Antenna Array Response & Beamforming
Educational tool for 5G Wireless Communication concepts
1. Array Geometry
End-fire (0°)
Broadside (90°)
End-fire (180°)
Theoretical Concept
As per Figure 2, the extra path distance to reach the next element is \(d \cos\theta\). For \(d = \lambda/2\), the phase shift \(\psi\) between elements is:
\[ \psi = \pi \cos(\theta) \]
The array response vector \(a(\theta)\) becomes:
[1, e^{j\psi}, e^{j2\psi}, ...]
2. Phase Vector Visualization
Live Matrix Calculation
Updating calculations...
3. Resulting Beam Pattern
The main lobe "points" to \(\theta\) by constructive interference.
How Antenna Array Response and Beamforming Work
The illustration shows incoming waves, but the same principles apply analogously to transmitted waves or signals due to the principle of reciprocity.
If d = λ/2, the phase difference between consecutive antenna elements is πcosθ, which always lies within the range -π to π. This prevents the formation of grating lobes (ghost beams).