JFYI, Attached are COMSOL simulations for the frustum (with coax coupling) I am going to build. It is now time for some sheet metal cutting and torch soldering... And then there will be the moment of truth.
D_big: 264 mm
D_small: 158 mm
L_center: 204 mm
TE012 freq: 2,323,xxx kHz COMSOL (vs. 2,402,xxx spreadsheet)
Hi RfPlumber,
Thanks for the data on your test setup and VERY LOW COST quasi VNA. Have ordered that unit as I have built a Forward & Reflected power monitor that should have almost zero insertion loss and should work well with that unit. If it works as expected, using it and this unit will make really low cost frustum resonance monitoring a reality. By low cost I mean like around $150.
Can you please confirm the frustum built length is 204 mm and not 240 mm?
...
Based on the frustum length being 240 mm (TE012 resonance at 2.324 GHz), the prediction is 4mN at unloaded Q of 50k (25k loaded Q) and 30W Rf forward power.
Hi TT,
You're welcome. I am glad this info ends up useful. Yes, all dimensions above are correct, and the center length is 204 mm (and the actual frustum as-built ended up within 1mm of that length). Spreadsheet does produce a different value for TE012 frequency (2,402 MHz) vs. 2,323 MHz per COMSOL, and unfortunately the COMSOL value ends up being much closer to reality.
...
The fact that a spreadsheet that models resonance of a truncated cone as a summation of constant cross-section cylinders gives a natural frequency higher than reality and higher than what Finite Element Analysis calculates is to be expected.
The spreadsheet approximation is
too stiff (higher stiffness results in higher natural frequencies) because the cylinder approximation does not properly take into account the interaction between the different segments. The Finite Element Analysis takes this coupling into account because the FEA solution involves inversion of a populated matrix with off-diagonal components that account for this interaction.
The difference: 2.402 vs. 2.323 GHz: (2.402-2.323)/2.323
is 3.40 % apart in frequency
The air bearing this is mounted on is virtually frictionless but he does have fans and pumps running plus the thrumming of the air compressor nearby.
It is not clear to me how the air bearing is done. It looks like an ordinary ball bearing turning table rotating around an axle. Do you have reference on about the air bearing he used in the Youtube static test?
TT had referenced it in a Pm to me 5-6 months ago. I'll dig for it. But until I dig it out I believe TT said Shawyer said it was designed for them by WestWind engineering in the UK.
Do a google search. I believe it was a simple rotary load bearing table riding on a cushion of air between two plates.
https://www.google.com/search?q=air+bearing+rotary+tableWestWind
http://www.westwind-airbearings.com/ I know who WestWind-Airbearings are. My company had a good open relationship with them when we were doing Air Bearing Spindles and air-slides for our semiconductor equipment.
JFYI, Attached are COMSOL simulations for the frustum (with coax coupling) I am going to build. It is now time for some sheet metal cutting and torch soldering... And then there will be the moment of truth.
D_big: 264 mm
D_small: 158 mm
L_center: 204 mm
TE012 freq: 2,323,xxx kHz COMSOL (vs. 2,402,xxx spreadsheet)
Hi RfPlumber,
Thanks for the data on your test setup and VERY LOW COST quasi VNA. Have ordered that unit as I have built a Forward & Reflected power monitor that should have almost zero insertion loss and should work well with that unit. If it works as expected, using it and this unit will make really low cost frustum resonance monitoring a reality. By low cost I mean like around $150.
Can you please confirm the frustum built length is 204 mm and not 240 mm?
...
Based on the frustum length being 240 mm (TE012 resonance at 2.324 GHz), the prediction is 4mN at unloaded Q of 50k (25k loaded Q) and 30W Rf forward power.
Hi TT,
You're welcome. I am glad this info ends up useful. Yes, all dimensions above are correct, and the center length is 204 mm (and the actual frustum as-built ended up within 1mm of that length). Spreadsheet does produce a different value for TE012 frequency (2,402 MHz) vs. 2,323 MHz per COMSOL, and unfortunately the COMSOL value ends up being much closer to reality.
