Array Factor
Understanding the Array Factor
The array factor separates the array design problem into two independent parts: the element design (each individual antenna) and the array design (how the elements are arranged and excited). This simplification is enormously powerful for array synthesis.
Array Factor for Linear Array
AF(theta) = sum[n=0 to N-1] of a_n x exp(j n (kd sin(theta) + delta)), where a_n = element amplitude, d = element spacing, delta = progressive phase shift, k = 2pi/lambda.
Array Factor Properties
- Beam direction: Controlled by progressive phase delta. Beam at theta_s where kd sin(theta_s) + delta = 0.
- Beamwidth: Decreases as N increases. Approximately 0.886 lambda / (Nd) radians.
- Sidelobe level: Uniform excitation gives -13.2 dB SLL. Amplitude taper reduces sidelobes.
- Grating lobes: Appear when d > lambda / (1 + sin(theta_max)).
Frequently Asked Questions
What is the array factor?
The array factor is the radiation pattern produced by an array's geometry and excitation, independent of the individual element pattern. The total pattern = element pattern x array factor. It determines beam direction, width, sidelobes, and grating lobes.
What is pattern multiplication?
Pattern multiplication states that the total array radiation pattern equals the product of the individual element pattern and the array factor. This allows designing the element and array independently, then multiplying the results.
How do you control sidelobe levels?
Sidelobe level is controlled by the element amplitude distribution (taper). Uniform excitation gives -13.2 dB sidelobes. Cosine taper gives -23 dB. Taylor distribution gives configurable near-in sidelobes. Lower sidelobes require wider mainlobe (gain trade-off).