I was looking at the notion of a typical Sweep tube / Audio power tube design being just a re-scaling of a basic 6L6GC (for example). Higher power = bigger plate, higher current rating = bigger cathode. So it seemed natural to expect some simple relation to the 6L6GC for the typical selection of an OT primary impedance too.
Since power scales as V * I or V*V/Ro, and impedance as Zo=V/I, a simple formula derivation would be:
W = V * V / Ro
so V = SQRT (Ro *W)
and the OT Zo = k deltaV/deltaI
k is a "constant" to be determined from typical tube/OT datasheet specs
so the magic formula is:
OT Zo = k SQRT(W)/Idc
the 6L6GC bogey Ro getting absorbed into the k for convenience, W is the tube plate Watt spec and Idc is the tube's max DC current spec in milliamps. (usually on the datasheet )
This formula assumes B+ and Idc current will BOTH scale as SQRT of the Watts spec ideally, with the Idc term in there to modify the scaling for tubes designed with a different balance of I to V versus the 6L6GC. Ie, if a scaled tube handles twice the Watts, it would be expected to handle 1.414 x the voltage and 1.414 x the current, so would use the same primary Z OT then. The Idc term fixes deviation of the scaling for different V to I design ratios from the 6L6GC.
Looking at some typical tubes with datasheet spec'd OTs for maximum power output, some typical k values:
6L6GC kSQRT(30)/110 = 5600 Ohms, so k = 112466
6973 kSQRT(12)/45 = 8000, so k = 103923
6AQ5 kSQRT(12)/40 = 10000, so k = 115470
6V6 kSQRT(14)/40 = 8000, so k = 85524
6CA7/EL34 kSQRT(25)/150 = 3400, so k = 102000
6550 kSQRT(42)/190 = 3500, so k = 102612
6BQ5/EL84 kSQRT(12)/65 = 8000, so k = 150111
8417 kSQRT(35)/200 = 3500, so k = 118322
7591 kSQRT(19)/85 = 6600, so k = 128702
6146B kSQRT(27)/175 = 4000, so k = 134715 (5600 Ohm case was right at the max B+, so didn't use it)
6BM8 kSQRT(7)/50 = 7000, so k = 132288
4D32 kSQRT(50)/300 = 3000, so k = 127279
the variations of k above are largely from deviation from the SQRT(W) term for B+ variation with Watts expected, versus the tube design models actually used from the datasheets.
for TV Sweep tubes, the Watt rating is generally more conservatively rated due to the constant high-stress usage in that mode. So for these I multiply the given Sweep Watt rating by 1.333 to use here:
6GE5 kSQRT(23)/175 = 4000 Ohms, so k = 145960
6HJ5 kSQRT(32)/280 = 3000, so k = 148492
6LX6 kSQT(44)/400 = 2500, so k = 150756
6LW6 kSQRT(53.3)/400 = 2000, so k = 109579
42KN6 kSQRT(40)/400 = 2000, so k = 126491
Well, these #s are not written in stone by any means, but maybe guidelines I would say for plotting a 1st load-line on the plate curves graph.
The B+ available would affect the load Z choice obviously, and efficiency goes up with higher B+ and higher load Z.
One needs to check that V and dissipation ratings are not exceeded. The screen V would be selected to just enable the max current on the load line.
Distortion is another matter for pentodes, since there is typically an optimum load Z due to screen current distortion at high load Z setting in. The later TV Sweep tubes typically had reduced screen current figures shown, so that allows using a higher load Z without distortion increasing. 21LG6A being a good example, very straight lines for plate curves. https://frank.pocnet.net/sheets/123/6/6LG6.pdf
Constant k in the above formula assumes B+ and OT Z will scale up or down as the SQRT of Watts (with modification for the cathode size deviating from SQRT(W) also). Since the 6L6GC starts at 450V B+ here, this may not be a desirable scheme if trying to stick with lower cost electrolytics in the power supply for bigger tubes. In which case, one should scale from the 6L6GC using current only (so a modded formula then: Zo = k2 / Idc, with different k2 factors from the datasheet models ).
Just having some fun looking for patterns.
Just for curiosity:
211 tube kSQRT(100)/175 =9000, so k = 157500
300B tube kSQRT(40)/100 = 7000, so k = 110679
Hmmm, works OK for triodes even. Upgrade that Magic formula to Miracle formula!
