This is a friendly group and I do not wish to get into some kind of argument with others. If I have posted something in this group which is wrong or confusing please quote what I said and tell me why it is incorrect and I will do my best to answer your question or if proven wrong admit my error. But please quote what I said NOT what someone else thought I said or meant about the subject at hand.
In a previous post on a graph I wrote "This is the S11 phase plot which is the angle of the reflection coefficient gamma. A common misconception by those new to S parameters is to confuse this with the impedance phase of the device under test (DUT)". Here is why I believe that to be true.
If we have a complex impedance attached to our NanoVNA and wish to measure its characteristics we can do this with an S11 or S21 measurement. For the purposes of this discussion I will focus on the S11 measurement.
Let us say our device under test (DUT) consists of a 50 ohm resistor in series with a 1.6 uH inductor. We perform the measurement at 5 MHz. The inductive reactance is X = 2*pi*freq*L which is equal to 50 ohms. So the complex impedance R+jX is 50+j50. At 20 MHz. the same DUT will have a complex impedance of 50+j200.
It is well known that the "impedance phase angle" is equal to the arctangent of X/R and this will range between +90 degrees to -90 degrees depending on the values of X and R and whether X is inductive or capacitive. For the case of 50+j50 the phase angle is arctan 1 or 45 degrees and fro 50 + j200 is arctan 4 or 76 degrees. This is shown on the attached diagram. We could easily do a plot of impedance phase versus frequency for the DUT and get a graph.
Now when we connect this example DUT to the CH0 port of a NanoVNA and do a measurement over the range of 5 to 20 MHz. we can set the traces to display a number of parameter plots. One that is very useful is to plot the "reflection coefficient" Gamma (Γ) . Gamma Γ = (Z - Zo) / (Z + Zo) with Z being a complex number and Zo typically set at 50 or 75. Note that Gamma will also be a complex number in the form a+jb or as magnitude @ an angle. The Magnitude is = sqrt(a^2+b^2) and the angle is the arctan (b/a). The angle is often referred to as the "S11 phase angle" and that can be displayed on the NanoVNA or in PC programs that work with the PC. There are calculators that calculate the reflection coefficient in both forms for a given R and X and the phase angle . Here is one that is easy to use.
If R and X are plotted on a Smith chart the vector from the origin to that point will have a length equal to the magnitude of the refection coefficient and the angle will be the S11 phase angle. I have plotted the 50+j50 and 50+j200 on a Smith chart and attached them to this post.
Here is a comparison of the "impedance phase angle" and "reflection coefficient phase angle" for the two cases above. One can clearly see that they are different which is what I originally stated. Yes reactance does have an effect on both and this is not in dispute. But they are different measurements!
Impedance phase reflection coefficient phase
50+j50 45 63.4
50+j200 76 26.6
It would be nice if the "impedance phase angle" could be added to the graphing capability of the NanoVNA or one of the PC programs. Someone requested this on the NanoVNA saver GitHub page last month.
Roger
Roger Need
