Phased Array Antenna Steering Angle Calculator & Formula

This online Phased Array Antenna Steering Angle Calculator allows you to compute the steering angle of phased array antennas based on essential parameters such as element spacing and signal wavelength. Simply input the required values, and the calculator will provide you with the steering angle at which the antenna array can effectively direct its beam.

Phased Array Antenna Calculator

Example Calculation:

Scenario : We have a linear array radar operating in the S-Band at 3 GHz. The antenna elements are spaced at the standard “half wavelength” distance (d =lambda/2) to avoid grating lobes. We want to steer the main beam 30 degrees to the right.

INPUTS:

• Frequency (f) = 3 GHz
• Target Steering Angle (θ) = 30 degrees

Constant:

• Speed of Light (c) = 3 x 10^8 meters/second

OUTPUT:

• Wavelength (λ) = 0.1 meters
• Element Spacing (d) = 0.05 meters
• Steering Phase Shift (in radian) = 1.57 radians
• Steering Phase Shift (in degrees) = 90 degrees

Phased Array Steering Angle Formula

Following formula can be used to calculate the steering angle of phased array antennas:

Where:

• Δφ = Phase Shift required between adjacent elements (Degrees)
• θ = Desired Beam Steering Angle (measured from broadside) (Degrees)
• d = Physical spacing between antenna elements (meters)
• λ = Wavelength of the signal (meters)

Results: To steer the beam 30 degrees off-center, the phase shifter for each successive element must add a 90 degree phase shift relative to the previous element. In 4 element array, this results in a total phase shift of 270 degrees from the first to the last element. (Element 1 : 0 degrees, Element 2 : 90 degrees, Element 3 : 180 degrees, Element 4 : 270 degrees)

References

1. “Phased Array Antenna Handbook” by Robert J. Mailloux, 2nd Edition, Artech House, 2005.
2. “Antenna Theory: Analysis and Design” by Constantine A. Balanis, 4th Edition, Wiley, 2016.
3. Skolnik, Merrill I. Introduction to Radar Systems. 3rd Edition. McGraw-Hill, 2001.