Having just played around with a Futterman and inverted Futterman OTL circuit in another thread, I became curious about how easy it was to change a grounded cathode stage into a cathode follower stage by just changing the bootstrap circuitry to the driver stage.
1st, I tried making something 1/2 way in between, a 50% CFB Futterman. This turned out to be really easy. Just put 1/2 the bootstrap voltage back to BOTH the driver plate loads. And then, you can even get ANY % CFB there, by altering the amount of each bootstrap.
Then I started thinking, there must be a way to do this with a conventional center tapped OT too. So I configured that setup similarly, and lo and behold, it is just the resistive feedback Schade circuit (a feedback resistor between plate and grid of the output tube). Never saw it in this light before.
One often hears questions about Schade feedback, and whether it sounds like a real triode using that feedback resistor. A different visualization obviously.
Looking at the bottom diagram, I have used Broskie's trick of moving a virtual ground around to the plate. Now the B+ is just a battery, swinging around to drive the load instead of the plate. The grid drive does not care about where ground is, with a current source driver just dropping voltage across Rfb. So this is 100% CFB.
Now look at the top diagram, left side. I have included the usual plate load resistor Rl for the driver stage (current drive, or pentode say), from B+, as well as the Rfb resistor. (I've included an additional R for the grid variation, will get rid of that below) Placing a virtual ground at their common point, one gets a certain % of the OT primary voltage variation dropping across Rl and Rfb on each side. If Rl = Rfb, then 50%. So plate and cathode are each varying 50% of the primary voltage from virtual ground. 50% CFB.
If Rl = 0.43 of (Rfb+Rl), then 43% of plate V variation occurs at their jucntion to the grid. It would have the same voltage variation as the typical UL tap.
So we can just replace those R's with the equivalent R and UL tap setup on the right side (top). Now its 43% CFB. Maybe a little more obvious that a virtual ground on the UL tap would have the cathode doing 43% of the primary, and the plate doing 57%. Or 43% CFB.
So one can get any % CFB by just arranging the divider R network. If the UL tap gives too much % CFB, then do an R divider between the UL taps and B+ to get lower %.
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Using a triode driver stage however breaks the floating B+ rules due to its Rp. One can look at this variant as that of the current driven arrangement analyzed above, plus a high Rp diode across the output tube's grid to cathode. Not helpful for a SE arrangement, since it will exacerbate the non-linearity of the output tube. But for a P-P arrangement, the diode(s) could be seen as compensating the opposite side's non-linearity in class A operation somewhat. Maybe. ??
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So no need to get a custom CFB OT wound. Two divider resistors (and maybe preferably a high Zo driver stage) is all it takes to get an exact equivalent.
1st, I tried making something 1/2 way in between, a 50% CFB Futterman. This turned out to be really easy. Just put 1/2 the bootstrap voltage back to BOTH the driver plate loads. And then, you can even get ANY % CFB there, by altering the amount of each bootstrap.
Then I started thinking, there must be a way to do this with a conventional center tapped OT too. So I configured that setup similarly, and lo and behold, it is just the resistive feedback Schade circuit (a feedback resistor between plate and grid of the output tube). Never saw it in this light before.
One often hears questions about Schade feedback, and whether it sounds like a real triode using that feedback resistor. A different visualization obviously.
Looking at the bottom diagram, I have used Broskie's trick of moving a virtual ground around to the plate. Now the B+ is just a battery, swinging around to drive the load instead of the plate. The grid drive does not care about where ground is, with a current source driver just dropping voltage across Rfb. So this is 100% CFB.
Now look at the top diagram, left side. I have included the usual plate load resistor Rl for the driver stage (current drive, or pentode say), from B+, as well as the Rfb resistor. (I've included an additional R for the grid variation, will get rid of that below) Placing a virtual ground at their common point, one gets a certain % of the OT primary voltage variation dropping across Rl and Rfb on each side. If Rl = Rfb, then 50%. So plate and cathode are each varying 50% of the primary voltage from virtual ground. 50% CFB.