...4 mN of thrust would send my poor pendulum into an orbit 
Do you have a link for your 30W Rf amp and can the freq gen you have drive it enough power to obtain the 30Ws at output?
Yes, it is the same unit someone else has recently pointed to. http://www.ebay.com/itm/30W-Class-A-Linear-RF-amplifier-2-3-2-45-GHz-2304-ATV-/221981664579?hash=item33af236543:g:Ro4AAOSw1S9WhALo
Note that it has a rather narrow band (2.30-2.35 GHz) where it can deliver 30W, hence all my trouble to make a frustum with a mode in this range.
No, my freq generator does not have enough power to directly drive this amp (just a few dBm short), so I am using a pre-amp. This one: http://www.ebay.com/itm/Mini-Circuits-Wideband-RF-Amplifier-ZX60-6013E-S-50-20-MHz-to-6-GHz-NOS-/261994189569?hash=item3d00121301:g:2jEAAOSwyQtVwsdG
The same guy www.windfreaktech.com has other generator models which do provide enough power to avoid the pre-amp, but they cost (way) more and are heavier. Note that I need a generator with EEPROM so it could fire at pre-programmed freq at power-up as I do not have an intelligent controller on the test platform to program it on the fly. You do, so can likely use any other synthesizer, even the one from that pseudo-VNA unit.
BTW what is the bandwidth and loaded Q if you measure 3dB up from the max rtn loss dB point, instead of 3dB down from the reference level.
Roger's Force equation works from unloaded Q, being twice the loaded Q, measured 3dB up from the max rtn loss dB point on a S11 VNA scan. This is how you measure power bandwidth as the max power xfer level becomes 0dB and you measure the point where the power xfer is 3dB down from the peak power xfer dB level.
Not trying to trigger an argument here. Just stating how Roger's Force equation works and what Q measurement technique it is based on.
That "Q" value (calculating UP from the _minimum_ of S11) would be around 10,000. It is what the scanner software calculates by default, but this value has very little sense, and so I didn't event include it in my screenshots. It is somewhat strange that this is what Roger is using... Think about it, assuming the minimum on S11 plot is say -20 dBm, this implies 99% of power goes into the cavity. Now take a +3 dBm up point, this will be S11 of -17 dBm, that is 98% of power going into the cavity. So moving from -20 dBm to -17 dBm of S11 changes the amount of power in the cavity by... 1%.
Apparently even the "3 dBm down" method is rather gross for S11 measurements, and they usually recommend calculating Q factor from complex S11 values (via Smith chart or otherwise). But since I don't have a vector NA... no complex S11 values for me.
Good luck with your tests.
Phil
Thank you, I will need it
Using a different than TTs calculation method I get ... please see below
JFYI, Attached are COMSOL simulations for the frustum (with coax coupling) I am going to build. It is now time for some sheet metal cutting and torch soldering... And then there will be the moment of truth.
D_big: 264 mm
D_small: 158 mm
L_center: 204 mm
TE012 freq: 2,323,xxx kHz COMSOL (vs. 2,402,xxx spreadsheet)
Hi RfPlumber,
Thanks for the data on your test setup and VERY LOW COST quasi VNA. Have ordered that unit as I have built a Forward & Reflected power monitor that should have almost zero insertion loss and should work well with that unit. If it works as expected, using it and this unit will make really low cost frustum resonance monitoring a reality. By low cost I mean like around $150.
Can you please confirm the frustum built length is 204 mm and not 240 mm?
...
Based on the frustum length being 240 mm (TE012 resonance at 2.324 GHz), the prediction is 4mN at unloaded Q of 50k (25k loaded Q) and 30W Rf forward power.
