Making 2-port measurements without S-Params - Page 1
Forum section: electronics / projects

author: Andrew_K
author_rank: Contributor
timestamp: July 18, 2022, 02:16:37 am
content: Hi,I would like to make some 2-port measurements of a few circuits. However, S-params are fairly useless, since my circuits are not at Z0=50 ohm, and I'm not sure there is a characteristic impedance. So, a standard VNA is basically useless for my purposes.Is there any standard test equipment that can measure, for example, Z params or ABCD params?I do have access to an Impedance Analyzer, the 4990A. It is a 1-port device. Measuring Z11 and Z22 is trivial. However, Z12 and Z21 might not be possible.Can multiple 1-port measurements be combined to create a 2-port model?Otherwise, I suppose, I could use a signal generator and 4-probe oscilloscope with active/differential probes.Make a shunt, measure voltage across the shunt, measure voltage across port 1, then measure voltage across port 2. That should give me Z11 and Z21.A sweep would be rather annoying, though, but I guess I could automate measurement with pyvisa...I've found that a scope's phase measurements aren't the most useful, either. Can't do expanded phase like a VNA or impedance analyzer might have.Has anyone done anything like this before?

author: Terry Bites
author_rank: Super Contributor
timestamp: July 18, 2022, 12:42:56 pm
content: Use a matching transformer?

author: mag_therm
author_rank: Frequent Contributor
timestamp: July 18, 2022, 02:01:51 pm
content: What type of circuits, are they linear?If not possible to get inside, there are 3 ways to measure:Open circuit impedance parametersShort circuit admittance parameters (does involve s/c on output though)Hybrid parametersUsually only one of those 3 test will give the 4 parameters.If non linear, parameters might become dependent on internal current or voltages. (partial derivatives are used)For example the small signal hybrid pi for bjt is only an approximation over certain input signal levels.A text book might be needed.I think it could be said that S params are a more recent subset of network measurement to make it easy for the 50 Ohm users. (swr etc)

author: TheUnnamedNewbie
author_rank: Super Contributor
timestamp: July 18, 2022, 03:14:06 pm
content: Quote from: Andrew_K on July 18, 2022, 02:16:37 amIf it is a passive circuit (or sometimes even an active circuit very far from any non-linearities, but don't quote me on that one), measuring s-parameters will still work. We do this all the time in simulations where we export s-parameter files based on 50 ohm impedances, even though they are (for example) complex matching networks matching something like say 16-56j ohm to 12-43j ohm.The only issues are that if your impedances are very far from 50 ohm, you get into problems with measurement uncertainty.After getting the s-parameters, you can just hook them up to ports with whatever impedance you want in a simulator, or even analyze thigs like gmax etc...And there is always an impedance - it is just how voltage and current are related at your ports.You cannot really combine one-port measurements to give two-port parameters. Just think of the following: Imagine two circuits, both black boxes, where each port is just connected to a 50 ohm resistor. However, in the second box, an idea amplifier is connected and amplifies the voltage over the resistor at port one and puts it at port 2. Both of these have the exact same S/Z11 and S/Z22, yet clearly very differnt 21 and 12 parameters.

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 19, 2022, 04:51:56 am
content: Quote from: Andrew_K on July 18, 2022, 02:16:37 amOver what frequency range do you need to make measurements? Do you need only a few discrete frequencies, or a complete parameterization over a band? Is you circuit passive or active?

author: Andrew_K
author_rank: Contributor
timestamp: July 19, 2022, 12:34:56 pm
content: Quote from: Terry Bites on July 18, 2022, 12:42:56 pmPerhaps. Few concerns: Frequency range is rather large. 5Hz to ~1MHz. Impedance changes dramatically throughout that range.Quote from: The Electrician on July 19, 2022, 04:51:56 amI'm looking for complete parameterization over a sweep, ideally.The part I'm looking to characterize is passive. This signal path feeds into an amplifier, but since those parameters are known, I'm looking to get the characterization of the passive circuit.I have schematics of everything that can be taken apart or separated into discrete elements.There are a few elements that don't have a nice lumped element model. One is a high impedance cable. It functions like a transmission line, but I'm having trouble getting parameters from it with an impedance analyzer.Quote from: mag_therm on July 18, 2022, 02:01:51 pmThat's a really good point about hybrid parameters!I do already have the open impedance(h22), short admittance(h11), and high impedance voltage transfer function (h12).And I see on wikipedia that h12 = -h21 for reciprocal networks (which mine happens to be)!Quote from: mag_therm on July 18, 2022, 02:01:51 pmI have been reading every appnote and book I can find. I would love recommendations on more books to read and study, though.Definitely lot of shortcuts from S-parameters being dedicated to 50 ohm. Has made my analysis more challenging/interesting, seeing as most app notes and literature is based on S.

author: virtualparticles
author_rank: Regular Contributor
timestamp: July 19, 2022, 01:11:20 pm
content: You may be able to extract a model of your circuit using chain parameter analysis. See the attached article written by yours truly. As noted earlier, impedances far from 50 ohms will add uncertainty to the measurement.

