Author Topic: Phase noise measurement  (Read 1453 times)

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Offline cncjerry

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Phase noise measurement
« on: November 22, 2020, 09:17:25 am »
I first started looking at phase noise (PN) as it related to radio transmitters and receivers.  I somehow got sidetracked for a couple of years on the other side of oscillator performance, that being stability.  I think I am now well equipped to measure stability having several different systems and references including a Cs beam,  a number of rubidium units, three or four GPSDOs as well as interval counters, Dual mixer setups, counters, etc.  So now I am going back to PN measurement and I've found that it still looks like you have to spend a fortune to get a decent PN plot.

I've read about a dozen papers on the various PN measurement methods.  I tried KE5FXs PN.exe with my spectrum analyzers and even with my 8568 and the companion 85685 preselector/preamp, I can't get a noise floor low enough to characterize anything more than maybe a poorly performing DDS or other synthesizer.   I also am looking at the old HP 3048 system because that uses a readily available interface that I might be able to couple with my 3562a baseband FFT analyzer.  If I can't put that system together, then the HP 70K spectrum analyzer has a PN measurement module I remember so I'll have to dig in there again too.

But going back to the documents like that written by KE5FX as well as Keysight, it seems like I might be able to get down to around -140dB or so by using one of the quadrature measurement methods.   There are two outlined in the docs.  The first uses a reference brought in phase with the DUT and then phase shifted 90 degrees so that when mixed within a DBM, the amplitude noise and primary frequency can be eliminated so that by then low pass filtering and amplifying the remaining phase noise, it should be able to be plotted on a baseband analyzer.  You might be able to also detect the PN by using a sound card with a 384k sample rate and 24bit or more ADC.  The second quadrature method skips the reference and splits the DUT signal itself into two paths with the second path being delayed or brought into quadrature with possibly a twisted wire quadrature device like those discussed by Breed(?) and others.

So armed with both a twisted wire quadrature module and a delay line (for 10Mhz), I tried mixing a 10Mhz signal with itselft 90 degree shifted .  I got the 20Mhz output from the mixer as expected with the 10Mhz greatly reduced in amplitude but still detectable, possibly due to shielding and coupling from input to output.  I then ran this directly into the 3562a as it has a 100Khz filter on the front end just to see what I would get.  I saw some of the typical phase noise plot but nowhere near as pronounced as expected.  For instance, and I'll post a plot as this continues, I had maybe a curve from -120dB down to -135 or so, maybe -140dB, but I would have thought the frequencies closer to 1hz to have more amplitude. I thought about it later that maybe it had something to do with the input coupling on the 3562a and I'll look at that again tomorrow.

If anyone can point me in the right direction, I'd appreciate it.  If this is hopeless within a hobbyist budget, I'll accept that advice as well.

Thanks,

Jerry

edit: Links to some doc:
Keysight:

https://www.keysight.com/upload/cmc_upload/All/PhaseNoise_webcast_19Jul12.pdf

One of the more interesting:

https://www.npl.co.uk/special-pages/guides/gpg68_noise

John's paper:
http://www.ke5fx.com/phase_noise.pdf

This link sent to me via PM  is very interesting and I'm trying to get more info.  He realized the analog mixing and baseband conversion with a high performance ADC with great results down to -170dBc:

http://www.aholme.co.uk/PhaseNoise/Main.htm

This R&S paper is better than some but the issue is with spectrum analyzers is the high noise floor:
https://www.rohde-schwarz.com/us/applications/phase-noise-measurements-with-spectrum-analyzers-of-the-fse-family-application-note_56280-15577.html

The picture in this doc is what I am trying to realize in hardware.  The issue remains though, if you can boost the PN to a level that can be measured to -170dBc by a typical baseband analyzer:

https://www.analog.com/media/en/technical-documentation/application-notes/AN-0982.pdf

Site with a simple discussion of measuring phase using correlation:

https://www.edn.com/measure-phase-difference-using-correlation/
« Last Edit: November 25, 2020, 05:47:51 pm by cncjerry »
 

Offline Villain

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Re: Phase noise measurement
« Reply #1 on: November 22, 2020, 01:08:58 pm »
How much are you willing to spend? What carrier frequencies are we talking about?
« Last Edit: November 22, 2020, 01:15:06 pm by Villain »
 

Online mawyatt

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Re: Phase noise measurement
« Reply #2 on: November 22, 2020, 01:21:09 pm »
Jerry,

We needed to measure PN of a newly developed over-moded acoustic wave resonator back ~1990, and didn't have the proper PN equipment (and no budget for such). Recall I was at the IEEE MTT conference where MaCom presented a paper utilizing two identical oscillators, which were mixed together resulting is a zero baseband since the oscillators would self inject lock to each other. The baseband residue is the PN from each like oscillator and can be amplified and displayed with a high resolution ADC or baseband analyzer.

