measurement of effective dielectric constant

[lag]

effective dielectric constant

I want to know how to measure effective dielectric constant using HFSS or ADS or ansoft designer. I am working on design of coupled strip line and i need information regarding measurement of effective dielectric constant.

 

[Manjunatha_hv]

effective dielectric

Hello,

Sonnet em lite version has the Eeff. Effective Dielectric Constatnt Measurement...
https://www.sonnetsoftware.com/products/lite/

& it Works with Agilent ADS

Eeff: Effective dielectric constant of the transmission line connected to the port.

Z0: TEM equivalent characteristic impedance of the transmission line, in ohms.


---manju---

 

[mauloftin]

z0 and effective dielectric sonnet lite

Hi,
may be try attachment.

 

[tayfeh]

you can contact Dr. Atabak rashidian : **broken link removed** , he is an expert in dielectric materials, especially dielectric resonator antennas, and willing to help interesting people.

 

[flyhigh]

Hi

You can determine the effective dielectric constant and characteristic impedance for the transmission line by using the S parameters of a section of line obtained by EM simulations or measurements.

Use the following set of equations:



Zo is the normalizing impedance of the system (50 Ohm).
For the best accuracy line length should be approximately one quarterwavelength.

Taken from:

Hong, Lancaster – Microstrip Filters for RF/Microwave Applications, John Wiley & Sons, 2001

flyhigh

 

[biff44]

You know, it is not so easy to curve match actual S parameter data on an unknown transmission line to figure out the real and imaginary parts of the dielectric constant. You will get ripples in insertion loss and vswr that do not exactly match up to the EM simulations, and then what do you do?
Been there, done that!

You might want to also use resonant structures, like half wave lightly coupled resonators, to augment the data.

 

[Joe_User]

... Taken from:
Hong, Lancaster – Microstrip Filters for RF/Microwave Applications, John Wiley & Sons, 2001

I believe that equation is only valid when the Z0 of the transmission line equals the Z0 of the S-parameters. So if you have a 60 ohm line, but your S-parameters are 50 ohm S-parameters, you need to renormalize your S-parameters to 60 ohms. Of course, if you don't know the Z0 of you transmission line, you can't use that equation.

Why not use ADS's transmission line tool, Linecalc? AWR also has one called TXline.

 

[flyhigh]

Hi

No Joe_User, Zc is the calculated transmission line characteristic impedance, Zo is the normalizing impedance of 50 Ohm, it is exact method and it works 100% fine for all the transmission lines one can imagine as opose to the ADS LineCalc that uses approximate formulas for a limited set of lines.

flyhigh

 

[umair67]

U can consult Microstrip filters for RF Microwave Applications By M J Lancaster 2001 edition CHAPTER 3 Or4.U will find equations to calculate effective dielectric constant.

 

[Joe_User]

No Joe_User, Zc is the calculated transmission line characteristic impedance, Zo is the normalizing impedance of 50 Ohm, it is exact method and it works 100% fine for all the transmission lines one can imagine as opose to the ADS LineCalc that uses approximate formulas for a limited set of lines.

flyhigh: I was talking about equation 5.31 which does not use Zc (TRL characteristic impedance) or Z0 (normalizing impedance). It only uses the phase of S21. If the line is not matched, then the added reflections can modify S21 phase. Thus, you can't use S21 phase to calculate the effective dielectric constant unless the line is perfectly matched... at least not using equation 5.31.

 

[flyhigh]

" If the line is not matched, then the added reflections can modify S21 phase."


Can you explain this please, looks very promissing!

flyhigh

 

[Joe_User]

I am not sure how well I can explain this, but let me try it with an example:

Matched Line Case: Let's say you have a lossless line that is 20 degrees long. The voltage wave travels 20 degrees from port 1 to port 2. Since there is no reflection, S21 = 1.0 <-20°.

Unmatched Line Case: Now let's say the line is not matched and 50% of the wave is reflected at port 2. The voltage wave travels 20 degrees, so if you stopped time right then, S21 would be 0.5 <-20°. But that reflected wave travels back towards port 1. Let's say 50% of this wave is reflected off port 1 back to port 2, so the forward wave (on its second pass) has a magnitude of 0.25 and a phase of 60 degrees (assuming the reflections don't change its phase) by the time it makes it to port 2. If 50% is reflected and 50% is transmitted, this voltage wave should have a magnitude of 0.125 and a phase of -60 degrees. This voltage wave ADDS to the first voltage wave. You need to add these two vectors: the 0.5<-20 and the 0.125<-60 to get the total voltage wave at port 2. This is just from the first two passes of the wave. There are an infinite number of them, each one with less effect than the previous one.