If Rl = 0.43 of (Rfb+Rl), then 43% of plate V variation occurs at their jucntion to the grid. It would have the same voltage variation as the typical UL tap.
So we can just replace those R's with the equivalent R and UL tap setup on the right side (top). Now its 43% CFB. Maybe a little more obvious that a virtual ground on the UL tap would have the cathode doing 43% of the primary, and the plate doing 57%. Or 43% CFB.
So one can get any % CFB by just arranging the divider R network. If the UL tap gives too much % CFB, then do an R divider between the UL taps and B+ to get lower %.
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Using a triode driver stage however breaks the floating B+ rules due to its Rp. One can look at this variant as that of the current driven arrangement analyzed above, plus a high Rp diode across the output tube's grid to cathode. Not helpful for a SE arrangement, since it will exacerbate the non-linearity of the output tube. But for a P-P arrangement, the diode(s) could be seen as compensating the opposite side's non-linearity in class A operation somewhat. Maybe. ??
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So no need to get a custom CFB OT wound. Two divider resistors (and maybe preferably a high Zo driver stage) is all it takes to get an exact equivalent.
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Still trying to wrap my head around your diagram... but what are you doing with the screen grid? Do you tie that to the UL tap or just pentode connection?
An externally hosted image should be here but it was not working when we last tested it.
The screen grids of the output tubes would be powered from floating supplies from the cathodes. (or the usual screen R divider from B+ to cathodes with a cap(s) between screen and cathode to hold it constant.)
I didn't draw anything in for the screen grids since that would just obscure the circuitry for this modeling. The outputs could just as well be triodes too.
I didn't draw anything in for the screen grids since that would just obscure the circuitry for this modeling. The outputs could just as well be triodes too.
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If you drive with a current source you can define every point you wish as ground.The source with infinite impedance has no reference, the current can come from where ever.
In real live it's a dipole source.Depending on where you put the other pole (signal ground) things change.
If it is the cathode you get Schade (low input impedance,low input voltage), with the anode a cathode follower (high input impedance, high input voltage).
Since B+ and cathode are the same for the signal, a devider between anode and cathode gives you a bit of both.
Mona
In real live it's a dipole source.Depending on where you put the other pole (signal ground) things change.
If it is the cathode you get Schade (low input impedance,low input voltage), with the anode a cathode follower (high input impedance, high input voltage).
Since B+ and cathode are the same for the signal, a devider between anode and cathode gives you a bit of both.
Mona
I built a push-pull KT88 amp like that for my brother once and it sounded great. I made the current drive by using a p-channel fet as a voltage source and putting a resistor in series. The advantage was I was able to eliminate the capacitor at the output tube and eliminate the possibility of charging that cap in overload conditions. The disadvantage of course was that I had to make extra negative supplies.
The amp gave .3% distortion at 10W, pretty darn good for an open-loop pentode amp. It sounded really good too. It seemed to be in control of the speaker as well. I regret that I didn't get a measurement of Zout before I gave the amp away. It would have been nice to know.
I shared the details here: http://www.diyaudio.com/forums/tubes-valves/248376-amp-kt88-push-pull-shunt-feedback-output-via-p-channel-fet.html
Heavy CFB is complex if you want to keep the advantages of a pentode due to the need for the floating screen supply, so the simple way to do it seems to be just a resistor divider to accomplish the same end, and it actually works very well in practice.
The amp gave .3% distortion at 10W, pretty darn good for an open-loop pentode amp. It sounded really good too. It seemed to be in control of the speaker as well. I regret that I didn't get a measurement of Zout before I gave the amp away. It would have been nice to know.
I shared the details here: http://www.diyaudio.com/forums/tubes-valves/248376-amp-kt88-push-pull-shunt-feedback-output-via-p-channel-fet.html
Heavy CFB is complex if you want to keep the advantages of a pentode due to the need for the floating screen supply, so the simple way to do it seems to be just a resistor divider to accomplish the same end, and it actually works very well in practice.
Mona K makes a good point here.