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 19, 2022, 02:12:07 pm
content: Quote from: Andrew_K on July 19, 2022, 12:34:56 pmI ask again: "Over what frequency range do you need to make measurements?"

author: TheUnnamedNewbie
author_rank: Super Contributor
timestamp: July 19, 2022, 02:48:08 pm
content: Quote from: Andrew_K on July 19, 2022, 12:34:56 pmAs I said earlier, there is no reason for s-parameters to be limited to 50 ohm,and for passive networks, even if you use a 50 ohm VNA to measure the s-parameters, you can still measure a network with non-50 ohm impedances. S-parameters completly define a network, just like ABCD or Y or Z or whatever parameters. There is math to transition between them.

author: mag_therm
author_rank: Frequent Contributor
timestamp: July 19, 2022, 03:31:58 pm
content: Frequency range already given post #5

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 19, 2022, 09:51:45 pm
content: Quote from: mag_therm on July 19, 2022, 03:31:58 pmHow embarassing!I missed it because I went directly to the part of his post where he was responding to my questions and the frequency range was not there; it was in response to a question about a matching transformer.My next question to Andrew_K is how much budget money do you have? Is this a company project, or are you a student?The instrument you need is the Hioki IM3570 impedance analyzer:https://www.hioki.com/us-en/products/lcr-meters/3-ghz/id_5772It covers the range 4 Hz to 5 MHz, and it only costs about $10000. It is available to rent. I've used one to determine the ABCD parameters of small audio transformers.

author: Andrew_K
author_rank: Contributor
timestamp: July 20, 2022, 02:47:14 am
content: Quote from: TheUnnamedNewbie on July 19, 2022, 02:48:08 pmThis is true, however, I was running into significant errors given the mismatch.Quote from: The Electrician on July 19, 2022, 09:51:45 pmI mentioned that I have access to an Impedance Analyzer, the 4990A.I used the impedance analyzer to get H11 and H22, then used a gain-phase analyzer (high impedance probes) to determine H12. I then determined H21 (H21 = -H12 by reciprocal network).So I now have h parameters across the frequency range I wanted. But, I may be a complete idiot.I had read that LT Spice could handle S parameters, and I assumed it could handle other network parameters, or, at the least, I could use behavioral sources and frequency tables to simulate:The S-parameter model seems to have issues. Because again, I'm not at 50 ohms. The mismatch seems too significant, even if it should be equivalent mathematically.Unfortunately, the behavioral R is largely undocumented and completely unstable.https://ltwiki.org/?title=B_sources_%28complete_reference%29Is there any sensible way to simulate 2-port networks with circuit elements together?

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 20, 2022, 04:51:26 am
content: Quote from: Andrew_K on July 20, 2022, 02:47:14 amCould you explain what you mean by this in some detail? How about a block diagram or schematic of what's in your two-port? Is the high impedance cable from another thread part of the signal path of this two port?

author: Andrew_K
author_rank: Contributor
timestamp: July 20, 2022, 01:53:41 pm
content: Quote from: The Electrician on July 20, 2022, 04:51:26 amSure, let me explain what I am trying / want to do.I have a few subcircuits that do not seem to play nice with lumped element analysis, or are complete black boxes to me. But, they are in the signal path and cannot be changed.Some of the "signal of interest" that my circuit measures is actually being "distorted" by the circuit response. If the transfer function is known, I can reasonably compensate the signal in a later (independent / buffered) stage by boosting. Much like Oscilloscope Probe compensation.https://www.electronics-notes.com/articles/test-methods/oscilloscope/scope-probe-compensation.phpI wanted to model the circuit to find the zeros/poles of the entire circuit. More importantly though, I want to determine how the input impedance or other changes will affect the response / zeros & poles.A simple H(s) transfer function is not sufficient for determining impact of input impedance or loading. And the transfer function of each piece individually does not correlate to the entire H(s).My understanding is that a proper 2-port network should encapsulate all of the necessary information.Quote from: The Electrician on July 20, 2022, 04:51:26 amYes, the high impedance cable is one of the circuits in the signal path. The LTRA model in spice does NOT play nice with high R.I would like to combine 2-port networks with circuit elements in the same simulation, so I can combine the "known" circuits with the "black box" circuits.Perhaps it would be better to convert the "known" circuits to 2-port networks, then use purely 2-port analysis?

author: mag_therm
author_rank: Frequent Contributor
timestamp: July 20, 2022, 02:41:18 pm
content: Sounds interesting.I use qucs and have not tried specifically, but it has VCIS and ICVS etc , presumably LT does too.As you are owner of the 2 port models , they don't have to follow the standard hybrid model.You can for example put lumped components inside yours .A classical example I think is to look at the way Giacoletto morphed the standard hybrid 2 port model of common emitter bjt into the hybrid pi.It is similar to Design of Experiment (DOE) where a model is created not so much based on physics of the real system, but on forcing the model to approximate your real system tests subject to limits on input variable range etc.

