# Output TX Power with complex impedances

I'm developing an application with my software defined radio (SDR) Board and it is very critical that I have some control over the actual power I am transmitting at every time.

In order to do this, I have first measured the impedance of the TX antenna port and unfortunately it is not a purely 50ohm impedance. In fact we can treat it as a complex Z = R + jX impedance, with the values of R and X known.

Knowing this, and assuming that I'm transmitting pulses with voltage U(t) well known, my question is the following:

I believe that if Z = 50 ohm, the total power P(t) of the signal would simply be (right?):

$$P = \frac{1}{t_1-t_0}\int_{t0}^{t1} \frac{U^2(t)}{50} \, dt$$

In general, since U(t) is known, I don't believe that I have to pursue any approximations in computing that pulse power.

However, if the impedance is complex, as it is the case, what is the relation between transmitted power and transmitted voltage? I mean, am I simply interested in the absolute of Z, i.e:

$$P = \frac{1}{t_1-t_0}\int_{t0}^{t1} \frac{U^2(t)}{|Z|} \, dt$$

or am I interested in the Real part of P only?

• how do you measure the impedance of a TX port?! – Marcus Müller Jan 27 '19 at 13:22
• (that's a very serious question here: Interpretation of the results really depends which operational state your PA to be in and how you measured.) – Marcus Müller Jan 27 '19 at 13:50
• @MarcusMüller I have used a VNA and observed the result in a smith chart. As expected the impedance measured in accordance to the center frequency of the channel, therefore I registed the impedance value for the center frequency of interest. – João Franco Jan 27 '19 at 14:27
• ok, but HOW did you use the VNA and in what operation mode was the SDR at the time? The impedance seen when trying to sink energy into the output of an amplifier depends on what the amplifier is doing at that time. – Marcus Müller Jan 27 '19 at 14:49
• @MarcusMüller I really wasn't aware of such criteria. I simply configured the SDR to the intended channel frequency and then performed the impedance measurement. I was not transmitting. I'm really not sure on how to proceed now. All I wanted to do was to make a calibration table that would tell me at every configuration of TX antenna gain and digital IQ word what was the power being sent. What do you suggest? How is my impedance approach wrong? – João Franco Jan 27 '19 at 15:27