For the past couple of days I have been trying to understand and perform Koji's method for impedance measurement using the Agilent 4395A Network Analyzer (without the impedance testing kit). I have made some headway, but I don't completely understand what's going on; here's what I've done so far.
I have made several transfer function measurements using the attached physical setup (ImpedanceTestingPhysicalSetup.png), after calibrating the setup by placing a 50 Ohm resistor in the place of the Z in the diagram. The responses of the various impedances I've measured are shown in the attached plot (ImpResponses.png). However, I'm having trouble figuring out how to convert these responses to impedances, so I tried to derive the relationship between the measured transfer function and the impedance by simplifying the diagram Koji drew on the board for me (attached, ImpedanceTestingSetup.png) to the attached circuit diagram (ImpedanceTestingCktDiagram.png), and finding the expected value of V_{A}/V_{R}. For the circuit diagram shown, the equation should be V_{A}/V_{R }= 2Z/(50+Z). 50 Ohms is good to use for calibration because the expected value of the transfer function for this impedance is 1 (0 dB).
So I used this relationship to find the expected response for the various impedances, and I also calculated the impedance from the actual measured responses. I've attached a plot of the measured (red) and expected (black) response (top) and impedance (bottom) for a 1 nF capacitor (1nF.png). The expected and measured plots don't really match up very well; if I add extra inductance (7.6 nH, plots shown in blue), the two plots match up a little better, but still don't match very well. I suspect that the difference may come from the fact that for my analysis, I treated the power splitter as if it were a simple node, and I think that's probably not very accurate.
Anyway, the point of all this is to eventually measure the impedance of the circuit I created on Friday, but I don't think I can really do that until I understand what is going on a little better. |