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QDX FST4W-300 Transmits only 2 tones? #qdx


 

This subject has been raised before, [ /g/QRPLabs/topic/94416795#94434 ] smaller frequency shifts than WSPR not being transmitted correctly.

I attach 2 shots, one a Softrock/WSJT-X and A QDX/WSJT-X.
While due to a hardware mod I can only use my version 1 QDXs with the 1.02 firmware it shows similar to a previous post.

Has this been rectified since October 18? I see no note of this in the 1.06 firmware.

73 Alan G4ZFQ


 

I am running firmware 1.05 on the V3 board, and the problem is pretty obvious, with FST4W-300 being unusable (one tone is entirely skipped over):


The 0.180 Hz tone spacing of FST4W-900 is even worse (only two tones output):


As a measurement check here is the FST4W-900 output from my IC-7200:


All measurements made with my home-built Time Interval Counter, using the internal digital mixer to translate the RF frequency down into the audio-frequency range.? The displayed frequency is the mixer output, and somewhat arbitrary.? What matters is the difference frequency of the tones.? These tests were done on the 30-meter band.

I will eventually install V1.06 firmware, but I think Hans would have mentioned it if this had been improved.
--
Paul Elliott - WB6CXC


 

V1.06 installed (quick and easy! -- Thanks, Hans!)

But as expected, the fine-frequency setting still exhibits the problem.? Whether the QDX emits two or three tones during FST4W-300 operation probably depends on where the tones fall within the set of tones?"achievable" with the current algorithm.
--
Paul Elliott - WB6CXC


 

Hello Alan?

Still a pending issue... Thought to be due to floating point precision limitations. I need to investigate..?

73 Hans G0UPL
http://qrp-labs.com
https://www.buymeacoffee.com/g0upl


-------- Original message --------
From: Alan G4ZFQ <alan4alan@...>
Date: Fri, Nov 25, 2022, 7:57 PM
To: [email protected]
Subject: [QRPLabs] QDX FST4W-300 Transmits only 2 tones? #QDX
This subject has been raised before,? [
/g/QRPLabs/topic/94416795#94434? ] smaller frequency
shifts than WSPR not being transmitted correctly.

I attach 2 shots, one a Softrock/WSJT-X and A QDX/WSJT-X.
While due to a hardware mod I can only use my version 1 QDXs with the
1.02 firmware it shows similar to a previous post.

Has this been rectified since October 18? I see no note of this in the
1.06 firmware.

73 Alan G4ZFQ






 

Paul

I will try to get to investigating it soon...?

73 Hans G0UPL
http://qrp-labs.com
https://www.buymeacoffee.com/g0upl


-------- Original message --------
From: "Paul WB6CXC (tech-blog: wb6cxc.com)" <paul@...>
Date: Sat, Nov 26, 2022, 3:46 AM
To: [email protected]
Subject: Re: [QRPLabs] QDX FST4W-300 Transmits only 2 tones? #qdx
V1.06 installed (quick and easy! -- Thanks, Hans!)

But as expected, the fine-frequency setting still exhibits the problem.? Whether the QDX emits two or three tones during FST4W-300 operation probably depends on where the tones fall within the set of tones?"achievable" with the current algorithm.
--
Paul Elliott - WB6CXC


 

On 26/11/2022 05:40, Hans Summers wrote:
I will try to get to investigating it soon...
Hans

Thanks.
And, as Paul suggested, someone is going to want to use the -1800 mode with 0.089Hz tone spacing. Especially as you are enabling the lower frequencies.

73 Alan G4ZFQ


 

First:? I think the QDX is a brilliant piece of engineering and a great little transceiver.? I have one, and have just ordered two more for use in "network base station" operation.? My interest in the frequency-setting issue is mostly because it's a topic I find interesting, and there are some modes I am exploring where this issue (soon to be corrected, I hope) will be a problem.? Most people using the QDX will neither notice, or care about this issue -- the rig will just work for them.

So I finally set up an audio frequency ramp feeding the QDX USB input channel.? Output frequency measurements were made with my home-brew counter.? The displayed frequencies are after down-conversion in my counter, the absolute values are arbitrary and what matters is are the frequency differences.? I was using a Windows program called "NCH Tone Generator" to create the frequency sweeps.
First, to check the sweep itself, I sent the audio to my IC-7200 transceiver, set for 20 meters.? This is a slow sweep, 1000 Hz - 1010 Hz, taking 60 seconds:

There is measurement noise, but the frequency ramp appears to be smooth.

