What to expect from your FCD

I’ve had some questions about the FCD and spikes on the passband.

Out of the box, like all zero IF direct conversion analogue mixer SDRs, incuding the FCD and the Softrock, there are two tweaks that immediately come to mind. Firstly there’s the DC offset which you’ll find in the middle of the SDR’s passband, and secondly there’s the image rejection. By adjusting these settings, you can null out the DC offset and image signals.

The pictures shown here are deliberately shown without any DC or image corrections so that you can compare your own unit. The precise amount of DC offset and image rejection will vary from unit to unit, and is also frequency and gain specific.

Below you’ll see marker 1 on the right as the main signal, in the middle is the DC offset marker 2, and marker 3 on the left is the signal image. Ignore the fourth marker!
Using Spectravue the DC offset and image rejection are corrected in the SoundCard In Setup menu item, but it’ll vary depending on the SDR software you’re using.

It is highly recommended that you use the “Defaults” button in the FCD Controller app each time the FCD’s plugged in: this sets the FCD’s gains and filters to sensible values.

When you have strong signals in the receiver’s pass band you will see the noise floor rise. This can be alleviated to some degree by reducing the mixer gain. This increases the dynamic range from 80dB to 90+dB at the expense of some sensitivity as you can see in the picture below. This shows a strong signal on the input. The rasied noise around the signal is as a result of the FCD’s LO phase noise. To the left hand side, we still have about a -103dB noise floor, with a -11dB input signal.

At this point we are now close to the physical abilities of the FCD. Firstly the LNA is close to saturation and secondly, we are very close to the ADC’s dynamic range.

One further point: the FCD is primarily designed to be sensitive enough to receive satellites directly. However it is also an exceptionally wideband receiver, and although there is fixed and programmable front end filtering, you may also find that if you are in a high RF environment, and particularly at VHF, a low loss band pass filter will help if you find the noise floor rises when you plug in your antenna. Typically, quality masthead preamps often have these installed anyway.

Howard

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63 Responses to What to expect from your FCD

  1. Frank PH2M says:

    Hello Howard & others,

    After the tips found above, I managed yesterday to start receiving several signals on 144, 430 & 1298 MHz. I started with receiving PI7CIS (beacon) in CW on 144.416, then I switched to PI2HGL (FM repeater) on 430.350 and finally I switched to PI6RTD (FM repeater) on 1298.625.
    All above received with the use of SpectraVue, the antenna I use is a Diamond U5000 (Tribander vertical for 144/430/1296 MHz.) Mixer gain on 4dB.
    Today I started to use the WRplus program http://www.wrplus.altervista.org/ , I used the standard Winrad program in the past with my 40m Softrock and I must say this program is must easier to use (at least for strait listening with the FUNcube Dongle).
    I say just give it a try.

    73 de Frank PH2M

  2. Matty MD0MAN says:

    I have mostly been using Simon Brown’s (author of Ham Radio Deluxe) SDR software.

    - With the ‘online’ SDR’s and a 40/80m SoftRock I built a couple of years back.

    He’s originally from the Isle of Man and has given us a few talks/demos at the local club meetings.

    http://sdr-radio.com/

    I have recently downloaded Spectravue, and this looks very good, I will also try WRPlus, thanks for sharing this Frank.

    Matty

  3. Matty MD0MAN says:

    In addition to my previous comment,

    The ‘built in’ soundcard on the PC I was using with the Softrock was terrible, so I hooked the I/Q from the Softrockto an old Mini-Disc player – to use this as an A/D convertor.

    Took the digital output from this and fed it into the PC – the difference was incredible!!

  4. Mike says:

    Obervations and questions.

    I concur regarding filtering. I connected No 108 up today – to an 8 element Yagi up on Winter Hill. My impression was that it is impressive hardware but the FCD is very deaf, which it should not be, so I suspect this is a wideband RF desense issue – there are 100s of kWs of Broadcast DTV just up the road, and line of sight and also all of Manchester and Liverpoolwithin view. On 144MHz, GB3VHF is about 559 on a TS2000 with the same antenna but is almost inaudible on the FCD maybe 10-20dB worse SNR The noise goes up markendly on attaching the antenna. Hopefully this will be less of an issue in less challenging locations. I was wondering what to set the various gains to to make the best of this – I reduced the mixer gain and LNA gains and I think it helped.