Hi TT,
You're welcome. I am glad this info ends up useful. Yes, all dimensions above are correct, and the center length is 204 mm (and the actual frustum as-built ended up within 1mm of that length). Spreadsheet does produce a different value for TE012 frequency (2,402 MHz) vs. 2,323 MHz per COMSOL, and unfortunately the COMSOL value ends up being much closer to reality.
...4 mN of thrust would send my poor pendulum into an orbit
Do you have a link for your 30W Rf amp and can the freq gen you have drive it enough power to obtain the 30Ws at output?
Yes, it is the same unit someone else has recently pointed to. http://www.ebay.com/itm/30W-Class-A-Linear-RF-amplifier-2-3-2-45-GHz-2304-ATV-/221981664579?hash=item33af236543:g:Ro4AAOSw1S9WhALo
Note that it has a rather narrow band (2.30-2.35 GHz) where it can deliver 30W, hence all my trouble to make a frustum with a mode in this range.
No, my freq generator does not have enough power to directly drive this amp (just a few dBm short), so I am using a pre-amp. This one: http://www.ebay.com/itm/Mini-Circuits-Wideband-RF-Amplifier-ZX60-6013E-S-50-20-MHz-to-6-GHz-NOS-/261994189569?hash=item3d00121301:g:2jEAAOSwyQtVwsdG
The same guy www.windfreaktech.com has other generator models which do provide enough power to avoid the pre-amp, but they cost (way) more and are heavier. Note that I need a generator with EEPROM so it could fire at pre-programmed freq at power-up as I do not have an intelligent controller on the test platform to program it on the fly. You do, so can likely use any other synthesizer, even the one from that pseudo-VNA unit.
BTW what is the bandwidth and loaded Q if you measure 3dB up from the max rtn loss dB point, instead of 3dB down from the reference level.
Roger's Force equation works from unloaded Q, being twice the loaded Q, measured 3dB up from the max rtn loss dB point on a S11 VNA scan. This is how you measure power bandwidth as the max power xfer level becomes 0dB and you measure the point where the power xfer is 3dB down from the peak power xfer dB level.
Not trying to trigger an argument here. Just stating how Roger's Force equation works and what Q measurement technique it is based on.
That "Q" value (calculating UP from the _minimum_ of S11) would be around 10,000. It is what the scanner software calculates by default, but this value has very little sense, and so I didn't event include it in my screenshots. It is somewhat strange that this is what Roger is using... Think about it, assuming the minimum on S11 plot is say -20 dBm, this implies 99% of power goes into the cavity. Now take a +3 dBm up point, this will be S11 of -17 dBm, that is 98% of power going into the cavity. So moving from -20 dBm to -17 dBm of S11 changes the amount of power in the cavity by... 1%.
Apparently even the "3 dBm down" method is rather gross for S11 measurements, and they usually recommend calculating Q factor from complex S11 values (via Smith chart or otherwise). But since I don't have a vector NA... no complex S11 values for me.
Good luck with your tests.
Phil
Thank you, I will need it
Using a different than TTs calculation method I get ... please see below
Your spreadsheet
for this TE012 case is EXCELLENT !
only -0.60% apart in frequency from COMSOL FEAWhile "the other" spreadsheet was 3.40 % higher frequency
Here:
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1469866#msg1469866 , I exhaustively compare NASA's COMSOL FEA vs. experiment and vs. exact solution for TE012 without dielectric.
JFYI, Attached are COMSOL simulations for the frustum (with coax coupling) I am going to build. It is now time for some sheet metal cutting and torch soldering... And then there will be the moment of truth.
D_big: 264 mm
D_small: 158 mm
L_center: 204 mm
TE012 freq: 2,323,xxx kHz COMSOL (vs. 2,402,xxx spreadsheet)
Hi RfPlumber,
Thanks for the data on your test setup and VERY LOW COST quasi VNA. Have ordered that unit as I have built a Forward & Reflected power monitor that should have almost zero insertion loss and should work well with that unit. If it works as expected, using it and this unit will make really low cost frustum resonance monitoring a reality. By low cost I mean like around $150.
