Why is CPW so dispersive !?

[jslee]

cpw current distribution

Hello everyone：
I do some simulations on Microstrip Line using HFSS. Please see the attachment. The conductor and substrate of Microstrip Line are copper and dielectric. The conductiviy of copper is 5.8*10^7 S/m. I wonder that the chracteristic impedance varies with frequency so sharply. The S11 is lowest at low frequeny width reference impedance of 50Ohm,but the simulation result of magnitude of Zo is around 56Ohm. I am curious how the HFSS calculate the Zo. I read the manu said that the Zo is obtained by Zpi, Zpv, or Zvi by calculting the fileds of 2D port structure. The method is right, but its result cannot make me believe. Microstrip line shall not be dispersive. If I use LineCalc in ADS to simuate the Zo， the Zo is almost const with frequency. Please give some comments on these issue. Thank you very much.

 

[rfmw]

zpi zvi zpv cpw

Why the title CPW, when you're asking help for microstrip?


Show a picture of your structure.

 

[elektr0]

@jslee
Hallo,

doesnt matter if we are talking about MSL or CPW. If there is more than one dielectric sheet in the transverse plane, the structure becomes dispersive.
The phase, shown in your ppt document agrees with measurements.
Anyway, try to enlarge the waveguide port a bit and look at the change in Z0.
You can specify a minimum mesh cell number for the port calculations in the solution menu.

At the moment I work on a similar problem - see my post about "gettin Z0 from gamma".
You should study the deviations between the ZPI and ZPU characteristic impedance. This is another side effect of arbitrary waveguides, Z0 definition becomes ambigious.
ZPI is default in HFSS. Never use ZUI.

elektr0

 

[jslee]

Sorry! The topic should be microstrip line. Actually, CPW also has the same phenomenon.

Added after 5 minutes:

The microstripline structure is shown in the figure.

Added after 22 minutes:

The microstripline structure is shown in the attachment.

 

[jslee]

Hi elektr0：
The micristrip line is dispersive, but the result is hard to believe. The low freuqnecy Zo is as high as 56 Ohm. If this is correct, the returen loss shall be the worst at low freuqeny. However, the return loss is lowest at low frequeny.The simulation results shown in attachment uses driven-terminal solution type. It will need to give a reference impedance with default 50Ohm.
I am curious about how the HFSS do caculate the S parameter. I have read the articles you have posted. Did you find out how the HFSS tranforms the S parameters to Z parameters as the chracteristic impedance is complex?
Besides, the size of waveport doesn't affect the response apprantly. This is reasonable as i expected.
If i wanna design a Zo of 50 ohm microstripline with practical material, how should i get the size of structure by using HFSS tool? This is the most concerned.
Anyone ever did the design?
Sincerely, Andy

 

[rautio]

Hi JSLee -- If you are going to use this microstrip line to connect to a 3-D arbitrary structure, then using a volume mesher like HFSS is appropriate, and you want to make sure you are getting reasonable results before proceeding.

However, if you are considering only planar strucutures (including metal thickness), then you should be using any planar solver. Planar solvers are much more efficient and much more accurate (both!) when applied to planar structures. I usually recommend Agilent Momentum for unshielded and Sonnet for shielded (I work for Sonnet). The shielded approach has the advantage of being the most accurate. You can get a free SonnetLite (shielded planar EM analysis, www.sonnetsoftware.com) that will solve this problem easily. When you download it and install it, do Help->Tutorials first. Then you will be ready to do this problem in about 45 minutes. If you have problems, put a posting on the Sonnet Forum. Some very capable people keep a close watch there and can be very helpuful. We often recommend using both Sonnet and Momentum to analyze the same problem when you have a high cost of failure situation. Why take chances "trusting" just one tool?

If you must use a volume mesher, I agree that the power-current definition is most likely to give a good answer. However, if you are going to use the Zo in a circuit theory (nodal, schematic) analysis, then you should use the TEM equivalent Zo. The TEM equivalent Zo will give the circuit theory tool (TEM) transmission line the same current and voltage at the transmission line terminals as you have in the EM analysis. One chacteristic of TEM eqivalent Zo is that as you increase frequency, the Zo first goes down, then it starts going back up. This has been verified by experiment. I can email you several papers on both the theory and experiment if you like. TEM equivalent Zo is what Sonnet calculates. And you don't have to worry about which kind of port to use, there is only one kind, and it is exactly calibrated. I can send you papers on that too.