Since power scales as V * I or V*V/Ro, and impedance as Zo=V/I, a simple formula derivation would be:
W = V * V / Ro
so V = SQRT (Ro *W)
and the OT Zo = k deltaV/deltaI
k is a "constant" to be determined from typical tube/OT datasheet specs
so the magic formula is:
OT Zo = k SQRT(W)/Idc
the 6L6GC bogey Ro getting absorbed into the k for convenience, W is the tube plate Watt spec and Idc is the tube's max DC current spec in milliamps. (usually on the datasheet )
This formula assumes B+ and Idc current will BOTH scale as SQRT of the Watts spec ideally, with the Idc term in there to modify the scaling for tubes designed with a different balance of I to V versus the 6L6GC. Ie, if a scaled tube handles twice the Watts, it would be expected to handle 1.414 x the voltage and 1.414 x the current, so would use the same primary Z OT then. The Idc term fixes deviation of the scaling for different V to I design ratios from the 6L6GC.
Looking at some typical tubes with datasheet spec'd OTs for maximum power output, some typical k values:
6L6GC kSQRT(30)/110 = 5600 Ohms, so k = 112466
6973 kSQRT(12)/45 = 8000, so k = 103923
6AQ5 kSQRT(12)/40 = 10000, so k = 115470
6V6 kSQRT(14)/40 = 8000, so k = 85524
6CA7/EL34 kSQRT(25)/150 = 3400, so k = 102000
6550 kSQRT(42)/190 = 3500, so k = 102612
6BQ5/EL84 kSQRT(12)/65 = 8000, so k = 150111
8417 kSQRT(35)/200 = 3500, so k = 118322
7591 kSQRT(19)/85 = 6600, so k = 128702
6146B kSQRT(27)/175 = 4000, so k = 134715 (5600 Ohm case was right at the max B+, so didn't use it)
6BM8 kSQRT(7)/50 = 7000, so k = 132288
4D32 kSQRT(50)/300 = 3000, so k = 127279
the variations of k above are largely from deviation from the SQRT(W) term for B+ variation with Watts expected, versus the tube design models actually used from the datasheets.
for TV Sweep tubes, the Watt rating is generally more conservatively rated due to the constant high-stress usage in that mode. So for these I multiply the given Sweep Watt rating by 1.333 to use here:
6GE5 kSQRT(23)/175 = 4000 Ohms, so k = 145960
6HJ5 kSQRT(32)/280 = 3000, so k = 148492
6LX6 kSQT(44)/400 = 2500, so k = 150756
6LW6 kSQRT(53.3)/400 = 2000, so k = 109579
42KN6 kSQRT(40)/400 = 2000, so k = 126491
Well, these #s are not written in stone by any means, but maybe guidelines I would say for plotting a 1st load-line on the plate curves graph.
The B+ available would affect the load Z choice obviously, and efficiency goes up with higher B+ and higher load Z.
One needs to check that V and dissipation ratings are not exceeded. The screen V would be selected to just enable the max current on the load line.
Distortion is another matter for pentodes, since there is typically an optimum load Z due to screen current distortion at high load Z setting in. The later TV Sweep tubes typically had reduced screen current figures shown, so that allows using a higher load Z without distortion increasing. 21LG6A being a good example, very straight lines for plate curves. https://frank.pocnet.net/sheets/123/6/6LG6.pdf
Constant k in the above formula assumes B+ and OT Z will scale up or down as the SQRT of Watts (with modification for the cathode size deviating from SQRT(W) also). Since the 6L6GC starts at 450V B+ here, this may not be a desirable scheme if trying to stick with lower cost electrolytics in the power supply for bigger tubes. In which case, one should scale from the 6L6GC using current only (so a modded formula then: Zo = k2 / Idc, with different k2 factors from the datasheet models ).
Just having some fun looking for patterns.
Just for curiosity:
211 tube kSQRT(100)/175 =9000, so k = 157500
300B tube kSQRT(40)/100 = 7000, so k = 110679
Hmmm, works OK for triodes even. Upgrade that Magic formula to Miracle formula!
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I'm not following your math, but....
