A Visual Introduction to Scattering Parameters - Page 1
Forum section: electronics / rf-microwave

author: 0xCoto
author_rank: Newbie
timestamp: December 11, 2021, 10:23:49 am
content: Hi folks,I just published a video covering the fundamental theory surroundingS-Parameters, and their applications toRF Networks:https://youtu.be/CEA8njh4tLUHere are the topics I cover:What is a 'Network'?Power WavesComplex Impedance & Phase AngleS-Matrix & S-ParametersReflection & Transmission CoefficientsStanding WavesExample NetworksDesignating S-ParametersReciprocity & LosslessnessReflection Coefficient and VSWRHope you find it helpful. Your feedback is very welcome!

author: Joel_Dunsmore
author_rank: Regular Contributor
timestamp: December 12, 2021, 03:11:21 am
content: Well, you did say feedback was welcome, so here is a little bit of feedback.at 1:00 you mention a forward power wave as a1, but really the forward power wave is a1 times a1* = |a1|^2. , then at 3:51 you call a1 a voltage wave. at 1:00 I would recommend you call a1 an incident wave (no other name, like voltage or power), where the mag squared represents the forward power and at 3:51 you should note that a1 is V+/sqrt(Z) with units of sqrt(power).At about 6:40 you have your standing wave graphic and one can easily see Vmax, but it's really hard to pick out the V-min value (maybe near 6:50); you might consider to slow and stop the animation right at Vmin to show the voltage does not go to zero but does reach a minimum value.At about 8:56 you introduce a Pi attenuator, and you show it has an increasing attenuation value with freq, as well as S11 increasing with frequency. But don't explain it. If you morphed your attenuator schematic to show the parasitic shunt C in the shunt elements and parasitic series L in the series element, you could explain why the S-parameters behave as they do. Now you show ideal resistors and it doesn't make sense that the S-parameters should change as you show that they do. Of course, if you used Keysight attenuators, they would be infinitely flat over their attenuation rangeAnd finally, you don't mention the real, key point of S-parameters: It allows you to concatenate circuit elements and get the proper gain value which might be different than expected due to mismatch effects. You could easily create a gain block that has non-ideal (say 25 ohm) output and 25 ohm input impedance. It would show flat gain, maybe 10 dB. But if concatenated them together you would get much different gain than the expected 20 dB, and if you did it with an ideal 50 ohm transmission line between, maybe 10 wavelengths long at center frequency, then you would get a big gain ripple. S-parameters let you see than and that is why they are better than just dropping your gain block numbers into an Excel spread sheet.Just for fun I ran a quick ADS simulation of a single amp and dual amp, with the amplifier having S21=10dB and S11=-10 dB or -6 dB (100 ohm or 150 ohm), for 2:1 and 3:1 mismatch, and 3600 degrees phase change transmission line at mid frequency.You get either 2 dB ripple or 4 dB ripple, for the cascade, even though the simple adding of gains would say it should just be flat 20 dB.My $0.02.

author: 0xCoto
author_rank: Newbie
timestamp: December 13, 2021, 12:42:11 am
content: Thank you for your comments!The incident and reflected power waves are defined by Kurokawa as a1 and b1 respectively ("Power Waves and the Scattering Matrix", IEEE Trans. Micr. Theory & Tech., Mar. 1965, pp. 194–202). You are correct that, strictly speaking, it should be V+/sqrt(Z), but given all ports have the same characteristic impedance (which I assumed earlier while elaborating on the ki coefficient), it makes no difference to set Sij equal to Vi-/Vj+, because the sqrt(Z) ratio becomes 1, so in most (real-world) cases, sqrt(Z) can be disregarded anyway.The point of the example networks is to highlight the applications of S-Parameters. Of course, I could go into explaining the frequency response of filters, amplifiers, attenuators etc., but that begins to step out of the scope of S-Parameters (which treat networks in a black box manner). As for the accuracy of the schematic, it depends on how you look at it. This could very well be the equivalent circuit of a network, but due to minor imperfections (somewhere in transmission lines etc. for example), the response may come with a bit of a frequency dependence. I think it's important to highlight some sample cases of what one might expect when measuring devices in the real world, with an equivalent circuit as a rough example.I agree that cascading S-Parameters is an interesting topic to bring up, and I definitely considered including it for some time, but that would require the introduction of T-Parameters, S-to-T transformations etc. (which goes beyond a simple 'introduction' to S-Parameters). I think referring to the cascading of S-Parameters as the "real, key point" is a bit of an exaggeration. That is certainly the main idea behind T-Parameters, but S-Parameters alone are a great 'tool' for covering other things. Perhaps it might have been an interesting idea to just briefly bring up the possibility of cascading in the conclusion, but that could carry the risk that one might misinterpret that you can just add up the values of S-Parameters to get the cascaded S-Parameters.