author: Andrew_K
author_rank: Contributor
timestamp: July 23, 2022, 04:29:46 pm
content: Quote from: mag_therm on July 20, 2022, 02:41:18 pmVCIS and ICVS do work reasonably well in LT spice for frequency analysis. Instead of doing an arbitrary impedance, I needed to use the VCIS and ICVS.So I'm able to measure the h parameters. h11 and h22 with an impedance analyzer, h12 by using a gain-phase analyzer.However, I'm noticing the model of the network isn't passive. For some reason, when hooked up to a voltage source, the output of the model goes above 0dB.This is strange, since the device is 100% passive.There must be error somewhere in my measurements. My hunch is the h22 open-circuit admittance isn't being measured well. I think the open-impedance is too high for my impedance analyzer.That, or, there is too much variation when switching between devices...Is there any alternate way to derive or measure h22? If the network is symmetrical, the determinant = 1. However, not all components are symmetrical.Could I, for example, use a known load to measure and solve for the open admittance?Could I take other measurements to derive or convert to the open admittance?Alternately, could I use a transformer, or cascaded transformers, to take proper S measurements to reduce the mis-match for a standard VNA?The DC R = 30k, 60k, for my components.I know some transformers are 50 ohm characteristic, but I'm not really sure what that means for a transformer.

author: mag_therm
author_rank: Frequent Contributor
timestamp: July 23, 2022, 06:01:38 pm
content: If there are reactive terms +/- j in the parameters, then it is possible the voltage (not power) can "ring up" above 0dBBut that would need both L and C ( + and - j terms)

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 23, 2022, 07:40:57 pm
content: Andrew_K, you say:"I have a few subcircuits that do not seem to play nice with lumped element analysis, or are complete black boxes to me. But, they are in the signal path and cannot be changed."How do you simulate your subcircuits? Do you have a parameterization of each one? Are their two-port parameters known? Which parameters are used to describe them? Can you show your signal chain as a cascade of two-ports; perhaps a block diagram of the signal chain?You said you've made measurements of several parameters such as z11, z12, h11, h12, h22, but you didn't say at what frequency you made those measurements.There is a lot of detail you're not telling us.It is not too hard to obtain the ABCD parameters of a passive network from measurement of the impedances at both ports. Using ABCD (chain) parameters for each block of a signal chain allows you to get the overall chain parameters for the signal chain by multiplying the parameters of each subcircuit or block in the chain. I'm sure you know this, but to help you, we need more details of your circuitry.

author: Andrew_K
author_rank: Contributor
timestamp: July 24, 2022, 05:53:14 pm
content: Quote from: The Electrician on July 23, 2022, 07:40:57 pmI mean, I really can't/don't without models. That is why I am attempting to pursue 2-port analysis.Using 2-port models, I can use LT Spice and VCIS/ICVS and frequency response tables to do a frequency analysis.I can also use Python and basic network analysis to calculate frequency response.Quote from: The Electrician on July 23, 2022, 07:40:57 pmIf the two-port parameters were actually "known", I wouldn't be asking on the best way to measure them.The parameters to describe them are arbitrary, since any parameter network can be converted to another.My equipment only allows 1-port impedance measurements and thru 2-port measurements, which is what hybrid parameters are, hence why I chose hybrid.I don't know how to measure Z12 or Z21, since they are current/voltage measurements on both ports of the DUT.Quote from: The Electrician on July 23, 2022, 07:40:57 pmIt's like 3-4 cascaded blocks, series connection. I'm not sure if drawing it out would really help here. I'll draw it out if you really think it would help.Quote from: The Electrician on July 23, 2022, 07:40:57 pmI've mentioned before.20Hz to ~1MHz. My equipment goes that low. I really don't care about anything above 1MHz.What other detail is needed? I'm asking advice on how to measure these parameters.Quote from: The Electrician on July 23, 2022, 07:40:57 pmGiven what I can physically measure, I only have A and D. Obviously B and C can be calculated, but I have no way to actually measure these at frequency.Simulation isn't my problem here, my issue is measurement.

author: Andrew_K
author_rank: Contributor
timestamp: July 24, 2022, 05:59:49 pm
content: Quote from: mag_therm on July 23, 2022, 06:01:38 pmInteresting, so would that indicate resonance in the circuit?

