula box?
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Exactly! A single dipole has a broad, doughnut-shaped pattern. When you line up multiple elements, their signals interfere—constructively in some directions, destructively in others. The Array Factor mathematically describes this interference effect. For instance, with N=4 and d/λ=0.5, you get a much narrower main beam. The simulator multiplies this factor by a single element's pattern to get the final result.
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So the spacing slider (d/λ) must be crucial too. What happens if I set it too high?
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Great question! If elements are too close (d/λ very small), they couple strongly and efficiency drops. If too far apart (d/λ > 0.5), you get extra, unwanted peaks called "grating lobes"—like having multiple main beams pointing in weird directions. Try sliding d/λ to 1.0 and watch those side lobes grow. In practice, designers tune this to maximize gain without creating these ambiguous beams.
Physical Model & Key Equations
The total radiation pattern of a uniform linear array is the product of the pattern of a single element and the array factor, which models the interference from multiple identical elements.
Where:
• $F_{\text{total}}(\theta)$: Normalized total field pattern.
• $F_{\text{element}}(\theta)$: Pattern of a single antenna (e.g., a dipole).
• $AF(\theta)$: Array Factor, governing the interference pattern.
For a linear array of N identical elements with uniform spacing d and phase, the Array Factor is given by:
Where:
• $N$: Number of elements (simulator slider).
• $d/\lambda$: Element spacing in wavelengths (simulator slider).
• $\theta$: Angle from the array axis (0° is end-fire, 90° is broadside).
• $\psi$: The phase difference between adjacent elements. The peaks occur where $\psi = 0, 2\pi, ...$.
Frequently Asked Questions
Increasing the number of elements N sharpens the main lobe and improves gain, but also increases side lobes. Increasing the spacing d narrows the beam width, but if d exceeds the wavelength λ, grating lobes (unwanted strong lobes) occur, so d ≤ λ/2 is generally recommended.
An array antenna arranges identical elements at equal intervals and controls the beam through phase differences, whereas a Yagi antenna concentrates gain in one direction by adjusting the lengths and spacings of directors and reflectors. This tool allows you to change the number of elements and dimensions of a Yagi antenna to observe changes in directivity.
This tool is based on an ideal free-space model, so it does not account for ground reflection, surrounding obstacles, or feed circuit losses. Therefore, while it is effective for relative pattern comparison and initial design considerations, adjustments through measurement are necessary in actual installation environments.
First, increase the number of elements N to sharpen the main lobe, then fine-tune the element spacing d around λ/2. If using a Yagi antenna, optimize the length and spacing of the directors. If side lobes are a problem, it is also worth trying the function (available in some modes) to taper the amplitude distribution instead of keeping it uniform.
Real-World Applications
5G Massive MIMO Base Stations: These use arrays with dozens or hundreds of elements (large N) for beamforming. By electronically steering the narrow beam (which you can simulate by changing phase), they can track individual users, drastically increasing network capacity and reducing interference for others on the same frequency.
Phased Array Radar: Military and weather radars use end-fire arrays (beam along the axis) to track fast-moving targets. The key advantage is electronic steering—the beam can be redirected in microseconds without any mechanical movement, allowing it to monitor multiple targets almost simultaneously.
Satellite Communications: Dish antennas on satellites need extremely high directivity (very narrow HPBW) to focus energy into a small "footprint" on Earth. This is achieved using large parabolic reflectors fed by array feeds, where the principles of array gain and side lobe suppression are critical to avoid interfering with adjacent satellites.
Wi-Fi Routers & IoT Gateways: Modern routers often use 2x2 or 4x4 MIMO arrays. The patterns are designed to provide wide coverage (broader HPBW) within a home while placing nulls in directions of potential interference from neighbors, optimizing both signal strength and network reliability.
Common Misconceptions and Points to Note
When you start using this simulator, there are a few common pitfalls to watch out for. First, remember that higher gain does not always mean better communication performance. While a sharper main lobe (smaller HPBW) makes it easier for radio waves to reach farther distances, it also means communication fails unless the antenna is pointed precisely. For example, this is essential for satellite communication, but in urban mobile communication, users move around, making it difficult for the beam to track them, which can actually be a disadvantage. It's important to consider the trade-offs for your specific application.
Next, a pitfall in parameter settings. Setting the element spacing "d/λ" to 1.0 or greater will always cause grating lobes (spatial aliasing). This is not a "calculation error" but a real physical phenomenon. For instance, designing with d/λ=1.5 creates beams of equal strength in directions other than the main lobe, potentially causing communication in completely unintended directions. In practice, d/λ is typically set around 0.5 to avoid this issue.
Finally, don't forget the simulator calculates an "ideal environment". The beautiful pattern displayed does not account for any influence from the ground or surrounding structures. In a real installation, pattern distortion from reflections off metal supports or nearby structures is normal. Don't be satisfied with just theoretical calculations; always get into the habit of comparing them with actual measurements from field tests.
Set element count (nVal) between 2 and 8 elements for linear or planar array configurations
Adjust spacing (dSlider) in wavelengths (0.25λ to 1.5λ) to control main lobe sharpness and grating lobe emergence
Select antenna type (dipole, Yagi, or phased array) and observe real-time polar plot updates showing gain distribution, then record directivity in dBi, HPBW in degrees, and side lobe level in dB
Worked Example
4-element linear array at 2.4 GHz (λ=125 mm) with 0.5λ spacing (62.5 mm element separation): directivity increases from 6.0 dBi (single dipole) to 12.1 dBi. HPBW narrows from 78° to 42°. Side lobe level remains at −13 dB with uniform amplitude weighting. Increasing spacing to 0.9λ raises directivity to 12.8 dBi but introduces grating lobes at ±38° requiring tapering or element count reduction for 5G base station compliance.