The grid input impedance, or Zin, goes very low as the %CFB gets higher in this setup. Essentially similar to the Miller effect, except here it is across the bootstrapped load R, or grid pull-up. The usual resistive Schade version (= 100% CFB) being the hardest to drive.
So practical circuits will prefer a lower %CFB arrangement for easier drive and gain, unless you use a reasonable size pentode for the driver stage.
Another difference is that the drive voltage swing does not increase towards 100% CFB, just the current demand. So a bit different than real CFB for the driver at least. Output tube doesn't know the difference though.
Maybe should call it CFB with shunt feedback, versus the usual series feedback.
The grid input impedance, or Zin, goes very low as the %CFB gets higher in this setup. Essentially similar to the Miller effect, except here it is across the bootstrapped load R, or grid pull-up. The usual resistive Schade version (= 100% CFB) being the hardest to drive.
So practical circuits will prefer a lower %CFB arrangement for easier drive and gain, unless you use a reasonable size pentode for the driver stage.
Another difference is that the drive voltage swing does not increase towards 100% CFB, just the current demand. So a bit different than real CFB for the driver at least. Output tube doesn't know the difference though.
Maybe should call it CFB with shunt feedback, versus the usual series feedback.
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re: SpreadSpectrum
Yes, I recall that design now. The P channel follower drive is novel for sure. The resistor from plate to grid on the output is the typical Schade setup (maybe a cap isolator usually), which would be equivalent to 100% CFB, if it were current source fed.
With a 10K Ohm driver source impedance, it is something in between (but likely closer to 100% CFB). Should be some easy way to calculate the equivalent % CFB in that case, one needs to know the effective gain of the KT88.
Yes, I recall that design now. The P channel follower drive is novel for sure. The resistor from plate to grid on the output is the typical Schade setup (maybe a cap isolator usually), which would be equivalent to 100% CFB, if it were current source fed.
With a 10K Ohm driver source impedance, it is something in between (but likely closer to 100% CFB). Should be some easy way to calculate the equivalent % CFB in that case, one needs to know the effective gain of the KT88.
It is basically the same circuit as an inverting op-amp. As long as the KT88 has much more gain that the gain we are trying to set with our feedback network, we should be able to use the same formulas that we use for op-amps, right?
I set my amp up for a mu of 5. I reached a limit of practicality here because with my circuit configuration with the feedback all direct-coupled, I shifted the negative bias required on the gate of the fet. With an effective mu of 5, I needed ~-125V on the gate of the fet, and I needed the negative supply even more negative to accommodate the large swing to drive the feedback network. I would say that doing effective mu of less than 4 starts to get very difficult this way due to large negative rails required and voltage ratings of p-channel parts.
I wanted to use a current source (pentode) to drive it directly but I never found one that I thought was linear enough and had constant enough rp, so I decided to make a device with the desired characteristics with a mosfet and resistor.
"I wanted to use a current source (pentode) to drive it directly but I never found one that I thought was linear enough and had constant enough rp, so I decided to make a device with the desired characteristics with a mosfet and resistor."
Well, I think a nice feature of the Schade type shunt Fdbk setup is that the driver voltage swing is not increased over the grounded cathode mode. (unlike the usual CFB setup) So the amount of variation of driver Rp with voltage is well minimised for a tube pentode. (but not with current variation unfortunately) Certainly, a Mosfet driver has the upper hand there.
The convertability between Schade and CFB modes also says something about typical UL mode I think. The screen grid is just another grid for input, the N Fdbk in that case, just like the Schade setup using g1. Some small difference due to screen currents when taken to the output tube screen grids.
I guess the main thing I see in this "equivalence" finding is that Schade mode is not really some weird non-linear triode emulator. Although it does set an effective stage Mu, just like %CFB does. One should not fear the sound quality that can be obtained this way.
