# Superposition of Rays

The individual rays are superposed with consideration of the phase information. This leads to constructive and destructive interference in the results.

Depending on the path length and frequency, the phase of the signal and the complex electric field vector are computed. The phase φi of ray i depends on the path length r and the wavelength λ of the signal (c0 is the velocity of light and f the carrier frequency):

(1) ${\phi }_{i}=\frac{r}{\lambda }×{360}^{\circ }=\frac{r}{{c}_{o}}f×{360}^{\circ }$

For each reflection in the ray, an additional phase shift of 180° is considered.

The total field strength Etot is the coherent (including phase) superposition of the electric field strengths of the different paths:

(2) ${E}_{tot}=\sum {E}_{i}=\sum {E}_{ef{f}_{i}\text{\hspace{0.17em}}}\left(\mathrm{cos}{\phi }_{i}+j\mathrm{sin}{\phi }_{i}\right)$

The generated output file does not contain any information concerning the phase (because all radio network planning tools would not consider this information). Therefore, in the generated results only the magnitude of the electric field strength relative to the isotropic radiator is considered:

(3) $G=\frac{|{E}_{tot}|}{|{E}_{iso}|}$