Amir, to calculate the loss per unit length we need to know the relative dielectric constant and the dielectric loss tangent of the dielectric and the frequency. This is assuming the loss is dominated by the dielectric, which it is for FR-4 and so we will ignore copper loss.
Example:
Relative dielectric constant of 4
Loss tangent of 0.02
1000 MHz
The propagation time per meter is (4^0.0.5)/ 300e6 meters/second = 6667 ps/m or 67 ps/cm
C = (prop time)/ Z = (67 ps/cm)/50 = 1.3 pF/cm
Xc = 122 ohms/cm
dielectric shunt loss resistance = 122 ohms x 1/0.02 = 6.1k ohms
Voltage = 158 V
Power dissipated in dielectric loss = (E^2)/R = (158^2)/(6.1k) = 4 watts
Now we need to know the thermal conductivity of FR-4, the PCB stack-up and flooding, and the thermal resistance to free air. If you want to continue I can go through that calculation.
We might find that this is too much power for FR-4 and start looking at other dielectrics such as Teflon. In that case the copper loss must be calculated to see if it is the dominant loss.
