Free Phased Array Beam Steering Calculator
Calculate progressive phase shift ($\Delta \phi = -\frac{2\pi d}{\lambda} \sin\theta_0$), 3dB beamwidth, grating lobe avoidance, and array factor for radar and 5G beamforming.
📡 Array Geometry & Steering Angle
📊 Progressive Phase Shift & Beam Metrics
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Phased Array Beamforming & Progressive Phase Shift Physics
A phased array steers its main radiation beam electronically without mechanical rotation by imposing a linear phase ramp across an array of individual radiating antennas. Because electromagnetic waves travel at light speed $c$, adjusting the phase delay between adjacent elements causes wavefronts to interfere constructively in the desired direction $\theta_0$: $$\Delta \phi = -k \cdot d \cdot \sin(\theta_0) = -\frac{2\pi d}{\lambda} \sin(\theta_0)$$ Where $\theta_0$ is measured relative to broadside ($0^\circ$).
Grating Lobes & The Half-Wave ($d \le \lambda/2$) Rule
Just like spatial aliasing in Nyquist sampling, if antenna element spacing $d$ is too large, secondary constructive interference peaks called grating lobes emerge in the visible hemisphere, wasting transmitter power and creating severe false target radar ghosting.
To steer across scan angles up to $\theta_{max}$ without grating lobes entering visible space: $$\frac{d}{\lambda} < \frac{1}{1 + |\sin(\theta_{max})|}$$ Setting $d = 0.5\lambda$ guarantees grating-lobe-free steering across all practical angles up to $\pm 90^\circ$.
Frequently Asked Questions
Why does the beam broaden (HPBW increase) as it steers away from broadside?
Because the projected effective aperture of the array shrinks geometrically by the factor cos(theta_0). At a 60-degree scan angle, cos(60) = 0.5, cutting the effective aperture in half and doubling the beamwidth.
What is phase quantization lobe error in digital phase shifters?
Digital phase shifters use discrete binary steps (e.g. 6-bit gives 5.625° increments). The rounding error between the ideal mathematical phase and the actual quantized bit setting introduces small periodic phase ripples across the aperture, raising the antenna side lobe level (SLL).
What is the difference between active (AESA) and passive (PESA) phased arrays?
PESA uses a single high-power central transmitter tube feeding phase shifters at each element. AESA (Active Electronically Scanned Array) equips every individual element with its own miniature solid-state Gallium Nitride (GaN) transmit/receive (T/R) module, providing superior reliability, efficiency, and multi-beam agility.