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I had an odd thought yesterday while driving. It seems to me that an SA with TG can be used in place of a VNA, but I'd like to discuss it with another knowledgeable person. My greatest surprise is that this had not occurred to me before.
This is a serious mathematical topic, so if you haven't spent a LOT of time doing time series analysis, please stay quiet. Except for the context this is all introductory time series analysis required of anyone going into reflection seismology.
In the 1950's Norbert Wiener's students in the Geophysical Analysis Group at MIT did pioneering work on time series analysis. A key aspect of this was exactly recovering the phase from a sample of the amplitude spectrum. Wiener recognized that while there are an infinite number of complex spectra which share the same amplitude spectrum, there are two cases which can be uniquely determined, the minimum and maximum phase cases.
Wiener then went on to argue that for a passive system, the impulse response was minimum phase. All of the research was done in the context of solving 1D elastic wave propagation problems. This is the elastic version of a transmission line. The argument is actually very simple. For the response to be other than minimum phase it must be acausal. The system must respond before the impulse. There is no basis for expecting a passive system to respond before a stimulus.
Mathematically there are two methods for recovering the phase information. Compute the inverse of the Wiener filter computed via the Levinson recursion or compute the Hilbert transform of the amplitude spectrum. While the mathematical correctness of the Hibert transform approach is well established, neither I nor any of my friends in grad school could ever get the Hilbert transform method to work correctly in a computer program.
For the benefit of non-mathematical readers, a quadrature detector computes the Hilbert transform of the input. It's a 90 degree phase shift operator.
Is all this familiar to anyone here? I find it hard to believe that the PhD level EE community would have overlooked this. So I presume there is some subtlety of instrumentation I'm overlooking.
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i know rat arse about time series analysis but i bet you cant unless...
1) you can extract complex number of FFT out of your interested SA. and...
2) you can control the TG from the PC to whatever freq you like however slow sweep you like.
another alternative is... using DSO + FG, people have thought about and have done this, not specifically for VNA purpose though but... any kind of convoluted spectral multi dimensions imaginary numbers you wish you can get, you can, but then... what bandwidth are you talking about? and then you are posting in metrology board, how can you expect metrology grade result out of non metrology grade equipments? are you from Greece?
but then i should keep quiet except just to link you to this recently discussed, if anything relevant of interest to you... https://www.eevblog.com/forum/rf-microwave/why-do-i-need-a-vna-rather-than-a-sa-with-directional-coupler-to-tune-antenna/msg1313893/#msg1313893
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The amplitude spectrum is pure real. The FT consists of two copies of the amplitude spectrum, the positive frequency part the SA displays and the negative frequency part which is the mirror image of the positive part.
The FT of the complete amplitude spectrum is the autocorrelation of the time domain signal. If you have a scope and single pulse generator which are fast enough you can FT the impulse response to get the complete magnitude and phase response. This is a routine procedure in processing seismic data to remove the transfer function of the recording system and the non-ideal source pulse. In the trade, it's called "signature deconvolution".
An SA+TG collects the transmission transfer function from which the reflection transfer function may be derived. I did a complete analysis of the general case in 1D in grad school in Z transform notation. I'd never ever thought about it in the context of a VNA but it should be the complete solution for quantifying instrument and fixture errors.
The autocorrelation is symmetric about time zero, so it is acausal. To make it causal the imaginary part of the FT must be the Hilbert transform of the real part. This also happens to be the minimum phase criterion.
I posted to metrology because it seemed the most likely place someone who had designed and built commercial VNAs might be found.
I'm not from Greece, but I have a very close friend who is. He has a PhD in geophysics from UT Austin and an MBA from UT Dallas. He's in the same class as our mutual friends with PhDs from Stanford or Colorado School of Mines.
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It seems to me that an SA with TG can be used in place of a VNA
Say you want to measure the transfer function of a matched transmission line (an ideal time delay, with no reflections). The SA with TG just gives you a constant amplitude at all frequencies. How do you get the phase?