As for the low frequency behavior of Zo, it might actually be OK. Remember that S11 is determined by Zo for an infinitely long line. You can simulate an infinite line by terminintating any actuall length 56 Ohm line in a 56 Ohm resistor. (You need a complex resistor for a complex Zo.) You will indeed have a high SWR. What you are probably doing is terminating a short length of line (a few degrees, perhaps?) in a 50 Ohm resistor and indeed you are getting a low SWR.

 

[jslee]

Hi rautio：
As far as I know, HFSS will solve the 2D waveport first. The results of 2D wave port will become the initial codition for the 3D structure. If checking the solve only option in the simulation setup, HFSS do planar simulation quickly and effeicienty. I have no ideal which EM tool is more accurate in planar simulation. Thank for your seggestion! I will try different tool to verify the results. Could you email the papaers to me? My email address is andy11.ee94g@nctu.edu.tw

 

[rautio]

Hi jslee -- I just sent the papers to you in an email. I would post them here, but I am not sure about copyright.

A 2-D analysis is restricted to using transverse field quantities to guess at Zo. Which definition is best is now a philosphical discussion, it is not an engineering discussion.

The TEM equivialent Zo requires a full field analysis of a length of line, a 2-D cross section analysis is not sufficient. Any kind of "wave port" is inappropriate for this purpose. The TEM equivalent Zo provides the only Zo that gives the correct current-voltage relationships at the terminals of a transmission line used in circuit theory. All other definitions of Zo necessarily give a different answer and thus are necessarily wrong when used in circuit theory... the TEM equivalent Zo is the only correct answer for microstrip, or any transmission line that is lossy or is inhomogenous.

I have published extensive reearch on EM analysis error. Go to IEEE Xplore and search on my last name to see some of that research. I find it to be an incredibly interesting and rich research area. However, most other researchers are uninterested, content to say, "We have good agreement," and then they are on to their next paper. A quick way to judge qualitatively the accuracy of an EM analysis result is to look at the current distribution. A good current distribution will be smooth with a clear high edge current. Keep in mind that while this is a necessary condition for a high quality result, it is not sufficient.

 

[jslee]

Hi rautio:
Thank you for your papers. I will read these papers in near future. Could you give some comments about the phenomenon in HFSS? I am still curious about the results I have gotten from HFSS. Of course, I will try another tool to verify this.
As to the dependence of Zo on frequency, actually, this depends on the transimission line structure. For conventional microstrip line, there is a layer of dielectricl between signal and ground. Therefore, the Zo will increase as the frequency decrease in low frequency band. For CPW, the behavior is opposite if the CPW has a lossy substrate. These behavior can be known from the formula of Zo in any texbook and HFSS also give the same trend, but too rapidly.
I am interisted that in microstrip line case, the Zo will approach infinity in very low frequency assuming that the dielectric is lossless. However, the reflection, definitely, will be very low. We just look the line as a lumped circuit. What does Zo mean in low freuqency or DC for the Microstrip Line with lossless dielectric and metal of Copper? Please give me some hints. Thank you very much.
Jslee

 

[rautio]

Hi Jslee -- Zo has very little significance at low frequency. At DC, when we connect a light bulb to a battery, the light bulb lights up, no problem, even though Zo is infinite. This is because what matters for Zo is the length of the line in terms of wavelengths. Thus, for a given length of line, when the line is very short compared to wavelength, Zo has no effect on the result.

How short (compared to wavelength) must a line be before Zo has no effect? That depends on your requirements. There is an equation for the reflection coefficient of a length of line of given Zo terminated in Zt. This is the equation that is used for the Smith chart. Play with that equation for Beta*L small and you will see what I mean.

 

[ptshao]

Hi, maybe I can answer your question.
Please take a look at the definition of characteristic impedance: Z=sqrt((jwL+R)/(jwC+G)). W (radian frequency) goes to zero if frequency f goes to zero, which means Z=sqrt(R/G) in this case. In most cases, G tends to be zero, which makes Z infitely large due to the large value of R/G.
Hope this is helpful!\]