Can you please confirm the frustum built length is 204 mm and not 240 mm?
...
Based on the frustum length being 240 mm (TE012 resonance at 2.324 GHz), the prediction is 4mN at unloaded Q of 50k (25k loaded Q) and 30W Rf forward power.
Hi TT,
You're welcome. I am glad this info ends up useful. Yes, all dimensions above are correct, and the center length is 204 mm (and the actual frustum as-built ended up within 1mm of that length). Spreadsheet does produce a different value for TE012 frequency (2,402 MHz) vs. 2,323 MHz per COMSOL, and unfortunately the COMSOL value ends up being much closer to reality.
...4 mN of thrust would send my poor pendulum into an orbit
Do you have a link for your 30W Rf amp and can the freq gen you have drive it enough power to obtain the 30Ws at output?
Yes, it is the same unit someone else has recently pointed to. http://www.ebay.com/itm/30W-Class-A-Linear-RF-amplifier-2-3-2-45-GHz-2304-ATV-/221981664579?hash=item33af236543:g:Ro4AAOSw1S9WhALo
Note that it has a rather narrow band (2.30-2.35 GHz) where it can deliver 30W, hence all my trouble to make a frustum with a mode in this range.
No, my freq generator does not have enough power to directly drive this amp (just a few dBm short), so I am using a pre-amp. This one: http://www.ebay.com/itm/Mini-Circuits-Wideband-RF-Amplifier-ZX60-6013E-S-50-20-MHz-to-6-GHz-NOS-/261994189569?hash=item3d00121301:g:2jEAAOSwyQtVwsdG
The same guy www.windfreaktech.com has other generator models which do provide enough power to avoid the pre-amp, but they cost (way) more and are heavier. Note that I need a generator with EEPROM so it could fire at pre-programmed freq at power-up as I do not have an intelligent controller on the test platform to program it on the fly. You do, so can likely use any other synthesizer, even the one from that pseudo-VNA unit.
BTW what is the bandwidth and loaded Q if you measure 3dB up from the max rtn loss dB point, instead of 3dB down from the reference level.
Roger's Force equation works from unloaded Q, being twice the loaded Q, measured 3dB up from the max rtn loss dB point on a S11 VNA scan. This is how you measure power bandwidth as the max power xfer level becomes 0dB and you measure the point where the power xfer is 3dB down from the peak power xfer dB level.
Not trying to trigger an argument here. Just stating how Roger's Force equation works and what Q measurement technique it is based on.
That "Q" value (calculating UP from the _minimum_ of S11) would be around 10,000. It is what the scanner software calculates by default, but this value has very little sense, and so I didn't event include it in my screenshots. It is somewhat strange that this is what Roger is using... Think about it, assuming the minimum on S11 plot is say -20 dBm, this implies 99% of power goes into the cavity. Now take a +3 dBm up point, this will be S11 of -17 dBm, that is 98% of power going into the cavity. So moving from -20 dBm to -17 dBm of S11 changes the amount of power in the cavity by... 1%.
Apparently even the "3 dBm down" method is rather gross for S11 measurements, and they usually recommend calculating Q factor from complex S11 values (via Smith chart or otherwise). But since I don't have a vector NA... no complex S11 values for me.
Good luck with your tests.
Phil
Thank you, I will need it
Using a different than TTs calculation method I get ... please see below
Your spreadsheet for this TE012 case is EXCELLENT ! only -0.60% apart in frequency from COMSOL FEA
While "the other" spreadsheet was 3.40 % higher frequency
Here: https://forum.nasaspaceflight.com/index.php?topic=39214.msg1469866#msg1469866 , I exhaustively compare NASA's COMSOL FEA vs. experiment and vs. exact solution for TE012 without dielectric.
I put a lot of work into it and compare it with VNA measurements of real cavities.
