Author Topic: An advanced question - sampling an oscillator's signal for analysis  (Read 22006 times)

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Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #275 on: February 18, 2019, 01:32:15 am »
When I first turn on the oscillator, my frequency counter shows 9,999,995Hz or thereabouts. As the oscillator warms up it reaches 9,999,999.5Hz.

Oops, I didn't pay enough attention to what you said there. The frequency change during warm up should be in the hundreds of hertz (it's 310Hz low when cold at 20°C ambient on my one), so that was a giveaway.

The HP5335A frequency error sounds like a fault rather than a calibration issue.
As you mentioned, the first thing to try would be an external reference.
I think that the HP5335A normally used a 10811 OCXO, which has a hole on the top for the frequency adjustment trimmer capacitor in it, but this will not adjust it by 150Hz.
The 10811 that I have is about 210Hz low when cold at 20°C ambient, so if your one is 150Hz low it might be worth checking if the oven is heating up - if it's there at all!

I took off the cover of the HP5335A and powered it up. It does indeed have a 10811 OCXO. After 1/2 hour there was no noticeable warmth coming from the exterior of the 10811. So, either it is busted, or something else is wrong (e.g., power not getting to it).

Right now fixing it will have to take a back door seat to building the MV89 enclosures. Did you happen to replace the fan in your HP5335A? If so, which model did you use? Mine is using a DC version of the original Pabst fan, which sounds like a small refrigerator.
« Last Edit: February 18, 2019, 05:39:50 am by dnessett »
 

Offline FriedLogic

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #276 on: February 20, 2019, 12:40:25 am »
I don't have that counter, just the oscillator - this thread has some info if you've not already seen it:
https://www.eevblog.com/forum/testgear/hp-5335a-timer-counter-anything-i-should-know/

If you get to looking at the oscillator, there are various versions of the manual and other info online, such as:
http://ftb.ko4bb.com/getsimple/index.php?id=manuals&dir=HP_Agilent/HP_10811_Crystal_Oven_Oscillator
The thermal fuse and its connections often cause problems, so if the power is getting to it that might be a good place to start.

 
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Offline Gerhard_dk4xp

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #277 on: February 24, 2019, 08:21:32 pm »
The MV89A that I have on my table definitely needs a +/- 5V tuning voltage.
I also have one that stops oscillating when Vtune > 0.5V. It seems they
drift down over time.

I had about 50% loss with my Chinese MV89As.
They have all a 20 year hot life behind them and are removed from their
boards in a most cruel way. There are lots of scars to prove that.

The MTI-260 also seem to have a lot of subtypes.
I'm just doing a PLL to lock all of them to an incoming reference frequency.
 

Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #278 on: February 28, 2019, 01:10:08 am »
One piece of design I need for the enclosure is an interface between the HP11729C Freq-Cont X-Osc output and the MV89A adjust input. This interface must convert the +/- 10 V swing of the Freq-Cont X-Osc output to the 0-5 V swing required by the adjust pin on the MV89A.

I came up with a simple divider network to achieve this conversion, shown in Figure 1

Figure 1 -

The 470 resistor divider pair converts +/- 10 V to +/- 5V. Using the 5V reference provided by the MV89A, the 10K resistor divider pair converts this swing to 0-5 V (in theory). I breadboarded this circuit and found that the actual swing is 1.06V - 4.3V. This reduced breadth is due to the actual voltage produced by the Freq-Cont X-Osc circuit when driving the interface. Instead of +/- 10 V, the range observed on the Freq-Cont X-Osc input was: -6.1V -> +7.2V. Since the output impedance of Freq-Cont X-Osc is specified as 100 ohms and it is driving ~940 ohms, this is a little surprising.

However, the circuit is not a simple passive network, because the MV89 Ref connection to the 10K resistor divider has an output impedance of 100 ohms (see previous message). I decided not to pursue a network analysis of the circuit, since the measured swing is sufficient to drive the MV89A adjust pin.

The SPDT switch allows the adjust pin to be driven either by the Freq-Cont X-Osc line or by a 2.5V constant voltage derived from the Ref pin. This means the MV89A can be used either as a reference oscillator in an HP11729C phase detector configuration or as a DUT analyzed by the HP11729C in a frequency discriminator configuration.

I would welcome thoughts about how to test this circuit with the HP11729C to insure it can keep the MV89A in quadrature with another oscillator over long time intervals when using a phase detection configuration.
 

Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #279 on: March 10, 2019, 03:23:29 pm »
If you get to looking at the oscillator, there are various versions of the manual and other info online, such as:
http://ftb.ko4bb.com/getsimple/index.php?id=manuals&dir=HP_Agilent/HP_10811_Crystal_Oven_Oscillator
The thermal fuse and its connections often cause problems, so if the power is getting to it that might be a good place to start.

Thanks for the pointers to the manuals for the 10811. Now that I have an enclosure built for one of the MV89s, I need to get the HP5335A repaired. I started with recalibrating the two adjustable power supply voltages. The 3.1 supply was off, but I was able to get it back into range. However, the 15.7 power supply was at 15V and I could not get it to 15.7 V by adjusting the controlling pot. I suspect the HP11811 might be causing the problem, so I plan to take it out of the 5335A and troubleshoot it.

However, the power supply is connected to it by an edge connector. I thought about using a alligator clip to attach power by clipping it to the pad for that purpose, but am concerned that it will slip and put 20V onto some other pad, thereby damaging the device.