We funded a grad student (ended up hiring him!) to build up a couple of these setups and wrapped two of the over-moded acoustic wave oscillators with towels for thermal isolation and powered by batteries, then a high gain low noise baseband amplifier followed. The PN measurements which were better than -140dBm at 1KHz offset for a ~2GHz oscillator about 5mm square, were impressive at the time. Later we confirmed these measurements with a proper HP PN instrument at another location.

Wish I could remember the MaCom paper, but my memory is fading :P 

Anyway, know this isn't exactly what you were looking for but maybe helps in your PN endeavors since it doesn't require any expensive specialized equipment.

Best,

Edit: MACOM paper courtesy of my colleague Alberto  ;)

« Last Edit: November 23, 2020, 12:27:01 am by mawyatt »
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Offline RoGeorge

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Re: Phase noise measurement
« Reply #3 on: November 22, 2020, 01:48:37 pm »
There are many ways to measure and characterize the phase noise.  Would be nice to link or name the documents you were talking about.

Just for an approximation, to see which oscillator is worst, I once did like this:
- set a Rigol DS1054Z oscilloscope on the biggest memory depth
- look at the oscillator's waveform at a later moment, a second later or so after the trigger.

Because constant phase noise accumulates as a time jitter over time, the zero crossing observed a second later after the trigger will slightly differ with each trigger event.  This is an example made with pulses instead of sinusoidal waveforms, just to better illustrate the idea of phase noise leading to time jitter accumulation over time.  The later we look after triggering, the more the pulse jitter around the ideal time spot.  The peaks that never move are there just as a helping reference on the screen, they are not live signals.  The bigger the delay from the trigger, the more time jitter is observed.



That method is in fact limited by the stability and phase noise of the DS1054Z internal PLL, but good enough for a demo or to compare which oscillator has lower phase noise.

An instrument can be improvised on the spot with some very clean reference oscillator and a counter, then some software to read the measured time jitter and display the statistic of the results.

Offline SilverSolder

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Re: Phase noise measurement
« Reply #4 on: November 22, 2020, 02:30:44 pm »

[...] Because constant phase noise accumulates as a time jitter over time [...]

I don't understand this part -  Wouldn't the noise introduce both positive and negative jitter,  so it nets out to zero in the long run?
 

Offline RoGeorge

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Re: Phase noise measurement
« Reply #5 on: November 22, 2020, 03:16:47 pm »
Wouldn't the noise introduce both positive and negative jitter,  so it nets out to zero in the long run?

Yes, both negative and positive, and zero in average, yet it accumulates as larger and larger time jitter.  In fact, I re-"discovered" that myself, by accident, while trying to measure something else.  At first I was intrigued by the same question, until it was kindly explained in another forum by somebody named "cirip", whom I want to thank for.

The explanation had some math in it, but I'll try an intuitive one (as in rough and no math):
- phase noise can be seen as a frequency modulation (an ideal oscillator is FM modulate by some noise)
- frequency modulation can be seen as a "lenght" modulation (the length between two consecutive zero crossings)
- the noise has both + and - variations, averaging on zero

- let's make an analogy with a (foot) walking down an alley, where each wavelenght of the oscillator is a step made in the same direction, and the phase will be a small error, let's say randomly distributed in the range of +/- 0.1 steps
- we make one step, we arrive at the distance 1 +/- 0.1 steps
- if we walk 100 steps, we arrive in average at a distance of 100 steps, correct, but what will be the range of the final error?

The real question here is what is the worst possible error?  That would be if by chance all the errors (at each step) will be +0.1 (or -0.1).  In conclusion:
- walk 1 step and arrive at the distance 1 step +/- 0.1, so the end point is at [1 step +/-0.1] steps
- walk 10 steps and arrive at the distance 10 steps +/-0.1*10, so the end point is at [10 steps +/-1] steps
- ...
- walk 999 steps and arrive at the distance 999 steps +/-0.1*999, so the end point is at [999 steps +/-99.9] steps
- the more we walk, the bigger the range of the final error.