    Setup questions:

    Spectravue is setup as indicated in Howards’ document. Unfortunatly I can’t figure out how to demodulate the “negative frequencies” in SSB – that is those on the left of 0Hz which are really just those below the centre frequency of the FCD. This leaves half the screen useless, I am not sure why I can’t demodulate below 0 but it could be a function of the software configuration. Is there a way to set it up?

    For the FCD How do I correct for the crystal error? There is a tempting box that does something, but not what I expected it to do.

    Any ideas on how to make Spectravue do the frequency tuning? Does it need a virtual radio application?

    Anyone written a spectrum sweep application yet?

    • admin says:

      Hello Mike

      Ouch, Winter Hill will indeed bury the poor old FCD’s front end! It’s been twenty years since I last went up there with a radio.

      There is some more tweaking I’m building into the new firmware that makes a rather more sensible judgement regarding the front end programmable filtering. At present for VHF in particular it’s wide open from 50 to 600MHz.

      The way we’ve resolved that here is to use an external hardware BPF. (For the educational outreach version we’ll be offering an appropriate antenna with a built in filter).

      You’ll find on a signal generator that the FCD is pretty sensitive – that’s one of the tests I run on every FCD. However being wide band as well means it’ll suffer in a harsh RF environment unless steps have been taken to calm things down. This is not unlike taking any wide band receiver into such an environment. Typically manufacturers mitigate against this to some degree with separate tuned RF sections for different bands (eg, the TS-2000 for example) and optimise for this, and this innevitably adds complexity and cost.

      The FCD uses the same RF front end througout its entire range in much the same way as your average handheld scanner. Unlike some scanners though, there is some fixed and programmable filtering, and the latter still needs some tweaking.

      The box is fixed at -115ppm (that’s 1,000,000-999,885). That is fixed in the software when you start it up and came about as the seemingly fairly constant characterisation of all the devices made so far. You can change it but it’ll reset next time you start the software.

      So, 999,900 is -100ppm and 1,000,100 is +100ppm. Be aware though that the FCD’s firmware currently only understands 1kHz steps! (That’s another fix coming in the next firmware).

      The Qt version lets you put in the number in directly as ppm, and it’s saved, however lots of other fancy things have yet to be incorporated. The Qt version will be the future as it’s cross platform.

      Negative frequencies in Spactravue: SoundCard IN setup: set the centre frequency to 48000Hz.

      Howard

    • David Barber says:

      Mike / Howard.
      I’m happy to help out if I can with any basic operational questions. Has to be with Howard’s OK though.

      Mike, in the “Soundcard IN Setup” set the centre frequency to 48000 that will allow you the use of the full sweep but remember the selected Dongle frequency remains at the centre of the screen. For best results you need to adjust the “I/Q Comp” figures to suit your unit. Adjust “I dc” & “Q dc” for lowest DC offset (hump at centre of screen) and “alpha” and “beta” for the lowest signal image however without a stable signal source of variable level the latter adjustment can be a bit trial and error.

  5. Mike says:

    It is certainly quite harsh up here. I am now using a 2m 1/4 wave whip and with 10dB LNA and 4dB mixer I can get the 145MHz noise floor down to -90dBm in 2.9Hz RBW. This is -47dBm in the continuum. No aerial but instead a precision 50 ohm load takes that down to -69dBm so the noise floor is 22dB above the front end. Defaults setting gives a continuum at -65dBm (of course there is 10dB more LNA and 8dB more mixer gain) and with the aerial the noise continuum is -35dBm. That puts the noise level at 30dB above the load. Of course it is not really noise but intermods and these can’t really be classed as Gaussian. A band pass filter will be needed.

    Incidentally, mobile phones give up up here too – no coverage and not because there are no signals. I found the mobile worked best inside the car on the floor.

    Mike

    • admin says:

      Hello Mike

      Yes, when we came up with the FCD we really had in mind a bunch of school children with a laptop, dongle and quarter wave in the middle of the playground listening the satellites going overhead rather than a hilltopping expedition!

      But your findings are invaluable, and reflect our own findings.

      I have been fiddling with homebrew hardware inline VHF BPFs on and off over the past weeks myself rather than using commmercial ones. It’s not really an area of expertise for me I’m afraid. I can tell you that they work beautifully with a DCI filter… but they cost three times as much as a dongle and are 100 times the volume!

