Coplanar Strip lines Z paramter graphs a spike using HFSS 12

Hello

I need help with Coplanar strip lines. I have attached the diagram and results with the formula used for the dimensions of the coplanar strips to find Zo, characteristic impedance of the striplines. I used formulas as described in the book by Simons called "Coplanar Waveguide Circuits, components and system". The formula involved elliptical integrals and I used Matlab to solve those formula.

The simulation results in a spike for Z21 (Z paramter between port 1 and port 2) at around 6 Ghz. I do not understand why this spike should appear at that frequency.

Specifications:

Strip length: 20mm
Strip width: 2.8mm
Gap between strips: 0.5mm
Thickness of strip: 0.017mm
material: Copper

Substrate height or thickness: 1.575mm
Substrate relative permittivity: 2.2 (Rogers 4880 Duroid)

Two wave ports at the ends of the strips.
No ground plane

Results:
Using Matlab, Zo, impedance = 130 ohm

Using HFSS version 12: Spike down all the way for for Real part of Z parameter at around 6.15 GHz. Spike down and then up for imaginary part at around the same frequency.

I will appreciate if somebody helps in understanding why this spike appears and what I could do to get the correct results.

Duuuhh my mistake, did not check what parameter you were plotting..... I think you can easily get the S parameters (in 50 ohm mode) in HFSS and then you can calculate Zo from the reflection coefficient equation.
Now, people are telling you that Zo does not change versus frequency....it does change, there is no such thing as zero loss transmission line, but if you have low loss the changes will be small and it will be close to the value of Zo=sqrt(L/C)

The peak you see is becasue you are hitting a resonance / impedance transformation at that point.... due to the natural impedance transformation tha occur when you have a tranmission line terminated in something different that a Zo load. the plot shows a reactive part that basically goes to zero and then changes sign.
How to fix it?? check what is generating the reactive element in the first place...

Z21 is something different than the line impedance Z0 that you calculated in Matlab.
The spike in Z21 is what you expect in theory for a transmission line with this length.

If you want to check the line Z0, you are looking at the wrong parameter.

Hello Volker,

Thanks for your reply. I will appreciate if you could explain why the spike should appear or tell me any reference sources like websites or books that explain about coplanar strip lines and explain the spike.

My goal for the design was to get the Zo, characteristic impedance, for the striplines with the specifications above. In theory I should have gotten 130 ohm for the above specifications. But HFSS results in spike for Z parameter port 2 vs port 1 (Z21).

I would assume that Zo, characteristic impedance, could be found by plotting Z parameter, and see where the imaginary curve crosses the zero line on the graph and then what is the value of the real curve at that point. The value on the real curve at Im(Z)=0 is the characteristic impedance, Zo.

If this is not the approach to find Zo, characterisitic impedance, for the case of coplanar strip lines, I will really appreciate if you please explain how can I find it using HFSS12. This is related to my work and I should find a way out for this.

Many thanks in advance.

mequitnever said:

In theory I should have gotten 130 ohm for the above specifications. But HFSS results in spike for Z parameter port 2 vs port 1 (Z21).

Click to expand...

You are looking at the wrong parameter. Z21 has nothing to do with line impedance Z0. These are completey different parameters.

With Z21, you calculate the voltage v2 at the end of the line (port 2) for a current i1 at the beginning of the line (port 1), when the line is open ended (i2=0).
As you know, at high frequency, the current and voltage are NOT everywhere the same over the length of the line. They will vary along the line according to the wavelength. This is why depending on the ratio of line length/wave length, the Z21 value changes. In other words, Z21 changes over frequency, as seen in your plot. It is not a useful parameter to define your line properties.

The "line impedance" Z0 is something different. It is not calculated from Z21. The line impedance is the impedance that your signal sees into the line (input impedance at port 1) if the line is infinitely long or perfectly match (i.e. if no signal is reflected back from the end of the line).

Sounds like you want to look at Z11 then? No, because you still have reflection from the other end of the line. Using Z11 for Z0 only works if your line runs into an absorbing boundary on the other end.

How to get Z0? That depends on the tool. I use Sonnet which plots Z0 as a side result of port calibration. I am not using HFSS, but maybe they habe something similar in the ports/modes data. You can also analyze short piece of line and calculate the R'L'C'G' values per unit length, and then calculate Z0 from these values. I had shown that method **broken link removed** on pages 7/8.
There are other ways to calculate Z0, too. I looked into my collection of equations files and found this: Z0 = (1/((y11*y11-y12*y12)^(1/2))) That should be easy, so maybe you want to try that.

volker_muehlhaus said:

Z0 = (1/((y11*y11-y12*y12)^(1/2))) That should be easy, so maybe you want to try that.

Click to expand...

Just like Z21 varies with frequency, then y11 and y12 would be varying with frequency as well. So how would I know which value of y11 and y12 to pick to find Zo, if I choose to go by this method.

Again, thanks for your reply. Your document is incredibly helpful.

Just select any one point as ref point, calculate all the parameters at this point, then can get Z0. Although parameters maybe change along with ref point, but Z0 shouldn't change at all.