The +/- n steps is the error after walking n steps (caused by the noise), and this length error is what we perceive as time jitter on the oscilloscope.
« Last Edit: November 22, 2020, 03:29:18 pm by RoGeorge »
 
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Offline SilverSolder

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Re: Phase noise measurement
« Reply #6 on: November 22, 2020, 03:27:18 pm »
Wouldn't the noise introduce both positive and negative jitter,  so it nets out to zero in the long run?

Yes, both negative and positive, and zero in average, yet it accumulates as larger and larger time jitter.  At the first I was intrigued by the same question until it was kindly explained in another forum by somebody named "cirip".  In fact, I re-"discovered" that myself, by accident, while trying to measure something else.

The intuitive explanation (as in rough and no math) is like this:
- phase noise can be seen as a frequency modulation (an ideal oscillator is FM modulate by some noise)
- frequency modulation can be seen as a "lenght" modulation (the length between two consecutive zero crossings)
- the noise has both + and - variations, averaging on zero

- let's make an analogy with a (foot) walking down an alley, where each wavelenght of the oscillator is a step made in the same direction, and the phase will be a small error, let's say randomly distributed in the range of +/- 0.1 steps
- we make one step, we arrive at the distance 1 +/- 0.1 steps
- if we walk 100 steps, we arrive in average at a distance of 100 steps, correct, but what will be the range of the final error?

The real question here is what is the worst possible error?  That would be if by chance all the errors (at each step) will be +0.1 (or -0.1).  In conclusion:
- walk 1 step and arrive at the distance 1 step +/- 0.1, so the end point is at [1 step +/-0.1] steps
- walk 10 steps and arrive at the distance 10 steps +/-0.1*10, so the end point is at [10 steps +/-1] steps
- ...
- walk 999 steps and arrive at the distance 999 steps +/-0.1*999, so the end point is at [999 steps +/-99.9] steps
- the more we walk, the bigger the range of the final error.

The +/- n steps is the error after walking n steps (caused by the noise), and this length error is what we perceive as time jitter on the oscilloscope.


Thank you for the excellent explanation. 

So, are we in effect depending on the low frequency components of the phase noise to "stack up" and cause enough jitter to become visible?
 

Offline RoGeorge

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Re: Phase noise measurement
« Reply #7 on: November 22, 2020, 03:59:43 pm »
are we in effect depending on the low frequency components of the phase noise to "stack up" and cause enough jitter to become visible?

This is the next very good question, after the previous one.  Kind of yes, but there is yet another very tricky thing here.

Our (wrong) intuition would say:
- OK, so if I look n edges later from the triggering point (let's assume it's a square wave instead of sinus) I would see all the n'th falling edges uniformly distributed in the range of the final +/- error, around the average point, but this is not what we see!

Most of the edges are right near the expected average, even if the error came from a white noise.  So, initially all the values in the range were equally possible in the +/- error range, yet after many steps we see most of the errors will like to "cluster" around the average, only a very few fall farther away from the expected average.  The final errors distribution after many, many steps has a Gaussian shape.

This is because of something very fundamental to statistics, called Central Limit Theorem.  For our case it means that if we "accumulate" many errors equally distributed (white noise) we will end up with errors that are not equally distributed, the final errors will have a Gaussian distribution (Gaussian noise). 

The resulting Gaussian shape is very convenient for us, because we know that standard deviation \$\sigma\$ directly relates with the RMS power of the noise, while the mean value \$\mu\$ directly relates with the DC component of the noise.

That Gaussian shape happens no matter what when "adding randomness", and is sometimes called Normal Distribution.
https://en.wikipedia.org/wiki/Normal_distribution

Here's an interactive model of a Gaussian shape (in general), and how it changes with its standard deviation and its mean values \$\sigma\$ and \$\mu\$. (drag the sliders)
https://www.geogebra.org/classic/ehkwndma
« Last Edit: November 22, 2020, 04:22:01 pm by RoGeorge »
 

Offline SilverSolder

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Re: Phase noise measurement
« Reply #8 on: November 22, 2020, 05:29:28 pm »
are we in effect depending on the low frequency components of the phase noise to "stack up" and cause enough jitter to become visible?