author: mag_therm
author_rank: Frequent Contributor
timestamp: July 24, 2022, 07:16:23 pm
content: For your post #18, In case you don't know it, I mention how a nanovna can be used to measure tuned circuit, filter etc even if HiZ.I have done this on HF radio tuned circuit/filters with and without coupling transformers.First connect a 20dB or 10 dB attenuator to CH0.Now connect that attenuator to a low Z part of the network input (make one with a tapped capacitor or tapped inductor if necessary)Connect CH1 to the network output.Now run a sweep using both LogMag and Smith (*)The LogMag response will ( always be below 0dB) and obtained by adding the attenuator value back to the sweep values.For your post #19, Yes the voltage can "ring up" even if the ciricuit did not actually get to resonance in the sweep.Correction: run Smithwithoutthe attenuator. Run LogMagwiththe attenuator

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 24, 2022, 08:44:54 pm
content: Quote from: Andrew_K on July 24, 2022, 05:53:14 pmUsing this page for reference:https://en.wikipedia.org/wiki/Two-port_networkA little over halfway down the page under the heading "Combinations of two-port networks" are several figures.My question to you is: are your two-ports connected in cascade as in Figure 16, or are they series connected as in Figure 10. Those are different things.

author: Andrew_K
author_rank: Contributor
timestamp: July 24, 2022, 09:08:14 pm
content: Quote from: The Electrician on July 24, 2022, 08:44:54 pmIt is cascaded, like figure 16.

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 24, 2022, 09:17:41 pm
content: So why must you determine the parameters of each individual block? Why not just determine the parameters for the whole chain as a single two port?

author: virtualparticles
author_rank: Regular Contributor
timestamp: July 25, 2022, 12:09:14 pm
content: Quote from: mag_therm on July 24, 2022, 07:16:23 pmThis is interesting. I'm not sure where you're going with this. Are you suggesting the low impedance tap in order to measure the resonance without loading it with the 50 ohm source of the VNA? How is the attenuator helpful other than improving the awful source match of the Nano? If the circuit is measured in the Smith Chart mode, measuring S21, impedances will only be accurate from about 20 ohms to 200 ohms for about 5% accuracy.Thanks

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 25, 2022, 12:40:06 pm
content: Andrew_K, read this page:https://en.wikipedia.org/wiki/Image_impedanceIt is possible to obtain the ABCD parameters by only making one-port impedance measurements.Consider that you have a two-port. Make 4 measurements with an impedance analyzer. Measure the impedances at the input port with the output port first open circuited and then short circuited. Then measure the impedances at the output port with the input port first open circuited and then short circuited.Using these formulas, calculate the ABCD parameters:Since your two-port is reciprocal, only 3 of the 4 measurements are needed to get the 4 ABCD parameters.

author: mag_therm
author_rank: Frequent Contributor
timestamp: July 25, 2022, 10:50:50 pm
content: Hi Virtual,Thanks for the comments at your #24, I will dice them up and reply:Are you suggesting the low impedance tap in order to measure the resonance without loading it with the 50 ohm source of the VNA?*Yes, that is necessary, as the Q of the inductor would be reduced by the 50 Ohm. In my case the tap was already existing, being the antenna input via a toroidal transformer to a tap on the inductor.How is the attenuator helpful other than improving the awful source match of the Nano?* The attenuator on CH0 will use CH1 and LogMag to give the magnitude of 2 versus 1, in my case it showed the peak of the resonance to enable turns adjustment. Also I am not sure, if the nanoVNA can measure LogMag > 0dB. I will check next time it is out.If the circuit is measured in the Smith Chart mode, measuring S21, impedances will only be accurate from about 20 ohms to 200 ohms for about 5% accuracy.*I did not try that yet. It probably would not work, as you mention, if Z is high.*I removed the attenuator and used CH0 to get Smith just on 11 with a sweep over 80 to 20 metre band, re-peaking the tuner at each band.* To show the method,here are test results on the antenna tuner with the 50 Ohm atten at antenna input. Note that there are taps selected for inductor and variable capacitor is adjusted at each band.Freq MHz Smith Z11 Ohm at resonance LogMag dB after -20dB atten is added back3.96 122 +37.07 45 +1410.05 65 +314.04 24 +9Note that these results will be different when the real antenna is connected, however the tuner can still peak over the above range.Thanks

author: virtualparticles
author_rank: Regular Contributor
timestamp: July 26, 2022, 11:52:13 am
content: Thanks Mag! Appreciate the detailed answer.

author: Andrew_K
author_rank: Contributor
timestamp: July 29, 2022, 12:44:36 am
content: Quote from: The Electrician on July 24, 2022, 09:17:41 pmThe reason is threefold1) I want to examine if I need to change pieces of the signal path.2) I can cascade the multiple individual blocks and compare against the measurement of combinations as a sanity check.3) Ease of measurement, the impedance analyzer I was using doesn't do well when the path is too long due to standing waves.Quote from: The Electrician on July 25, 2022, 12:40:06 pmThis is seriously fascinating.Did you find those equations in a book somewhere? Or did you derive them youself?I'd really love to read more, if there is a book or paper.

