Building Bridges Pt. 3 – Time And Time Again

Let’s talk about time for a moment. As in Time Domain. In the previous chapter I stated that one problem with transient\time-domain (TD) methods is the structured mesh, limiting accurate modeling to square-ish structures. What I’m presenting here is not necessarily a problem with TD methods, rather a designation for it. Namely, TD methods are not suitable for some problems, but more suitable than frequency-domain (FD) methods for others.

Consider the case of this patch Antenna:

I know you are thinking to yourself how the meshing is significantly better, right? Well, that’s because I’ve been debugging like crazy and it is a lot more robust and useful now. Back to our subject, however, one would expect such a simple and square structure to run very fast, right?

Well, no. Before I answer why, I’ll drop one more hint. This patch was printed on a 1.6_{mm} thick substrate and designed for 2.4_{GHz}. Do you know now why it’s going to run very slowly?

One more hint: Here is the return loss graph:

That’s it, no more hints. Got it?

Going back to signal processing: A narrower frequency domain impulse response of a filter, results in a longer time domain response. Meaning, such a narrow-band structure would “ring” for a very long time, once excited by a pulse. Let’s see how long:

Or in run-time:

As you can see, the energy in this simulation keeps going up and down, even if the general trend is downward. However, as it approaches the -50_{dB} marker, it barely dissipates. This means that either there is a larger resonator (such as the PCB ground) in the simulation that is still ringing, or that there is a numerical problem, e.g. floating point precision trouble that sometime happens with small numbers. This could be resolved by adding more losses to the simulation, or maybe just designing a proper patch with a thicker substrate.

So as my Sensei says: Know your enemy, know yourself. When dealing with narrow-band structures, choose the right solver. Of course, it’s not always available open-source, is it.

Short post this time, but I’m wrapping up this series for now. I would like to thank Thorsten Liebig for publishing this cool piece of software as open-source and also taking the time to answer some of my annoying questions.

Let’s start designing!

Leave a Reply

Your email address will not be published. Required fields are marked *