I purchased the LibreVNA, which allows two port vector network analyzer measurements up to 6 GHz. I have the original model that cost about $600. Here is a link to purchasing the new one on Amazon.
The unit comes with coaxial calibration standards: open, short, and load. I wanted to calibrate the unit to allow waveguide measurements. I looked and looked on the World Wide Web, assuming someone else in the world wanted to do the same thing. All I can find are videos talking about the coaxial calibration. Yeah, I get it. I want to do something else.
WR-187 is a waveguide I am using at work for some current projects. It is actually perfect for the LibreVNA since its frequency range is 3.95 to 5.85 GHz. I found a pair of coax to waveguide launchers on eBay for $75, and I found a short piece of waveguide that matches these flanges at work.
The trick to calibrating the LibreVNA for waveguide is modifying the TRL calibration. You need to modify the frequency range to match the waveguide, you need to change the single port calibration from open to short, and you need to change the line delay to match a piece of calibration waveguide that you have. I am using a 20 mm long piece of waveguide machined as a block that had different flanges. I plan to CNC machine a shorting plate and a 20 mm long waveguide at home for future calibrations.
Use Calibration > Edit Calibration Kit > TRL. Change Refletion to Short, change the min and max frequencies to 3.95 and 5.85 GHz, and change the delay to match your waveguide. Mine is 20 mm, so use vgroup = c * sqrt (1 – (2/2af)^2) and group delay = length / vgroup. My center frequency is 4.9 GHz, and my waveguide is 20 mm long, so delay is 66.76 ps.
Next perform the TRL calibration. Make sure to set the frequency range to 3.95 to 5.85 GHz for Port 1 Short, Port 2 Short, Through Standard (launchers face to face) and Line Standard (the 20 mm waveguide). Click Measure on each of these choices.
Here are the launchers face to face, used for the THRU measurement.
You can see that I tied my LibreVNA down to a heat sink. It gets pretty hot without this addition.
Here is what the thru calibration looks like when it completes.
My line was not necessarily perfectly aligned since the flanges were different. I also could not press it when I measured it. When I CNC machine my calibration standards, this result should improve.
The measurement I wanted to make is permittivity and permeability of a sample. I 3D printed a block of PLA plastic for a first test. Its length is 10 mm. I moved it to the center of an 82.5 mm long waveguide.
Here is the sample attached to the LibreVNA.
I used bolts (no nuts) and clamps to make the measurement.
Here is a side view showing the het sink on the LibreVNA.
I exported S11, S12, S21, and S22 as real and imaginary data using the LibreVNA export feature. One can export Touchstone or CSV format.
I wrote a MATLAB program based on the paper Characterisation and Comparison of Material Parameters of 3D-Printable Absorbing Materials found at this link. I can equate manipulations of the complex values of the S parameters to compare to formulas including the dielectric and magnetic properties of the material sample. The code can be found here.
Setting er = 2.55 and ur = 1, I plot left-hand side and right-hand side, and they match really well. I can use any MATLAB solver or write a least squares routine to determine the best values.
While er for PLA is published as 3.11, my 3D printed puck is not 100% dense. I need to weigh it to find the fill percentage. Plastic mixed with air has a reduced dielectric constant. If the puck is F% dense, then er = 3.11F+1.0*(1-F). That means my puck should be 73.45% dense. I will weight it to verify.
Here are the plots of the real part of LHS and RHS for the two equations in the paper.
To find er’, er”, ur’, and ur”, I will need to apply a fitting routine to compare the real and imaginary parts of the two equations. I have four equations and four unknowns.
The most important part of this blog is telling everyone how you can take a $600 box and use it to make valid waveguide measurements. Anything below 6 GHz is available. I hope my blog pops up when people search for LibreVNA Libre VNA waveguide calibration. I have not found it anywhere, so here it is.
I changed the MATLAB program to a function that takes er’, er”, ur’, ur” as inputs an outputs the sum of squares of the real and imaginary parts of the two fitting equations. I run FMINSEARCHBND, which is the bound version of FMINSEARCH. Since the minimum values are 1 , 0 ,1, 0, I set that as a lower bound. The function is here and the search routine that runs the function is here.
Here is a result of running this program. The results are reasonable. This is the PLA data, so now I have it in more detail. The fit of all four functions looks great. I can move on to measuring other pucks now.
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