      Howard

  6. Matty MD0MAN says:

    Managed to puck up my FCD on the evening of 23rd, hooked it up for a quick play, but didn;t really get anywhere.

    Was too busy Christmas eve to play with it, so had another go today – didn;t seem to want to pick up anything on the satellite front, so tired our local 70cms repeater.

    Still no joy, going over the connections, I found the centre pin missing from the SMA end of the SMA to N adaptor I had picked up !!

    Managed to find an SMA > BNC connector and have now been receiving packet from the ISS and some ssb on the transponder on VO-52.

    Thanks for a fabulous bit of kit Howard.

    Matty

    • Mike says:

      That was probably a reverse SMA connector – used for WLANs to stop you changing the antenna! Either that or broken. The FCD has fairly good screening even though it is in a plastic case as it picks very little up with no antenna connected.

      I am pleased you are seeing signals. I can hear the local 23cms repeater on a small whip so it certainly works up there. I noticed a little frequency drift but not much.

      I happened to have a low pass filter for 150MHz to hand for use with the VNWA and I put this in line hoping it would resolve my overload issue – it didn’t help much so my overloading must be due to strong signals below 150MHz – probably pagers and VHF broadcast. A simple bandpass is probably what I need to make.

      As I had the VNWA out, I also measured the input matching from DC-1.3GHz. It is OK.

      Mike

  7. Mike says:

    What is the performance of the built-in UHF BPF’s at around 435MHz?
    Is there any need for external BPF for UHF as well?
    Thanks.

  8. David Barber says:

    I have been experimenting with data modes this morning (26/12/10).

    1) Using the FCD with Spectravue via ‘Virtual Audio Cable’ software to WSJT and using an attenuated signal from GB3VHF as a source. Perfecting decoding.

    2) Using the FCD with Spectravue via ‘Virtual Audio Cable’ software to AGWPE and on to UISS. Copying terrestrial packet OK but signal levels required for reliable decode seem surprisingly high when compared to the usual transceiver/sound card setup.

    Due to high levels of local hash across 2m I have found it beneficial to run the mixer gain at 4dB and experiment with the LNA gain.

  9. David Barber says:

    With setup as described above the following copied from the ISS during the 17.45utc UK pass. Antenna = co-linear at 10m, LNA gain 10dB, Mixer gain 4dB, other settings default.

    Port2 with SoundCard On COM2: 1200 Soundcard

    Fm EA1JM-6 To APRS Via RS0ISS-4* [17:48:13]
    :BLNQSL1/1:EA7AHA,EA1AXY,EA2AUK,EC4AMQ,ON3URT,DG4BR,SQ1FTK

    Fm SV2KGA To ARISS Via RS0ISS-4*,WIDE [17:48:48]
    =/:-UhT1_7- TORNG0002/

    Fm F8BPU To RS0ISS-3 Via RS0ISS-4* [17:50:05]
    =5018.03NI00304.14E&PHG12503 Philippe Estrees dp 59 {UIV32N}

    Fm RS0ISS-11 To IK5FEV [17:50:07]
    Fm RS0ISS-11 To IK5FEV [17:50:27]
    Msg# Size TS Date Time From To @ BBS Subject

    Fm RS0ISS-11 To IK5FEV [17:50:37]
    Fm RS0ISS-11 To IK5FEV [17:50:49]
    Fm YO8RBY To APRS Via RS0ISS-4* [17:53:01]
    :D G4BR :73′ Narcis yo8rby@yahoo.com

  10. Rob says:

    Iv’e had much success with most SDR software with the FCD bar Spectravue,I may of just missed a setting but the modes on the right hand side are greyed out,so I’m unable to change the mode,plus I’m unable to change the Demod freq.In Howards screenshot of Spectravue the freq is set to 0.024500 mine is 0000000 and I’m unable to change it.

    any clues?
    Rob

    • Mike says:

      What do you have set in soundcard setup?

      The input device is set to soundcard – in the setup for this:
      It should say Funcube Dongle V0.0 in the selection box
      The sample rate should be 96000
      The BW limit should be 96000
      The center (sic) freq should 48000
      Stereo…. should be checked.
      Invert spectrum unchecked.

      Have you checked “Demod on” on the right hand side.