Thus S21 phase is not equal to -20 degrees but some other value.

Does this make sense? I think most people are familiar with this concept but sometimes only think about the effect on S11, but it also affects S21 phase.

 

[flyhigh]

"Thus S21 phase is not equal to -20 degrees but some other value. "

What is that other value? We are engineers, not phylosophers!

Equation, Please!

flyhigh

 

[loucy]

Equation 5.31 above is valid when there is only one forward propagating wave on the transmission line. In this case the phase (of the voltage along the line) is linear with respect to the length L, with a factor proportional to the square root of effective Epsilon. If the transmission line is not connected to a matched load, then there will be both forward and backward propagating wave, then the phase of the voltage will no longer be linear with respect to the length, hence eq. 5.31 is no valid.

 

[flyhigh]

Equation 5.31 above is valid when there is only one forward propagating wave on the transmission line. In this case the phase (of the voltage along the line) is linear with respect to the length L, with a factor proportional to the square root of effective Epsilon. If the transmission line is not connected to a matched load, then there will be both forward and backward propagating wave, then the phase of the voltage will no longer be linear with respect to the length, hence eq. 5.31 is no valid.

It is valid for quarterwavelength line, as stated above, try it yourself!

flyhigh

 

[loucy]

L should be around a quarter wavelength for better accuracy. L doesn't have to be exactly a quarter wavelength. In fact if you know beforehand the exact value of quarter wavelength, there is no need to perform the measurement, all quantities on the right hand side of eq. 5.31 are known.

The keyword in the paragraph after eq. 5.31 is "de-embedded". De-embedding could mean different things. In this case, it should be interpreted as requiring the matched load to have the same characteristic impedance of the transmission line.

 

[flyhigh]

Loucy

the trick is that cos and sin of 90deg are 1 and 0 respectfully and the phase information of bouncing waves are gone. Within +/- 10 deg it is still a very good approximation and doesn't affect the accuracy of the calculation.

Make a simple circuit in a simulator and tune Zc of a quarterwavelength line and observe phase of S21 if you have any doubt about it.

If you are still not convinced, perhaps you should complain to Wiley Interscience for letting Hong and Lancaster publish a complete rubish in their book!


flyhigh

 

[loucy]

flyhigh,

I am not sure how to interpret your statement that the "phase information of bouncing waves are gone". Do you mean that the phase of S21 would not be affected by the phase of the bouncing (multiply reflected) wave(s)?

I agree equation 5.31 could give a good approximate effective epsilon when the mismatch is small. This might be sufficient for one's application, but it doesn't change the fact that eq 5.31 is invalid when the load is not of a characterisitic impedance.

There is well established literature for calculation of the permittivity when the source and load are not matched. Just go to IEEEXplore and search for "transmission reflection method" for dielectric measurement. Among other things, you can find the euqation for s11, s21, and uncertainty analysis (and on how to choose the length for higher accuracy). For the case of inserting a segment of transmission line of Zc into an otherwise uniform transimission line of Zo, S21=(1-gamma^2)*T/(1-gamma^2*T^2), where gamma=(Zc-Zo)/(Zc+Zo), T=exp(-j*K0*Sqrt[Epsilon_r*Mu_r]*L). The phase term of Eq5.31 is the phase of T here (when gamma=0).

There is nothing wrong in the above book section by Hong and Lancaster. What is lacking is a clearer explanation for the statement "the S-parameters are de-embedded". This could mean different things in the eyes of different readers.

 

[flyhigh]

"I am not sure how to interpret your statement that the "phase information of bouncing waves are gone". Do you mean that the phase of S21 would not be affected by the phase of the bouncing (multiply reflected) wave(s)?"

Yes! That is the trick with quarterwavelength!

"I agree equation 5.31 could give a good approximate effective epsilon when the mismatch is small."

Works for 10<Zc <150 Ohm


"the S-parameters are de-embedded"

Having a book in my hands it means that in Eeff calculation the length of a line is taken between reference planes as set in Sonnet simulation.

Regarding a search on IEEEXplore, I published a paper there myself!

flyhigh

 

[Joe_User]

I think you are right, that if you are close to a quarter wave and your Zc is relatively close to your Z0, you can use the simple equation. Flyhigh suggested 10<Zc <150 Ohm and +/- 10 degrees. I tried simulating a case on the extreme of this: Zc=10 ohms, 80 degree long line. This gives 86 degrees. If I did my math right, that works out to be about a 15% error in Ere. That's probably the worst case error.

You could also take Manju's advice and just simulate the thing in Sonnet (Lite?). It reports the Ere value.