I have no problem to say that for some other modes (especially TM
) the difference is much bigger in comparison with field calculation software and real measurements. But its a good indication to identify modes in a given VNA plot!
Beside of my own I have a second spreadsheet available (thanks to a great old MW Prof.!) that calculates the resonant frequency based on the complex input impedance iterative for a number of diameters of the cavity.
For some models it fits better for others it's worse than my. The point is that it's a bad idea to believe in a specific spreadsheet it's only an indication/ approximation of the real world and have to be checked again and again against reality. I believe more in field simulation programs than in this kind of spreadsheet.
That gives more precise/usable results.
The difference is, a spreadsheet delivers a result (however correct or not) in seconds while a field simulation costs more time and experience (and maybe expensive licenses for easy to use programs).
EDIT:
@Rodal
You gave me great support to get such results! The reason I expanded my old version of this spreadsheet was your advice. Thanks!
None of this is meant as a criticism of any particular individual or spreadsheet of course. It must be taken into account that all engineering companies start a design using such simpler tools (many times proceeding from a drawing) for first cut analysis, and only proceeds to more sophisticated methods like FEA or FD or Boundary Element Method or spectral methods when really required. Also the spreadsheet has been made freely available to the general community by the author while the more sophisticated methods (COMSOL FEA or using Wolfram Mathematica for an exact solution) are not free. The comparison is made rather to get a sense of realism in a comparison vs. experiments and more sophisticated methods, so that the general community has a sense of what errors to expect when using such spreadsheet methods vs the real world.
As a result of an excellent question from RotoSequence, in
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1470613#msg1470613 I showed that
no numerical solution is close to the precision needed to find the bandwidth of resonance for the high Q that one is seeking for. The higher the Q, the more precision is needed.
The precision is unattainable because one does not know the exact geometry of the resonant cavity to that precision.
All that one can do with the numerical solutions for a resonant cavity with a high Q (>10,000) is to tell where the resonance is, to a precision less than 1%, perhaps 0.1%. Finding the actual bandwidth of resonance and the resonance peak has to be done empirically, experimentally by S21 and S11 measurements.
None of this is meant as a criticism of any particular individual or spreadsheet of course. It must be taken into account that all engineering companies start a design using such simpler tools (many times proceeding from a drawing) for first cut analysis, and only proceeds to more sophisticated methods like FEA or FD or Boundary Element Method or spectral methods when really required. Also the spreadsheet has been made freely available to the general community by the author while the more sophisticated methods (COMSOL FEA or using Wolfram Mathematica for an exact solution) are not free. The comparison is made rather to get a sense of realism in a comparison vs. experiments and more sophisticated methods, so that the general community has a sense of what errors to expect when using such spreadsheet methods vs the real world.
As a result of an excellent question from RotoSequence, in https://forum.nasaspaceflight.com/index.php?topic=39214.msg1470613#msg1470613 I showed that
no numerical solution is close to the precision needed to find the bandwidth of resonance for the high Q that one is seeking for. The higher the Q, the more precision is needed.
The precision is unattainable because one does not know the exact geometry of the resonant cavity to that precision.
All that one can do with the numerical solutions for a resonant cavity with a high Q (>10,000) is to tell where the resonance is, to a precision less than 1%, perhaps 0.1%. Finding the actual bandwidth of resonance and the resonance peak has to be done empirically, experimentally by S21 and S11 measurements.
These are good commentaries on what we used to call "canned" software in the filter biz. We used a (now antiquated) piece of software called flysyn:
http://www.alkeng.com/sfilsyn.htmlFrom those numbers, we'd use our own, in-house, software loaded with standard values of chip caps and realistic Qs of the components inclusive of high-density packaging (miniaturization). We'd tweak inductors in old style LC filters to achieve resonance with the standard ATC multilayer caps.
Bottom line is, QA and bench inputs would make exceptional in-house software for engineers, but we always had to start from a fixed design program, or in this particular case, spreadsheet.