      • Rob says:

        Yes above setting is what I have,Demod is ticked but grey out.
        Like I say,no problems with any other software..
        I have tried removing Spectravue, and installing again, but still got the problem.
        Rob

  11. Oscar says:

    Hi Folks,

    the postman delivered this morning the Funcubedongle serial number 115 to my home :-)

    I just gave it a try on various frequencies and it works great. I am very please with the relatively high sensitivity of the front end (no LNA or mixer overloading here, due to modest RF levels)

    I tried FM stereo reception, which works quite well with WRplus SDR software (yet another Winrad clone, but wit a few very usefull additions)….works great as well…

    Then followed by NOAA overpass (WRplus allows for doppler tracking with internal AFC !), airband sigs in AM worked with great sensitivity as well, 2m and 70cm ham bands w/o problems, 250MHz military satellite band picked up one of the strong FLTSATCOM broadcast channels with 20dB SN on my ham radio vertical :-)
    Finally also tested some 1090 MHz aircraft transponder signals (bursts nicely audible and visible on the waterfall) on my ham vertical….

    Overall I am very happy. Thanks Howard for developing this nice little gadget…

    One remark though….it would be very nice if the LO frequency could be directly controled from the SDR receiving software instead from an external tool.

    Winrad and its clones (e.g.HDSDR and WRplus) as well as the well known PowerSDR use an external DLL file called EXTIO.DLL to control frequency agile SDR radios….this concept works very well…

    I wonder if there are any plans to come up with an EXTIO.DLL for the funcube dongle?

    Cheers,

    Oscar

  12. Roger G7RUH says:

    Rob,
    The setting for the soundcard in Spectravue MUST be the same as the actual soundcard setting: e.g. if soundcard is set to 48000, then Spectravue setting must also be 48000 otherwise Demod is grayed out. I know, because it foxed me for a while, the answer is in the help somewhere.

    Roger G7RUH

  13. admin says:

    VHF & filtering

    Folks,

    If you are seeing substantially raised noise floors when you plug in your antenna, particularly on VHF, it’s likely that you’re in a high RF area. The front end of the FCD is very wide band but it does have some front end filtering, both fixed and programmable. I am aware of a firmware problem on VHF where the incorrect filter is being used. This is ar least partly due to using some code from the tuner chip manufacturer that I believe is buggy. I am fixing that now. However it may be thats even with this firmware fix we’ll have some raised noise floors and apparent insensitivity in harsh RF scenarios.

    Certainly it seems that reducing the mixer gain to 4dB is beneficial at the expense of a small amount of sensitivity.

    Today as well as working on the new firmware, I tried my luck with some more filters and also some diplexers/triplexers I have here, with quite a bit of success! You may well have a di/triplexer yourself.

    The best one I found was the middle port of a Comet CFX-514 triplexer. The middle port is 130-200MHz. Even with a handful of connectors, this port shows only 0.3dB loss on 145MHz.

    I also tried the VHF ports of a Diamond MX-72 diplexer and a Diamonf MX-3000N triplexer. Again, quite some success. These are low pass filter only.

    I tried the V/UHF port of a Comet CF-530 (125-470MHz) but this made very little benefit for me.

    Howard

  14. Doug Phillips, W7RDP says:

    OK a FUNcube Dongle arrived in the Seattle, WA, USA in today’s mail, very cool!

    73, Doug W7WRP

  15. Frank PH2M says:

    A very nice promo by Henk PA3GUO:

    http://www.youtube.com/watch?v=xFZGlqKPPQo
    (HD video: set to 720p and Fullscreen)

    YouTube video featuring the first results;
    - HO68 CW
    - HO68 FM
    - AO51 FM
    - VO52 SSB
    - OOREOS 1k2 AX25 (packet radio with MixW)

    Results are amazing. The FUNcubeDongle gives
    results similar to the Kenwood TS2000x.

    Tests are done with the dongle straight out
    of the box, no tweaking.

    Great achievement Howard & team !

    Henk, PA3GUO, The Netherlands
    http://www.pa3guo.com

    ps: where can I nominate you for the most innovative design of 2010 ?

  16. Tim Bucknall says:

    very tempting i’ll almost certainly get one eventually, depending on what opportunities for dxpeditions come up in 2011 (home is rubbish for dxing)
    does the FCD have any problems with the evil windows vista?
    the laptop i intend to use is vista (sadly) with 1.73ghz processor speed,
    i already use winrad HD, spectravue & perseus on it with no probs but vista is an unpredictable beast so i thought it best to double check

    the fcd will be a real boon for fm/tv dxers

    • admin says:

      Hi Tim.