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 29, 2022, 02:17:47 am
content: I derived them.All you need is any three (since your two-ports are reciprocal) of the ordinary two-port parameters. The driving point (single port) parameters are easy to get with an impedance analyzer; it's the transfer parameters that need another instrument, a gain-phase analyzer. There are 4 transfer parameters: transfer impedance, transfer admittance, voltage transfer ratio, current transfer ratio. A gain-phase analyzer can only measure the transfer ratios, not the transfer impedance and admittance.Suppose you want to get the impedance parameters, z11, z12, z21, z22. z11 and z22 can be obtained with an impedance analyzer, but z12 and z21 cannot be obtained with a gain-phase analyzer, since they are transfer impedances, not transfer ratios.But there's another way to get a transfer impedance from a voltage transfer ratio (Av measured with a gain-phase analyzer).If you have the Z parameters for a two-port, the forward (from input port to output port) voltage transfer ratio is given by Av = z21/z11.So, if you have z11 (and z22 on the side) and measure forward Av, then z21 = Av*z11. So now you have z11, z21 and z22; if the two-port is reciprocal, z12=z21, and you have all four Z parameters. You could then convert the Z parameters to the ABCD parameters.You need to use the ABCD parameters to be able to calculate the parameters of combined two-ports in cascade.

author: Andrew_K
author_rank: Contributor
timestamp: July 31, 2022, 04:06:20 pm
content: Quote from: The Electrician on July 29, 2022, 02:17:47 amThat's seriously impressive.I'd love to read a short article about how you did that, if you ever wrote one.Quote from: The Electrician on July 29, 2022, 02:17:47 amUnderstood.So I have a few options: open/short impedance measurements to form ABCD, impedance analyzer to find h11 and h22 then use a G-P for h12, impedance analyzer to find Z11 and Z22 then find Av to get Z21.

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 31, 2022, 04:28:49 pm
content: Let us know how it goes, periodically.

author: Andrew_K
author_rank: Contributor
timestamp: July 31, 2022, 07:01:41 pm
content: Quote from: The Electrician on July 25, 2022, 12:40:06 pmSo, I did try this method.I think this method should have less measurement error. Changing from Impedance Measurement to Gain-Phase will mean changing fixtures/equipment. Two sets of Calibrations and two sets of systematic error.One issue I was observing was that open-circuit impedances were garbage at low frequencies. This makes sense, since the impedance approaches infinity at DC, and the impedance measurement is limited.To remedy this, I decided to add a shunt R at the output. This term preserves the impedance measurement at low frequencies. By measuring DUT+Shunt, then Shunt alone, I should be able to separate out the DUT, in theory...For clarity, here is my measurement setup:For the shunt, I did measure Z1O Z1S, Z2O Z2S, and confirmed that the network is reciprocal and symmetrical.The ABCD for the DUT+Shunt, and Shunt, both look reasonable on their own.When I attempt to remove the shunt by division, something strange happens. Here is the A parameter of the isolated DUT matrix. There are a few discontinuities in both the A and C parameters.I think I have isolated how this is happening.Since the shunt is of the form (The measured shunt is approximately this)$$ \begin{bmatrix} 1 & 0\\ Y & 1 \end{bmatrix}$$The equation for the DUT without Shunt is:$$ \begin{bmatrix} A*1 + B * -Y & A*0 + B*1\\ C*1 + D * -Y & C*0 + D*1 \end{bmatrix}$$So the $$A-B*Y$$ and $$C-D*Y$$ have a subtraction in them. Complex add/sub seems to give some messy results. I plotted A, B*Y, and the subtraction to better understand.The discontinuity seems problematic. Still, I continued to see what the final results would look like.As a sanity check, I wanted to compare the individual measurements with the measurements of the entire network:I used the ABCD of the shunt, removed it from the ABCD of DUT1, DUT2, and DUT1&2.Then I calculated DUT1 * DUT2 (cascading) to get the calculated DUT1&2Here are the plots:While they roughly have a similar shape, they do not match as I would expect.There must be measurement error somewhere. The low frequency, low-impedance measurements in the shunt and low-z DUT, seem to have a slight imaginary component where there shouldn't be. This causes significant phase shift at very low Z.I think my next step will be to try measuring only high-frequency response with the impedance analyzer. Then, use DC measurements to fill a point at, say, 0.1Hz. Then use curve-fitting to generate the transfer function equation I am after.

author: The Electrician
author_rank: Frequent Contributor
timestamp: July 31, 2022, 07:39:01 pm
content: The formulas I gave for the ABCD parameters have an aspect that is not conducive to numerical robustness. In the denominator of each expression is the difference zoo-zos. This is the difference between a large quantity and a small quantity. Not a good thing to have in any formula.When I've used these formulas, since only 3 measurements are needed to get the four parameters, one can choose which 3 measurements. I found that not using zio was a good choice, since my input port was a high impedance port, and parasitics tend to seriously contaminate the measurement.It has occurred to me that it might be better to make the measurements on each port with the two conditions on the other port being not open and short, but with a moderately high impedance load and a short. Using a moderately high impedance rather than an open would, hopefully, decrease the contamination by parasitics.I think I was working on deriving the formulas for this case, but I didn't finish. I'll see if I can find my unfinished work.In the meantime, the formulas I gave you are theoretically correct, but may not be as numerically robust as one might want.

