Baseline correction in Smith Chart

[hmalissa]

I'm looking at the measured S-data of a resonator on a Smith Chart. I can clearly see the loop when I scan across resonance, but I'm getting a substantial insertion loss from other components in the circuit - S is below 1 when I'm off resonance.
I'm trying to fit the theoretical curve a resonator to the measured data. The theoretical curve doesn't take the additional insertion losses into account and goes all the way to 1 off resonance.
I'm wondering if I can do some kind of baseline correction with my data in order to do the fit properly. How is this to be done? Is it just a subtraction of the background, or a multiplication? Since S is complex, I need to take the baseline in real and imaginary channel into account simultaneously. Is there a proper way of doing this background correction? Or maybe even software that will allow me to do that?
Thanks a lot.

 

[FvM]

The correction will be ususally done by a VNA when calibrating the measurement setup in a suitable way. A numerical correction would be possible, too. A S11 and S22 curves (the only s-parameters that are usually plotted in a Smith chart) would shrink towards the origin by adding losses, or a different point along the real axis, depending on the matching.

 

[hmalissa]

The correction will be ususally done by a VNA when calibrating the measurement setup in a suitable way. A numerical correction would be possible, too. A S11 and S22 curves (the only s-parameters that are usually plotted in a Smith chart) would shrink towards the origin by adding losses, or a different point along the real axis, depending on the matching.

Thanks a lot for the reply.
The VNA is calibrated, but unfortunately I cannot measure close to the resonator since it's an experimental setup. Therefore I will have to correct for the losses numerically.
If the S parameters are just shrinking towards the origin, then I should be able to multiply the whole curve with a non-complex scaling factor in order to take that into account, right?

 

[E Kafeman]

The VNA is calibrated

Misunderstanding maybe but VNA calibration and actual measurement setup calibration are two very different things, and you have not done measurement calibration?
Measurement calibration is a must to be done if it is a complex and unknown load between VNA and actual measurement object.
A complex loss involving several loss-factors causes amplitude and phase values that varies with frequency in a non linear way.
Calibration which includes compensation for complex losses near measurement object can be done in several ways and depends a bit on type of calibration procedure that actual VNA can handle.
Method resulting in most reliable result is in my opinion in place calibration, Short Open Load, and manual setting of correct electrical delay if it not is a part of standard calibration procedure.
If losses are purely real and not causing any phase delay can a fixed scaling factor be used.
If losses have low impedances will it make calibration less precise, due to VNA dynamic limitations. Most simple solution is to cut PCB traces that connect these lossy parts during measurement and measure that part later, if needed, to get the whole circuit status.
For low frequencies and short measurement distances relative wavelength can maybe both phase and component losses be omitted or replaced with their theoretical values.
If lossy part complex values are known, as an S11-parameter table, can these be subtracted from S11 measurement. Problem is that without calibration can not either the losses be defined.

 

[hmalissa]

I believe the measurement setup calibration was done correctly. The VNA firmware has a procedure that asked me to connect short, open, load, and thru to both ports, one at a time.
The problem is that I cannot measure close to the actual device. The feed lines consisted of multiple segments (SMA cables, CPW, wire bonds), and I believe there could be several inductive losses in between. The setup doesn't allow any other access to the resonator.
Would it help if I approximate the Smith Chart baseline with a circle, and then transform the whole dataset in the same way that would bring the circle to the origin, and scale it to 1?

 

[FvM]

Would it help if I approximate the Smith Chart baseline with a circle, and then transform the whole dataset in the same way that would bring the circle to the origin, and scale it to 1?

To at least guess about the answer, we would need to understand the nature of the circuit, respectively expectable S-parameter characteristic. You didn't tell yet, which S-parameters you are measuring and if it's a single port (reflection) or two-port (transmission) setup.

 

[hmalissa]

It is a 2-port measurement on a continuous feed line, consisting of various interconnects. And the quarter wavelength resonator is capacitively coupled to the feed line, so it's basically a reflection setup. I have measured all 4 S parameters.

 

[FvM]

If you have reason to assume that the resonator is almost lossless, you can normalize its |S11| to 1. Second assumption is no considerable resonances in the other circuitry, which might be difficult to prove.

 

[hmalissa]

The resonator is superconducting and should be low loss.
I'm unsure about the other resonances, the baseline is messy.
I will try this approach anyway.
Thanks a lot!

 

[FvM]

I fear, at the end at the day, you won't get much realible measurements from the resonator without an in-place SOL calibration. In a cryo experiment, if feasible at all, it most likely involves diassembling part of the setup several times.

Part of the measurements might be possibly avoided by a-priori knowledge about the system, e.g. the low-loss assumption. The question is, which information can be reliably get by the resonator measurement then?

 

[E Kafeman]

it most likely involves diassembling part of the setup several times.

I agree with this. Calibration of a part of the setup is no calibration at all. It is not possible to omit SMA cables, waveguides and wire bonds as it will add irregular inductive and capacitive losses.

The problem is that I cannot measure close to the actual device.

It was possible to place the DUT at that location? A side cutter and you have just prepared it for calibration of open. A solder ball is all that is needed for Short.
Superconducting, is it a permanent cryo or low pressure environment? It is probably enough to calibrate in room temperature.
If it is absolutely impossible to get access, build a exact copy and perform calibration in normal environment.