This is the next very good question, after the previous one.  Kind of yes, but there is yet another very tricky thing here.

Our (wrong) intuition would say:
- OK, so if I look n edges later from the triggering point (let's assume it's a square wave instead of sinus) I would see all the n'th falling edges uniformly distributed in the range of the final +/- error, around the average point, but this is not what we see!

Most of the edges are right near the expected average, even if the error came from a white noise.  So, initially all the values in the range were equally possible in the +/- error range, yet after many steps we see most of the errors will like to "cluster" around the average, only a very few fall farther away from the expected average.  The final errors distribution after many, many steps has a Gaussian shape.

This is because of something very fundamental to statistics, called Central Limit Theorem.  For our case it means that if we "accumulate" many errors equally distributed (white noise) we will end up with errors that are not equally distributed, the final errors will have a Gaussian distribution (Gaussian noise). 

The resulting Gaussian shape is very convenient for us, because we know that standard deviation \$\sigma\$ directly relates with the RMS power of the noise, while the mean value \$\mu\$ directly relates with the DC component of the noise.

That Gaussian shape happens no matter what when "adding randomness", and is sometimes called Normal Distribution.
https://en.wikipedia.org/wiki/Normal_distribution

Here's an interactive model of a Gaussian shape (in general), and how it changes with its standard deviation and its mean values \$\sigma\$ and \$\mu\$. (drag the sliders)
https://www.geogebra.org/classic/ehkwndma

Just testing my understanding....    as an example let's look at 100 edges 1 second apart...  we trigger on the first one, and look at how far edge no. 100 is away from the mathematically expected value of 100 seconds.   The distribution around the 100 second mark will be Gaussian if we do that - just like the error of each step along the way is also Gaussian.   Effectively, we end up amplifying the small Gaussian error of each step into something large enough that we can actually sample and measure - and from that we can work backwards to what the per-step error must be?








« Last Edit: November 22, 2020, 05:42:52 pm by SilverSolder »
 

Online mawyatt

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Re: Phase noise measurement
« Reply #9 on: November 22, 2020, 06:30:37 pm »
I would think the "scope method" would limit the range of measurement to something that has only moderately good PN since the measurement result is the root-sum-squared of the scope jitter and the DUT.

I don't think our moderately prices DSOs have really high quality low PN reference oscillators internally (they tend to be expensive) but if the DSO had an external reference input then one could supply a really low PN reference. Unfortunately my DSO doesn't have an external reference input  :P

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
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Offline cncjerry

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Re: Phase noise measurement
« Reply #10 on: November 22, 2020, 06:48:33 pm »
How much are you willing to spend? What carrier frequencies are we talking about?

trying to keep it below $1k and I'm only looking at 10Mhz right now.
 

Offline TexasRanger

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Re: Phase noise measurement
« Reply #11 on: November 22, 2020, 07:23:36 pm »
I have little experience with high-frequency stuff, but I was recently fiddling around with some Jitter Cleaner for ADC Clocking, I figured that something like in the appended picture should work for high offset frequencys (>1kHz).

Jitter Cleaner ICs and EVMs for Jitter Cleaner ICs are quite cheap and low frequency offset phase noise should mainly be limited by the used VCXO.
 

Online mawyatt

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Re: Phase noise measurement
« Reply #12 on: November 23, 2020, 12:29:27 am »
There are many ways to measure and characterize the phase noise.  Would be nice to link or name the documents you were talking about.


My colleague supplied the IEEE MACOM Paper. See my edited post earlier.

Best
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Offline cncjerry

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Re: Phase noise measurement
« Reply #13 on: November 23, 2020, 04:39:23 pm »
There are many ways to measure and characterize the phase noise.  Would be nice to link or name the documents you were talking about.


My colleague supplied the IEEE MACOM Paper. See my edited post earlier.

Best

Thanks, but correct me if I am wrong, but it looks like they are using the term "injection" for phase (e.g. injection locking v. phase locking) and if so, this is the procedure I'm currently evaluating.

I've been communicating via email with Andrew Holme and plan to build his system.  I'll post as i progress thru his FPGA based system and my analog version.

Thanks for all the comments.