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 01, 2022, 12:03:38 am
content: You have a result of:[A∗1+B∗−Y A∗0+B∗1][C∗1+D∗−Y C∗0+D∗1]after multiplying the ABCD matrix:[A B][C D]Times the matrix for a shunt Y, which is:[1 0][Y 1]How did the result end up with the minus sign in front of the Y? I don't get that; I get:[A+BY B][C+DY D]

author: Andrew_K
author_rank: Contributor
timestamp: August 01, 2022, 01:22:39 am
content: Quote from: The Electrician on July 31, 2022, 07:39:01 pmWelp, that makes a lot of sense! That matches what I was observing. Impedances too high (full open) or too low (full short) were being contaminated by parasitics.Perhaps the solution to make the 1-port-impedance method work would be using an L pad (resistive) attenuator instead of just a shunt. That way the Open and Short circuit impedances are guarded, rather than just the open-circuit found in a shunt. Then, the attenuator block could be measured and removed by matrix division. I believe that (should) keep the ZOO-ZOS term reasonable?One other interesting thing I observed: the open-circuit impedance is actually lower than the short-circuit impedance for some frequency range. Initially I thought that shouldn't be possible. Playing around in LT Spice, I found I could replicate the effect with LC Resonators. A small R could detune the resonance and cause the impedance to be higher than if the low R wasn't present at all.Perhaps that could be another source of instability in my measurements. ZOO and ZOS may cross... At the least, they will approach at high frequency (in my case).The active probe I have, which I have used for gain-phase, does have a small parasitic capacitance. This actually severely limits my frequency range significantly.

author: Andrew_K
author_rank: Contributor
timestamp: August 01, 2022, 01:25:10 am
content: Quote from: The Electrician on August 01, 2022, 12:03:38 amMy measured ABCD was ABCD of the DUT, as well as the shunt.I multiplied by the inverse matrix of the shunt to remove the contribution of the shunt.Inverse matrix of the shunt is \begin{bmatrix} 1 & 0\\ -Y & 1 \end{bmatrix}

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 01, 2022, 02:11:25 am
content: Why are you making your impedance measurements with a VNA rather than the 4990A?

author: Andrew_K
author_rank: Contributor
timestamp: August 01, 2022, 02:29:32 am
content: I don't have direct access to the 4990A, not for a while anyway. Also, it is an autobalancing bridge device. As such, it cannot take balanced measurements. The ports are unbalanced, as the LCur is a virtual ground driven by an amplifier.The VNA has impedance analysis functionality, and as I understand, should give better result for balanced measurements. It's also accurate enough for the impedance range and frequency range I'm interested in.I tried using baluns, but the results I was getting were garbage. Even with significant effort in calibration.

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 01, 2022, 04:31:33 am
content: Quote from: Andrew_K on August 01, 2022, 02:29:32 amGiven the fact that a VNA doesn't do well when circuit impedances are substantially different from 50 ohms, trying to get the 4 measurements for deriving an ABCD matrix using a VNA might be expected not to give good results.With an open on one port, the impedance at the other might be expected to be about as high as possible. Similarly, when there's a short on one port, the impedance at the other might be as low as possible.Not a happy situation.Just to satisfy my curiosity, what are the 4 measurement results you got on DUT1, at what frequency?

author: Andrew_K
author_rank: Contributor
timestamp: August 02, 2022, 04:40:36 am
content: I took some measurements using all methods discussed.1) Gain Phase and Impedance2) 1-Port Impedances using the impedance analysis functionality (S ports and GP ports offer this function)3) S-Parameter to ABCD using math functionsS-Parameter had some obvious inaccuracies due to mismatch. Gain-Phase gave poor results, as the probe capacitance was too high (~0.5pF active differential probe).1-Port impedance gave the best results by far.Quote from: The Electrician on August 01, 2022, 04:31:33 amThat is true if I use the S ports for 2-port analysis. There is obvious mismatch uncertainty in my results.I don't know if the VNA is using math to decouple things, or if there is something hardware based on the S ports, but itisintended for impedance analysis. It's one of the features of this analyzer.In the impedance measurements I took today, I didn't use the shunt. I took impedance measurements with both the S-ports, and the gain-phase ports (both are supported as impedance ports). The measurements agreed fairly well. I'm noticing that the Gain-Phase had better impedance measurement stability at high frequency, while the S ports had better impedance measurement stability at low frequency.So far, the ABCD parameters lookmuchbetter than when I tried using a shunt to preserve the open impedance at low frequencies.The fact that the ABCD parameters agree, using two different methods of impedance measurement, give me confidence in the measurements.(DUT1 B parameter for reference, both curves were obtained using different impedance measurement techniques)Also, now the calculated cascade  *  is approximately equal to the measurement of [DUT1 & DUT2](B parameters of [DUT1&2] and * for reference)I think with some clever tricks, like forcing reciprocality (and symmetry where applicable), curve fitting, and some averaging, these 2-port parameters will do what I want.