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If you have a scope and single pulse generator which are fast enough you can FT the impulse response to get the complete magnitude and phase response.
but an SA wont give you phase respond, except an realtime SA maybe... which RTSA that can spit out phase respond to USB?To make it causal the imaginary part of the FT must be the Hilbert transform of the real part.
how can (from any unknown signal) the imaginary part (phase) has any correlation to the real part (magnitude)? to make it causal you have to make it up. how do you make it up if you dont know the signal (DUT transfer) in the first place? even if you do, how can it possibly has to obey hilbert transform and your minimum phase criterion?
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For a real 1-port, there is only one possibility, given by the Kramers–Kronig relation. This is convenient for reconstructing the complex Z of a component (like a ferrite bead), though it's also not a very sensitive method (you won't reconstruct a reasonable Q factor, without making assumptions about the system, or having extremely accurate data to start with).
For N-ports, the phase might not be minimum, and you need to use other measurements to solve it. For example: a spec can't tell what a transmission line is, based on its transmission characteristics (because |H| ~= 1). But you might use a one-port-mismatch measurement to identify that that transmission line is probably a stub of Zo impedance.
The benefit of a VNA is it doesn't need to make assumptions about the DUT; it's just a black box with complex numbers coming out of it.
Realizing a physical circuit from that, say, might not be trivial (or indeed physically correct, given that some physical processes are neither pole-zero nor time-delay, e.g., Warburg impedance).
Tim -
What exactly would be a VNA and a SA?
In the classical sense, an SA have only 1 input, and can measure only the amplitude at each frequency. A VNA have 4 inputs, and can measure both the amplitude and the phase at each frequency, on all the 4 ports.
What do you want to measure with the VNA?
Also, a block diagram with the whole setup would be very helpful.
Without them, the short answer will be that it's not possible, because a VNA extracts both the phase and the amplitude information, while an SA extracts only the amplitude. -
Arbitrary static phase shift can't change the spectrum with an unmodulated sine wave input, so I don't see a simple TG->DUT->SA connection working. Add some 90 degree couplers and controllable switches and that changes.
There is the NIST designed dual six port VNA which only uses amplitude measurements via power sensors. The 6 ports are made up of 0 degree and 90 degree power splitters. It's not very practical except for metrology or in waveguide at extreme frequencies.
Another amplitude only technique is the old fashioned slotted line. It's workable with multiple fixed amplitude detectors rather than a one moving one. -
Responses in no particular order:
Causality is the argument for why you can extract the phase from the magnitude. I understand David Hilbert's argument, but I'm not smart enough to offer a critique. Quite frankly, I wouldn't dare try.
I can't say about N ports. The only thing I've considered closely is 2 ports. Just the notion of analyzing a circular N port makes my head hurt.
Never heard of "Warburg impedance". Can you provide a reference?
A Hilbert operator is the mathematical version of a 90 degree phase shift. The point of this is that it looks to me as if one can replace a bunch of expensive hardware with a computer program.
A LimeSDR mini is under $200 once you put it in a proper enclosure. Turning that into a 100 KHz to 2 GHz VNA strikes me as worth a significant chunk of my spare time.
I posted here because despite knowing a lot of people with PhDs I don't know anyone who knows this particular chunk of mathematics AND knows electronics. My good friend, the Greek, doesn't know which end of a soldering iron to hold. Another friend just got his first scope. I'm not looking for someone to tell me I'm right. I'm looking for someone who can explain why I'm wrong. The math is not trivial nor is the physical world. So it is depressingly easy to get one of them wrong.
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Causality is the argument for why you can extract the phase from the magnitude. I understand David Hilbert's argument, but I'm not smart enough to offer a critique. Quite frankly, I wouldn't dare try.
from reading the wiki. from what i understand, Kramers–Kronig relation or Hilbert transform is only applicable on some particular cases, predictable and causal where one property that need to be seek, correlates in some way or abide to some law with the known property. such as in electron energy loss spectroscopy, Hadronic scattering and magnetooptics. much like the falling object F = mg. g is a known universal constant (well "approximately" constant), we only need to know one property to get another, either m or F. but not in the VNA business. if we can predict, we will just do it on the bench with pencil and papers..A Hilbert operator is the mathematical version of a 90 degree phase shift. The point of this is that it looks to me as if one can replace a bunch of expensive hardware with a computer program.... I posted here because despite knowing a lot of people with PhDs I don't know anyone who knows this particular chunk of mathematics AND knows electronics
trust me, if it can be applied, the pHD Dr and universities that continue the work will be the first to realize it, even if they wont, those engineers and expert in the field who use it will. in fact it is this objective (applications) that motivate them to come up with better formulations/theories. we have a problem here, lets solve it mathematically, thats what they do... do you think they picked the topic or solution by random? undeniably some are pure God given luck, but most are just causal.. brain, sweat and raw muscles. i dont have master doctorate let alone pHD, just a happy hobbiests who apply (or try to) what they have discovered, without going deepest into the abstract mathematical nuts.
