Array Factor Equation

The above equation can be factor simply as The quantity AF is the Array Factor. The Array Factor is a function of the positions of the antennas in the array and the weights used. By tayloring these parameters the antenna array's performance may be optimized to achieve desirable properties.

Radiation pattern of array antenna is called an Array Factor AF. Array factor can be expressed using this formula 2 sin 2 sin92 92 N N AF Where N Total Element k 2 is the polar angle is the difference of phase between any two successive elements forming the array.

Note that because of reciprocity, the array works similarly in transmit mode except the direction of the phase gradient is reversed to produce a plane wave leaving the array in the direction shown. 2 Plotting the Array Factor It is not obvious what the radiation pattern produced by the array factor looks like by examining Equation 7.

Positions of the elements of a sensor array, specified as a 1-by-N vector, a 2-by-N matrix, or a 3-by-N matrix.In this vector or matrix, N represents the number of elements of the array. Each column of pos represents the coordinates of an element. If pos is a 1-by-N vector, then it represents the y-coordinate of the sensor elements of a line array.

In this page, we'll derive a general equation for the array factor or antenna array response for an N element uniformly spaced linear antenna array. The weights will be simple phased weights when the antenna array is steered towards direction , the weights are given by. Assuming that element n is at location given by. This implies that the inter-element spacing is constant and equal to d.

In order a true grating lobe to occur, both equations 16.16 and 16.17 must have a real solution , mn mn. The array factors of a 5 by 5 uniform array are shown below for two spacing values d 4 and d 2 . Notice the considerable decrease in the beamwidth as the spacing is increased from 4 to 2 .

The array factor for an N element linear array of equal amplitude is given by Equation 17.14. 17.14 E N sin N 2 sin 2 This is similar to the pattern of a line source aperture, Equation 17.5 , and it is possible to synthesise an aperture with a planar array.

The factor multiplying jE 0jabove is also called the array factor. The above can be used to plot the far- eld pattern of an antenna array. Equation 27.1.6 has an array factor that is of the form jsinNxj jsinxj. This function appears in digital signal processing frequently, and is known as the digital sinc function. The reason why

Here, the phase factor exp 1 2j N reflects a phase advancement associated with the last Nth array element relative to the center of the linear array. It represents the phase shift of the array's centre relative to the origin, and it would be equal to one if the origin were to coincide with the array centre.

That normalized array factor can be written as Equation 11. We have already defined beam angle 0 as a function of phase shift between elements therefore, we can also write the normalized antenna factor as Equation 12. The conditions assumed in the array factor equation include The elements are equally spaced.