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 02, 2022, 07:06:09 am
content: Again, to satisfy my curiosity, what is the manufacturer and model of the VNA?

author: Andrew_K
author_rank: Contributor
timestamp: August 02, 2022, 02:13:16 pm
content: Keysight E5061B

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 03, 2022, 05:24:13 pm
content: Quote from: Andrew_K on August 02, 2022, 02:13:16 pmI want one of those. Are you a student, and that gives you access to the E5061B at school, or is your project something you're doing as part of your job?I went looking for my derivation of those ABCD formulas, and I found the file that contains the ones I gave you, and some others.In particular I found that I had derived a set that required measurement of a transfer function, but I never tried it out because I don't have a gain/phase analyzer (and I'm retired, so I no longer have access to one at work).I derived these formulas using Mathematica to solve for them. The next image shows the derivation, which is a fairly easy one. There is a variable name "fvtfr" that stands for "forward voltage transfer ratio". As you can see, the expressions are simple and they don't involve any measurements of a port impedance with the other port open circuited; they only involve the short circuited impedances. These formulas might work very well for you. Let me know if you try them and what results you get. Here are the formulas:

author: Andrew_K
author_rank: Contributor
timestamp: August 04, 2022, 02:12:26 pm
content: It's technically a work project. But learning about transfer functions, 2-port analysis, has been a personal learning goal of mine for a while. Just so happened that some of the things I've been learning about apply nicely to work.I may have found a better way to calculate the transfer functions given these impedance measurements.By reciprocity, $$Z12 = Z21$$ and $$Y12 = Y21$$Using$$Z_{IS} = \frac{1}{Y_{11}}, Z_{OS} = \frac{1}{Y_{22}}, Z_{IO} = Z_{11}, Z_{OO} = Z_{22}$$$$ \begin{bmatrix} Y_{11} & Y_{12} \\ Y_{21} & Y_{22} \end{bmatrix} = \frac{1}{det(Z)} * \begin{bmatrix} Z_{22} & -Z_{12} \\ -Z_{21} & Z_{11} \end{bmatrix} $$then for Z12 and/or Z21,$$ Z_{11} * Z_{22} - Z_{12} * Z_{21} = \frac{Z_{22}}{Y_{11}}$$$$ Z_{11} * Z_{22} - \frac{Z_{22}}{Y_{11}} = Z_{12} * Z_{21}$$Since $$Z_{12} = Z_{21}$$,$$Z_{12} = Z_{21} = \pm \sqrt{Z_{11} * Z_{22} - \frac{Z_{22}}{Y_{11}}}$$I feel like this should be similar (or the same) mathematically. Yet, the results are much better numerically. There are far fewer random discontinuities.Only "issue" is that the angle may be offset after the square root operation. This is corrected fairly easily by complex multiplication.Then, converting to ABCD or H parameters, gives a result that simulates very well in QUCS.

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 04, 2022, 03:48:10 pm
content: You have: zis=z11, zos=z22, zio=y11, zoo=y22but this is wrong. It should be:zis=1/y11, zos=1/y22, zio=z11, zoo=z22When I want to verify this sort of thing, I draw a schematic of some simple resistor network and calculate the Y and Z parameters, then see if the equalities like those above are true.For example consider a simple T network consisting of, left to right, a 3 ohm series resistor, a 5 ohm shunt resistor, and a 7 ohm series resistor. The Z parameters for that network are:[8 5][5 12]and the Y parameters are the inverse of the Z matrix:[12/71 -5/71][-5/71 8/71]Clearly, zio is equal to 8, which is z11.zoo is equal to 12, which is z22.zis is equal to 3 + 5||7, which is 71/12, and that is equal to 1/y11.zos is equal to 3||5 + 7, which is 71/8, and that is equal to 1/y22.

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 04, 2022, 04:21:05 pm
content: Quote from: Andrew_K on August 04, 2022, 02:12:26 pmIf you're serious about this, you should buy this book:https://www.amazon.com/Electronic-Engineering-Applications-Two-Port-Networks/dp/148317154X/ref=sr_1_1?crid=9ZDR89KUB7EM&keywords=electronic+engineering+applications+of+two+port+networks&qid=1659629785&s=books&sprefix=electronic+engineering+applications+of+two+port+networks%2Cstripbooks%2C118&sr=1-1And this one:https://www.amazon.com/Circuits-Matrices-Electrical-Engineering-Paperback/dp/B011MDTJUU/ref=sr_1_2?crid=258BXP6FK4H9E&keywords=circuits+matrices+and+linear+vector+spaces&qid=1659630033&s=books&sprefix=circuits+matrices+and+linear+vector+spaces%2Cstripbooks%2C114&sr=1-2

author: Andrew_K
author_rank: Contributor
timestamp: August 04, 2022, 09:43:19 pm
content: Quote from: The Electrician on August 04, 2022, 03:48:10 pmTyped it out wrong as I was copying from my notes and trying to format in LaTeX for the post.Quote from: The Electrician on August 04, 2022, 04:21:05 pmThanks for the recommendations! Definitely going to check these out.