Do you have any suggestions? Is there a way to test the thermal fuse and connections without applying power to the 10811? If not, are mating connectors for the edge connector widely available (eBay or perhaps an electronic parts distributer)? How do you power your 10811?
 

Offline Gerhard_dk4xp

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #280 on: March 10, 2019, 06:33:50 pm »
The mating plug is

EDAC 305-030-520-202

That's what is printed on it. I can't find where I have ordered them, at least not quickly.
Probably Mouser or Digi Key.

I'm just doing version 2 of my OCXO support board. It hosts one of 10811A, MV89, MTI260
or CVHD-950 or ECOC2522, KVG O-30-ULPN-100M, KVG O-40-ULPN-100M for 100 MHz.

There is a Xilinx Coolrunner2 that creates a 1pps out and that has a dual Flipflop PFD.
The Oven can be synchronized to an incoming reference frequency or an incoming 1pps.
There is also a doubler for 5 -> 10 MHz if needed.

This is V1:
<     https://www.flickr.com/photos/137684711@N07/30952252115/in/album-72157662535945536/     >
<     https://www.flickr.com/photos/137684711@N07/30952263115/in/album-72157662535945536/     >
It used a ring mixer as phase detector. That could not work for 1pps.

But this is still work in progress.

regards, Gerhard
« Last Edit: March 10, 2019, 06:46:38 pm by Gerhard_dk4xp »
 
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Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #281 on: March 18, 2019, 12:51:31 am »
If you get to looking at the oscillator, there are various versions of the manual and other info online, such as:
http://ftb.ko4bb.com/getsimple/index.php?id=manuals&dir=HP_Agilent/HP_10811_Crystal_Oven_Oscillator
The thermal fuse and its connections often cause problems, so if the power is getting to it that might be a good place to start.

Instead of trying to fix the HP10811, I decided to buy one from eBay and replace the one that came with the instrument. This fixed the problem. By tweeking the frequency adjust screw on the new 10811, I got the HP5335A to measure one MV89A oscillator frequency to within .01Hz of 10 MHz. Also, the new 10811 is warm to the touch after 10-15 minutes, whereas the old one did not warm up at all.

Of course, in effect I am using the MV89A as a calibration oscillator, so there is no guarantee that the HP5335A is actually calibrated properly. But at least it should be possible to get within 1-2 Hz of an accurate measurement.

In regards to the HP10811, I did buy a connector, so at some future point I could attempt to fix it. However, I was already sidetracked by trying to get the  HP5335A to work properly. I didn't want to get sidetracked on a sidetrack. My goal is measuring phase noise, which now, after building enclosures for the other 2 MV89As, is within reach.
 

Offline jpb

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #282 on: April 19, 2019, 12:55:19 pm »
I have an MV89 I got from China years ago and it seems to work fine (though I don't have anything that will measure its phase noise though.

The main issue with them I seem to remember for Time Nuts postings is that the 10MHz devices are frequency doubled 5MHz devices:

https://www.mail-archive.com/time-nuts@febo.com/msg58269.html

The reliability issue is to do with a capacitor going bad but that shows up as a low level output I think.

It will be interesting to see what your measurements show.

Thanks for the info, jpb.

Given your experience with the MV89, I have a question. When I ran one of the MV89s for an hour or so, I noticed it became quite hot. I am still able to pick it up and hold it my hand, but it is on the borderline of that. When you were working with yours, did you have a heatsink on it? If so, how did you attach it (as there are no screw holes for this purpose on the top)?
Sorry, I've only just seen this and now it is rather too late to reply!
Just for the record, my MV89 did not have a heat sink and it did get warm but almost all OCXOs do - in fact some get quite hot. This is not that surprising as the temperature of the crystal is around 70C or more, an OCXO that is specced to operate up to 70C must keep the crystal at some temperature above that as it has no means of cooling only heating.

On the subject of the 10811 - I had one which was broken, (weird waveform). I managed to mend it using the repair manual which is very good but then I was doing one last probe of all the voltages and managed to blow up one of the transistors. I replaced it with one I had but it was not the right specs. The original type is unobtainable but recently I got round to ordering a similar part but it has been a couple of years and one house move since I last worked on it so I'm going to have to start over when I have time.

I'm looking forward to seeing how your phase noise measurements go dnessett.
I am thinking of getting a 16bit picoscope myself but I'm torn between this and an audio interface with word clock. Are you still happy with the picoscope?
I wish it had 4 inputs instead of 2. I want to use it for ADEV measurements but for three-cornered-hat measurements I really need 3 or 4 inputs.
Also it would be nice to have an external clock reference option - I can't work out if this matters or not if one input is used for a reference.
 

Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #283 on: April 19, 2019, 10:06:50 pm »
I'm looking forward to seeing how your phase noise measurements go dnessett.
I am thinking of getting a 16bit picoscope myself but I'm torn between this and an audio interface with word clock. Are you still happy with the picoscope?
I wish it had 4 inputs instead of 2. I want to use it for ADEV measurements but for three-cornered-hat measurements I really need 3 or 4 inputs.
Also it would be nice to have an external clock reference option - I can't work out if this matters or not if one input is used for a reference.