author: Joel_Dunsmore
author_rank: Regular Contributor
timestamp: December 13, 2021, 01:22:27 am
content: Quote from: 0xCoto on December 13, 2021, 12:42:11 amI always speak strictlyQuote from: 0xCoto on December 13, 2021, 12:42:11 amWell since it doesn't make a difference, why not state it correctly? Then you don't have strict people questioning it.Quote from: 0xCoto on December 13, 2021, 12:42:11 amNormally one wouldn't use idealized representations of resistors to indicate frequency dependence, one would include a little L and C for spiceQuote from: 0xCoto on December 13, 2021, 12:42:11 amNaw, just use equation 2.18 from my book. Easy little bit of loop stuff. No S-T needed, just simple algegra, e.g. S21cascade=(S21A*S21B)/(1-S22A*S11B).Quote from: 0xCoto on December 13, 2021, 12:42:11 amNot if you include the formula (as above) that shows how they are related.

author: 0xCoto
author_rank: Newbie
timestamp: December 13, 2021, 04:47:37 am
content: It is stated correctly under the assumption that all ports share the same impedance (which is usually the case), but I agree, let's elaborate to avoid potential confusions. I'm planning to add this clarification in the description, let me know if it looks OK: "Note: At 4:07, Sij is equal to (Vi-/Vj+) * sqrt(Zj)/sqrt(Zi), but because we've assumed an equal impedance for all ports, it has been simplified to Vi-/Vj+."S21cascade=(S21A*S21B)/(1-S22A*S11B) does work for the case of a cascade of just 2 two-port networks (and I could give out the S-matrix for the other parameters), but I think an explanation on why and how each cascaded S-parameter is actually derived (because the formula isn't very obvious) along with the applications of scattering transfer parameters would deserve its own video. (By the way, a version of your book I found has the equation in 2.19 and S21AB seems to be in place of S12AB and vice versa, but I assume the 2012 version I'm looking at is outdated)

author: Joel_Dunsmore
author_rank: Regular Contributor
timestamp: December 13, 2021, 02:15:27 pm
content: Quote from: 0xCoto on December 13, 2021, 04:47:37 amYup. That's been fixed in the 2nd edition, 2020; although perhaps it is like the deliberate mistake in a Persian rug?

author: jwet
author_rank: Frequent Contributor
timestamp: December 13, 2021, 07:22:01 pm
content: I think this is a fantastic video and would have loved something like this in 1979 when I was first exposed to S parameters at the University of Illinois- EE453 IIRC.I understand the other poster's issues with power ratios vs. voltage ratios- this is a confusing part of S parameters- I like thinking of them as voltage ratios and its generally more useful.The other comment that I had was more visual. At around 6:30 in the video, you show forward and reflected waves and the resultant standing wave. The reverse wave is the forward wave modified by the complex reflection coefficient of the load- this affects amplitude and phase. This is excellent and very subtle- it took me a long time to understand this. I remember a lab using a slotted line that tried to get this across. The slipping phase is caused by the relative length of the line and the frequency of the forward signal. I don't know if labs still include slotted lines but it was really critical to my finally understanding how this VSWR stuff works. Back in the dark ages, we worked the first half of the course with vector voltmeters only. In the last half, the instructor pulled out this impossibly modern VNA (HP 8503 probably). I remember how awesome this instrument was- it made a real impression on me.I also loved the circulator/isolator explanation and showing its operation in the s domain and with the EM simulator software.Excellent.