Try it on a real tube. HK257/4E27
HK 257, Tube HK257; Rohre HK 257 ID11255, Transmitting Tube,
http://www.tubecollectors.org/h&k/archives/hk257.pdf
Try it on a real tube. HK257/4E27
HK 257, Tube HK257; Rohre HK 257 ID11255, Transmitting Tube,
http://www.tubecollectors.org/h&k/archives/hk257.pdf
Attachments
Sure.
1st , note that the HK257 data is for class A P-P, which is not a problem. We just use the 6L6GC data for class A:
6L6GC kSQRT(30)/110 = 5000 Ohm
so k = 100415.8 for the 6L6GC in class A
(only difference is 6L6GC has 5000 Ohm load for class A versus 5600 Ohm for class AB1)
Solving for the HK257 with that k we get:
Zo = k SQRT(75)/150 = 5797 Ohm, however that is for 450V x SQRT(75/30) = 711 V B+. That is assuming a scaled 6L6GC to 75 Watts rating.
The HK257 datasheet models are using 1000V B+ and 500V B+ however, so we have to convert for different B+ :
For 500V B+ we would change that by 500/711 factor for the numerator, and by 711/500 factor for the denominator for the same 75 Watts tube rating. Giving (500/711)/(711/500) x 5797 = 2863 Ohms for the 500V case. Comparing with the datasheet 2600 Ohm for 500V.
For 1000V B+ at 75 Watt tube rating, we would change the 5797 Ohm figure by 1000/711 for the numerator and 711/1000 for the denominator, giving 11467 Ohms. Comparing with the datasheet 12000 Ohm for 1000V.
Using the 6L6GC class AB figure of 5600 Ohms instead gives 6493 Ohms at 711 V B+ which converts to 3210 Ohms at 500V and 12844 Ohms at 1000V. Similar.
1st , note that the HK257 data is for class A P-P, which is not a problem. We just use the 6L6GC data for class A:
6L6GC kSQRT(30)/110 = 5000 Ohm
so k = 100415.8 for the 6L6GC in class A
(only difference is 6L6GC has 5000 Ohm load for class A versus 5600 Ohm for class AB1)
Solving for the HK257 with that k we get:
Zo = k SQRT(75)/150 = 5797 Ohm, however that is for 450V x SQRT(75/30) = 711 V B+. That is assuming a scaled 6L6GC to 75 Watts rating.
The HK257 datasheet models are using 1000V B+ and 500V B+ however, so we have to convert for different B+ :
For 500V B+ we would change that by 500/711 factor for the numerator, and by 711/500 factor for the denominator for the same 75 Watts tube rating. Giving (500/711)/(711/500) x 5797 = 2863 Ohms for the 500V case. Comparing with the datasheet 2600 Ohm for 500V.
For 1000V B+ at 75 Watt tube rating, we would change the 5797 Ohm figure by 1000/711 for the numerator and 711/1000 for the denominator, giving 11467 Ohms. Comparing with the datasheet 12000 Ohm for 1000V.
Using the 6L6GC class AB figure of 5600 Ohms instead gives 6493 Ohms at 711 V B+ which converts to 3210 Ohms at 500V and 12844 Ohms at 1000V. Similar.
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I want to try to understand this. Can you do a 6CU5? its a miniature 7 pin beam tube with what seems to be an oversized cathode. Would this work on such a tube so proportionally smaller plate than 6L6GC but a relatively massive cathode in such a small bottle:
https://frank.pocnet.net/sheets/127/6/6CU5.pdf
https://frank.pocnet.net/sheets/127/6/6CU5.pdf
There are some problems using that tube in the model, but we can still try.
First of all, at 7 Watts 6CU5 versus 30 Watts rating for the 6L6GC would lead to 350V x SQRT(7/30) for B+, which at 169 V is a little above the 6CU5 rating of 150V.
We can still translate the load Ohm results to a lower B+ V if necessary.
The other problem is the max DC current rating is not given on the datasheet.
Neither is the peak current rating (usually about 3.3x the average rating). We can make some guesstimates:
1st, lets assume it IS comparable to a scaled 6L6GB, so we can work the equation backwards to see what DC max current would be.
The datasheet gives 2500 Ohms load for class A single tube 6CU5 with 49 mA idle. While the 6L6GB gives 4200 Ohms class A single tube for best output power.