I only use my Picoscope as a spectrum analyzer. It has the advantage of analyzing down to 1 Hz, whereas my Siglent 3032X only goes down to 9 KHz. For phase noise measurements, the Picoscope is crucial. Also, the 16 bits of the 4262 is necessary to get enough precision to capture low power phase noise values.

My mother broke her hip and I have had to dial back my work on this project in order to interact with doctors and help her with her rehabilitation. However, I hope to have some results in the next week or two.
 

Offline jpb

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #284 on: April 20, 2019, 06:59:52 pm »
I only use my Picoscope as a spectrum analyzer. It has the advantage of analyzing down to 1 Hz, whereas my Siglent 3032X only goes down to 9 KHz. For phase noise measurements, the Picoscope is crucial. Also, the 16 bits of the 4262 is necessary to get enough precision to capture low power phase noise values.

My mother broke her hip and I have had to dial back my work on this project in order to interact with doctors and help her with her rehabilitation. However, I hope to have some results in the next week or two.
I'm sorry to hear about your mother. I wish her a speedy recovery.

I look forward to reading the outcome of your measurements.

I've been having fun making ADEV measurements but at present I'm using my counter and despite best efforts with mixers to provide some heterodyne gain (if that is the right term) the measurements are buried in noise (particularly quantisation noise)below about 20 or 30 seconds. I'd like to get down to about a second. There are lots of approaches to take, but most of them require acquisition of more equipment!
 

Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #285 on: May 27, 2019, 10:51:47 pm »
It has been a long, hard and onerous journey of about a year, but I am now in the position to run some experiments. The test setup is in place and working. There have been changes since I originally described this setup, which I now document.

HP11729C Based Frequency Discriminator Configuration



Figure 1

HP11729C Mechanical Configuration

For this test setup, the HP11729C has the following mechanical configuration:

  • 50 ohm terminator on the 640 MHz output. Since the oscillators tested are all 10 MHz, the 640 MHz signal (which generates down converting frequencies to put the oscillator signal into the 10-1028 MHz range) is unused.
  • 50 ohm terminator on the 10Hz-10Mhz (unused) noise spectrum output.
  • The Mode selector is set to phi(phase), CW and the Local selector is on.

Device Under test

The Device (oscillator) Under Test (DUT) must output a signal having power within the range of the HP11729C input limits. The output of the directional coupler (see below) between the DUT and HP11729C is connected to a variable attentuation pad (shown in the figure) to ensure the input to the HP11729C does not exceed 3.5 dBm. This constraint is necessary because exceeding this input power drives the HP11729C into compression.

Directional Couplers

The HP11729C inputs terminate the coaxes that are connected to them. However, to monitor the signals during a test, two directional couplers are used to tap the oscillator and Delay Complex (see below) inputs. The signals from these taps are displayed on an oscilloscope (Rigol 1104Z), which allows the use of the Delay Device to bring the two signals into rough quadrature. The Phase Lock indicator on the HP11729C is then used to bring the signals into tight quadrature. The directional couplers are MiniCircuit ZDC-10-1 devices.

Delay Line and Delay Device

The Delay Line is 400'+2*25'+2x50' = 550' of RG-58 coax. The total delay of the signal between the IF output and the mixer input varies depending on the delay value selected for the Delay Device. The Delay Device is described in this EEVBlog topic. Normally, the signal is delayed about 875 ns (8 full periods plus an extra 275 degrees) by the combined Delay Line and Delay Device (the Delay Complex). The Delay Complex reduces the power of the IF output by 8.268 dB.

The maximum sensitivity of the frequency discriminator occurs when the Delay Complex attenuates the IF output by 8.7 dB. While the value provided by the Delay Complex is somewhat less than this optimal value (around 8.268 dB), the need to put the two signals into quadrature and to utilize coaxes that were available necessitated use of this slightly non-optimal value.

Low Frequency Spectrum Analyzer

The Low Frequency Spectrum Analyzer used in these experiments is a PicoScope 4262. This is an FFT SA, the use of which results in some differences in the measurement procedures specified in the HP11729C Operating and Service Manual. These changes are documented in the next message that I will post to this topic.

The 1Hz-1MHz output of the HP11729C feeds the PicoScope through a Tee. One end of the Tee connects to the PicoScope while the other end is terminated by a 600 ohm terminator. 600 ohm termination is necessary, since the 1Hz - 1MHz output has a source impedance of 600 ohms. (The coax connecting the 1Hz-1MHz output to the Tee is 50 ohm RG-58. However, it is only about 5 feet long and at 10 Mz should not behave as a transmission line, so this impedance mismatch can be safely ignored.)
« Last Edit: May 27, 2019, 11:26:09 pm by dnessett »
 

Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #286 on: May 27, 2019, 10:53:51 pm »
The measurement procedures for an HP11729C operating in Frequency Discriminator mode are somewhat complicated and require documentation and comment. In addition, the procedures as described in the HP11729C Operating and Service Manual are predicated on the use of a swept-tuned spectrum analyzer. However, the test setup utilizes an FFT spectrum analyzer (a PicoScope 4262), which has some significant differences to a swept-input SA. These differences create changes in the computations required to characterize phase noise in oscillators.

In regards to the use of a PicoScope in the test setup, I gratefully acknowledge the help given me by Gerry, a tech specialist active on the PicoScope forum, navigating through several issues that affect such use. The most prominent of these is the effect of processing gain on stochastic signals (i.e., noise), which requires compensation in order to obtain valid spectrum data.