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Probably should stay quiet, but never was much good at that
As long as you can get IQ data from the SA, because of the 90 degree phase shift, then you already have a single frequency VNA.
The older SignalHound SA software did this, you had to calibrate at each frequency though so it was never practical.
I think modern SA's now all use quadrature data internally. So they are not really magnitude devices any more - whether they expose it or not.
However the hard part is getting it to work at multiple frequencies as the oscillators in the system (LO and TG) are not phase coherent. The underlying 'system' is not static as the TG and LO PLL's are jumping to different relative phases when the retune at each frequency step.
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This is a serious mathematical topic, so if you haven't spent a LOT of time doing time series analysis, please stay quiet.
It might be just one of those cultural differences, but telling people to stay quiet on a forum is not polite.
You can always specify you are interested only in answers coming from people with a specific level of expertise, but you can not tell anybody to shut up. Also, all math is serious, but I don't want to go into rant mode.
Judging from the fact that you are talking about SA, VNA and SDR in the same subject, i guess we are using the same terms, like SA, to name different instruments.
Here is the block diagram of an SA: http://www.rfwireless-world.com/Terminology/spectrum-analyzer-basics.html
With that architecture, you can not have a fully functional VNA.
Also, you want to use the instrument in some geologic mesurements. What exactly do we need to measure? You must specify that, unless you are asking the questions in a geology forum.
Without that info:
- can we just use some software instead of expensive seismology equipment? No. Whenever some instrument is expensive, there are reasons.
- can an SA be a VNA? No.
- can an SDR architecture be used to do measurements like a VNA? Yes.
- can a limeSDR be used in geology? I don't know what we need to measure, and with what precision or accuracy. -
I don't want to argue about whether it's right or wrong. I want to find out. If there are edge cases I want to know what they are.
As stated, this is a serious mathematical physics topic. I'm trying to find people with appropriate skills and experience who are interested and are intimately familiar with the mathematics and the physics. It is not easy stuff and many very capable people don't ever get involved with it at a rigorous mathematical level. It is not something you learn from a wiki. You learn it by spending many long hours doing numerical experiments to accompany graduate level math books.
Testing the idea is quite simple. Get some magnitude and phase data from a good VNA of a quartz crystal or a microstrip bandpass filter. Compute the phase spectrum from the magnitude and compare the two.
So if anyone reading this has access to a recent calibrated VNA and is willing to investigate, please measure something and post a photo of the setup and CSV files of the data as frequency, magnitude and phase.
Until I have that I have nothing more to say.
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So if anyone reading this has access to a recent calibrated VNA and is willing to investigate, please measure something and post a photo of the setup and CSV files of the data as frequency, magnitude and phase.
Until I have that I have nothing more to say.
my oh my! what a masterpiece of arrogance.
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Never heard of "Warburg impedance". Can you provide a reference?
An element where |Z| = w * sqrt(f). Accordingly, Arg(Z) = 45 degrees. They arise from diffusion processes, like skin effect (EM field diffusing into conductor), or ionic diffusion (supercapacitors, batteries), or thermal diffusion (might be relevant for thermal tails in precision test equipment?).
They're not hard to emulate, at least: you can cover three decades within a fractional dB with six RC or RL stages. See AoE3 p.559.
Tim -
I don't want to argue about whether it's right or wrong. I want to find out. If there are edge cases I want to know what they are.
Testing the idea is quite simple. Get some magnitude and phase data from a good VNA of a quartz crystal or a microstrip bandpass filter. Compute the phase spectrum from the magnitude and compare the two.
