Question

A 20 dBm power source is connected to the input of a directional coupler having a coupling factor of 20 dB, a directivity of 35 dB, and an insertion loss of 0.5 dB. If all ports are matched, find the output powers (in dBm) at the through, coupled, and isolated ports.

Answer 1

`P_O = 0.989 watt = 19.9 dBm`

Step-by-step explanation:

Given data:

P_1 power = 20 dBm = 0.1 watt

coupling factor is 20dB

Directivity = 35 dB

We know that

coupling factor
`= 10 log (P_1)/(P_f)`

solving for final power

`20 = 10 log(P_1)/(P_f)`

`2 = log (P_1)/(P_f)`

`100 = (0.1)/(P_f)`

`P_f = 0.001 watt = 0 dBm`

Directivity
`D =  10 (P_f)/(P_b)`

`35 = 10 (0.001)/(P_b)`

`P_b = 3.162 * 10^(-7) wattt`

output Power
`= P_1 -P_f - P_b`

`= 0.1 - 0.001 - 3.162 * 10^(-7)`

`P_O = 0.989 watt = 19.9 dBm`