So for 6L6GB: k SQRT(30)/ 110 = 4200 so k = 84349
Then putting that in for the 6CU5: 84349 SQRT(7) / Imax = 2500 so Imax DC would be 89 mA
Considering the heater power is at 6.3V and 1.2 Amps, it better be able to do that. The 6L6GB does 110 mA max DC with only a 0.9 Amp heater. So maybe we have a good Imax DC figure.
Working the equation forwards now will just give the 2500 Ohm load figure back again obviously.
We have a discrepancy though, since that 6CU5 model is at 120V B+ and the scaled 7 Watt 6L6GB would be at 169V B+. Knee voltages are significant at these low B+ voltages, and are not being adjusted for with this simple modeling either. But both 6CU5 and 6L6GB look to have similar knee voltages around 40V.
We can adjust the 6CU5 load for 169V using 169/120 over 120/169 factors for numerator and denominator in the Zo equation. Giving 4958 Ohms load.
Then going back to the 84349 SQRT(7) / Imax = 4958, gives Imax DC of 45 mA. But the class A data model for the 6CU5 is running at 49 mA idle. The truth is out there somewhere, probably in between. Well the 6CU5 doesn't quite fit the k = 84349 of the 6L6GB scaled model. Making k bigger than 84349 for the 6CU5 would resolve the discrepancy. To get the 89 mA max DC current back again would take k = 166823. So I would use that k factor in the equation, unless you can find a real DC max current spec for the 6CU5.
For a P-P case, you still need a P-P model load Z for the 6CU5. But can probably just fudge with the scaled 6L6GB P-P model till it fits for B+ and idle current to find the k factor there for P-P 6CU5. (assuming the 89 mA DC max at least for the 6CU5 until further info is found)
First of all, at 7 Watts 6CU5 versus 30 Watts rating for the 6L6GC would lead to 350V x SQRT(7/30) for B+, which at 169 V is a little above the 6CU5 rating of 150V.
We can still translate the load Ohm results to a lower B+ V if necessary.
The other problem is the max DC current rating is not given on the datasheet.
Neither is the peak current rating (usually about 3.3x the average rating). We can make some guesstimates:
1st, lets assume it IS comparable to a scaled 6L6GB, so we can work the equation backwards to see what DC max current would be.
The datasheet gives 2500 Ohms load for class A single tube 6CU5 with 49 mA idle. While the 6L6GB gives 4200 Ohms class A single tube for best output power.
So for 6L6GB: k SQRT(30)/ 110 = 4200 so k = 84349
Then putting that in for the 6CU5: 84349 SQRT(7) / Imax = 2500 so Imax DC would be 89 mA
Considering the heater power is at 6.3V and 1.2 Amps, it better be able to do that. The 6L6GB does 110 mA max DC with only a 0.9 Amp heater. So maybe we have a good Imax DC figure.
Working the equation forwards now will just give the 2500 Ohm load figure back again obviously.
We have a discrepancy though, since that 6CU5 model is at 120V B+ and the scaled 7 Watt 6L6GB would be at 169V B+. Knee voltages are significant at these low B+ voltages, and are not being adjusted for with this simple modeling either. But both 6CU5 and 6L6GB look to have similar knee voltages around 40V.
We can adjust the 6CU5 load for 169V using 169/120 over 120/169 factors for numerator and denominator in the Zo equation. Giving 4958 Ohms load.
Then going back to the 84349 SQRT(7) / Imax = 4958, gives Imax DC of 45 mA. But the class A data model for the 6CU5 is running at 49 mA idle. The truth is out there somewhere, probably in between. Well the 6CU5 doesn't quite fit the k = 84349 of the 6L6GB scaled model. Making k bigger than 84349 for the 6CU5 would resolve the discrepancy. To get the 89 mA max DC current back again would take k = 166823. So I would use that k factor in the equation, unless you can find a real DC max current spec for the 6CU5.