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 05, 2022, 12:52:46 pm
content: Regarding the formulas I posted in reply #25, I have mentioned that since only 3 impedance measurements are needed to get the 4 ABCD parameters, one of the impedance measurements can be unused. In those formulas, it was zio that went unused.Here is another set of formulas that does use zio, and neglects zoo:If these equivalencies: zis=1/y11, zos=1/y22, zio=z11, zoo=z22are used in the final formula you derived for z12 in reply #44, and after some algebra, you will arrive at the result for C in the set of formulas just above because C = 1/z12Try the set of formulas in this post. You should get the same results you get with your derivation for z12 in reply #44, which have fewer discontinuities.

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 08, 2022, 08:23:37 pm
content: Andrew_K, what's happening? Are you getting any good results?in one of your posts you show how you have hooked and measured a couple of two-ports labeled "DUT1" and "DUT2". Does one of those include that high resistance cable you described early on? If so, does that mean that the other DUT only contains passive components capacitors, inductors and resistors connected in a network? Can you post a schematic of what's in that particular DUT?

author: Andrew_K
author_rank: Contributor
timestamp: August 17, 2022, 12:45:34 pm
content: Quote from: The Electrician on August 08, 2022, 08:23:37 pmSorry, it's been a while. Took a much needed vacation.I do get reasonable results using the first set of equations you provided. The results agree with my own at lower frequencies. At higher frequencies, my method seems to be more inaccurate when Zopen approaches Zshort. Which makes sense. I think this will always be a limitation with this method of measurement.Once I have measurements that I (mostly) agree with, I convert to H parameters, then attempt to estimate the transfer functions to import into QUCS for "Function Defined" network blocks.H parameters give the best results for fitting. If I were to fit Zshort/Zopen directly, or fit to Z parameters, the estimated fits might not agree where Zshort approaches Zopen. The estimated functions may cause one parameter to shoot past the other, when really they approach asymptotically. It's more robust to fit to H parameters.Approaching F->0 or F->∞, I can remedy measurement noise by chopping my measurements to the region where they make sense. Then fill in data using assumptions. For example, the voltage gain -> 1 at DC, voltage gain -> 0 at HF. I can use the measured results to get the shape in the area where measurements seem valid.I am getting fairly good results with this method. Importing into QUCS, I can calculate the AC response with the rest of the circuit. Then, I can use the AC response to calculate the step or impulse response. This seems to agree fairly well with the real-world measurements.This may not be important anymore, since I am getting results that work for what I am trying to do... But I am struggling to find how my version of derivations has equivalence to your derivations algebraically. Numerically they agree. I might have to play around some more with the algebra to really understand the differences there.To answer your other question, the DUTs I am measuring are all passive devices (cables).

author: The Electrician
author_rank: Frequent Contributor
timestamp: August 19, 2022, 07:54:16 pm
content: Quote from: Andrew_K on August 17, 2022, 12:45:34 pmI start with this:zis=1/y11, zos=1/y22, zio=z11, zoo=z22Keeping in mind that your two-ports are reciprocal.Using the conversion from Z to Y parameters, we can get:Y11 = Z22/(Z11 Z22 - Z12 Z21)Y22 = Z11/(Z11 Z22 - Z12 Z21)Using this, we get Y11/Y22 = Z22/Z11and then (Z11 Y11)/Y22 = Z22Using the equivalences from the beginning, this becomes:(Zio Zos)/Zis = ZooNow starting with your formula Z12 = Z21 = Sqrt(Z11*Z22 - Z22/Y11)Leaving the Sqrt off until the end, we can convert Z11*Z22 - Z22/Y11 to Zio*Zoo - Zis*Zooand then Zio*Zoo - Zis*Zoo to Zoo(Zio-Zis)Now using (Zio Zos)/Zis = Zoo, we replace Zoo in Zoo(Zio-Zis) to finally get Z12 = Z21 = Sqrt((Zio Zos*(Zio-Zis))/Zis)And since the C element of the ABCD parameters is 1/Z21, the just above expression for Z21 can be reciprocated to give:C = 1/Z21 = 1/Sqrt((Zio Zos*(Zio-Zis))/Zis) which is the formula for C in these formulas:Those are the second set of formulas I posted in reply #48