Below is presented the procedure used to compute phase noise using the test setup described in the previous message. This procedure is presented in some detail so that others may evaluate it and, if desired, use it to conduct their own experiments. It should be noted that this procedure is general and, with suitable minor modifications (e.g. elimination of step 1), should apply to any double balanced mixer implementing a frequency discriminator based phase noise analyzer.

Procedure to Test An Oscillator with the HP11729C in Frequency Discriminator Mode

1. Make sure the 640 MHz output and the 10 Hz-10MHz output are terminated by 50Ω.
2. Connect a signal generator to a swept-tuned spectrum analyzer (to make these instructions concrete, it is assumed here that the signal generator is a Rigol DG1022 and the swept-tuned spectrum analyzer is a Siglent SSA3032X. The latter is used since the Picoscope 4262 has a maximum input frequency of 5 MHz, which is insufficient to execute the next steps.). Set the output frequency of the DG1022 to 10 MHz and the amplitude to 200 mVp-p (-10 dBm).
3. Select the FM modulation function on the DG1022; set the modulation frequency to 1 KHz and the frequency deviation to 100 Hz.
4. Using the SSA3032X, measure the difference in dB between the 10 MHz and 10.001 MHz lines and note the value (call it Delta_SB-cal). This value is the sideband power minus the carrier power. For example, if the carrier power is -10 dBm and the sideband power is -30 dBm, then Delta_SB-cal would equal -20 dBm.
5. Disconnect the DG1022 from the SSA3032X. Connect the DG1022 to the Microwave Test Signal input of the HP11729C and the IF output of the HP11729C to the SSA3032X. Measure and note the output power of the 10.001 MHz line on the SSA3032X (call it P-cal).
6. Connect the oscillator to the input of a directional coupler. Connect the output of the directional coupler to the SSA3032X, adding enough 50Ω attenuation padding so the output from the directional coupler is less than or equal to 3.5dBm. (It is convenient if the pad is adjustable in 1 dB increments.)
7. Disconnect the padded directional coupler output from the SSA3032X and connect it to the Microwave Test Signal input of the HP11729C.
8. Connect the IF output of the HP11729C to the input of the Delay Complex. Connect the output of the Delay Complex to the input of a second directional coupler. Connect the output of that coupler to the SSA3032X and measure the output power. The difference between the IF output and Delay Complex output power should be close to 8.7 dBm, if the coax cable length is properly chosen.
9. Connect the Delay Complex output to the 5-1280 MHz input of the HP11729C.
10. Connect the 1 Hz-1MHz output of the HP11729C to a Tee at the PicoScope 4262 input. Connect the other end of the Tee to a 600Ω terminator.
11. Set up the PicoScope to use Blackman-Harris windowing, dBm@50 ohm scale and select an appropriate number of bins for the FFT. (Assuming the use of a PicoScope 4262, in the channel setup menu, choose 200 KHz hardware low pass filtering.) Choose display mode as "Average" and select an appropriate number of segments over which to compute the average (using the “Statistics Captures” box on the General tab of the Tools->Preferences window). Set the Frequency Span of the PicoScope to an appropriate value. If desired, set the primary view of the PicoScope to “Scope Mode” and the secondary view to “Spectrum Mode”. This allows the adjustment of spectrum properties so that bin width can be adjusted precisely (see this discussion on the PicoScope Fourm)
12. Connect the coupler ports of the directional couplers to two channels of the oscilloscope with the output of the oscillator directional coupler Tee'd at the oscilloscope input. Connect the Tee'd output of the oscilloscope input to a Frequency Counter (e.g. HP5335A), so that the frequency of the oscillator can be monitored. Connect the Tee'd output of the Delay Complex coupler port to a 50 ohm terminator. Adjust the Delay Device so the two signals are roughly in quadrature.
13. Using the quadrature LEDs on the HP11729C, fine tune the Delay Device so that the green LED is lit.
14. After the chosen number of segments have been averaged (as indicated when the capture count equals this value), copy the PicoScope spectrum in CSV format to a file and move it to the analysis computer.
15. Using Octave, convert to mW by first applying 10^(dBm-value/10). If necessary sum the bins so the spectrum is presented in 1 Hz increments (or as close to that as is possible). That is, if necessary, sum the bins between x±.5, x=1…(upper range of spectrum) to yield bins 1 Hz wide. Ignore the bins with offset freqencies less than .5 Hz. Convert the millwatt values to dBm and correct each 1 Hz bin for processing gain by adding to each 10 log10(number of bins/2). Added 6/01/2019: The order in which summing of bins and correction for processing gain occurs is important. In particular, the bins should be corrected for processing gain first and then summed.
16. To convert the measurements to phase noise, add 10 dB and the value of Delta_SB-cal noted in step 4 to each data point. (NB: there is a mistake in step 22 of the HP11729C Operating and Service Manual. This step, which appears on page 3-24, stipulates that the Delta_SB-cal value should be subtracted, not added to each data point. However, in the example given at the end of step 22, it is added. The error is also apparent when the mathematics behind the corrections are derived. See the mathematical justification for Phase Noise corrections.) Adding 10 dB normalizes each data point value to a carrier power level of 0 dBm (recall that the calibration uses a carrier of -10 dBm). Subtract P-cal from each data point. Subtract 20 log(f-off/1 Khz), where f-off is the offset frequency of a bin, from the bin power value (to compensate for differences between the calibration Fourier frequency (1 KHz) and the offset frequency).
17. The result of the adjustments is the phase noise spectrum of the oscillator.