author: Mechatrommer
author_rank: Super Contributor
timestamp: December 13, 2021, 07:55:57 pm
content: looking forward for the next video... how VNA get the S11 after calibration and the math involved

author: Bud
author_rank: Super Contributor
timestamp: December 13, 2021, 10:00:40 pm
content: @0xCoto I second the comment you got on the YT regarding background music. It may be just me but I am unable to take seriously videos with background music, to me they fall into pop-cartoons category rather tnan technical presentations.Edit: Also at 2:40 and abouts, why not use a plain and simple notation Re() and Im() instead of the funny symbols which may only be appropriate for an academic style papers. The symbols used may be confusing to a beginner and hard to refer to if one would want to reference them in most of usual communications including this forum.

author: Bud
author_rank: Super Contributor
timestamp: December 13, 2021, 10:12:19 pm
content: Quote from: Mechatrommer on December 13, 2021, 07:55:57 pmAs a happy owner of Joel's book, I can recommend you to get one and you will be set for life with all the VNA math and much more than you will ever need.

author: Mechatrommer
author_rank: Super Contributor
timestamp: December 14, 2021, 04:34:42 am
content: who is Joel? you meanHandbook of Microwave Component Measurements: with Advanced VNA Techniques?

author: Bud
author_rank: Super Contributor
timestamp: December 14, 2021, 06:04:48 am
content: Yes , Dr. Joel Dunsmore, and he is right here with us in this topic.

author: 2N3055
author_rank: Super Contributor
timestamp: December 14, 2021, 08:50:13 am
content: Quote from: Bud on December 13, 2021, 10:12:19 pmAgree, really, really, good book. And very nice to have author here...

author: Mechatrommer
author_rank: Super Contributor
timestamp: December 14, 2021, 03:31:13 pm
content: Quote from: Bud on December 14, 2021, 06:04:48 amif i can give half of my post count to him i will do that...

author: Joel_Dunsmore
author_rank: Regular Contributor
timestamp: December 14, 2021, 04:33:30 pm
content: Quote from: Mechatrommer on December 14, 2021, 03:31:13 pmI appreciate the thought; maybe I'll slowly catch up. But I try to post only on things I really know about (on EEVblog forum, only posting things you know, and not what you guess? who knew it was possible?)

author: 2N3055
author_rank: Super Contributor
timestamp: December 14, 2021, 05:07:32 pm
content: Quote from: Joel_Dunsmore on December 14, 2021, 04:33:30 pmI, for one, thank you for your valued contributions.Quality is always better than quantity.Take care!Sinisa

author: Bud
author_rank: Super Contributor
timestamp: December 14, 2021, 05:49:53 pm
content: @Mechatrommer I loved you reaction

author: Bud
author_rank: Super Contributor
timestamp: December 14, 2021, 05:54:36 pm
content: Quote from: Joel_Dunsmore on December 13, 2021, 02:15:27 pmIs Errata sheet available for the 1st edition?

author: Joel_Dunsmore
author_rank: Regular Contributor
timestamp: December 16, 2021, 01:17:46 am
content: Quote from: Bud on December 14, 2021, 05:54:36 pmWell, no, actually the Errata currently consists of a couple a dozen post-it notes stuffed into my copy of the first edition. Maybe I will get motivated to write them all down on a single sheet and post it.Mañana.

author: xmo
author_rank: Regular Contributor
timestamp: December 16, 2021, 04:26:52 am
content: "perhaps it is like the deliberate mistake in a Persian rug?"----------So you slipped a couple errors into the book just to see if anyone is paying attention?