So if anyone reading this has access to a recent calibrated VNA and is willing to investigate, please measure something and post a photo of the setup and CSV files of the data as frequency, magnitude and phase.
You don't need any hardware. This can be proven impossible on paper. Get QUCS or ADS or other similar software and try it.
Proof: Take two 2 ports A and B. A is your DUT with arbitrary S Parameters. B has no loss and is perfectly matched but has an arbitrary phase shift vs frequency. The code below computes the S parameters of a pair of series connected two ports. inv_denom is 1.0 given that s11b is 0 (perfectly matched), so our new s21 is simply s21*s21b. As s21b has a magnitude of 1, there amplitude response of A in series with B is the same as just A proving that magnitude is insufficient to compute phase. The Dunsmore book referenced is worthwhile.Code: [Select]// Concatenate 2 2 ports
// Ref: Dunsmore, Handbook of Microwave Component Measurements 2.4.3
// Note typo in book: S21/S12 swapped
// [a]--[b]
void SParameter::cat_2_2(const SParameter &a, const SParameter &b)
{
a.require_ports(2);
b.require_ports(2);
ports = 2;
a.require_freqmatch(b);
f = a.f;
s.resize(4*f.size());
for(unsigned i=0; i<f.size(); i++)
{
auto s11a = a.s[i*4+0];
auto s12a = a.s[i*4+1];
auto s21a = a.s[i*4+2];
auto s22a = a.s[i*4+3];
auto s11b = b.s[i*4+0];
auto s12b = b.s[i*4+1];
auto s21b = b.s[i*4+2];
auto s22b = b.s[i*4+3];
auto inv_denom = 1.0 / (1.0 - (s22a * s11b));
s[i*4+0] = s11a + (s11b * s21a * s12a) * inv_denom;
s[i*4+1] = s12a * s12b * inv_denom;
s[i*4+2] = s21a * s21b * inv_denom;
s[i*4+3] = s22b + (s22a * s21b * s12b) * inv_denom;
}
}
Yes, something like a LimeSDR or R&S FSQ can measure phase. That's because there are two mixers, one being fed with a 90 degree LO. The phase is thrown out in detection by a traditional SA. -
Mathematically there are two methods for recovering the phase information. Compute the inverse of the Wiener filter computed via the Levinson recursion or compute the Hilbert transform of the amplitude spectrum. While the mathematical correctness of the Hibert transform approach is well established, neither I nor any of my friends in grad school could ever get the Hilbert transform method to work correctly in a computer program.
You can get LabVIEW (or MATLAB) to do a Hilbert transform for you. It's useful if you want to convert a real signal (from a receiver) into an analytic signal (e.g., for calculating first- or second-order coherence). But I don't think it'd be very helpful if you're exciting your system with a sine wave from a tracking generator and measuring it with a spectrum analyser. -
@edavid
The wikipedia quote you cited says the same thing somewhat more succinctly.
@CD4007UB
Please show your work for the case of an SA & TG
Does anyone have a citation to the mathematical analysis of short-open-load responses? Or better yet, can provide a copy of the papers. It's likely to be paywalled by IEEE. I *think* I've figured out how to analyze the responses in Z transform notation, but it would be reassuring to compare my result to a peer reviewed solution.
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There are some spectrum analysers out there that can already act as a VNA. My old Advantest spectrum analyser has a tracking gen and also it has the impedance measuring option fitted. This also required some external hardware in the form of a Wiltron return loss bridge but this analyser can measure impedance just like a VNA. It won't be as accurate as a modern VNA and it is very fiddly to calibrate but it can measure stuff like the impedance of an antenna as long as the internal option is fitted and you have a suitable external bridge. It's marketed as a spectrum analyser and it was one of the best spectrum analysers of its day (30-35 years ago?) but it can also measure impedance using the tracking gen and the external RLB.
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Quote
Testing the idea is quite simple. Get some magnitude and phase data from a good VNA of a quartz crystal or a microstrip bandpass filter. Compute the phase spectrum from the magnitude and compare the two.
