The array factor (AF) for a uniform linear array is given by:
\[AF(\theta) = \sum_{n=0}^{N-1} e^{jn(kd\cos\theta + \beta)}\]Where:
The directivity can be approximated as:
\[D \approx 10 \log_{10}(N)\]For an array with 4 elements:
\[D \approx 10 \log_{10}(4) \approx 6.02 \text{ dB}\]This visual shows a simplified representation of an antenna array pattern. The actual pattern would depend on various factors including the number of elements, spacing, and phase shift.
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