Seems we are moving towards an "in-house" FRUSTUM CAVITY modeling tool.
Seems we are moving towards an "in-house" emdrive modeling tool.
uh oh
Uhhhh...I mean an in-house frustum/cavity tool...LOL! Ya got me there, Glenn. Well done...cavity spreadsheet modeling tool in my brain, emdrive on my keyboard...forgive me.
Note to self - try to minimize posting when actually doing work elsewhere
Seriously, my apologies to all. After looking back on my posts the past few days, I am host-chatting way too much without much substance. Ya'll do just fine without my encouragement, so I'm going to exile myself into modtown for a few days and let everyone here do their own thing without my needless 2 cents
Sorry gang, I get carried away sometimes...
Seems we are moving towards an "in-house" emdrive modeling tool.
uh oh
Uhhhh...I mean an in-house frustum/cavity tool...LOL! Ya got me there, Glenn. Well done...cavity spreadsheet modeling tool in my brain, emdrive on my keyboard...forgive me.
Note to self - try to minimize posting when actually doing work elsewhere
You didn't quite read my
uh oh thought. I was trying to calculate how many "free" hours I have in 2016 in my
copious free time to devote to writing some simulation software given some empirical data and builder requirements that forces it to be written.
There are a few other coders in this forum... an open source development project was where my brain was at, and how much pain it is to make that work. I wasn't correcting your word usage.
I was calculating my personal pain threshold at doing lots of billable work for free. Have to do some market research to see if I could license it to someone in the RF industry without violating an existing NDA....
That "Q" value (calculating UP from the _minimum_ of S11) would be around 10,000. It is what the scanner software calculates by default, but this value has very little sense, and so I didn't event include it in my screenshots. It is somewhat strange that this is what Roger is using... Think about it, assuming the minimum on S11 plot is say -20 dBm, this implies 99% of power goes into the cavity. Now take a +3 dBm up point, this will be S11 of -17 dBm, that is 98% of power going into the cavity. So moving from -20 dBm to -17 dBm of S11 changes the amount of power in the cavity by... 1%.
Apparently even the "3 dBm down" method is rather gross for S11 measurements, and they usually recommend calculating Q factor from complex S11 values (via Smith chart or otherwise). But since I don't have a vector NA... no complex S11 values for me.
Roger did say his S11 Q method x2 generates an approximation of the unloaded Q that is used in the Force equation.
He went on to say the best way to measure loaded Q is to use a 2nd sample port attached to a power meter. Then adjust the input freq to obtain max power on the meter Next slowly adj freq until 50% power is noted on the high & low sides Then the real 1/2 power points are known and true loaded cavity Q can be calculated, with unloaded Q being twice that value.
So for Roger, either S11 or S21 is just a quick way to get a rough idea of loaded Q.
BTW at the indicated 2.312 GHz, the small end is below cutoff when calculated as a constant diameter circular waveguide. According to what Roger has taught me, there should be no thrust. This is not to say the small end is actually cutoff, just a rule of thumb situation to avoid.
Please trust me to investigate all this in intimate detail once my 1st frustum and test system is operational. If the spreadsheet Roger helped me to create stands up to the test data, so be it. Likewise if it falls short, so be it. At least I'll have real data to compare against the predicted data, be it from my spreadsheet or from some other source.
Take a look of Shawyer's original turning table experiment on YouTube. Surely it needs vibration (or tapping) to overcome the initial static friction. But such a vibration is not needed for a torsion balance or a boat on water experiment to overcome static friction that is zero.
The air bearing this is mounted on is virtually frictionless but he does have fans and pumps running plus the thrumming of the air compressor nearby.
Think of an imagined perfect air cushion hovercraft on the land. The land is not perfect, with tiny highs and lows that is not detectable by bear eyes. When stay idle, the perfect hovercraft will find itself a local low position and stay there. now suppose we apply a small force on the hovercraft (say, very light wind). If the force is not enough to overcome the initial climbing out of the local low position, the hovercraft will not move away. Only when a small earthquake shakes the land so the hovercraft overcomes the initial obstacle, will it start to move; and with built-up momentum it will overcome any new small low lands.