Discussion

When I first worked my way through the procedure described in the HP11729C Operating and Service Manual, it seemed like voodoo. There was very little justification for its prescriptions and even that (found mostly in the appendices) was vague and puzzling. Fortunately, I found an HP product note that went into much more detail on the theory behind the practice (i.e., HP product note 11729C-2: Phase Noise Characteristics of Microwave Oscillators - Frequency Discriminator Method). However, even that very helpful document contained many inscrutable passages and I had to work hard to extract a working understanding of what was going on.

I thought it would be useful to present my current understanding of several issues, in order to relieve others from the onerous work necessary to dig this understanding out of the product note.

Steps 1-5

The basic goal of these steps is to measure the values required to compute the discriminator constant. Delta_SB-cal is required to convert dBm measurements to dBc units. P-cal is the system response to a known sideband value. Both are used in the corrections described in step 16.

Step 6

Setting the padded input from the oscillator under test (DUT) to a level equal to or less than 3.5 dBm is required to ensure the HP11729C doesn't go into compression, thereby invalidating the frequency discriminator calibration procedure.

Steps 7-10

Keeping the difference between the IF output power and Delay Complex output power as close to, but not exceeding 8.7 dBm yields the optimum system sensitivity, as described in Appendix C of Product note 11729C-2.

Steps 11-15

The selection of a Blackman-Harris window was somewhat arbitrary, but did have support from this article. The Blackman-Harris window used by the PicoScope is 4-term See this post. After some experiments, a different choice of FFT window may recommend itself.

Serendipitously, the PicoScope 4262 makes available a 200 KHz hardware low-pass filter. This has to be enabled in the Channel setup menu and provides significant anti-aliasing protection for the signal coming out of the HP11729C.  Step 15 includes corrections for processing gain created by the FFT algorithm and sums the power in adjacent bins in order to make the final bin result 1 Hz wide. It should be noted that for noise signals, summing power values is the correct approach, whereas for non-stochastic signals the proper technique is to sum amplitudes. Also, I chose to sum those sub-Hertz bins that were +/- .5 Hz on either side of the integral Hz value. Bins associated with Hz values less than or equal to .5 Hz were dropped.

Step 16

The motivation for these corrections is not self-evident and requires some explanation. As mentioned previously, at first they seemed to me to be something like voodoo. The justification is mathematical and while not particularly difficult (only algebra is involved), it is somewhat long. Consequently, I decided to make it the subject of a separate message. This will allow those not interested to simply skip it and accept the correctness of the corrections made in step 16 as given.
« Last Edit: June 01, 2019, 10:37:44 pm by dnessett »
 

Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #287 on: May 27, 2019, 10:54:51 pm »
The corrections made to the measurements described in step 16 of the Frequency Discriminator test setup procedure are somewhat inscrutable. For those who wish to understand the rationale behind them, I provide the mathematical justification in this message. Those who don't like or can't be bothered with math are encouraged to skip the remainder of this message.

Warning: Algebra ahead

HP product note 11729C-2 provides the mathematical justification for the corrections specified in step 16. However, this justification is not isolated to a single section of the product note; although most of the material is found on pgs 16, 24-27 and 40. One complication that arises is the product note includes some corrections required when using a swept-tuned spectrum analyzer, corrections that are not applicable to an FFT spectrum analyzer. Specifically, the Noise Bandwidth of analog HP spectrum analyzers is used for one correction; whereas the Effective Noise Bandwidth correction of the FFT windowing function is already applied by the PicoScope 6 software and requires no further correction. In addition, a correction factor for the "log-shaping and detection circuitry of an analog spectrum analyzer" is applied. Again, this is not applicable to FFT spectrum analyzers. Consequently, the correction procedure given in the test setup description elides these steps and the mathematics justifying their use is modified to eliminate terms corresponding to them.

In the derivation of the equation for the frequency discriminator constant the final result is: \$\nu(t)=K_{d}\varphi(t)\$, where \$\nu(t)\$ is the voltage output of the Phase Detector after low-pass filtering, \$K_{d}\$ is the (frequency) discriminator constant, and \$\varphi(t)\$ is the instantaneous frequency corresponding to the output voltage.

In the HP product note, this is presented in a slightly different form: \$\Delta V = K_{d}\Delta f\$, where \$\Delta V\$ is the change in output voltage and \$\Delta f\$ is the change in instantaneous frequency. These are mathematically equivalent formuations.

The equations above are time domain descriptions, whereas the spectrum measurements are in the frequency domain. Consequently, additional notation is necessary to identify these measurements. (Subsequent page references are citations to the HP product note).

On page 6, two symbols are defined to identify the relevant spectral data. First, \$S_{v}(f_{m})\$ identifies the "power spectral density of the voltage fluctuations out of the detection system" at the offset frequency \$f_{m}\$. \$S_{\Delta f}(f_{m})\$ is the spectral density of the frequency fluctuations at the offset frequency \$f_{m}\$ . Thus, \$S_{v}(f_{m})\$ represents the power spectral density of the signal \$\nu(t)\$ (this is what is measured by the low frequency spectrum analyzer during an experiment) and \$S_{\Delta f}(f_{m})\$ represents the frequency spectral density of the signal \$\varphi(t)\$.