Then I sent the same audio sweep to the QDX, on 20 meters:

You can see that there are nine frequency steps over the 10 Hz range, each step roughly 1.25 Hz.? It is obvious that this will not work with the 1.46 Hz steps used in FST4W-120, and will cause some frequency error with the?1.4648 Hz steps used in WSPR.

Things got slightly better on the 30 and 40 meter bands, on 40m there were eleven steps (per 10Hz), but while I had expected better frequency resolution here, strangely the steps were less even than the 20m band:? The 30m band also showed eleven steps, although the spacing distribution was somewhat different.

40 meters:


Fractions are funny things, and perhaps if I had tried other audio frequencies the results would have been a bit different.

Finally, I set the audio sweep for 1000 - 1100 Hz, this time on the 10-meter band:

While the steps were uneven, there were no major discontinuities over this 100Hz range

So there you have it.
--
Paul Elliott - WB6CXC


 

Hi Paul, all

I worked on this problem this afternoon. Solved in Beta 1_06_005?

First step, reproduce the problem. To do this I used two QDX. My "Franken-QDX" Rev 3a having the Rev 4 mods and connected VGA monitor and PS/2 keyboard as the transmitter (dummy load); For reception, my 10-20m high-bands QDX prototype on 20m band. Testing at 14.044 for no good reason other than that was where the equipment was set up. I generated a 60 second audio clip in audacity with a linear sweep from 1000 to 1010Hz, and fed this audio to the transmitting QDX with VOX enabled. The receiving QDX audio was analyzed in Argo set to 10s QRSS mode and Fast speed. Results are as attached before.png which shows a few attempts to get a clean shot. It's a perfectly similar result to what Paul reported.

Many hours later...

Turns out there are THREE causes of the problem. Floating point accuracy is the first one, the major one, which hides both the others; but all three need to be solved to get fine-resolution transmit frequency control.?

1) A bug: the floating point frequency was passed into the Si5351A transmit configuration function where it was used as a floating?point number; but the actual parameter declared as an unsigned 32-bit integer. Dumb. This limits the transmit resolution to 1Hz. Resolving this was easy of course.?

2) Frequency shift threshold introduced to help the "popping" problem; remember that Rev 3 and Rev 3a boards suffer this "popping" sound in the transmit audio? That was solved by a combination of various strategies in firmware version 1_04. Each of the strategies didn't eliminate the pops but reduced them; one of these strategies was to reduce the amount of frequency updates to the Si5351A (100 times per second by default) by setting a 0.5Hz threshold; the frequency had to shift more than this amount in order for the Si5351A to be configured to a new frequency. This threshold itself had another bug which was covered up by the bug mentioned in 1) above.?

I resolved the bug easily; and I have created a new parameter on the Configuration screen called "TX shift threshold" which defines the shift threshold in milli Hertz and defaults to 500. More any mode such as WSPR and FT8 whose frequency steps are larger than 0.5Hz this would be fine; for modes with narrow-spaced frequency steps less than this, you could reduce it as needed.?

For anyone with a Rev 4 PCB, the popping problem was totally eliminated in hardware so setting 0 threshold is fine.?

3) Finally the main issue is one of floating point accuracy; if you have a frequency such as 14,044,000 USB Dial Frequency such as in my tests, then a frequency shift of 0.1Hz on this is just too small a fraction and single precission?IEEE 754 cannot represent it accurately enough in the calculations of Si5351A parameters. The significand is 24-bit which is roughly equivalent to 7 decimal digits see?

To solve this I could have simply changed the relevant parts of the code to use double precision floating point representation. I am sure this would have worked. However this could not then have used the STM32F4 microcontroller's hardware floating point unit which is only single precision IEEE 754. So it would have compiled in some double precision?floating point library presumably. Which would probably have been large, probably been slow to execute (both of which could potentially have created new problems) and definitely been about as elegant as a troll swinging a sledgehammer in a glassware shop.?

So instead I devised some careful tricks to let me use regular single precision floating point and 32-bit integer arithmetic and handle the main USB dial frequency and the audio offset as two separate components. The result should be that the frequency steps are now precise to better than a one millihertz resolution, which is about the accuracy of the audio cycle measurement on the incoming USB audio stream from the PC.?