Jerry
 

Online mawyatt

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Re: Phase noise measurement
« Reply #14 on: November 23, 2020, 06:37:37 pm »

Thanks, but correct me if I am wrong, but it looks like they are using the term "injection" for phase (e.g. injection locking v. phase locking) and if so, this is the procedure I'm currently evaluating.

I've been communicating via email with Andrew Holme and plan to build his system.  I'll post as i progress thru his FPGA based system and my analog version.

Thanks for all the comments.

Jerry

Injection locking and phase locking are slightly different, check the Reference by Adler (7) at the end of the IEEE paper, also see figure 2 in the IEEE paper. Phase locking tends to attempt to keep the phase fixed whereas injection locking tends to keep the phase within a range.

Injection locking takes advantage of an oscillator's inherent non-linearity to "mix" with the injected signal and if the injected signal is within a frequency range called the locking range the oscillator will move frequency wise towards the injected signal. This works very similar to a PLL, but doesn't require the separate components of a PLL as the basic oscillator provides everything that's needed. We've used this concept many times for various applications, including one where a microwave receiver LO would injection lock to an incoming RF signal and demodulate the data for a very small single silicon chip direct downconversion receiver developed in ~1990 and later patented (5603111).

Best,

Edit:

This injection locking concept was first described by Van der Pol when he was experimenting with relaxation oscillators based upon neon bulbs.
« Last Edit: November 23, 2020, 07:12:52 pm by mawyatt »
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Offline cncjerry

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Re: Phase noise measurement
« Reply #15 on: November 25, 2020, 05:40:06 pm »
I decided to build the system Andrew Holme built.  It is basically a DSP based version of what I'm still trying to do with with the phase shifted and mixed DUT, translated to baseband.  But even after filtering and amplifying the remaining phase noise after mixing, I'm still not getting the expected trace but getting closer.  I think I need more amplification.

So I ordered the sp605 board, the quad ADC, etc and plan to build Andrew's phase splitters.  He seems like a good guy and is providing a little help in addition to the basic layouts and the code.  It's amazing that he, as well as at least two others that built the system, are getting noise levels below -180dBc.

I'll post pictures as thing arrive.

Jerry
 

Online mawyatt

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Re: Phase noise measurement
« Reply #16 on: November 25, 2020, 06:46:37 pm »
Just looked at Andrew's work, impressive indeed!!

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
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Offline cncjerry

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Re: Phase noise measurement
« Reply #17 on: November 27, 2020, 06:16:16 am »
With regards to power splitters, Andrew used his own design:

MCL PSC-2-2+  ---> pad -> 1Mhz Filter -> pad -> HMC580 AMP -> output to ch1
                       ---> pad -> 1Mhz Filter -> pad -> HMC580 AMP -> output to ch1

I'm going to build his splitter as I have the parts but after he had recommended I follow the path of one of the other builders and use connectorized parts from Minicircuits.  But instead I was thinking of just making a couple of changes to his design.  First, I would probably use some shielding between stages.  Then I was wondering about the PSC2-2.  Since most of my testing will be in either 5Mhz or 10Mhz, I can quickly design a Wilkinson Power Splitter for each frequency.  then even though I have the amp chip, it doesn't have the best noise figure so I was thinking of changing that out as well.  The HMC580 is obsolete anyway (I have 4 or 5 of them, need 4 for each frequency) but it had a NF over 4 and the new chip that is up to 4Ghz now, has an even higher NF.  There are a lot of LNAs that have lower NF but I have to look for one with the same footprint.  Ideas?


 

Online mawyatt

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Re: Phase noise measurement
« Reply #18 on: November 27, 2020, 03:26:15 pm »
I would be concerned about any amplifiers placed in the DUT signal path, since all amplifiers are fundamentally mixers as they "mix" any 1/f, Power Supply or bias noise with the signal to some extent. So select an amp with very low 1/f noise as well as low NF, and pay close attention to the bias and power supply. This is why 30 years ago we went to the trouble of designing the baseband amplifier based upon a selected low 1/f noise npn differential pair as an input to a low 1/f noise op-amp, all powered by batteries.

Now you've pinged my interest in ultra-low phase noise measurements, like I need another topic of consideration  ???

Anyway, good luck with your phase noise endeavors and keep us posted on your progress.