While discussing symbols representing spectral densities, it is convenient to mention another quantity that plays an important role in the characterization of phase noise, \$\mathscr{L(\mathcal{\mathrm{f_{m}}})=\frac{\mathcal{P_{SSB}}(\mathrm{f_{m}})}{\mathcal{P_{\mathrm{Carrier}}}}}\$. \$\mathcal{P_{\mathrm{Carrier}}}\$ is the power of the (oscillator) carrier signal. \$\mathcal{P_{SSB}}(\mathrm{f_{m}})\$ is the single side-band power of a phase modulation sideband at the offset frequency \$f_{m}\$. When discussing phase noise, most specifications provide values of \$\mathscr{L(\mathcal{\mathrm{f_{m}}})}\$, so there is a requirement to convert the spectra measured by the frequency discriminator into the form \$\mathscr{L(\mathcal{\mathrm{f_{m}}})}\$. On page 6 is derived the relationship between \$S_{\Delta f}(f_{m})\$ and \$\mathscr{L(\mathcal{\mathrm{f_{m}}})}\$:

\$\mathscr{L(\mathcal{\mathrm{f_{m}})}} = \mathcal{\frac{S_{\Delta f}(f_{m})}{{2f_{m}}^2}}\$.

Spectral densities are continuous functions of frequency. When the set of frequencies associated with a power measurement is countable, this is not true and the result is referred to as a spectrum. Since the measurements by a frequency discriminator test setup quantize frequency, phase noise characterizations based on measurement deal with spectra rather than spectral densities. We continue to use the notation \$S_{v}(f_{m})\$, \$S_{\Delta f}(f_{m})\$, and \$\mathscr{L(\mathcal{\mathrm{f_{m}}})}\$ to identify the spectra arising from quantization of the identically named spectral densities.

Phase noise is canonically described as arising from FM modulations of the carrier signal by stochastic (noise) processes within the oscillator. The products of these processes add linearly to create the total phase noise spectrum or spectral density.

Consider the value associated with \$S_{v}(f_{m})\$, for a particular offset frequency \$f_{m}\$. This is the power of the \$f_{m}\$ component of the spectrum and the total phase noise spectrum is mathematcially equivalent to a sum of spectra, where each comprises a single tone spectrum for the frequency \$f_{m}\$ (m ranging over all values for \$S_{v}(f_{m})\$). To be clear, the single tone spectra are not those produced by the noise processes, which generally create multi-tone spectra. The single tone spectra are a mathematical decomposition useful when considering how to measure the discriminator constant. In particular, measurement of the system response to a single tone input contains all the information needed to compute the discriminator constant. This is the objective of the calibration steps described in the test setup procedure presented previously, specifically in steps 3-5.

The mathematical justification for the corrections specified in step 16 is found on page 40. It begins with the casual assertion that for m<0.2rad, where m is the modulation index of the modulation:

\$\frac{P_{ssb}}{P_{carrier}} = \frac{m^2}{4}\$

I searched for hours on the internet to find a justification for this result without success (it may be that it exists in some textbook, of which I do not have a copy). Finally, I found enough information to dervive it. On this web page, it is noted that for sufficiently small FM modulation indices (which on other web pages is given as m<0.2), the Bessel J coeffients are: \$J_{0} = 1\$, \$J_{1} = \frac{m}{2}\$, and \$J_{n} = 0, n>1\$. As an aside, the correct constraint on the modulation index is m<.2, not m<0.2rad, since the modulation index is defined as: \$ m = \frac{\Delta f_{peak}}{f_{m}}\$, where \$\Delta f_{peak}\$ is the peak frequency deviation of the FM modulation and \$f_{m}\$ is the FM rate. This is a unitless ratio. The constraint m<0.2rad is appropriate for Phase Modulation and I found several references on the internet where it is erroneously cited for FM modulation.

In the calibration procedure (step 3), the FM rate is set to 1 KHz and the frequency deviation to 100 Hz. This yields a modulation index of .1, which satisfies the given constraint.

In a slide presentation available on the internet (on slide "Angle and Pulse Modulation - 7"), the total power \$P_{T}\$ of an FM modulated signal with carrier \$P_{C}\$ is given as:

\$P_{T} = P_{C}({J_{0}}^2 + 2({J_{1}}^2+{J_{2}}^2+ ...))\$

Noting the values of \$J_{i}\$ when the constraint m<.2 holds and substituing into this equation:

\$P_{T} = P_{C}(1 + 2(\frac{m^2}{4})) = P_{C} + P_{C}\frac{m^2}{2}\$

In the last expression to the right of the equal sign, the first term represents the carrier power and the second term represents the power of the double sideband. The single sideband power is 1/2 of this, i.e., \$P_{ssb} = P_{C}\frac{m^2}{4}\$. Dividing this expression by \$P_{C}\$ (aka \$P_{Carrier}\$) yields the assertion made at the beginning of page 40.

