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Entry  Wed Jul 29 12:00:49 2009, Stephanie, Update, General, Multiply Resonant EOM Update ImpedanceTestingPhysicalSetup.pngImpResponses.pngImpedanceTestingSetup.pngImpedanceTestingCktDiagram.png1nF.png
    Reply  Thu Jul 30 19:55:23 2009, Koji, Update, General, Multiply Resonant EOM Update imepedance.pngimpedance_meas.jpg
Message ID: 1813     Entry time: Thu Jul 30 19:55:23 2009     In reply to: 1804
Author: Koji 
Type: Update 
Category: General 
Subject: Multiply Resonant EOM Update 


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 VA/VR. For the circuit diagram shown, the equation should be VA/VR = 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.

 I checked the setup and found RF reflection at the load was the cause of the unreasonable response in the impedance measurement.
So, I have put a total 22dB attenuation (10+6+6 dB) between the power splitter and the load to be measured. See the picture.
This kind of attenuators, called as PADs, is generally used in order to improve the impedance matching, sacrificing the signal amplitude at the load.

Then, It looks the measurements got reasonable up to 100MHz (at least) and |Z|<1kOhm.
For the measurements, I just followed the procedure that Stephanie described.
Stephanie has measured the impedance of her resonant circuit.

As a test of the method, I measured impedances of various discrete devices. i.e. 50Ohm, 10-1000pF Cap, Inductances, circuit opened.

a) 50Ohm (marine-blue) was calibrated to be recognized as 50Ohm.

b) The mica capacitances (orange 10pF, yellow 100pF, green 1000pF) appeared as the impedances f^-1 in the low freq region. It's nice.
At high frequency, the impedances deviate from f^-1, which could be caused by the lead inductance. (Self Resonance)
So 1000pF mica is not capacitance at 50MHz already.

c) Open BNC connector (Red) looks have something like 5pF. (i.e. 300Ohm at 100MHz)

d) I could not get good measurements with the inductors as I had 200nH (and some C of ~5pF) for a Pomona clip (blue).
This is just because of my laziness such that I avoid soldering the Ls to an RF connector!

Attachment 1: imepedance.png  141 kB  Uploaded Thu Jul 30 21:48:01 2009  | Hide | Hide all
Attachment 2: impedance_meas.jpg  54 kB  Uploaded Thu Jul 30 21:48:47 2009  | Hide | Hide all
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