Best,
Research is like a treasure hunt, you don't know where to look or what you'll find!
~Mike
 

Offline cncjerry

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Re: Phase noise measurement
« Reply #19 on: November 27, 2020, 10:39:13 pm »
Parts are beginning to arrive.  I have the ADC and ADC clock in-hand and the FPGA is out for delivery.  I'll post pictures a little later when I have time.

I sent Andrew a note today asking a few simple questions about his oscillators, but then added this:

6) Dual Mixer Time Difference: I don’t see any reason why the system couldn’t be used for DMTD as well. Using two incoming channels for DUT and reference, you would reduce the incoming noise using a 2nd channel for each. Then with the digitized DUT and Reference, mix them both with an NCO offset by 1hz or 10hz, low pass filter, zero crossing detect, and measure the ZCD delta from one channel (Ref x Offset) to the 2nd channel (DUT x offset).  You now have the delta that is scaled by 10e-6 for the 10hz offset and 10e-7 for the 1hz offset.  Moving the data to the PC, it would be plotted using TimeLab or Stable32 to produce Allan Deviation, Modified Allan deviation, etc charts.  So now your system is fully competitive with all the much more expensive alternatives.

So, now I have an extension to the project.  I've written a lot of DSP code but not on FGA but this shouldn't be all the complicated to implement.  I would love to have help on this aspect of the project.
 

Offline RoGeorge

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Re: Phase noise measurement
« Reply #20 on: November 27, 2020, 11:50:35 pm »
So, now I have an extension to the project.  I've written a lot of DSP code but not on FGA but this shouldn't be all the complicated to implement.  I would love to have help on this aspect of the project.

I would try to minimize any processing done on the FPGA side, and do as much processing as possible (if not all of the processing) in software, on the PC side.

If this is the first time working with FPGAs you'll have a surprise.  Verilog or VHDL (HDL = Hardware Description Language) are very different from being "yet another programming language".

HDL (Hardware Description Language) are not programming languages.  Think about HDL as a text file to describe a digital schematic.  HDL is not a programming language, does not describe an algorithm, HDL describes a schematic diagram.  For example, in a HDL source code there is no order of execution of the text lines, like it would be in a programming language.

Same with the HDL toolchain, very different from a compiler, and certainly not trivial to work with.

My point is:  forget about previous DSP implementations.  In fact, forget about any programming experience.  Nothing applies to FPGAs.  Programming knowledge will only add confusion when doing anything with a FPGAs, including DSP (unless you are using them with a HLS compiler, of course).  Not to say, depending on the FPGA manufacturer and the FPGA model, DSP IPs might not even be available in the toolchain without buying a very expensive license.

Sure, the math and the DSP theory still stands, but the rest of the implementation/optimization techniques, not so much.  OTOH, data acquisition and some local processing then streaming is somehow a standard application for an FPGA, so there might be some example FPGA projects out there with just the right hardware, as inspiration or to modify it. 

Anyway, not a weekend project (unless you have everything already written/developed), but rather a couple of months.
« Last Edit: November 27, 2020, 11:57:41 pm by RoGeorge »
 

Offline cncjerry

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Re: Phase noise measurement
« Reply #21 on: Yesterday at 12:10:13 am »
i'm not trying to minimize the FPGA effort but I should be able to use some of his code already to help me understand what is going on.  I've been doing a lot of reading already.

I'm attaching some of the pictures of parts arriving. Everyone loves pictures.  The only interesting one is the Crystek oscillator as I haven't seen that format before.  Basically you mount it to the ADC board and then inject 3.3V into the other end.  Andrew had made a very low noise power supply for his.  I plan to make a small PCB with the 3.3v regulator on it with a prominent SMA connector to allow it to attach directly to the back of the oscillator.

On the back of the ADC board is the connector compatible with that on the FPGA, name escapes me.  I'm going to look for an extension but I suspect it isn't avaiable.  Andrew cut the corner off his ADC board to allow it to clear an SFP cage on the FPGA when mounted. Others decided to remove the SFP cage as it wasn't being used.

The FPGA is due to be here today as well.

Getting back to the power splitter, it surprised me to see the pad->filter->pad->amp path as why reduce a signal that is already very low.  So I'm going to think about that more and probably just use connectorized modules and if I don't get as-good results, then go back and build his splitters.

More to come.

Jerry
 


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