Given \$\frac{P_{ssb}}{P_{carrier}} = \frac{m^2}{4}\$, we can substitute the values measured during calibration in steps 3-5 and develop an expression for the single-sideband to carrier power ratio in terms of these values. First, to ensure clarity, the derivation on page 40 identifies the calibration values as \$\Delta f_{peak_{cal}}\$ and \$f_{m_{cal}}\$ and uses them to express the modulation index, \$m = \frac{{\Delta f_{peak_{cal}}}}{f_{m_{cal}}}\$, so:

\$\frac{P_{ssb}}{P_{carrier}} = \frac{m^2}{4} = \frac{1}{4}\frac{{(\Delta f_{peak_{cal}})}^2}{(f_{m_{cal}})^2}\$

At this point it is useful to mention that, so far, we have not been dealing with values expressed in logrithmic units. Rather, the values used in the expressions are in linear units. This is important in the next step of the derivation. The measurement of P-cal and Delta_SB-cal on the spectrum analyzer generally will be made in logrithmic units (e.g. dBm). To use these values in the derivation, we must express them in linear units. To retain clarity, the distinction between these values in linear and logrithmic units is made by appending them with either [Lin] or [dBm]. Thus, from this point, P-cal in linear units (e.g. milliwatts) is represented by the symbol \$P_{cal}[Lin]\$ and in logrithmic units by the symbol \$P_{cal}[dBm]\$. Simlarly Delta_SB-cal in linear units is represented by \$\Delta SB_{cal}[Lin]\$ and in logrithmic units by \$\Delta SB_{cal}[dBm]\$. The [Lin] and [dBm] notation applies to the other symbols as well.

In step 4 of the test setup procedure, the difference between the carrier and sideband power is measured by subtracting the former from the latter (this assumes the SSA3032X is displaying results in dBm). In other words, \$P_{ssb}[dBm] - P_{carrier}[dBm] = \Delta SB_{cal}[dBm]\$. In linear units the subtraction becomes division and therefore:

\$\frac{P_{ssb}[Lin]}{P_{carrier}[Lin]} = \Delta SB_{cal}[Lin]\$.

Consequently, we can write:

\$\frac{P_{ssb}}{P_{carrier}} = \frac{m^2}{4} = \frac{1}{4}\frac{{(\Delta f_{peak_{cal}})}^2}{(f_{m_{cal}})^2} = \Delta SB_{cal}[Lin]\$

The last equality can be re-expressed as:

\$\Delta {f}^2_{peak_{cal}} = 4 {f}^2_{m_{cal}} 10^{{\frac{\Delta SB_{cal}[dBm]}{10}}}\$, since \$10^{{\frac{\Delta SB_{cal}[dBm]}{10}}} = \Delta SB_{cal}[Lin]\$

The derivation of the equation for the frequency discriminator constant specifies voltage amplitudes for the oscillator (DUT),\$V_{DUT-AMP}\$ and the referenced signal, \$V_{R-AMP}\$. However, it fails to indicate whether these amplitudes are peak-to-peak values or RMS values. This follows the formuation in Appendix A (page 34), on which the derivation is based, which also does not indicate whether peak-to-peak or RMS voltages are meant. On page 40, however, the discriminator constant is defined implicitly as:

\$K_{d} = \frac{\Delta V_{rms}}{\Delta f_{rms}}\$

So far, we have derived the equivalent expression for \$\Delta {f}^2_{peak_{cal}}\$, not \$\Delta {f}^2_{rms_{cal}}\$. This is easily fixed, since \$\Delta {f}_{peak_{cal}} = \sqrt{2} \Delta {f}_{rms_{cal}}\$ and therefore:

\$\Delta {f}^2_{rms_{cal}} = 2 {f}^2_{m_{cal}} 10^{{\frac{\Delta SB_{cal}[dBm]}{10}}}\$

Substituting this expression into the definition of \$K_{d}\$ yields:

\$K^2_{d} = \frac{\Delta V^2_{rms}}{2 {f}^2_{m_{cal}} 10^{{\frac{\Delta SB_{cal}[dBm]}{10}}}} = \frac{P_{cal}[Lin]}{2 {f}^2_{m_{cal}} 10^{{\frac{\Delta SB_{cal}[dBm]}{10}}}}\$, since \$P_{cal}[Lin]\$ is the response expressed as power (\$\Delta V^2_{rms}\$) to the calibration input.

Applying \$10 log_{10}()\$ to both sides of the equation re-expresses it in terms of dB:

\$2K_{d}[dBm] = P_{cal}[dBm] - (\Delta SB_{cal}[dBm] + 20 log_{10}(f_{m_{cal}})+3dB)\$

Note: There is a mistake on page 40, which is corrected in the equation given above. On page 40, the left hand side of the equals sign is given as \$K_{d}[dBm]\$, rather than \$2K_{d}[dBm]\$. It turns out that this mistake is cancelled out by an error in the equation given for \$S_{\Delta f}(f_{m})\$ on page 16, which should be:

\$S_{\Delta f}(f_{m}) = S_{v}(f_{m}) - 2K_{d}\$

I am deliberately leaving off the units in this equation, since as stated on page 16, \$S_{\Delta f}(f_{m})\$ is in units of [dBHz/Hz], whereas both \$S_{v}(f_{m})\$ and \$K_{d}\$ are given in units of [dBm]. How one gets a quantity in [dBHz/Hz] by subtracting two quantities in [dBm] is beyond my comprehension. In fact the whole document is riddled with equations that combine units in such a way as to be completely baffling.

