# Step 4-B: Field Strength of the Configuration (Actual Value)

*P*is determined. The computation is similar to the computation for the isotropic radiator.

- Distance
*d*between*P*and radiation center of the antenna (*x*,_{ant}*y*,_{ant}*z*)_{ant}(1) $d=\sqrt{{\left({x}_{1}-{x}_{geo}\right)}^{2}+{\left({y}_{1}-{y}_{geo}\right)}^{2}+{\left({z}_{1}-{z}_{geo}\right)}^{2}}$ - Computation of power density
*S*of the direct ray at point_{ant}*P*with(2) ${S}_{ant}\text{\hspace{0.17em}}=\frac{{P}_{{t}_{ant}}}{4\pi {d}^{2}}\text{\hspace{0.17em}}$*P*representing the Tx power of the antenna._{tant} - Computation of effective electrical field strength
*E*at_{an-FSt}*P*based on power density*S*and impedance of free space_{ant }*Z*= 120 πΩ_{F0}(3) ${\left|{\underset{\_}{E}}_{iso}\right|}^{2}\text{\hspace{0.17em}}={S}_{iso}\times {Z}_{F0}$ - Computation of penetration / transmission loss
*L*._{T} - Subtraction of penetration / transmission loss
*LT*leads to actual received electric field strength at point*P*(based on direct ray):(4) ${\underset{\_}{E}}_{ant\text{\hspace{0.17em}}0}\text{\hspace{0.17em}}={E}_{ant-FS}-{L}_{T}$Depending on the path length

*d*and the frequency*f*, the phase φ of the signal is determined (with wavelength λ and velocity of light*c*):_{0}(5) ${\phi}_{i}=\frac{d}{\lambda}\times 360\xb0=\u2942\frac{d}{{c}_{0}}f\times 360\xb0$ - Additionally, the computation of reflected rays is possible.
For the computation of reflected rays, each object is examined whether a reflection is possible or not.

Additionally, the penetration / transmission must be considered if the reflected ray intersects further.

If the reflected rays exist (point of reflection

*Q*is inside the object), this leads to the power densitywith(6) ${S}_{ant}\text{\hspace{0.17em}}=\frac{{P}_{{t}_{ant}}}{4\pi {\left({r}_{1}+{r}_{2}\right)}^{2}}\text{\hspace{0.17em}}$*P*representing the transmitter power of the antenna._{tant} - Computation of the effective electric field strength
*E*at point_{an-FSt}*P*based on power density*S*and impedance of free space_{ant}*Z*= 120 πΩ:_{F0}(7) ${\left|{\underset{\_}{E}}_{ant-refl}\right|}^{2}\text{\hspace{0.17em}}={S}_{ant}\times {Z}_{F0}$ - The contributions of the direct and reflected rays are superposed considering their
phases:
(8) ${E}_{Ant}={\displaystyle \sum {E}_{i}={\displaystyle \sum {E}_{an{t}_{i}\text{\hspace{0.17em}}}\left(\mathrm{cos}{\phi}_{i}+j\mathrm{sin}{\phi}_{i}\right)}}$ - Computation of the reflection loss
*L*of the reflected ray._{R} - Computation of the transmission/penetration loss
*L*of the reflected ray._{T} - Subtracting the transmission loss
*L*and the reflection loss_{T}*L*leads to the received field strength at point_{R}*P*(on the basis of the reflected ray):(9) ${\underset{\_}{E}}_{ant\text{}\text{\hspace{0.05em}}\text{\hspace{0.05em}}i}\text{\hspace{0.17em}}={E}_{ant-refl}-{L}_{T}-{L}_{R}$Depending on the path length

*d*of the reflected ray and the frequency*f*(and wavelength λ), the phase j of the reflected ray is determined by the velocity of light*c*:_{0}(10) ${\phi}_{i}=\frac{d}{\lambda}\times 360\xb0+{n}_{R}^{}\times 180\xb0=\u2942\frac{d}{{c}_{0}}f\times 360\xb0+{n}_{R}\times 180\xb0$For each reflection (

*n*reflections are in the ray), an additional phase shift of 180° is added._{R}

These rays are determined for each antenna, and all rays are superposed with the equation
above. The total field strength * E _{Ant}* is the magnitude of the coherent
(including phase) superposed field strengths of the rays of the individual antennas.