written 5.4 years ago by |
Consider a transmitter and receiver separated in free space as shown in Figure 1(a) .
Let an obstructing screen of effective height h with infinite width (going into and out of the paper,) be placed between them at a distance $d_1$ from the transmitter and $d_2$ from the receiver.
It is apparent that the wave propagating from the transmitter to the receiver via the top of the screen travels a longer distance than if a direct line-of-sight path (through the screen) existed.
Assuming $h \lt \lt d1$, $d_2$ and $h \gt \gt \lambda $, then the difference between the direct path and the diffracted path, called the excess path length ($\Delta$) , can be obtained from the geometry of Figure as
$$\Delta \approx \frac{h^{2}}{2} \frac{\left(d_{1}+d_{2}\right)}{d_{1} d_{2}}$$
The corresponding phase difference is given by
$$\phi=\frac{2 \pi \Delta}{\lambda} \approx \frac{2 \pi}{\lambda} \frac{h^{2}}{2} \frac{\left(d_{1}+d_{2}\right)}{d_{1} d_{2}}$$