Obtain equivalent circuit parameters of an inductor (from s-parameter) - Page 1
Forum section: electronics / projects

author: Yansi
author_rank: Super Contributor
timestamp: October 13, 2020, 11:44:26 am
content: Hello,I am facing kind of a doh moment, as I can't figure something out I should be able to: I have measured an inductor using a VNA and obtained the s1p measurement file. I need to build a model of the inductor: i.e. get the inductance, ESR and parallel capacitance.The first issue I am facing is how the hell do I obtain the denormalized complex impedance from scatter parameter data? The touchstone file is in the formatCode:# HZ S RI R 50.00which after consulting the specification of the file (here:https://ibis.org/connector/touchstone_spec11.pdf) means the values are in real-imaginary form, normalized to 50 ohms.An example line from the file is:Code:1.355937500000000E7 7.658597047300226E-1 6.614757071629931E-1So what I have is 13.56 MHz, s{Re=0.7659, Im=0.6615}How do I convert to impedance? I thought I can look on the s11 measurement data as a reflection coefficient directly (Gamma), then the impedance should be Z = Z0* (1+Gamma)/(1-Gamma). But it seems I get a strange result, per below:50*(1+.7659+.6615j)/(1-.7659+.6615j) = 86.4 - j102.9 ohm.That huge real part is worrying me, does not look right. It also looks the inductor looks more like a capacitor, doesn't it? What have I done wrong? The calculation seem incorrect. But where?Thanks for any hints. I feel like I am stupid or what.

author: Yansi
author_rank: Super Contributor
timestamp: October 13, 2020, 12:21:59 pm
content: Okay, first thing, seems a basic fuckup: Correctly I should calculate like so:50*(1+(.7659+.6615j))/((1-.7659+.6615j)) = -2.46 + j134 ohm.I forgot the parenthesis around the gamma term, so in result did not flip the sign of the imaginary part in the denominator. Corrected that, I get -2.46 + j134 ohm. Now it looks like an inductor, in fact a 1.57 uH one. Which should be about correct. But why do I get negative resistance? And how do I obtain the model of the inductor (L, ESR, Cp)? I have measured a sweep from 5 to 20 MHz. In fact, I have done about 10 measurements of different setup of the inductor but if I compare the values at the same frequency (for example 13.56 MHz), they all result in about the same values (around 2.5 negative ohms plus 130 johms).I know there is also not insignificant amount of parasitic capacitance in parallel to the coil, but I think that should still not result in negative resistance, should it?

author: Yansi
author_rank: Super Contributor
timestamp: October 13, 2020, 12:42:33 pm
content: So, another progress: if I pick a sample S11 value at 5MHz, I get a completely different result:5MHz, Re{S11}= - 0.2154, Im{S11}= 0.9449 ---> Z = 1.28 + j39.9 ohm.So, it seems the impedance differs wildly, likely due to the parasitic parallel capacitance. But how to extract the data for the inductor model?//EDIT: Ewwww. The trace indeed lies outside the chart, having a negative resistance. I haven't notice during the measurement. Does not look right, does it?

author: suj
author_rank: Regular Contributor
timestamp: October 13, 2020, 03:56:41 pm
content: I prepared a spreadsheet according to this article:https://www.ieee.li/pdf/essay/s_parameters_of_passive_components.pdfNothing special, but it works. I am enclosing an xls sheet (file "Extraction.zip" below) with my sample coil measurements. You need to take care of the decimal separator sign when importing data, in my language settings there is "," and the file with s-parameters uses ".".I verified by building the filter and the results agreed with the simulations.EDIT:I used this sheet to measure self-wound coils for a designed filter. I was interested in the inductance and Q value of a specific coil after being enclosed in a shielding housing. I made an in-situ calibration on the target PCB. I used 0 Ohm and 50 Ohm resistors. It's only 94 MHz, so I think a simple model without additional capacitance and inductance would be enough. After measuring, the data of each coil was entered into the simulator and corrected other elements. This action has proven successful. I designed the filter for center f=94 MHz and the measurements showed center f=94.175 MHz. The 3 dB band was designed at 10 MHz and the measurement was 9.8 MHz. I used ATC 600S series capacitors, maximum of two connected in parallel so that the values are closer to the calculated ones. The filter does not contain tunable elements, so the precise measurement of the parameters of the coils was the key to precise results (of course, precise for my amateur capabilities).