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For practical circuits, I think I would just take a small amount of UL tap signal(s) and feed that back to the (differential) driver screen grids (crossed over for phase). That way the power handling of the output tubes is not reduced as in UL mode. And more local loop gain (driver + output gains) can be used for maintaining the linear closed loop gain. The screen grids are more linear than the g1 grids, being typically 1.4 power law, versus 2.0 power law for g1. So N Fdbk to the driver screen grids is unexpectedly more effective, even at the typically lower effective levels (1/Mu internal). The small screen grid voltage variation here (UL to the driver case) eliminates screen current issues.
Well, I think a nice feature of the Schade type shunt Fdbk setup is that the driver voltage swing is not increased over the grounded cathode mode. (unlike the usual CFB setup) So the amount of variation of driver Rp with voltage is well minimised for a tube pentode. (but not with current variation unfortunately) Certainly, a Mosfet driver has the upper hand there.
The convertability between Schade and CFB modes also says something about typical UL mode I think. The screen grid is just another grid for input, the N Fdbk in that case, just like the Schade setup using g1. Some small difference due to screen currents when taken to the output tube screen grids.
I guess the main thing I see in this "equivalence" finding is that Schade mode is not really some weird non-linear triode emulator. Although it does set an effective stage Mu, just like %CFB does. One should not fear the sound quality that can be obtained this way.
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For practical circuits, I think I would just take a small amount of UL tap signal(s) and feed that back to the (differential) driver screen grids (crossed over for phase). That way the power handling of the output tubes is not reduced as in UL mode. And more local loop gain (driver + output gains) can be used for maintaining the linear closed loop gain. The screen grids are more linear than the g1 grids, being typically 1.4 power law, versus 2.0 power law for g1. So N Fdbk to the driver screen grids is unexpectedly more effective, even at the typically lower effective levels (1/Mu internal). The small screen grid voltage variation here (UL to the driver case) eliminates screen current issues.
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Indeed, I just was never able to convince myself that it would be as linear overall from looking at real pentode characteristics. Maybe I'm wrong. I wish I had more time and energy to experiment.
Playing around some more!
Futterman and Inverted Futterman => Schade and Inverted Schade
so the Inverted Schade now:
This allows one to have anything from 100% to 0% CFB effectively, using a cathode follower output configuration. The difference here, is that the drive signal is now high impedance, high voltage swing. (instead of the low impedance input, low voltage swing for the usual Schade version)
Futterman and Inverted Futterman => Schade and Inverted Schade
so the Inverted Schade now:
This allows one to have anything from 100% to 0% CFB effectively, using a cathode follower output configuration. The difference here, is that the drive signal is now high impedance, high voltage swing. (instead of the low impedance input, low voltage swing for the usual Schade version)
How easy is it to make a very linear tube V to I converter that would be capable of driving these circuits? I mean, what always stopped me from doing something like this was the uneven spacing of curves on real pentodes. If we add a little cathode degeneration, do we get curves that are spaced evenly enough so that the current drive wouldn't be the dominant source of distortion in the amp? I wish I had a curve tracer to play around with.
I just built an amp with a Unity-Coupled output stage and had to develop 560Vpk-pk at low distortion to drive the output stage with 50% CFB. In the end I was able to get .25% distortion at 30W out of the amp without a bootstrapped driver and with no global feedback loop. If I were to take a different approach with a current driver, one of these CFB equivalent circuits, and a conventional output transformer, would I be able to match that performance in a real amp?
Something tells me that developing linear current drive is the hard part. Maybe I just haven't thought about it enough.
I just built an amp with a Unity-Coupled output stage and had to develop 560Vpk-pk at low distortion to drive the output stage with 50% CFB. In the end I was able to get .25% distortion at 30W out of the amp without a bootstrapped driver and with no global feedback loop. If I were to take a different approach with a current driver, one of these CFB equivalent circuits, and a conventional output transformer, would I be able to match that performance in a real amp?
Something tells me that developing linear current drive is the hard part. Maybe I just haven't thought about it enough.
Well, I guess one can always brute force the V to I with massive gain. (diagram)
That gets to be a lot of parts and alignments. And one would like to have differential drive outputs usually too.
