what is step 2 of TRL calibration?

[mtxx]

Good day everyone.


I'm would like to measure the S parameters of a thin specimen, which is my DUT.
i sandwich it between 2 Xband waveguides and measured its S parameters using a VNA.
knowing that calibration is required, i chose the TRL calibration.

I've read alot of TRL info on the web, and numerous agilent application notes.
They all have something in common, which it they only mention what T,R & L means.
they do not provide the next step which is how to use these information to get the calibrated S parameters,


anyway, when measuring the S parameter of my DUT, i also measured the S parameters of my TRL standards.
since i'm using waveguides,
T: i connect both waveguides directly.
R: attach a shorting plate to both waveguide
L: i tried 2 types of line standard in case one of them is not correct, a fix attenuator waveguide, a flap attanuator waveguide.

So now i have the S parameters (S11,S12,S21,S22) of the DUT, T,R,&L standards.

i would like to perform the calculations to convert my DUT uncalibrated S parameters to the calibrated S parameters.

I've search all over the web, and read alot of research papers from IEEExplorer, science direct,
but all of them did not mention how they do it. most of the researchers used the TRL method, and the paper they quote from is
“Thru-Reflect-Line”: An Improved Technique for Calibrating the Dual Six-Port Automatic Network Analyzer
by author GLENN F. ENGEN,

i've read this paper, and did not find any steps involved on how to use the TRL s parameters to do the calibration.

Finally i found a book written by Pozar, "microwave engineering"
the one i'm reading is the 2nd edition. on page 217-221 there is a very detail explaination on how TRL works, and how it should be done.
it goes like this, the entire setup is represented as bellow

VNA port1---error box1---DUT---error box2---VNA port2

the DUT is replaced with a Thru standard, and a signal flow chart is formed
the same is done for the Line and Reflect standard.

from the signal flow chart of the T,R,L, 5 equations with 5 unknowns are obtained
the 5 unknowns are S11,S12,S22 of the error box, the propagation constant, and the reflection coefficient.

do note that there is a mistake in equation 4.77a, this mistake is not corrected in the 3rd and 4th edition of the book.
equation 4.77a is obtained by inserting equation 4.74b into 4.76b and simplified it.

equation 4.74b:
T12 = S12^2 / (1-S22^2)

equation 4.76b
L12 = S12^2 * e^(-gamma*L) / 1 - S22^2 * e^(-2*gamma*L)

equation 4.77a (as stated in the book, the WRONG one)
L12*e^(-2*gamma*L)-L12*S22^2 = T12*e^(-gamma*L) - T12* S22^2 * e^(-gamma*L)

equation 4.77a (The correct one)
L12*-L12*S22^2 * e^(-2*gamma*L)= T12*e^(-gamma*L) - T12* S22^2 * e^(-gamma*L)

have a look at the above equations, its a careless mistake in the left hand side of the equation 4.77a.
the term e^(-2*gamma*L) is placed at the wrong location.

after correcting the mistake, i used MATLAB to solve it.
there will be many answers, but the correct one will be the one that satisfied this condition,
both the real and imaginery terms of the propagation constant must be positive.

now here is the problem.
in half of the results i got, they dont satisfy this condition.
i ignored the ones that does not satisfy the condition, and only take the data that does.

but the final output i got, quite a number of the S11 and S22 parameters are larger than 1.
which i know is not possible, meaning that the calibration calculations are wrong.

what am i doing wrong here, are my TRL standards incorrect? or pozar's method is incorrect?
i've done many reading, and still searching for a correct way to do the TRL calibration.

my friend recomend me to try asking in this forum. i hope you guys will give me some idea.
its strange that such a famous method TRL calibration is so widely used, but i cant find any detail source on how it is being done.

anyone know where else can i get information on how to perform TRL calibration?

 

[pstuckey]

First, I take my hat off to you for your persistence, but I think the answer is much simpler than this.

The VNA will do the calibration for you, you don't have to collect S-parameters for your cal standards. Go to calibration menu, do full two port cal. When you finish the calibration, the VNA will do the math and adjust the measured numbers accordingly. So after you complete the two-port cal, the data on the screen (or exported to a file) is the calibrated S parameters for your DUT. Also, note that analyzers will typically have a symbol or notation somewhere on the screen that will indicate whether the displayed results are calibrated or uncalibrated.

