A reader of Cooking the books on VSWR asked
…so you are telling me that I could measure this Prev>Pfwd with a directional wattmeter like my Bird43… I have never seen it and I don’t believe it.
For clarification, I did not discuss Prev or Pfwd in respect of the three scenarios (other than to say Pref cannot exceed Pfwd).
I did discuss line voltage
measurements you can make with a simple RF volt meter which was in the article’s reference quote. But, let’s discuss what you might measure by inserting a 50Ω Bird43 directional wattmeter in the Load case 2 scenario.
Above is a calculated plot of the expected Pfwd and -Prev readings, Prev is shown negated so you can add it by eye with Pfwd to obtain the net power Power (blue line).
Note that Pref is never greater then Pfwd, there is no implied breach of the law of conservation of energy.
So, what is the implied ρ?
Above is a plot of calculated ‘actual’ ρ and ρ(50), ρ wrt Zo=50+j0Ω, which would be derived from the Bird43 measurements.
The ‘actual’ ρ is a smooth exponential curve, a consequence of transmission line loss. The ρ(50) curve oscillates, and the error is due to the fact that its reference impedance is not the transmission line actual Zo. You will also see that whereas ρ>1.0 at the load, ρ(50) is never greater than 1.0. When Zref is purely real, ρ(Zref)<=1.0.
Even though ρ(50) is not a good estimator of ‘actual’ ρ, the blue Power line in the previous chart is correct.
Further, that given the shape of the blue Power line in the previous chart, it is clear that it cannot be derived from the ‘actual’ ρ line in the second chart, many of the operations based on ρ depend on Zo being purely real (ie a Distortionless Line).
The same response can be expected of any directional wattmeter, VSWR meter, antenna analyser or VNA calibrated for a purely real impedance such a 50+j0Ω.