Now the results are shown in attached "after.png" which shows the 10Hz, 60 second sweep with three settings of "TX shift threshold": 0.5Hz (500mHz the default); 2Hz (2000mHz) and 0Hz. 0Hz is run twice in the image. Note that the line thickness is a little variable, this is because between the transmitting QDX and receiving QDX there is no direct coupling, just leakage from the dummy load to my antenna.?

I believe this will comprehensively solve the problem and Paul I will be very interested if you re-run your tests on this beta version.?



Clearly QDX works extremely well already; however I do believe that use of this improved firmware version should be recommended for everyone (once I release an official 1_06, after a few people confirm there are no unintended issues with the beta version). Improved accuracy of the transmitted frequency does result in increased probability of decode, particularly under DX circumstances or other weak conditions.?

Thusly expired my Wednesday...

73 Hans G0UPL



On Wed, Nov 30, 2022 at 6:12 AM Paul WB6CXC (tech-blog: ) <paul@...> wrote:
First:? I think the QDX is a brilliant piece of engineering and a great little transceiver.? I have one, and have just ordered two more for use in "network base station" operation.? My interest in the frequency-setting issue is mostly because it's a topic I find interesting, and there are some modes I am exploring where this issue (soon to be corrected, I hope) will be a problem.? Most people using the QDX will neither notice, or care about this issue -- the rig will just work for them.

So I finally set up an audio frequency ramp feeding the QDX USB input channel.? Output frequency measurements were made with my home-brew counter.? The displayed frequencies are after down-conversion in my counter, the absolute values are arbitrary and what matters is are the frequency differences.? I was using a Windows program called "NCH Tone Generator" to create the frequency sweeps.
First, to check the sweep itself, I sent the audio to my IC-7200 transceiver, set for 20 meters.? This is a slow sweep, 1000 Hz - 1010 Hz, taking 60 seconds:

There is measurement noise, but the frequency ramp appears to be smooth.

Then I sent the same audio sweep to the QDX, on 20 meters:

You can see that there are nine frequency steps over the 10 Hz range, each step roughly 1.25 Hz.? It is obvious that this will not work with the 1.46 Hz steps used in FST4W-120, and will cause some frequency error with the?1.4648 Hz steps used in WSPR.

Things got slightly better on the 30 and 40 meter bands, on 40m there were eleven steps (per 10Hz), but while I had expected better frequency resolution here, strangely the steps were less even than the 20m band:? The 30m band also showed eleven steps, although the spacing distribution was somewhat different.

40 meters:


Fractions are funny things, and perhaps if I had tried other audio frequencies the results would have been a bit different.

Finally, I set the audio sweep for 1000 - 1100 Hz, this time on the 10-meter band:

While the steps were uneven, there were no major discontinuities over this 100Hz range

So there you have it.
--
Paul Elliott - WB6CXC


 

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Hey Hans,

Wow, it's always more than one thing, and as always I'm amazed at your perseverance, diagnostic skills, and clever use of software to work around what could have been another problem! ?Congrats for finding and solving the problem, and thanks as always for your educational posts!

73, Willie N1JBJ

On Nov 30, 2022, at 11:06 AM, Hans Summers <hans.summers@...> wrote:

Hi Paul, all

I worked on this problem this afternoon. Solved in Beta 1_06_005?

First step, reproduce the problem. To do this I used two QDX. My "Franken-QDX" Rev 3a having the Rev 4 mods and connected VGA monitor and PS/2 keyboard as the transmitter (dummy load); For reception, my 10-20m high-bands QDX prototype on 20m band. Testing at 14.044 for no good reason other than that was where the equipment was set up. I generated a 60 second audio clip in audacity with a linear sweep from 1000 to 1010Hz, and fed this audio to the transmitting QDX with VOX enabled. The receiving QDX audio was analyzed in Argo set to 10s QRSS mode and Fast speed. Results are as attached before.png which shows a few attempts to get a clean shot. It's a perfectly similar result to what Paul reported.

Many hours later...

Turns out there are THREE causes of the problem. Floating point accuracy is the first one, the major one, which hides both the others; but all three need to be solved to get fine-resolution transmit frequency control.?