 

[mtxx]

First, I take my hat off to you for your persistence, but I think the answer is much simpler than this.

The VNA will do the calibration for you, you don't have to collect S-parameters for your cal standards. Go to calibration menu, do full two port cal. When you finish the calibration, the VNA will do the math and adjust the measured numbers accordingly. So after you complete the two-port cal, the data on the screen (or exported to a file) is the calibrated S parameters for your DUT. Also, note that analyzers will typically have a symbol or notation somewhere on the screen that will indicate whether the displayed results are calibrated or uncalibrated.

i could only wish it was that simple.
the VNA i use does have a auto calibration kit. but the connector type is SMA. means from the VNA, i connect the SMA cable to the calkit, it will auto cal for me. but this means the measurement plan will be at the tip of my SMA cable.

the setup of my stuff is like this. The SMA cable from the VNA is connected to a coaxial to waveguide converter, then to a wave guide, then only reach my DUT.
if no additional calibration is done, the measured S parameters will include the all of the following: converter, waveguides and DUT.

i only want the S parameter of the DUT, hence the TRL calibration is required to eliminate the effects of the waveguides and converter

 

[pstuckey]

Yes, you'll have to do a manual calibration of the VNA (put the auto cal kit away using all your sma and waveguide components, but still let the vna do the math for the adjustment.

Get to the manual cal menu, then for the thru measurement, you'll connect your sma cables, coax/waveguide adaptor, and connect both waveguides exactly as you described above. When it's connected, press the thru button, the VNA will collect and store the data, and you'll move on to the R and L using your waveguide components as you described above. Then at the completion of the cal the VNA will crank through the math and come up with the adjustments which will include the effects of the sma/waveguide components since they were attached during the cal.

 

[enjunear]

Yes, you'll have to do a manual calibration of the VNA (put the auto cal kit away using all your sma and waveguide components, but still let the vna do the math for the adjustment.

Get to the manual cal menu, then for the thru measurement, you'll connect your sma cables, coax/waveguide adaptor, and connect both waveguides exactly as you described above. When it's connected, press the thru button, the VNA will collect and store the data, and you'll move on to the R and L using your waveguide components as you described above. Then at the completion of the cal the VNA will crank through the math and come up with the adjustments which will include the effects of the sma/waveguide components since they were attached during the cal.

Agree w/ pstuckey. To check your calibration after the adjustments are done, reconnect the "thru" configuration and look at S21 and S12, they should be nearly 0 dB (since the loss of the cables/adapters/transitions are being offset by the cal factors). Then check S11 and S22, they should show a good return loss (haven't worked with waveguide in a long time, but in the 10's of dBs should be a good sign... for coax, I'd say better than 20 or 30 dB return loss is typical).

 

[mtxx]

Agree w/ pstuckey. To check your calibration after the adjustments are done, reconnect the "thru" configuration and look at S21 and S12, they should be nearly 0 dB (since the loss of the cables/adapters/transitions are being offset by the cal factors). Then check S11 and S22, they should show a good return loss (haven't worked with waveguide in a long time, but in the 10's of dBs should be a good sign... for coax, I'd say better than 20 or 30 dB return loss is typical).

thanks for the reply guys.
i'm not sure how to use that VNA for TRL calibration, but i now i have no access to the VNA anymore, its in another institution, i was given a chance to use it for a limited time only :-(

now i have with me the S parameters of T,R,L, and DUT.
was hoping able to produce the calibrated S parameters of DUT with these inputs.

since the VNA has its own method of processing the TRL calculations, and the TRL calculation has been defined and digitalized,
is it possible to find such function block or tool box in matlab? CST, or AWR or any RF related software?

i really need to get this done with soon. stuck at the calibration part for so long already.
sorry if i sound desperate or pushy. i really spend alot of effort, and it puzzles me why the original fundamental calculation technique has been lost for TRL, seems that really no one knows how its done anymore, if one day all VNA spoil, TRL method will be just a myth.