Basically I want to measure how impedance (Ohm) relative to Z0 (50 Ohm) waveguide is changing by varying a parameter. I currently measure the reflection coefficient S11 in a 1-port setup. Our VNA can store complex S11 parameters, but also magnitude (dB or linear) and phase.
As far as I understand it's not so easy now to get from S11 to Ohm and Smith Chart was designed for that reason. A webpage says:
In order to convert S-parameters to impedances, you must specify Z0. Usually it's 50 ohms, sometimes 75 ohms.
The calculation to get from S-parameters to impedances is more complicated than, for example, VSWR. This is one of the reasons the Smith Chart was invented, you could enter coordinates either way and the graph would solve the equations for you. Here's one form of the equations, sent by an alert engineer named Steve:
REAL=(Z0*(1-(MAG*MAG)))/(1+(MAG*MAG)- (2*MAG*COS((ANG/360)*2*PI()))) IMAGINARY=(2*MAG*SIN((ANG/360)*2*PI())*50)/ (1+(MAG*MAG)-(2*MAG*COS((ANG/360)*2*PI())))
He sure like brackets! Here's the input and output impedance, with real and imaginary parts plotted separately. Ideally the real part is 50 ohms, and the imaginary is zero.
So with REAL and IMAGINARY R and X in Z=R+jX are meant here or this again real and imaginary numbers of the S11 parameters?
As I recorded now some data where only the S11 real and imaginary pair numbers where stored, I'm wondering if I can deduce from S11 the magnitude to get with above formulas to Ohm, so I don't have to measure again? I'm using origin for post-processing the data, also matlab. Both have tools to plot smith charts and read VNA data to my knowledge.
Thanks for your kind help