Radiowave Reflection Homework | Calculate Voltage Vab

[leocfm]

Homework Statement

As shown in the attachment, a radio signal travels down a tunnel, reflected by the walls and floor. Assuming that at most 2 hops contribute, calculate the voltage Vab at A due to current Ib in antenna B. Obtain a formula that depends on various parameters of the problem.

Homework Equations

Assuming antennas are polarization matched, the voltage Vab in receiver antenna A (effective length Ha) is given by Vab=Ha*Eb,
where Eb (the field at A due to source at B) and
Eb=((jωμIbHb)/4∏)*(exp(-jβd)/d) (where β is wavevector, d distance between A and B)

The Attempt at a Solution

What I have got is for single reflection, the field at A due to source at B is Eb=R*((jωμIaHa)/4∏)*(exp(-jβd)/d) where R is reflection coefficient of ground and d the reflected distance. But for multiple reflection, just like shown in the graph, how I can get the field at A?

 

[KataKoniK]

To calculate the field at A due to multiple reflections, we can use the principle of superposition. This means that we can calculate the field at A by considering the contribution from each individual reflection separately and then adding them together.

Let's assume that the signal from B first reflects off the floor and then off the wall before reaching A. The field at A due to the reflection off the floor can be calculated using the formula Eb=Rf*((jωμIbHb)/4∏)*(exp(-jβdf)/df), where Rf is the reflection coefficient of the floor and df is the distance between B and the first reflection point on the floor.

Similarly, the field at A due to the reflection off the wall can be calculated using the formula Eb=Rw*((jωμIbHb)/4∏)*(exp(-jβdw)/dw), where Rw is the reflection coefficient of the wall and dw is the distance between the first reflection point on the wall and A.

Now, since we are considering at most 2 hops, the total field at A will be the sum of these two contributions, i.e. Eb = Eb(floor) + Eb(wall).

Plugging in the values for Rf, Rw, df, and dw, we can obtain the total field at A. This can then be used to calculate the voltage Vab using the formula Vab=Ha*Eb.

The final formula for Vab will depend on the various parameters of the problem, such as the reflection coefficients of the floor and wall, the distances between the antennas and the reflection points, and the effective lengths of the antennas.