Possible to get permittivity from quality factor?

I'm trying to measure Q, DF, and complex permittivity (real and imaginary part) of a DUT, its a thin material similar to paper. by the way, DF = dissipation factor, also known as tangent delta.
i know that DF=1/Q, and DF is imaginary part of permittivity / real part of permittivity.

i read from a NIST note that Q can be measured by looking at the S21,
and use this formula. Q = resonant frequency / 3dB bandwidt frequency.

i made a simple capacitor model fixture by using round metal plates as the conductor and my DUT as the dielectric.
2 female sma connectors are soldered to the metal plates. and connected to the vector network analyzer to observe the S21.

in the example given in NIST note, the S21 is a the shape of y=-x^2 graph. so the calculations of Q iis very easy and straigh forward. the maximum point of S21 is the resonant frequency.

but in the S21 that i measured, there are many many maximum peaks. which one of them is considered resonant frequency? i treat every peak as the resonant frequency and calculate Q, its very consistant, about 3.9-4.0.
is this Q value logica? i have the impression that Q should be above 100.

if this is indeed the Q value, i can get the DF by taking the reciprocal of Q, but how can i get the complex permittivity from Q?

[QUOTE=mtxx;1087965]I'm trying to measure Q, DF, and complex permittivity (real and imaginary part) of a DUT, its a thin material similar to paper. by the way, DF = dissipation factor, also known as tangent delta.
i know that DF=1/Q, and DF is imaginary part of permittivity / real part of permittivity.

i read from a NIST note that Q can be measured by looking at the S21,
and use this formula. Q = resonant frequency / 3dB bandwidt frequency.

i made a simple capacitor model fixture by using round metal plates as the conductor and my DUT as the dielectric.
2 female sma connectors are soldered to the metal plates. and connected to the vector network analyzer to observe the S21.

in the example given in NIST note, the S21 is a the shape of y=-x^2 graph. so the calculations of Q iis very easy and straigh forward. the maximum point of S21 is the resonant frequency.

but in the S21 that i measured, there are many many maximum peaks. which one of them is considered resonant frequency? i treat every peak as the resonant frequency and calculate Q, its very consistant, about 3.9-4.0.
is this Q value logica? i have the impression that Q should be above 100.





I am not aware about using S21 to measure the permittivity. I have used S11 at normal incidence to determine the complex permittivity of concrete and other materials at 50 GHz. Please find Agilent handbook on measuring the permittivity; also Damaskos company offers a variety of test jigs and measurement methods for sample permittivity.

Many things are important; sample type and size and shape. Low permittivity values call for specific methods as well as high ones, the imaginary part is usually determined with a lower precision than the real part.

Thank you for the information on the test jig.

I will look at the website tomorrow.

Can you explain in more detail how you get your dut complex permitivity using s11?
What are the calculations you used?

Previously I tried using NRW method to get complex permitivity using s11 and s21 as the input but I fail because I can't calibrate the s parameters.

I am now not able to give you the exact reference on my S11 concrete measurement method. It was published in ~1996 in the Internat.Journal of IR and MM Waves. Please refer to another paper: Polivka, J., Overview of Microwave Sensor Technology, High Frequency Electronics, April 2007, pp. 32-42. You can find the above paper in References and some details were included.

Sorry for my inability at the moment.

Thank you very much!

I'll look into it first thing tomorrow morning.

Q of a component is different from Q of a circuit.

Q of a component is 1/DF

Q of a circuit (sometimes called loaded Q) is f.c/BW

Hi pstuckey,

I'm referring to this technical note.
http://www.eeel.nist.gov/advanced_ma...%20TN%2001.pdf

at page 27&28,
it says for thin film material, the Q is f.c/ 3db bandwidth.

from the Q, easily can get DF, but how to get complex permittivity form Q, that is the question.

and question 2, if there are multiple peaks in S21, which is considered resonant frequency? is there only one which is the highest peak?