author: Yansi
author_rank: Super Contributor
timestamp: November 25, 2020, 04:54:48 pm
content: I'd like to bump this thread up, now that I have my own VNA.So, now to figure out, how to properly measure the inductor to obtain the equivalent circuit as precise as possible.What I have is just an SAA-2N, so not a full-featured 2-port analyzer, only I'd say a "1 and half" port analyzer (S11, S22), so the only measurement method that seems usable is to just slap the measured object against ground on the port 1 and measure the S11.If I'm right, I should likely sweep far enough to see the self-resonance. I could then take the SRF for an estimation of Cp, knowing the Ls first, by looking at an impedance value at a frequency well below the SRF. Am I right?

author: virtualparticles
author_rank: Regular Contributor
timestamp: December 02, 2020, 10:36:12 pm
content: There is a pretty good treatment of this in this article written by yours truly.. :-)https://www.microwavejournal.com/articles/34236-rlc-parameter-extraction-using-the-transfer-matrix?v=previewBest,Brian

author: Yansi
author_rank: Super Contributor
timestamp: December 02, 2020, 11:00:02 pm
content: yours truly who? The article is behing a register wall.Anyway, have figured out already, how to obtain the basic model with Cpa and Rpa. Just need an impedance sweep wide enough to obtain the Ls+Rs at low frequency, then read out the Rpa at self resonance and from that you can calculate Cpa quite easily.My mistake was making the sweep in just small window of frequencies, where you can not see the SRF, which is an important point to know.

author: virtualparticles
author_rank: Regular Contributor
timestamp: December 03, 2020, 02:17:50 pm
content: The Journal does like to have people register, but here is the article if you don't want to do that.https://drive.google.com/file/d/1SK6PBR2Fl-SttptWGNv3Erk_tqNk3Ajq/view?usp=sharing

author: Yansi
author_rank: Super Contributor
timestamp: December 03, 2020, 04:39:41 pm
content: Thank you for the article, will have a read.

author: jrive
author_rank: Newbie
timestamp: January 22, 2022, 04:04:50 am
content: Quote from: Yansi on October 13, 2020, 11:44:26 amI think you have a sign error . 1-gamma should be 1-(0.7659+j0.6615)=1-0.7659-j0.6615

author: cdev
author_rank: Super Contributor
timestamp: January 22, 2022, 07:09:55 pm
content: The key to measuring series component parameters is using the right fixture, whether commercially made/purpose built or home made.Because they are often insanely expensive, I often just use PCBs from junk that I chop up with tinsnips, and solder whatever I need ad-hoc. I collect as much RF junk as I can, for that purpose. If anybody has any good sources, I'd love to know them!You might also be able to use copper tape and styrofoam poster board as if it was PCB, or copper tape on glass. (with the right dielectric constants, styrofoam is easy, its usually very close to 1, the same as air. You can just use 1.Stripboard is not 50 ohms, but if you want you can make your own reusable fixtures to chop up, and have them made at a PCB house.You might also be able to use copper tape and styrofoam poster board as if it was PCB, or copper tape on glass. (with the right dielectric constants, styrofoam is easy, its usually very close to 1, the same as air. You can just use 1.Stripboard is not 50 ohms, but if you want you can make your own reusable fixtures to chop up, and have them made at a PCB house.Thats has been the way my fixtures have usually been made. Chopping up RF PCBs. Like older, obsolete wifi equipment. Coax works too. Since its a controlled impedance. You can use coax as your transmission line in several ad hoc ways without messing up the impedance too much to make your measurements inaccurate. Just watch out for heat as the styrofoam is flammable and also melts almost instantly. So be quick. Dry Cardboard also works (well) and doesnt melt instantly like styrofoam, it is also close enough to 1 for dielectric constant, to just use that... Cardboard is great for this sometimes, actually, its super easy and cheap and cuts with a scissors.Better quality corrugated cardboard's thickness is also consistent enough to be useful saving for use for this.See the attached PDF which gives example of how pros might do it. When sold, all of this stuff is way too pricey for me. Ridiculously so, for what it is. IMHO.Also, this link has additional info.https://coppermountaintech.com/calibration-types-and-considerations/