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My next approach would be to use two pentodes in a non-differential pair (no CCS tail), with a specially selected operating point. The plates then giving the current outputs directly. With complementary Vg1 inputs.
Now this has some caveats. The pentodes need to be operating in the region where their gm curves versus Vg1 are flat ramping (or inflecting at least). Take a look at the 6JC6 datasheet linked, last page. That flat (linear ramping) section in the middle current range is from 2.0 power law operation (I = kV^2) which gives 1.0 power law gm (hence the flattening out to a linear gm ramp in that region).
Note, that using a CCS tail does not work here. If you look at a datasheet where gm is plotted versus Ip, you will always find it bending over, no inflection point to the curvature.
Now in differential usage for the output currents, the gm's add up, so the result is constant gm (for differential current output, but not for individual current outputs). As long as the gm curves look reasonably complementary (symmetric S curves) then the gm sum should hold near constant.
Fortunately, with a CT'd OT, differential drive is all that matters, common mode stuff will cancel. So this should be good enough. Although, common mode currents do still heat up the output tubes somewhat needlessly. I guess one could put an interstage xfmr in the drive path to eliminate the common mode.
http://frank.pocnet.net/sheets/135/6/6JC6A.pdf
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By the way, how does one get stuff to show up in a post, so that one does not have to be logged on to see or use it?
That gets to be a lot of parts and alignments. And one would like to have differential drive outputs usually too.
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My next approach would be to use two pentodes in a non-differential pair (no CCS tail), with a specially selected operating point. The plates then giving the current outputs directly. With complementary Vg1 inputs.
Now this has some caveats. The pentodes need to be operating in the region where their gm curves versus Vg1 are flat ramping (or inflecting at least). Take a look at the 6JC6 datasheet linked, last page. That flat (linear ramping) section in the middle current range is from 2.0 power law operation (I = kV^2) which gives 1.0 power law gm (hence the flattening out to a linear gm ramp in that region).
Note, that using a CCS tail does not work here. If you look at a datasheet where gm is plotted versus Ip, you will always find it bending over, no inflection point to the curvature.
Now in differential usage for the output currents, the gm's add up, so the result is constant gm (for differential current output, but not for individual current outputs). As long as the gm curves look reasonably complementary (symmetric S curves) then the gm sum should hold near constant.
Fortunately, with a CT'd OT, differential drive is all that matters, common mode stuff will cancel. So this should be good enough. Although, common mode currents do still heat up the output tubes somewhat needlessly. I guess one could put an interstage xfmr in the drive path to eliminate the common mode.
http://frank.pocnet.net/sheets/135/6/6JC6A.pdf
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By the way, how does one get stuff to show up in a post, so that one does not have to be logged on to see or use it?
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Seeing as an interstage xfmr is quite inconvenient for a current source driver to eliminate the CM current, I'm thinking along the lines of a scheme to remove the common mode (CM) currents actively.
If one were to monitor the grounded tail current sum of the two driver pentodes with a small sampling resistor, one could derive the deviation from constant current sum. This could be used to control two SS CCS's which would be summed with the pentode outputs to null out CM currents.
It's tempting to just put a CCS under the pentode(s) tail, but that unfortunately doesn't work correctly. The gm sum has significant 3rd harmonic then.
To see that, take a look at the gm versus current plot on page 9 of the linked E55L tube datasheet below to see that complementary current tubes won't add up to a constant gm that way.
Page 7 also gives a gm versus Vg1 plot, where it is more obvious that a complementary (symmetrical S) gm set is available that way.
http://frank.pocnet.net/sheets/009/e/E55L.pdf
Could there be an easier way to eliminate the CM current?
Maybe just actively control both screen grid voltages, of the two pentodes, using a single controlled SS CCS, monitoring V on the low R tail?
Need to simulate that one I think. My guess is that it works as long as the pentode tail sampling R is low compared to 1/gm of the pentodes.
Looks like that's the way to do it. Just need's to keep the pentode tail impedance low. And the servo action tries to keep the tail V constant anyway, so the pentode Vg1 environment is preserved.
