Measurement of S21 (transmission) of glass

Hi everyone,
I've measured the transmission of a glass material at microwave frequency range, using two horn antennas, and absorbers(RAM) to limit reflections. The S21(dB) received using the VNA gave me unconvincing results( not really sure though). There was insignificant change in magnitude between S21(air) dB and S21(glass) dB. However there was significant difference of around 11deg in phase between S21(air) deg and S21(glass) deg. Can any experienced person say whether the readings I got are ok or not?
Many Thanks
Henry797

I would expect frequency independent Er of glass in a first order, so the microwave value would be around 1.5 as for visilible light. Other than for visible light, reflection losses depend strongly on window thickness and wavelength.

I think your measurement should be correct. When an EM wave pass through a dielectric material a part of it is reflected back, another part is absorbed and another part is transmitted. The reflection also strongly depends from the angle of incidence of the wave to the surface of the medium.
In order not to have negligible reflection and absorption losses the glass have to be very thick or should be a special type.
Furthermore the wave will change its velocity according to the dielectric constant of the medium [vm=c/sqrt(epsilon) where c is the speed of the ligth], then the phase will vary depending from both dielectric constant an thickness.
Can you specify the type of glass (if known) the thickness, the frequency and the angle of incidence (probably it's normal to the surface of the glass)

Thanks guys for replying
@FvM: I'm sorry, but might have not understood my question. And was wondering what the term "microwave value" stands for? I only asked whether it is usual to get a narrow change in magnitude between air and any glass material if you want to measure the dielectric of that very material.
@ albbg: Thanks a lot for your answer. Was indeed very informative. I already knew why the phase changed, but expected the magnitude of transmission(S21) to drop at least 2 dB below. For air it was -42.52 & glass -42.59. However, this is sodalime glass, fr=3.0 GHz, normal to the surface of the glass.
And also albbg, if you happen to have program that extracts the epsilon value of the material under test could you perhaps give me the value for sodalime glass using the above magnitude and phase(air) 0; phase(glass)=11. Or else could suggest a way I could extract epsilon using any website( if known), as I will be using this value in a simulation, but later will write my own coding when I have ample time.
Thanks alot!

I was in fact talking about the microwave value of Er (epsilon) and assumed it to be around 1.5 as it's for visible light. This approximate value should be sufficient for a rough calculation of reflections.

Unfortunately you didn't tell yet about the geometry of your test.
Reflections are a simple consequence of Er discontinuity and will occur in any case. In some cases, the reflection at first and second surface cancel out, this happens if the effective path length is a multiple of λ/2.

I know the refractive index of sodalime glass is 1.5, is that what you're referring as microwave value? And the Er of sodalime glass at microwave range is 7.75, just wanted to measure it myself. While doing so, when I measured the transmission coefficient (S21) of the microwave radiation between two horn antennas and the MUT(sodalime glass) in between, there was no significant degradation in the magnitude of the power of the signal when measured as compared to air.

You are right, I confused n and Er.

Which means that the reflections are stronger. And there are interference effects depending on the glass thickness. You need to consider the complete 3D geometry, including the antennas.

I know my arrangement(setup) for measurement is perfectly alright, as I've measured the S21 of different absorber materials and the magnitude seemed to drastically drop. I was just surprised to see that the insertion loss(dB) was almost insignificant as the glass was introduced in the system.

If the electrical thickness of the glass is a multiple of lambda/2, it does a perfect impedance transformation and the reflections from the air>glass and glass>air interfaces cancel.

The wavelength of the radiation incident on the MUT(glass) is 10cm [lamda=c/(f=3.0 GHz)] and the thickness of the glass I measured is 1mm. The electrical thickness is much lower than the wavelength of the incident radiowave signal. And also I think in this case, the insignificant amount of loss taken place is mostly due to absorption rather than reflection, as I measured S11(dB) reflection coefficient at 3.0GHz frequency and found very low. However, maybe the absorption of the material(glass) is reflected in the phase of the transmission as albbg suggested using the phase velocity concept.

The wavelenghts in air and in the medium are:

λair=c/f and λmedium=c/(f?√ε)

then for a thickness "d", we will have a difference of path, relative to λair, given by:

Δpath=λair?(d/λmedium-d/λair)

so we can calculate the phase as:

λair:360 deg = Δpath:phase

from which:

phase = 360?(d/λmedium-d/λair)

or:

phase = 360?d?f?(√ε-1)/c

from which you can solve with respect to ε.
The problem is that using your figures I have a different result:

f=3GHz, d=1mm, ε=7.75

phase≈6.4 deg.

To obtain 11 deg, instead, you should have a thickness of 1.7 mm or a ε≈16 !

Hi albbg,
Many Thanks for the classical theory for figuring out Er. However, I guess taking into account both S21(dB) and S21(deg) would lead to a more precise value. Using your way I'm sure a phase difference of 11deg wouldn't give a dielectric value close to 7.75, rather gives a very large and unfeasible value of dielectric for glass.

You suggest to use your insertion loss measurement 42.52 dB (air) vs. 42.59 dB (glass) with measured 0.07dB difference? And suggest this loss doubles the electrical delay? Seriously?

It seems that your measurement setup is sensitive to errors, especially with such a thin DUT. Why don't you test with a KNOWN sample, e.g. teflon?