Good day,
My title is perhaps a little vague, but I wasn't sure how to phrase it. I'll try to make it clear in as few words as possible, although I think I'll have to explain at least a few of the aspects to make it clear.
I am using AWR Microwave Office to simulate a planar EM structure using the AXIEM simulator. The planar structure looks like this:
![]()
For scale, the central rounded rectangle is about 500um wide.
Now, it might be a bit of an unconventional shape (this work relates to superconducting qubit design). What we see here is essentially an LC circuit (the large island has C to ground, and hard to see is the little wiggle on the side, which forms the L to ground due to the reactance of the material). That LC circuit is capacitively coupled to a (50 Ohm) transmission line predominantly via the little extrusion in the center, and there are 50 Ohm Edge ports on either side of the transmission line. Also present, but at this point not doing much, is another floating metallic island above the LC circuit. It has no connection to ground, so it simply floats for now and has a C. As for the layer stack, there is 500um of lossless silicon below, the material itself is a lossless (super)conductor of no thickness (but with some inductive reactance), and above is 500um of lossless air.
With this structure I can run an S21 simulation, and I'll find this Lorentzian lineshape centered at the resonance frequency, which is about 6.4 GHz here. As may or may not be obvious to you, this lineshape has a width and depth, related to its quality factor, set by two contributions: the internal quality factor Qi and the coupling quality factor Qc. The first comes from losses intrinsic to the LC circuit, such as losses in the dielectrics (which are set to 0 here). The second comes from the fact that the circuit is coupled to the transmission line, which has its 50 Ohm ports, acting as dissipation channels. This coupling thus causes losses as well, captured by Qc. In an S21 measurement these two contributions can be separated; after all the Qc essentially sets how much the LC circuit radiates into the transmission line, while Qi sets how much is lost in an unmeasured channel.
![]()
What I thus do is export this S21 data (both magnitude and phase) and use expressions known for this effective geometry to find the value of Qi and Qc. For this simulation there are no internal losses, and consistent with that I find a Qc of about 1000, and a Qi of about 5e6; practically infinite compared to Qc and just a result of numerical accuracy.
So far, so good! This is all consistent with my expectations, and in fact it turns out that if I make this structure in the lab, we get very similar numbers for the resonance frequency and Qc. Qi does turn out to be finite, but that is due to the lossy materials I have neglected.
But now we get to my actual question. In a next step, I add an additional structure to the design:
![]()
Added is another 50 Ohm impedance line (but currently without 50 Ohm port!), which ends up close to the floating island that (still) does essentially nothing. In practice it is intended as a way of sending microwaves to that structure, but for the purposes of this simulation, it is again just a floating piece of metal. Now, if I rerun the exact same simulation as above, I would expect to see more or less the same result; the new structure hardly influences the capacitances of the LC circuit and the transmission line. In fact, simulating these capacitances (I do not know how with AWR, so I used COMSOL), they are at least an order to 2 orders of magnitude smaller than any of the other relevant capacitances. So I would expect that most quantities are unchanged, with perhaps a small shift in the resonance frequency.
![]()
But what I find instead is that the structure has now apparently become 'lossy'; simulating S21 and fitting the lineshape, I now find that the lineshape has become much broader and more shallow. Fitting it there has to be a Qi of about 5000.
My question is, where are these perceived losses coming from? Why did the lineshape become broader and more shallow? Everything is still lossless, so I don't understand. At first I thought it was related to grounding issues; this new line now breaks the ground plane. But to overcome this I added some 'bridges' across the line with vias, and the result remains largely unchanged.
Does anyone have an idea for why this seems to happen? Maybe relevant to add is that my goal was to add another 50 Ohm edge port to that new structure (a port 3), and to find out exactly how much losses the LC circuit does get from its parasitic coupling to that port. Measuring S21 these would enter exactly into Qi, because they are losses into an unmonitored dissipation channel. But in the current iteration, that channel does not yet exist!
![]()
