How to find permittivity and dissipation factor from a given S11

[bbvv]

does anyone have any clue how to find permittivity and dissipation factor from a given S11?
thanks in advance

 

[jiripolivka]

Closest to this problem I have used the normal-incidence method to determine the complex permittivity of concrete at ~50 GHz.
Details can be found in olivka, J,: Measuring Concrete Permittivity at MM waves, Internat. Journal of IR and MM Waves, Vol.17, No. 10, 1997, pp. 1673-1683.
From S11 you can derive the standing-wave ratio ; for a full reflection, SWR o, for a particular-material boundary reflection, SWRx. Then the reflection ratio gamma, G = ( SWRo-1)(SWRx+1) / (SWRo+1) (SWRx-1).
Then the complex permittivity k = k' - j k" = [ (G +1) / (G+1)] squared.
I have not thought about using S11 directly as it would involve the transducer parameters between your transmission line and a tested material.

Please let me know your results, it may be quite interesting. Thank you

 

[kspalla]

I guess you need S21 too.

Otherwise you will not be knowing the accuracy of the measurement due to calibration issues.

 

[volker_muehlhaus]

Hewlett Packard (now Agilent) offered several text fixtures for dielectric property measurement, and documented the methods in their application notes.

One example application note: **broken link removed**

 

[jiripolivka]

In my normal-incidence method the S21 is not needed as the complex permittivity is determined from the boundary only.
To verify the measurement, with my colleagues we used the S21 as well as the Brewster angle ; the agreement was good and the normal-incidence method was, in fact, more accurate than the verification method.
Please see the paper for details.

I also agree that Agilent White paper on testing dielectrics is useful; the problem is that calibrated fixtures are needed.
I have found the normal-incidence method very good and can recommend it. Nothing more than a signal source, a detector and an antenna are needed, and a good sliding mechanism to adjust the antenna to boundary distance.
I used it at 50 GHz which is usually a problem with other test methods.

If you calibrate e.g. a coaxial probe on known dielectrics, I think only measuring S11 can give you good results, too.

 

[Kohi_boy]

Closest to this problem I have used the normal-incidence method to determine the complex permittivity of concrete at ~50 GHz.
Details can be found in olivka, J,: Measuring Concrete Permittivity at MM waves, Internat. Journal of IR and MM Waves, Vol.17, No. 10, 1997, pp. 1673-1683.
From S11 you can derive the standing-wave ratio ; for a full reflection, SWR o, for a particular-material boundary reflection, SWRx. Then the reflection ratio gamma, G = ( SWRo-1)(SWRx+1) / (SWRo+1) (SWRx-1).
Then the complex permittivity k = k' - j k" = [ (G +1) / (G+1)] squared.
I have not thought about using S11 directly as it would involve the transducer parameters between your transmission line and a tested material.

Please let me know your results, it may be quite interesting. Thank you

Your complex permittivity will always be 1 +J0. Maybe you could correct the formula.

 

[kspalla]

Hope these two papers will help you.

 

[biff44]

There are coaxial one-port test fixtures made specifically for computing the above. I think HP/agilent made one. Google them.

I think the theory revolves around a coaxial open circuit should look like S11= 1 with an angle of zero. If S11 magnitude is less than one, then you know the dissipation factor. If the angle is not zero, then you know the er.

(BTW, I once tried making my own coaxial OC transmission line 1 port once out of copper pipe to measure oil permitivity. It did not work out so well...there are lots of parasitics that can dominate. You will need a precise test fixture)

 

[jiripolivka]

Thanks Kohi Boy!

You are right, the first bracket should read (G-1), so the correct formula is
2
k' - jk" = [(G-1)/(G+1)]

Otherwise please see the details in my paper. It did work quite well.

---------- Post added at 16:44 ---------- Previous post was at 16:42 ----------

the [...] should be squared; the text editor shifter the exponent to the left