      No problems with Vista, 32 or 64 bit. I’ve turned to using a netbook to do my checkout tests, a really neat solution with oodles of battery life. It only has a 1.6GHz CPU. It also runs on an old Toshiba Portege M100 running Vista, that’s only a 1.2GHz CPU.

      Howard

  17. Mike says:

    OK – after some prompting I finally realised it is not that hard to write an “ExtIO” for WRPlus/Winrad. It is a lot easier than making PowerSDR work reliably.

    So, I can now control the FCD frequency and do the usual things with WRPlus – I am not yet able to set any registers as Howard is understandably keeping that info to himself until he finishes the firmware. We don’t want FunCubeBricks.

    Does anyone know how to get WRPlus out of single window mode? It is a bit frustrating.

  18. Rob STyles says:

    Hi Mike

    WRplus.exe -wv

    The -wv option makes it run in a window :)

  19. Rob Styles says:

    WRplus.exe -wv

    The -wv option makes it run in a window :)

  20. Bruce N1RX says:

    If by “single window mode” you mean full screen, then see the documentation:
    6.5 Window view
    WRplus can run in its “legacy” full screen mode or in a standard window, if launched with the command line option “–wv”; this is actually a useful feature already implemented by DG0JBJ,
    Mario in his WinradHD. If started in “window view” mode the program will try to build a window as highest as possible (up to 1024 internal pixels) using the available screen space: I recommend keeping only the Task Bar active.
    The current window position is saved in the registry when the program terminates and restored at the next program start-up.

  21. Alf DG8YHH says:

    Hi Mike ,
    is it possible , that you post your ExtIO – File or send it to me via Mail ?

    I think WR-Plus is the Best programm for our FCD ( maybe Sodira for FM Broadcast ist quiet better )
    with a Winrad-DLL everybody can trie many programms

    73 de Alf

    • Rob says:

      Hi Mike ,yes would be nice to have a copy of the ExtIO
      Regards
      Rob
      m0tfo@m0tfo.co.uk
      and well done…

      • Mike says:

        It is alpha at best, all it does is set the frequency, but if you want it, where can I put it?

        http://www.flickr.com/photos/ad6xy/5356705891/

        • Frank PH2M says:

          Hello Mike,

          Please just start to be a (free)member of the FUNcube Yahoogroup and put any file overhere:
          http://uk.groups.yahoo.com/group/funcube/files/
          You can make your own directory or put the file(s) in the WRplus directory I made in the past…

          Best 73 and thanks for the work so far.
          Frank PH2M (FCD #111)

          • Mike says:

            Ah – OK. I am a member of that group but was not aware that was where we could put files. I see the firmware is there as is WinRad.

            So – can someone quickly test it works – I am not sure I compiled it properly and it might be looking for libraries.

        • Rob says:

          If you could email it to me Mike, I can put it into the file section of the FUNcube yahoo group.
          Rob

          m0tfo@m0tfo.co.uk

          73

        • Mark N8MH says:

          Thanks, Mike! When starting WRPlus, I get an error saying vcl100.bpl is missing.

          • Rob says:

            I’m of to Walmart to buy a vcl100 hihi

          • Mark N8MH says:

            You find it yet, Rob? hehe

          • Rob says:

            No Still looking :-) , I see Mike has removed the file, so no doubt, the working one will be there soon.

          • Mike says:

            Ah – Right. Thought it was a bit small – it was attempting to use run time libraries. I have tried again. There are so many options in BDS2006. This might not work either….

          • Rob says:

            thanks Mike all working now..Keep up the good work
            73

          • Mark N8MH says:

            Thanks, Mike—no errors, loads fine.
            Now, silly question—how do we change frequencies, etc.? Just by tuning the freq in WRPlus?
            Does the full front end need to be running too?
            Just a bit of simple direction will help :) Thanks!!

          • Rob says:

            I have it running under Winrad, but not a lot happening at the moment,no freq change. I will take a look after some food.

          • Mark N8MH says:

            I don’t see the freq changing either…no errors, but no freq change.

