# Directivity

Directivity is the ratio of the radiation intensity in a given direction from the antenna in relation to the radiation intensity averaged over all directions.

If the main direction of radiation is known, the directivity $D$ can be calculated for each antenna pattern with the following equation:

(1) $D={\left(\frac{{S}_{\mathrm{max}}}{{S}_{i}}\right)}_{r=const\text{,}{P}_{t}=const}$

${S}_{\mathrm{max}}$ indicates the maximum radiated power density and ${S}_{i}$ indicates the power density radiated by the isotropic radiator.

It is also possible to determine $D$ from the directional characteristic with:

(2)

If the antenna pattern consists of a discrete number of values, the integrals in the equations must be substituted with a summation with increments $\Delta \vartheta$ and $\Delta \phi$ :

(3) $D=\frac{4\pi }{\Delta \text{\hspace{0.17em}}\vartheta \cdot \Delta \text{\hspace{0.17em}}\phi \cdot {\sum }_{\text{\hspace{0.17em}}i\text{\hspace{0.17em}}=\text{\hspace{0.17em}}1}^{\frac{2\text{\hspace{0.17em}}\pi }{\Delta \text{\hspace{0.17em}}\phi }}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\sum }_{j\text{\hspace{0.17em}}=\text{\hspace{0.17em}}1}^{\frac{\pi }{\Delta \text{\hspace{0.17em}}\vartheta }}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{C}^{2}\text{\hspace{0.17em}}\left(i\text{\hspace{0.17em}}\cdot \Delta \text{\hspace{0.17em}}\vartheta ,j\cdot \Delta \text{\hspace{0.17em}}\phi \right)\cdot \mathrm{sin}\text{\hspace{0.17em}}\left(j\cdot \Delta \text{\hspace{0.17em}}\phi \right)}$

Often the directivity of an antenna is given in dB. The logarithmic value ${D}_{db}$ in dB can be obtained from the linear value $D$ of the directivity with the following equation:

(4) ${D}_{dB}=10\cdot \mathrm{log}D$