Win, win, a new linear "differential" stage paradigm. (the old tube books are rolling over, falling off the shelves!!)
If one were to monitor the grounded tail current sum of the two driver pentodes with a small sampling resistor, one could derive the deviation from constant current sum. This could be used to control two SS CCS's which would be summed with the pentode outputs to null out CM currents.
It's tempting to just put a CCS under the pentode(s) tail, but that unfortunately doesn't work correctly. The gm sum has significant 3rd harmonic then.
To see that, take a look at the gm versus current plot on page 9 of the linked E55L tube datasheet below to see that complementary current tubes won't add up to a constant gm that way.
Page 7 also gives a gm versus Vg1 plot, where it is more obvious that a complementary (symmetrical S) gm set is available that way.
http://frank.pocnet.net/sheets/009/e/E55L.pdf
Could there be an easier way to eliminate the CM current?
Maybe just actively control both screen grid voltages, of the two pentodes, using a single controlled SS CCS, monitoring V on the low R tail?
Need to simulate that one I think. My guess is that it works as long as the pentode tail sampling R is low compared to 1/gm of the pentodes.
Looks like that's the way to do it. Just need's to keep the pentode tail impedance low. And the servo action tries to keep the tail V constant anyway, so the pentode Vg1 environment is preserved.
Win, win, a new linear "differential" stage paradigm. (the old tube books are rolling over, falling off the shelves!!)
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Here we go, the new paradigm differential stage:
(linear complementary current outputs, provided the pentodes are biased correctly at the gm versus Vg1 curvature inflection point) (linked datasheet, page 7 graph as example)
http://frank.pocnet.net/sheets/009/e/E55L.pdf
(linear complementary current outputs, provided the pentodes are biased correctly at the gm versus Vg1 curvature inflection point) (linked datasheet, page 7 graph as example)
http://frank.pocnet.net/sheets/009/e/E55L.pdf
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So that would be clever to have non-linear characteristics in both halves that sum to something that is linear. So distortion would go up if the output tubes were operated outside of class A for that scheme, right, since you don't have something opposing the nonlinearity when one tube cuts off?
Well, I was thinking of this for a linear driver stage, which would be class A.
Yeah, it won't work for an actual output stage in class AB.
However, there is a technique even for that, where one measures the difference of the two output tube currents and then feed that back to the driver stage as N Fdbk. (difference of the two tube currents is proportional to the actual load output current) One could just sample the two tube currents and send them both back to a differential (CCS tail type) driver stage to take the difference.
Trying to combine both these schemes will require some more burning the mid-night oil I'm afraid.
Yeah, it won't work for an actual output stage in class AB.
However, there is a technique even for that, where one measures the difference of the two output tube currents and then feed that back to the driver stage as N Fdbk. (difference of the two tube currents is proportional to the actual load output current) One could just sample the two tube currents and send them both back to a differential (CCS tail type) driver stage to take the difference.
Trying to combine both these schemes will require some more burning the mid-night oil I'm afraid.
There is this kind of cheat. A class A cascode with class B up top. I've been thinking this might actually be do-able with some refinements. Mosfet cascodes up top, and the new paradigm differential on the bottom say.
http://www.diyaudio.com/forums/tube...utput-without-all-heat-cheat.html#post4167018
http://www.diyaudio.com/forums/tube...utput-without-all-heat-cheat.html#post4167018
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I have an old hacked-up Fisher X-101-B that I was going to convert to run 6AR6s, since I have many of them and I don't want to keep buying 7591s. So I was going to do the p-channel fet/plate-grid feedback thing again on the output stage, but you have me wondering if there isn't something more interesting I can do and try something new. I'm kind of limited on space there though, so it couldn't be too complex. It's fun thinking about this stuff.
The p-channel fet thing was just awesome performance for the complexity, though, so I may end up sticking with that. I've always got my eye out for something better, though.
The p-channel fet thing was just awesome performance for the complexity, though, so I may end up sticking with that. I've always got my eye out for something better, though.
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