S-Parameter extraction from FDTD

I have written a 2D fdtd code in matlab and am simulating a simple waveguide. I have been trying to extract the s-parameters from the fields but haven't had any luck yet.

I am not really even sure where to begin. Do i need to take the fft of an applied pulse at the input and output for insertion loss? then integrate over something to get the voltage? I am basically just stuck, seems to pretty much just guess work for me.

Can anyone point me to any useful papers or give me some advice. Thanks

Hi,

try reading these great books, I think they contain the answer to your problem.





enjoy.
aze.

thanks, just checked out 1 of the books and it does clarify a few things that i was doing but wasn't sure if it was right. And it seems that i have the right concept but just must be messing something up. thanks again

Never seen anyone extracting S-parameter from a "2D" field solution. Suggest you take some time to figure what you really want.

why couldn't you get s-params from a 2 d problem? i eventually will go to 3D but I am just trying to go step by step until I understand each part before moving all teh way to 3D. Suppose i excite a wave guide with a TE10 mode, the third-dimension shouldn't matter when extracting the s-params? or am I missing something. I would like to see the s-params showing the cutoff freq or even implement a simple filter and show the s-params. If accuracy is the issue in 2D, I am just doing this for my own understanding, not for alot of accuracy.

Suppose you excite a waveguide with a TE10 mode, and ONLY the TE10 mode, then you have ONLY TE10 mode in the waveguide, which is considered infinitely long in your 2D problem. Without referring to the 3rd dimension, you can't define any s-parameter--where is the port, what is the "voltage" and "current"? Suggest you check a textbook on the definition of the term s-parameter.

or, do you want to calculate the transmission and reflection coefficients?

Won't the s-parameters be equal to the reflection and tranmsission coefficient assuming that each end of the waveguide has an ABC.

Also, why do i need three dimensions to define a port? I did look for a reason but i guess i still don't understand. And from my understanding, can't I just use the E-fields to calculate s-params becasue they should be proportional to voltage, or is that just in the TLM method.

hy alffnot,

I can not help very much in the FDTD technicalities but for sure you can solve for the S parameters of a rectangular waveguide without using the third dimension (that is wg. hight) provided that your discontinuities (wg. steps) do not change the wg. hight and provided that the wg is excited by a TEX0 mode (second index must be 0 so that the field is constant in the y direction).

thats what i thought but loucy says different, so i am just a little thrown off. thanks

lagrange is correct. I thought you were solving a waveguide "eigen-wave" problem and your 2D were the cross-section of the waveguide. Now I recognize in fact 1 of your 2D is actually the longitudinal direction (which was the 3rd dimension that I talked about above), and you are solving a 2D wave propagation problem. Obviously you know beforehand all the modes that could be excited in the waveguide. Yes you can get the s-parameter. Sorry for the misleading comments above.

There are many ways to "EXTRACT" the s-parameter. Each method is appropriate at only a certain circumstance corresponding to:
1. the pusle shape -f(t)- of your excitation.
2. the mode shape -f(x)- of your excitation (are you excitating only 1 mode, or in fact a series of modes?)
3. the way your excitation applied (hard source or soft source).
4. the ability to record the fields at only a few locations or a large number of them.
5. the absorbing boundary condition and the specifics of the problem, which determine the modal contents at the locations where you record the field.
6. other factors... (that I am not able to recall at this point)

Let's denote your 2D as x and z. One assumption in your "project" is that the field distribution along y is known (found in separate analysis). It could be uniform (f=constant), as pointed out by lagrange. f could also be non-uniform, but remain unchanged along the longitudinal dimension z. Somebody would call this latter case a 3-D problem that can be solved in 2D, (this might be the source of the confusion in my end.)

In the most simple senario, you implement some absorbing boundary condition, apply some source at z=zs, record the time signals (fields) at z=zin and z=zout. Normally one would make |zin-z0| big so that "higher order modes have decayed significantly". In other words, it is better to carefully select the "measurement" points (zin, zout) so that they are at some distance from any discontinuities. In this way, you can easily get Vin(t), Iin(t), Vout(x,t) and Iout(t) corresponding to the foundametal mode. Then these four V and I are transformed into the frequency domain. With the knowledge of mode-impedance (found from textbook or separate analysis), the V(f) and I(f) are "transformed" into the so-called "wave signals" coming in and out of the planes zin and zout. You can then calculate the s-parameter's in a straightforward manner.

The above senario is most simple because you don't need to pay much attention to the items (1-6) listed earlier. The signals you "measured" at zin and zout are "pure" (only foundamental mode component). It is simple also because you know the mode shape, the propagation constant, the mode impedance. Otherwise, you really need to "extract" the "wave signals" and the s-parameters. I think this "extraction" processe is partially science and partially "art". There are too much to talk about here. If you have any specific question, I would be happy to discuss it further with you.

thanks alot, i guess i should have been more clear on the problem i was solving. thanks again