          • Rob says:

            From Mike via yahoo group Should work now. The front end needs to be running. It is a form. I suppose it could be invisible as it does not do much except allow you to set offsets. This really is basic.

            How to use?

            Copy the DLL to the WRPlus directory.
            Go to Soundcard Menu
            Set up WRPlus with the FCD as the sound card – 96kb/s
            Go to Options Menu
            I found I needed to swap I/Q to get the passband the right way up
            In the select input sub-menu select the FCD option.
            Then
            Set a frequency within the range of the FCD – E.g. 145MHz.
            Start WRPlus decoding.
            Repeat – this time correctly…

            Now a few points – the offset for the IF is zero I think, unless you feel otherwise. The downside is the DC spike in the middle of the passband.

            The Error is the crystal offset, mine is about -108 but it seems to vary a bit for reasons I have not quite tied down. This is something to do with the dongle itself.

            You must run the HID application if you want to change filters and gains, but it is not a problem to run that as well – just don’t use it to set the frequency or WRPlus will not know.

            __._,_.___

          • Mark N8MH says:

            Here is a key instruction!

            Okay, the trick is…in WRPlus 1.04, use the first menu button

            ShowOptions button, Select Input, and then choose FCD-G0MJW Control (NOT sound card…)

            A little window then pops open

            Oh one more tidbit…click on the LO numbers in WRPlus to change the actual frequency of the FCD now!

            The “tune” is just showing you where you are decoding the audio…

            Working well here now. Thanks so much, Mike!!

  22. Rob says:

    Thanks Mike, Can see the file ok.

  23. Rob says:

    yes all working now, thanks Mike

  24. Rob - W7TBE says:

    I was finally able to carve out the time to try out the FCD. At the outset, I will admit to being completely new to SDR and very eager to learn. I attempted to adjust the DC offset using the directions on your site. I think I got pretty close. I checked it using Spectravue’s phase plot and tried to make sure the point “blob” was pretty much centered. The only question I had was in order to get it close to centered, I had maxed out the I dc compensation at 2000, the Q dc comp was down around 322. Am I doing this right? Is there a way to get a little more room in the adjustment? I used the default settings in FCHid.

    As long as I’m asking rookie questions, are you aware of any programs for OSX that will work with the SDR?

    Thanks,
    Rob – W7TBE

    • admin says:

      Hi Rob

      No problem. I had some success with DSP Radio a few weeks ago. This was running OSX under VMWare on a PC.

      I had a quick go again more recently in an attempt to make a short guide, but clearly I’m not pressing the right buttons.

      I am aware of other Mac SDRs, there is a treatise here. I personally have found many of the SDRs for the Mac and Linux to be half finished: they tend not to be plug and play, there’s a bunch of configurtation to do, and documentation can be sparse, so much so that I gave up after days of tinkering. DSP Radio and LinRad I found to be exceptions in this case.

      I bought a real Mac this week, so I’ll have some real hardware to use!

      Howard

  25. mike says:

    Great news that you have purchased a new Mac.

    The MacHPSDR is open source. It is now called Heterodyne.
    You can file tickets here:
    http://mcdermj.lighthouseapp.com/projects/47142-machpsdr/overview

    Source is here:
    https://www.xenotropic.com/ham-svn/MacHPSDR/branches/Heterodyne/

  26. mike says:

    Great news that you have a new Mac.

    MacHPSDR is now called Heterodyne.
    You can file tickets here:
    http://mcdermj.lighthouseapp.com/projects/47142-machpsdr/overview

    Source is here:
    https://www.xenotropic.com/ham-svn/MacHPSDR/branches/Heterodyne/

  27. Edgar Neukirchner says:

    Last year I bought a Funcube Dongle from you (S/N 0003463). I soon found out that there is a frequency error of approx. 14 kHz at 145 MHz, which seemed to be no problem because I assumed it to be constant over the whole frequency range. But recently I realized that frequency error is more than 40 kHz at 440 MHz! Is this some hardware error?

    I made the recommended firmware update. Generally, I use the FCD with gqrx under Linux, but a cross check under Windows with FCD frequency control gave the same result.

    Edgar

    • admin says:

      Hello Edgar,

      It is proportional to the frequency, and this is the function of the frequency correction fields on the FCHID control application. By adjusting the number of parts per million, you can make it resolve this across the entire frequency range. For your example, it looks like the factor should be about 999904.

      Many thanks, Howard

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