About this tool
An antenna array consists of many identical elements whose signals add up or cancel depending on the direction. Its radiation pattern is the product of the element pattern and the array factor, which follows from layout, spacing, amplitudes and phases. Shifting the phase from element to element steers the main beam without any mechanics – the principle of the phased array.
The antenna array simulator calculates linear arrays and planar N×M arrays of isotropic radiators, half-wave dipoles, short dipoles, dipoles in front of a reflector or patch elements. It shows the pattern as polar and cartesian plots, for planar arrays also the second principal plane and a u–v map, and determines directivity (integrated over the full sphere), half-power beam width, first-null beam width, highest side lobe and front-to-back ratio.
Amplitude tapers such as cosine, Hann, Hamming, Taylor and Dolph-Chebyshev lower the side lobes at the cost of directivity and beam width. The advanced parameters simulate phase shifters with few bits, let you switch off single elements and take a frequency for physical spacing and delays. The excitation of every element is listed in a table. Use the gain in the Link Budget Calculator. Everything is calculated in your browser.
How it works
- Choose linear or planar, the number of elements, the spacing in wavelengths, the element and the amplitude taper.
- Steer the beam with the slider and watch pattern, directivity, beam width and side lobes.
- Switch off elements with a click if needed, turn on the advanced parameters for phase shifter bits and frequency, and read the phases per element from the table.
Frequently asked questions
Why is the element spacing usually λ/2?
If the spacing is too large, steering creates additional main beams of equal strength – grating lobes. They stay away as long as d/λ < 1 / (1 + |sin θ0|). At λ/2 the beam can be steered up to 90°, at 0.7 λ only to about 25°. Smaller spacings also avoid grating lobes but increase the number of elements and the coupling.
What does a Taylor or Chebyshev taper do?
With uniform weighting the first side lobe is only 13.3 dB below the main beam. Driving the edge elements more weakly lowers the side lobes – Dolph-Chebyshev produces equal side lobes exactly at the chosen level, Taylor produces decaying ones. The price is a wider main beam and slightly lower directivity, shown as taper efficiency.
How is the directivity calculated?
The simulator integrates the radiated power numerically over the full sphere and divides the power in the main direction by the average: D = 4π·Pmax / ∮P dΩ. For N isotropic elements at λ/2 this gives exactly N (8 elements = 9.03 dBi); a half-wave dipole has 2.15 dBi. Gain is directivity times efficiency; losses and coupling are not part of the ideal model.
What happens with phase shifters of few bits?
Digital phase shifters only set steps of 360°/2^n, i.e. 45° with 3 bits. The rounding errors repeat periodically across the array and create extra quantisation lobes and a slightly shifted beam direction. Choose the number of bits in the advanced parameters and see the effect in the pattern.
Why does the main beam get wider when steering?
Seen from the steering direction the array looks shorter; its effective aperture shrinks with cos θ0. The half-power beam width therefore grows roughly with 1 / cos θ0, doubling at 60°. Real elements also lose gain, because their own pattern falls off towards the side.