Anyway, the desired final result is \$\mathscr{L(\mathcal{f_{m}})}\$ and this is expressed in terms of \$S_{\Delta f}(f_{m})\$ on page 7:

\$\mathscr{L(\mathcal{f_{m}})} = S_{\Delta f}(f_{m}) - 20 log_{10}(\frac{f_{m}}{1 Hz}) - 3 dB\$
\$\;\;\;\;\;\;\;\;\;= S_{\Delta f}(f_{m}) - 20 log_{10}(f_{m}) - 3 dB\$,

where \$20 log_{10}(f_{m})\$ in the last expression to the right of the equal sign is written without the explicit reference to its units.

Substituing the equation for \$S_{\Delta f}(f_{m})\$ and in that the equation for \$2K_{d}\$ gives:

\$\mathscr{L(\mathcal{f_{m}})} = S_{v}(f_{m}) - (P_{cal}[dBm] - (\Delta SB_{cal}[dBm]\$
\$\;\;\;\;\;\;\;\;\;\;\;\;\; + 20 log_{10}(f_{m_{cal}})+3dB)) - 20 log_{10}(f_{m}) - 3 dB\$
\$\;\;\;\;\;\;\;\;\;= S_{v}(f_{m}) - P_{cal}[dBm] + \Delta SB_{cal}[dBm] - 20 log_{10}(\frac{f_{m}}{f_{m_{cal}}})\$

Recalling that \$S_{v}(f_{m})\$ is what is measured by the low frequency spectrum analyzer during an experiment, the last equation to the right of the equal sign justifies the corrections made in step 16 (except adding 10 dBm, which is already justified in the description of the step).
« Last Edit: May 28, 2019, 12:39:14 am by dnessett »
 

Offline dnessett

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Re: An advanced question - sampling an oscillator's signal for analysis
« Reply #288 on: May 27, 2019, 11:11:22 pm »
6/01/2019: While working on the writeup for the MV89A oscillator tests, I discovered a bug in my Octave code that removes processing gain and sums frequency bins to 1 Hz width. Specifically, I did these things in the wrong order. I first summed the bins and then corrected the result by adding 10 * log10(rows(summed spectrum)/2) to each bin. I should have corrected each bin in the original data and then summed the bins. I have corrected this, but the plots in the original version of this post were incorrect. I have replaced them with corrected plots and also added a comment (shown in red) focused on why the noise floor shown in the plots doesn't seem to agree with the noise floor implied by the PicoScope 4262 spec.

Note that the conclusions about the PicoScope 4262 noise floor with respect to the MV89A data output by the Frequency Discriminator haven't changed. The corrected plots show these two signals in the same relationship as before. However, the absolute power values have changed.


Prior to testing oscillators using the frequency discriminator mode of the HP11729C, it was necessary to ascertain whether its output is above the PicoScope 4262's noise floor. To explore this question, I analyzed one of the MV89A oscillators I obtained. This device is an ultra low phase-noise double oven oscillator and I reasoned that if the output of the HP11729C in frequency discriminator mode with the MV89A as DUT is above the noise floor of the PicoScope, then the PicoScope should be suitable for the analysis of most oscillators.

Figure 1 compares the noise floor of the PicoScope with the output of the HP11729C in frequency discriminator mode with the MV89A as DUT. The PicoScope noise floor is in red and the HP11729C output is in blue.



Figure 1 (Corrected on 6/01/2019)

It is important to understand that the blue plot is not the phase noise of the MV89A. It represents the output of the HP11729C before the corrections indicated in step 16 of the test setup procedure are applied. Specifically, both red and blue plots are normalized according to the instructions in step 15 in order to correct for processing gain, and sum bins to normalize the spectra to 1 Hz bin width. Only these corrections are made, since it would make no sense to apply the phase noise corrections given in step 16 to the PicoScope noise floor data. This comparison only determines whether the signal from the HP11729C is hitting the PicoScope noise floor, which would invalidate the measurement.

Figure 1 clearly shows the PicoScope noise floor being below the signal output by the HP11729C. However, as the offset frequencies near 0, the two approach each other. Figure 2 shows the two plots in the range 1-100 Hz.



Figure 2 (Corrected on 6/01/2019)

It is clear that the two approach each other at the low end of the spectrum. This introduces some uncertainty in the measurements. Keep this in mind when evaluating the results of oscillator tests. At just what offset the output of the HP11729C are corrupted by the PicoScope noise floor is a judgement call.

One prominent feature of the MV89A noise plot are the significant spurs occuring at the low end of the spectrum. It turns out most of these are due to 60 Hz frequency modulations of the oscillator carrier. These will be discussed in more detail when the test results of various oscillators are published.

One issue requires comment. In the PicoScope 4262 spec, the maximum sensitivity of the device is give as 8.5 uV. At 50 ohms, this corresponds to -99 dBm. However, the noise floor shown in figure one is only about -82 or -83 dBm. How is this difference reconciled?

Figure 3 shows a plot of the PicoScope 4262 before bin summing, but after processing gain elimination. Clearly the noise floor is roughly -99 dBm, which corresponds to the quoted maximum sensitivity.




Figure 3 (Added on 6/01/2019)

As of this writing I have tested two oscillators and am in the process of writing up the results. I have decided to publish these results in a new forum topic, since this topic is focused on how to measure phase noise. I assume many will be interested in the test results who have no interest in the details of phase noise measurement. When I create the new topic, I will fill in this link (which at present is dead which is now active) so those who have followed the discussions here are directed to the results.
« Last Edit: June 05, 2019, 04:21:04 am by dnessett »
 


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