I have no experience with air bearing; but I have spent lots of time thinking of magnetic bearing that will suffer from similar problems.
It is a Man Shed dear,The stored furniture is GONE. Up bright & early to get my workshop back on stream. Who beat me to the space? SWMBO. "Just need to sort a bit of stuff out Darling? OK?"
Yes Dear. #$#×%€$#&
...
BTW at the indicated 2.312 GHz, the small end is below cutoff when calculated as a constant diameter circular waveguide. According to what Roger has taught me, there should be no thrust. This is not to say the small end is actually cutoff, just a rule of thumb situation to avoid.
...
Umm.. How do you calculate the cut-off freq? I am using attached, and so for 0.158 m smaller end one would get:
P01 = 3.832
Cut-off Freq = 3.832 * c / (6.28 * 0.158 * sqrt(1)) ~= 1,159 MHz.
The TE012 frustum mode at 2.312 GHz seems to be way above the cut-off for the smaller end... What am I missing?
...
BTW at the indicated 2.312 GHz, the small end is below cutoff when calculated as a constant diameter circular waveguide. According to what Roger has taught me, there should be no thrust. This is not to say the small end is actually cutoff, just a rule of thumb situation to avoid.
...
Umm.. How do you calculate the cut-off freq? I am using attached, and so for 0.158 m smaller end one would get:
P01 = 3.832
Cut-off Freq = 3.832 * c / (6.28 * 0.158 * sqrt(1)) ~= 1,159 MHz.
The TE012 frustum mode at 2.312 GHz seems to be way above the cut-off for the smaller end... What am I missing?
The guide wavelength turns imaginary when the small end is <= cutoff.
Need to do the cutoff calc 1st and then calc the guide wavelength.
Inside the frustum, freq is the same as outside. Need to work in wavelengths, Lambda.
None of this is meant as a criticism of any particular individual or spreadsheet of course. It must be taken into account that all engineering companies start a design using such simpler tools (many times proceeding from a drawing) for first cut analysis, and only proceeds to more sophisticated methods like FEA or FD or Boundary Element Method or spectral methods when really required. Also the spreadsheet has been made freely available to the general community by the author while the more sophisticated methods (COMSOL FEA or using Wolfram Mathematica for an exact solution) are not free. The comparison is made rather to get a sense of realism in a comparison vs. experiments and more sophisticated methods, so that the general community has a sense of what errors to expect when using such spreadsheet methods vs the real world.
As a result of an excellent question from RotoSequence, in https://forum.nasaspaceflight.com/index.php?topic=39214.msg1470613#msg1470613 I showed that
no numerical solution is close to the precision needed to find the bandwidth of resonance for the high Q that one is seeking for. The higher the Q, the more precision is needed.
The precision is unattainable because one does not know the exact geometry of the resonant cavity to that precision.
All that one can do with the numerical solutions for a resonant cavity with a high Q (>10,000) is to tell where the resonance is, to a precision less than 1%, perhaps 0.1%. Finding the actual bandwidth of resonance and the resonance peak has to be done empirically, experimentally by S21 and S11 measurements.
Haven't I been saying this all along? One cannot design the frustrum to the source, one must tune the source to the actual frustum!
On that note:
http://scitation.aip.org/content/aip/magazine/physicstoday/news/10.1063/PT.5.7231brings up the idea that, if there is already the couplers available for S parameter measurements then a very straightforward S12 vs S11 comparison using a mixer (as would be used for phase noise measurement), would yield extremely fine grained "doppler" measurement of what is going on within the frustum. Of course, the source must be phase locked, but current phase noise measurements are below -215 dBc/Hz. This techique should give picometer (or better) resolution of frustum acceleration.