1) A bug: the floating point frequency was passed into the Si5351A transmit configuration function where it was used as a floating?point number; but the actual parameter declared as an unsigned 32-bit integer. Dumb. This limits the transmit resolution to 1Hz. Resolving this was easy of course.?

2) Frequency shift threshold introduced to help the "popping" problem; remember that Rev 3 and Rev 3a boards suffer this "popping" sound in the transmit audio? That was solved by a combination of various strategies in firmware version 1_04. Each of the strategies didn't eliminate the pops but reduced them; one of these strategies was to reduce the amount of frequency updates to the Si5351A (100 times per second by default) by setting a 0.5Hz threshold; the frequency had to shift more than this amount in order for the Si5351A to be configured to a new frequency. This threshold itself had another bug which was covered up by the bug mentioned in 1) above.?

I resolved the bug easily; and I have created a new parameter on the Configuration screen called "TX shift threshold" which defines the shift threshold in milli Hertz and defaults to 500. More any mode such as WSPR and FT8 whose frequency steps are larger than 0.5Hz this would be fine; for modes with narrow-spaced frequency steps less than this, you could reduce it as needed.?

For anyone with a Rev 4 PCB, the popping problem was totally eliminated in hardware so setting 0 threshold is fine.?

3) Finally the main issue is one of floating point accuracy; if you have a frequency such as 14,044,000 USB Dial Frequency such as in my tests, then a frequency shift of 0.1Hz on this is just too small a fraction and single precission?IEEE 754 cannot represent it accurately enough in the calculations of Si5351A parameters. The significand is 24-bit which is roughly equivalent to 7 decimal digits see?

To solve this I could have simply changed the relevant parts of the code to use double precision floating point representation. I am sure this would have worked. However this could not then have used the STM32F4 microcontroller's hardware floating point unit which is only single precision IEEE 754. So it would have compiled in some double precision?floating point library presumably. Which would probably have been large, probably been slow to execute (both of which could potentially have created new problems) and definitely been about as elegant as a troll swinging a sledgehammer in a glassware shop.?

So instead I devised some careful tricks to let me use regular single precision floating point and 32-bit integer arithmetic and handle the main USB dial frequency and the audio offset as two separate components. The result should be that the frequency steps are now precise to better than a one millihertz resolution, which is about the accuracy of the audio cycle measurement on the incoming USB audio stream from the PC.?

Now the results are shown in attached "after.png" which shows the 10Hz, 60 second sweep with three settings of "TX shift threshold": 0.5Hz (500mHz the default); 2Hz (2000mHz) and 0Hz. 0Hz is run twice in the image. Note that the line thickness is a little variable, this is because between the transmitting QDX and receiving QDX there is no direct coupling, just leakage from the dummy load to my antenna.?

I believe this will comprehensively solve the problem and Paul I will be very interested if you re-run your tests on this beta version.?



Clearly QDX works extremely well already; however I do believe that use of this improved firmware version should be recommended for everyone (once I release an official 1_06, after a few people confirm there are no unintended issues with the beta version). Improved accuracy of the transmitted frequency does result in increased probability of decode, particularly under DX circumstances or other weak conditions.?

Thusly expired my Wednesday...

73 Hans G0UPL



On Wed, Nov 30, 2022 at 6:12 AM Paul WB6CXC (tech-blog:?) <paul@...> wrote:
First:? I think the QDX is a brilliant piece of engineering and a great little transceiver.? I have one, and have just ordered two more for use in "network base station" operation.? My interest in the frequency-setting issue is mostly because it's a topic I find interesting, and there are some modes I am exploring where this issue (soon to be corrected, I hope) will be a problem.? Most people using the QDX will neither notice, or care about this issue -- the rig will just work for them.

So I finally set up an audio frequency ramp feeding the QDX USB input channel.? Output frequency measurements were made with my home-brew counter.? The displayed frequencies are after down-conversion in my counter, the absolute values are arbitrary and what matters is are the frequency differences.? I was using a Windows program called "NCH Tone Generator" to create the frequency sweeps.
First, to check the sweep itself, I sent the audio to my IC-7200 transceiver, set for 20 meters.? This is a slow sweep, 1000 Hz - 1010 Hz, taking 60 seconds:
<IC7200 20m sweep 1000-1010.png>
There is measurement noise, but the frequency ramp appears to be smooth.

