1. Antenna Engineering EC 544
Lecture#1

2. Linear, Circular, Planar
Uniform Arrays
Linear, Circular, Planar

4. Two Isotropic elements array (Far field observation)

12. If the reference point is chosen to be the physical center of the array, the array factor will be:

13. For small values of ψ, the expression of the AF can be approximated by:

14. To find the nulls of the array, the array factor is set to zero
To find the nulls of the array, the array factor is set to zero. That is
For n = N, 2N,…, the (AF)n attains its maximum values because it reduces to a sin(0)/0 form. The values of n determine the order of the nulls (first, second, etc.). Since the argument of the arccosine cannot exceed unity, so the number of nulls that can exist is a function of the element separation d and the progressive phase excitation β.

15. The maximum values of the array factor occur when

17. The 3 – dB point for the array factor occurs when
The half power beamwidth (HPBW) can be determined once the angles of the first maximum (θm) and the half-power point (θh) are determined. For a symmetrical pattern
HPBW = 2| θm - θh |

19. There are secondary maxima (maximum of minor lobes) which occur approximately when the numerator AF attains its maximum value . That is,

20. The maximum of the first minor lobe occurs when
At that point, the magnitude of AF reduces to
Thus the maximum of the first minor lobe of AF is dB down from the maximum at main lobe.