Edit: Be very careful of slinging around S parameters. They are only defined in a 50 ohm system, unless otherwise transformed. You cannot directly compare S parameters unless the system is normalized to a particular impedance across the board. I'm also seeing confusion between dBm (decibels referrenced to one milliwatt), and dB (the decibel, a logarithmic ratio). -3 dB at -100 dBm is a hell of a lot less POWER than -3 dB at +40 dBm. I noticed this as rookie mistake reading the screen of a "network analyzer" earlier.
Acceleration does give a calculable frequency shift (Need to calculate it...)
Note: Then you have to compensate for velocity relative to your reference frame.
None of this is meant as a criticism of any particular individual or spreadsheet of course. It must be taken into account that all engineering companies start a design using such simpler tools (many times proceeding from a drawing) for first cut analysis, and only proceeds to more sophisticated methods like FEA or FD or Boundary Element Method or spectral methods when really required. Also the spreadsheet has been made freely available to the general community by the author while the more sophisticated methods (COMSOL FEA or using Wolfram Mathematica for an exact solution) are not free. The comparison is made rather to get a sense of realism in a comparison vs. experiments and more sophisticated methods, so that the general community has a sense of what errors to expect when using such spreadsheet methods vs the real world.
As a result of an excellent question from RotoSequence, in https://forum.nasaspaceflight.com/index.php?topic=39214.msg1470613#msg1470613 I showed that
no numerical solution is close to the precision needed to find the bandwidth of resonance for the high Q that one is seeking for. The higher the Q, the more precision is needed.
The precision is unattainable because one does not know the exact geometry of the resonant cavity to that precision.
All that one can do with the numerical solutions for a resonant cavity with a high Q (>10,000) is to tell where the resonance is, to a precision less than 1%, perhaps 0.1%. Finding the actual bandwidth of resonance and the resonance peak has to be done empirically, experimentally by S21 and S11 measurements.
Haven't I been saying this all along? One cannot design the frustrum to the source, one must tune the source to the actual frustum!
On that note:
http://scitation.aip.org/content/aip/magazine/physicstoday/news/10.1063/PT.5.7231
brings up the idea that, if there is already the couplers available for S parameter measurements then a very straightforward S12 vs S11 comparison using a mixer (as would be used for phase noise measurement), would yield extremely fine grained "doppler" measurement of what is going on within the frustum. Of course, the source must be phase locked, but current phase noise measurements are below -215 dBc/Hz. This techique should give picometer (or better) resolution of frustum acceleration.
I agree, you have been right all along.
Also credit is shared by
Robert Ludwick who was stating that <<One cannot design the frustrum to the source, one must tune the source to the actual frustum>> all the way back in thread 2.
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BTW at the indicated 2.312 GHz, the small end is below cutoff when calculated as a constant diameter circular waveguide. According to what Roger has taught me, there should be no thrust. This is not to say the small end is actually cutoff, just a rule of thumb situation to avoid.
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Umm.. How do you calculate the cut-off freq? I am using attached, and so for 0.158 m smaller end one would get:
P01 = 3.832
Cut-off Freq = 3.832 * c / (6.28 * 0.158 * sqrt(1)) ~= 1,159 MHz.
The TE012 frustum mode at 2.312 GHz seems to be way above the cut-off for the smaller end... What am I missing?
The guide wavelength turns imaginary when the small end is <= cutoff.
Need to do the cutoff calc 1st and then calc the guide wavelength.
I wondered about this cutoff point for some time and aero and Dr. Rodal susgested months ago we run a frustum past a cutoff point.
I stopped the video when the wavefront reached the part of the frustum that was its cutoff.
After the wave propagates past the cuttoff and hits the small end it bounces back hitting the cutoff area again and the frustum begins to make the cavity resonate in two directions.
For your viewing pleasure and some insight.
Shell
BRB with a gif that runs.
) the difference is much bigger in comparison with field calculation software and real measurements. But its a good indication to identify modes in a given VNA plot!