Then I sent the same audio sweep to the QDX, on 20 meters:
<QDX 20m sweep 1000-1010.png>
You can see that there are nine frequency steps over the 10 Hz range, each step roughly 1.25 Hz.? It is obvious that this will not work with the 1.46 Hz steps used in FST4W-120, and will cause some frequency error with the?1.4648 Hz steps used in WSPR.

Things got slightly better on the 30 and 40 meter bands, on 40m there were eleven steps (per 10Hz), but while I had expected better frequency resolution here, strangely the steps were less even than the 20m band:? The 30m band also showed eleven steps, although the spacing distribution was somewhat different.

40 meters:
<QDX 40m sweep 1000-1010.png>

Fractions are funny things, and perhaps if I had tried other audio frequencies the results would have been a bit different.

Finally, I set the audio sweep for 1000 - 1100 Hz, this time on the 10-meter band:
<QDX 30m sweep 1000-1100.png>
While the steps were uneven, there were no major discontinuities over this 100Hz range

So there you have it.
--?
Paul Elliott - WB6CXC


<before.png><after.png>


 

Hi Alan

Hi all

Just to close this thread too -?

I posted here?/g/QRPLabs/message/95590?about 1_06_005 beta which I believe will solve the transmit frequency resolution issues.??

73 Hans G0UPL



On Sat, Nov 26, 2022 at 8:40 AM Hans Summers via <hans.summers=[email protected]> wrote:
Hello Alan?

Still a pending issue... Thought to be due to floating point precision limitations. I need to investigate..?

73 Hans G0UPL


-------- Original message --------
From: Alan G4ZFQ <alan4alan@...>
Date: Fri, Nov 25, 2022, 7:57 PM
To: [email protected]
Subject: [QRPLabs] QDX FST4W-300 Transmits only 2 tones? #QDX
This subject has been raised before,? [
/g/QRPLabs/topic/94416795#94434? ] smaller frequency
shifts than WSPR not being transmitted correctly.

I attach 2 shots, one a Softrock/WSJT-X and A QDX/WSJT-X.
While due to a hardware mod I can only use my version 1 QDXs with the
1.02 firmware it shows similar to a previous post.

Has this been rectified since October 18? I see no note of this in the
1.06 firmware.

73 Alan G4ZFQ






 

Hans, good news!? I just ran a 10Hz audio input frequency sweep on the 30-meter band (1000 Hz - 1010 Hz) and found that the QDX generated 20 steps, evenly-spaced 0.5 Hz resolution


This is a big improvement, certainly for WSPR modes.? But it's still shy of what we need for some FST4W modes.? Here's FST4W-300 on 30 meters, using the new QDX firmware:

This actually looks pretty good, and certainly *much* better than before where there were missing tones!, but I think still not usable for the slower FST4W modes

I also ran the 10Hz frequency sweep with the QDX on 20 meters, and again there were 20 steps, evenly-spaced 0.5 Hz resolution

Again, a huge improvement!




--
Paul Elliott - WB6CXC


 

Ignore my previous!? I hadn't set the "TX shift threshold" parameter to zero.? Hans told me to, and I forgot.? New tests coming up...

The default is 0.5 Hz, and that's what I measured, so that part's good!
--
Paul Elliott - WB6CXC


 

Hans, you've nailed it!? As perfect as I can currently measure.? Here's a 10Hz sweep on 20 meters:

I'm going to try some of the FST4W modes, but this looks absolutely great!? Thank you.
--
Paul Elliott - WB6CXC


 

And here is the v1.6.5 firmware running FST4W-900 on 39 meters (0.18 Hz tone spacing).? The tones look perfect.? However, the frequency drift (thermal) is probably excessive for the -900 mode.? This measurement was taken halfway through the second of two back-to-back transmissions (900 seconds each), so the QDX temperature was fairly stable by this time.? The drift after a long idle period is much more dramatic, and the FST4W spec says the drift over a transmit cycle needs to be less than the tone-spacing.? But still, great work by Hans!

--
Paul Elliott - WB6CXC


 

On Wed, Nov 30, 2022 at 09:06 AM, Hans Summers wrote:
?
Clearly QDX works extremely well already; however I do believe that use of this improved firmware version should be recommended for everyone (once I release an official 1_06, after a few people confirm there are no unintended issues with the beta version). Improved accuracy of the transmitted frequency does result in increased probability of decode, particularly under DX circumstances or other weak conditions.?
?
Thusly expired my Wednesday...
Hans and all,
Since I am rather a culprit in starting this general topic I thought I should respond near its end.