If you want something to play with then here is a recent s2p file I took of an old KVG crystal filter. It's only taken over a 20kHz bandwidth centred on 9MHz. This is an s2p plot of an 8 pole LSB filter about 3kHz wide if that helps? There are 801 test points spread across 20kHz so the frequency step size is 25Hz.
Note that the filter isn't a 50R filter and so it needs an external matching network. So what you get below is the raw s2p data taken with a fairly modern Agilent VNA with 50R ports.
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Thank you. I'll take a look at it as soon as I get some free time. For current purposes, the mismatch doesn't matter.
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To give you some confidence that the data is decent, see below for some test results. The top SP1 is a simulation of the same raw s2p file but this time is with an external (simulated) matching network. With this simulated matching network the filter is matched to 50R and it shows a low insertion loss with low passband ripple in the simulation.
The SP2 file below it is the real filter after being measured again with a real version of the same matching network fitted to it. So this is real measured data of a real filter with a real matching network. You can see that the plots overlay quite well for both insertion loss and return loss and complex impedance at the input port.
I think this type of filter is supposed to be matched when the source and load look like 1000R in parallel with 24pF. However, this filter matches better with 850R and 24pF. I have another filter with the same part number that does match with 1000R and 24pF so there is some spread due to ageing or other effects. But either way, the data in the file looks to be good to me because it agrees so well with the real filter once matched and measured again on the VNA. The VNA was calibrated using an E4431B-60006 Ecal module and I also used the fixture simulation option in the VNA to de-embed right to the pins of the crystal filter. So I think you can have fairly high confidence that the s2p file is valid
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@G0HZU
Thank you. You've been very helpful. I should be able to take a day off to work on this towards the end of the week. I'm still stuck remodeling my mother's house so my sister and her husband can move out of my bedroom. My other sister showed up and tossed me out of the guest room. So I'm bunking on the couch in the TV room.
Extracting the reflection transfer function from the transmission transfer function will take some time. In seismology all we can collect is the reflection, so if we want the transmission we have to solve the opposite problem. Actually doing this is very specialized and the mathematical details are probably not publicly available, So I'll need to sit down and solve the problem of extracting the full S parameters from the transmission myself from scratch. Best guess is that will take several days. I've not done such things in a very long time.
Figure 6 in:
Calibration of vector network analyzers on the basis of the LRR-method
I. Rolfes and B. Schiek
Advances in Radio Science (2003) 1: 21–25
which is available via google scholar, shows the Hilbert transform relationship very nicely for S11. The Hilbert operator is nicely shown on the lower plot. Based on causality and the Kramers-Kronig relationship one expects the phase response to be the magnitude response convolved with a Hilbert operator. There's a sign reversal lurking somewhere, but the magnitude response is a good approximation of a spike in frequency and the phase in frequency is a good approximation to the "time domain" Hilbert operator. We're actually in frequency, but the mathematics are symmetric, so you just need to keep track of which representation you're using for the various terms and use the appropriate transform domain. -
As far as I have understood, the signal generator and the receiver needs to be phase-locked and frequency-locked so that you can compute the [complex-valued] transfer function of the DUT. If you think about the situation from the receiver point of view, you take the real signal coming from the tracking generator through the DUT and multiply the signal with sin and cos generated by the LO of the receiver, getting the quadrature complex signal comprising of two real signals (Q and I). Now, when you plot the complex signal on a XY-plane (IQ-plane) you will get a phasor with a certain length (amplitude) and angle (phase). Without knowing the the phase relation between the tracking generator and the receiver's LO generating the sin and cos signals, you will end up with a phasor which has a random phase but correct amplitude. Thus, in order to be able to resolve the phase information, the transmitter and the receiver needs to be synchronized in phase. However, you can get the phase information if you measure both tracking generator's signal and signal coming from the DUT: The phase and the amplitude will be relative to the tracking generator's phase and the amplitude. If your tracking generator is stable enough, you could possible measure those signals one at a time by first measuring the tracking generator's signal and the the signal coming through DUT, and the resolve the relative phase and amplitude differences.
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To me this is not what OP was talking about. He was saying he takes the screen trace data (DUT response) from an SA and extract phase information from it. Not hacking into the SA architecture , which would defeat the purpose of using a plane vanila spectrum analyzer, which in general may have no phase locked tracking generator.