Help, measuring dielectric constant with parallel plate capacitor

[mtxx]

I wish to make a fixture/tool that is able to measure dielectric constant.

after researching through the web and read numerous papers and application note.
i decided to try this **broken link removed**
at page 5. using parallel plate capacitor method.

The idea is simple, as long i am able to measure the capacitance the air and my MUT (material under test)
the dielectric constant er is the ratio of MUT capacitance over air capacitance.

So this is what i made.
i used 2 round copper plate, 2.5cm diameter, 0.05cm thick, to be the conducting plate.
solder 2 SMA connector to each copper plate.
connect one copper plate to the ground of the SMA connector, this makes one of the plate the ground.
this setup is attached to a sliding fixture so that it can move freely.
VNA is used to measure the S11, from the S11, the impedance can be found.

The VNA is calibrated using calkit before measurement, but the measurement plane is at the tip of the SMA cable.
this means the unwanted effects such as SMA connector, are included as well.
so the impedance measured includes everything between the tip of the SMA cables.

first i insert the MUT between plates, and clamp it tightly. take the S11 reading.
next, remove the MUT carefully without moving the plates, take the S11 reading.

this way i have 2 set of impedance.
Zt,sample = total impedance of the test fixture and the MUT
Zt,air = total impedance of the test fixture and air

the impedance of air i assume to be
Zco = 1/ (i*w*Co)
Co is air capacitance, Co = eo*(area of plates)/(distance between plates)
distance between plates = my MUT thickness

i assume my fixture has impedance of Zs.
so,

Zt,air = Zs + Zco----------------(1)
Zt,sample = Zs + Zsample -------(2)

from eq(1)
Zt,air is measured by VNA
Zco is calculated, so i can get Zs

from eq(2), i can get Zsample

with Zsample, i can calculate what is
Cp & Rp, the parallel equivalent capacitor and resistor.

then i use the formula in the agilent note above
er'=Cp/Co
er''=1/w.Rp.Co

ideally the above method should work,
but i tried measuring a FR4 board, the dielectric constant i got is 0.9 - 1.1
FR4 dielectric constant should be 4 right?

what could be wrong in my method?
Please if you spot any error or have any suggestions,
please let me know, i will be very grateful.

 

[BradtheRad]

1.

Are you applying AC or DC? It isn't clear from your description.

The linked document has graphs showing Hz as the X axis. I guess you're supposed to apply AC.

It may make a difference what frequency you apply (low or high).

Applying DC can only give a momentary reading.

2.

Do your plates make electrical contact with the MUT?

If your MUT conducts in the slightest, it can throw off the outcome. I suppose it would raise the reading. However you seem to have a low reading, so that suggests there is no leakage through the MUT.

 

[mtxx]

1.

Are you applying AC or DC? It isn't clear from your description.

The linked document has graphs showing Hz as the X axis. I guess you're supposed to apply AC.

It may make a difference what frequency you apply (low or high).

Applying DC can only give a momentary reading.

2.

Do your plates make electrical contact with the MUT?

If your MUT conducts in the slightest, it can throw off the outcome. I suppose it would raise the reading. However you seem to have a low reading, so that suggests there is no leakage through the MUT.

1. Its AC, i mentioned using VNA to measure, its measuring in AC.
the frequency i start from 40MHz to 8GHz, but readings higher than 200MHz are dont make sense, such as negative value. so i only take from 40MHz-200MHz
2. The MUT is not a conductor, its a dielectric, FR4 to be exact.

After some brain storming, i suspect probably its the fringing capacitance causing error.
the formula i use to calculate air capacitance is an ideal one,
i look through information on this, and found some info on fringing capacitance
**broken link removed**

however, using fringing capacitance correction mentioned in this paper, all 3 of them,
one by the auther, one by kirchhoff, and one by Shen,
all 3 of them does not provide the correct dielectric constant. in fact the results is worst. between 0.6-1.5

 

[volker_muehlhaus]

The way how you use and connect the coax cable between the plates does not make sense to me. You make a single connection, so this behaves like a simple wire. The series inductance of that wire is part of your results and changes the resonance frequency.

 

[mtxx]

The coaxial wire is indeed a simple wire to connect the 2nd plate to the ground.
Based on previous experience, if use normal wire, every time it change position or slightly bend, it will change to a difference inductance value.
Its too sensitive to changes, causing the vna reading to change as well.

If use coaxial wire, it won't varies a lot, I can bend it a little, and it won't cause any change to the vna reading.

- - - Updated - - -

The coaxial wire is indeed a simple wire to connect the 2nd plate to the ground.
Based on previous experience, if use normal wire, every time it change position or slightly bend, it will change to a difference inductance value.
Its too sensitive to changes, causing the vna reading to change as well.

If use coaxial wire, it won't varies a lot, I can bend it a little, and it won't cause any change to the vna reading.