First, Hans thank you so much for expending a perfectly good work day on curing this. I believe that I can concur that the fixes have worked.? I greatly appreciate that and your interest and willingness in improving the performance in this 'narrow band' domain.? I know that like myself, many others appreciate it as well.

What I'm not sure many appreciate is how important these improvements may prove to be.? I'm especially still thinking of FST4(W) but more generally in the application of narrow/long digital modes at not only LF and MF as FST4W was initially targetted but also at HF-microwave.? As you know, several of us have spent some effort in applying the mode, increasing the number of transmitting beacons and ireceive sites and seeking to better understand the characteristics and limitations. What we've found is that in some situations, perhaps many, even at mid-HF there exists the ability to decode "well behaved" transmissions in a way that may extend the performance of amateur beacon and QSO communications far more than the existing popular modes such as FT8 and WSPR.??

This can have the effect of 'digging deeper' into the noise by 10-20 dB beyond what has been the current limit.? This is several S units, the same as a 10 to 100 times increase in transmitter power and may allow investigation and QSO at times and to locations not previously possible within all of amateur radio.? Because of its performance and price point the QDX may become a key player in harnessing these new possibilities.? Not only beacon spots and? QSO? but new propagation and ionospheric study have already become a reality. Better communication and geophysical science are clearly benefitted. This potential is not limited to HF but probably is now available at VHF-microwave.? Very long DX on 2m through X band, where ionospheric limitation isn't present starts to become a reality.?

It may be that yet newer modulation formats and protocols are required to take full advantage of this but WSPR and FT8 have taken a while to catch on so with patience some really interesting possibilities may be furthered by the presence of more stations worldwide operating.? I think the QDX may be a key contributor to that future.?

I have quickly looked at v1_06_6? and have found that once I reduced the tx shift from 500 to 0, FST4W with fully GPSDO external clock substitued for the QDX's TCXO and GPSDO LOs on the receive side?produce extremely low spectral spreading.? I'm now seeing total end-end spreading well under 10 mill-Hz on 20m over LOS paths.? This is low enough to take essentially remove HW as a limitation and allows both better FST4W DX and also better examination of ionospheric, its modulation by the earth's magnetosphere, effects of CME events from the sun, travelling ionospheric waves and no doubt other effects not previously recognized.

I'm hoping that these possibilities will be recognized and that the QDX with suitable clock may greatly stimulate all of this.??
Thanks again for making these improvements !

Glenn n6gn
Fort Collins, CO


 

Since ' a picture is worth a 100 words' which I seem to already have produced, here is a measurment of total 20m system spectral spreading comparing a? GPSDO phaselocked IC7300 with an externally clocked QDX and new version code:



The QDX begins at 1930 with the tx shift set to 500. that value is changed to 0 at 2055 where the QDX and the (reference) IC7300 system are effectively the same and 'perfect'.


 

Hello Paul and Glenn

Thanks for your confirmation?of the successful change. Your observations and testing have helped make a great device even greater! Thanks again!

73 Hans G0UPL



On Thu, Dec 1, 2022 at 5:58 AM Glenn Elmore <n6gn@...> wrote:
Since ' a picture is worth a 100 words' which I seem to already have produced, here is a measurment of total 20m system spectral spreading comparing a? GPSDO phaselocked IC7300 with an externally clocked QDX and new version code:



The QDX begins at 1930 with the tx shift set to 500. that value is changed to 0 at 2055 where the QDX and the (reference) IC7300 system are effectively the same and 'perfect'.


 

And here is the QDX transmitting FST4W-1800:

Note that the tone spacing is only 0.089 Hz, and the QDX is tracking these accurately and cleanly.? Pretty amazing!?
But there does remain a frequency drift issue, caused by temperature rise during the transmit cycle.? I'm measuring slightly less than 1Hz drift during the thirty minute transmit time. This won't affect most modes, but will be a problem for FST4W-300/900/1800.? Either a GPSDO or an OCXO will probably be required to improve the already good temperature stability, and I doubt if either of these would make sense in a standard QDX (cost / size / power / diminishing returns / etc.)? But there are always other ways to do this, so we shall see...

And again, thank you Hans!
--
Paul Elliott - WB6CXC