About the additional inductance, I include it in the fixture impedance, Zs. It should be the same whether measuring air or my mut. Thus they should cancel out. At least I hope so.

 

[pstuckey]

This test setup is not actually measuring S11 of the DUT.

Think of it this way, you are presenting some power (at a frequency) through port 1 of the VNA and then measuring how much comes back into port 1. Some portion of that power is reflected by the sample (S11) and some passes through the sample. However, with your test setup the power that passes through the sample sees an open circuit and gets reflected right back into port 1 of the VNA. To measure S11 you need to terminate the power that passes through the DUT. A fifty ohm load on the second SMA would do that, or you could just connect it to port two of the VNA.

Also, I agree with Volker, I don't understand why the coax is connecting the two plates.

 

[FvM]

If I remember right, Agilent has published application notes about microwave permittivity measurements.

For GHz frequencies and FR4 substrate, a transmission line (e.g. microstrip) measurement seems much better suited.

 

[mtxx]

I see, I will try it tomorrow when I get back to my lab.
I will connect the 2nd plate to port 2 and try again.

Thank you for your suggestion. I remember you told me this in my other thread I asked.
But I don't have a 50 ohm termination. I will connected it to port 2 if its the same.

- - - Updated - - -

If I remember right, Agilent has published application notes about microwave permittivity measurements.

For GHz frequencies and FR4 substrate, a transmission line (e.g. microstrip) measurement seems much better suited.

Yes, indeed, i I've read those notes. Previously I used wave guides. But this method and the microsrip method require calibration, TRL calibration to be exact. Unfortunately I realise its impossible to be done without agilent vna. Even if I have a perfect trl standard, the method of calculation is proprietary to agilent. There really is no way to calculate it manually. Even simulation in mat lab using the fundamental theory in pozar text book fail. That's why I'm, avoiding trl calibration.

 

[mtxx]

This test setup is not actually measuring S11 of the DUT.

To measure S11 you need to terminate the power that passes through the DUT. A fifty ohm load on the second SMA would do that, or you could just connect it to port two of the VNA.

Dear pstuckey,

i've did as you suggested, i connect the 2nd ground plate to the VNA port 2.
and repeat my measurement. using the method i stated in the first post, these are my results.

top left: S11 in dB vs frequency
Bottom left: S11 phase vs frequency
top right: |Z| vs frequency
bottom right: calculated er' vs frequency.

the calculated er is higher than previous value, but still not in the 4.7 range.
this material is a PCB board, it is written in the spects sheet to have er of 4.6, the thickness is 1.6mm

 

[godfreyl]

Why are you plotting results on a linear scale from 0 to 4 GHz?

You said earlier that the results above 200MHz don't make sense, which is understandable. Surely it would be better to test between 0 and 100MHz?

- - - Updated - - -

IMHO, If you want to measure at very high frequencies, you need to change your whole wiring layout.

To start with, the connection points should not be soldered to the center of the plates, but rather at the edge. That way the conection points are right next to each other and you don't need a big loop of wire going right around the DUT.

 

[mtxx]

Why are you plotting results on a linear scale from 0 to 4 GHz?

You said earlier that the results above 200MHz don't make sense, which is understandable. Surely it would be better to test between 0 and 100MHz?

- - - Updated - - -

IMHO, If you want to measure at very high frequencies, you need to change your whole wiring layout.

To start with, the connection points should not be soldered to the center of the plates, but rather at the edge. That way the conection points are right next to each other and you don't need a big loop of wire going right around the DUT.

Just to show you guys the overall results on a large scale.
other than this, all my results are from 40MHz-200MHz. (40MHz is the lowest my vna able to measure)

i did a change to the model, i'm measure using a 2 port network. both plates are connected to each port.
and their ground connected by a wire.

First i directly take the S11 measured and change it into Z using Z=50(1+S11)/(1-S11), but the output pattern is totally weird.
then i read some notes saying that in order to get a 1port S11 from a 2 port measurement, need to do conversion.
S11_1port= S11-S12*S21/(1+S22)
using this S11 to get Zo and proceed with the calculations also yields completely unregonizable results.

finally, i read something useful
according to this book: RF Circuit design, theory and application, written by reinhold lidwig and pavel bretchko

the impedance of a 2 port network is the B parameters.
B parameter is a member of the ABCD parameter, which can be calculated using the S parameters.
impedance = B =Zo*( (1+S11)(1+S22)-S12*S21 ) / (2*S21)

using this impedance value and proceed with my calculations, i got

red color: without any fringging capacitance correction
blue&green: using fringging capacitance correction based on 2 different formular. one is kirchoff, one more from a conference paper.

i'm begining to think the calculation method that i use is inaccurate. the one described in the first post.
or maybe the fixture impedance cant be represented as a whole Zs and be cancelled of by subtraction.

is there a difference if the sma connector pin being soldered at the center and at the edge?