For a P-P case, you still need a P-P model load Z for the 6CU5. But can probably just fudge with the scaled 6L6GB P-P model till it fits for B+ and idle current to find the k factor there for P-P 6CU5. (assuming the 89 mA DC max at least for the 6CU5 until further info is found)
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The 6CU5 is a 6 volt version of the 50C5 used on old AA5 radios. That was a miniaturized version of the octal 50L6. It is derated some due to the smaller size, but 50C5's will run all night long making 20 watts from a pair on 340 volts in an UNSET circuit as long as you keep the screen grid in the 130 volts or less range. See post #57 in the UNSET thread.
UNSET is coming?
The ratings are quite conservative in these tubes due to their intended use. They ran in class A SE in a table radio at a time when many people like my mother left the radio on from morning until evening nearly every day. When these old radios finally needed service due to a weak tube it was nearly always the rectifier (35W4 or 35Z5), not the output tube.
The 50L6 is just a 50 volt 6W6 (compare all the curves and specs). All of the octal versions, 6W6, 6DG6GT, 12W6, 12L6, 25W6, 25L6, and 50L6 (the 35L6 is NOT the same tube) have the same curves, as do the 9 pin 6GC5 and the smaller 9 pin 6DB5.
The 6W6 and all of its relatives behave more like a TV sweep tube than a typical audio tube and can be treated as such, including respecting the screen grid ratings.
Most sweep tubes have a larger cathode and higher powered heater than similar sized audio tubes to allow for higher peak currents at lower saturation voltages (purveyance) possibly needing a different k factor. The 6W6 and its offspring including the 6CU5 have a 7.5 watt heater compared to 5.7 watts for the 6L6GC and 2.8 watts for the similar sized 6V6GT.
Note that the 6W6 is specified for 300 plate volts, but 150 screen volts as a pentode audio amp. It is specified for 300 volts in triode as a vertical sweep tube, its original intended use. Do NOT run it as a triode audio amp at 300 (or more volts) they will slow cook into a runaway death when left idling without signal, something that does happen in audio use, but never happens in a (working) TV set. As with my failed trioded 6LW6 amp, it may take months, but I have seen two 6W6's and a 6DG6 (same tube) die in this manner in a Tubelab SSE amp (cathode biased).
UNSET is coming?
The ratings are quite conservative in these tubes due to their intended use. They ran in class A SE in a table radio at a time when many people like my mother left the radio on from morning until evening nearly every day. When these old radios finally needed service due to a weak tube it was nearly always the rectifier (35W4 or 35Z5), not the output tube.
The 50L6 is just a 50 volt 6W6 (compare all the curves and specs). All of the octal versions, 6W6, 6DG6GT, 12W6, 12L6, 25W6, 25L6, and 50L6 (the 35L6 is NOT the same tube) have the same curves, as do the 9 pin 6GC5 and the smaller 9 pin 6DB5.
The 6W6 and all of its relatives behave more like a TV sweep tube than a typical audio tube and can be treated as such, including respecting the screen grid ratings.
Most sweep tubes have a larger cathode and higher powered heater than similar sized audio tubes to allow for higher peak currents at lower saturation voltages (purveyance) possibly needing a different k factor. The 6W6 and its offspring including the 6CU5 have a 7.5 watt heater compared to 5.7 watts for the 6L6GC and 2.8 watts for the similar sized 6V6GT.
Note that the 6W6 is specified for 300 plate volts, but 150 screen volts as a pentode audio amp. It is specified for 300 volts in triode as a vertical sweep tube, its original intended use. Do NOT run it as a triode audio amp at 300 (or more volts) they will slow cook into a runaway death when left idling without signal, something that does happen in audio use, but never happens in a (working) TV set. As with my failed trioded 6LW6 amp, it may take months, but I have seen two 6W6's and a 6DG6 (same tube) die in this manner in a Tubelab SSE amp (cathode biased).
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Ahh, 6CU5 is a 6W6 relative, thanks George.
Looking at the 6W6 datasheet, I see max DC current rated at 65 mA, using the same 1.2 Amp Htr at 6.3 V.
Putting that into the 6CU5 single tube class A model data:
k SQRT(7)/65 = 2500 we get k = 61419
I obviously messed up above with that earlier k =166823 estimate to get 89 mA.
Lets see what the 6W6 single tube class A model data gives using its 12 Watt rating:
k2 SQRT(12)/65 = 4000 we get k2 = 75055
Well, close enough I guess. The 6W6 model is using 200V B+ so efficiency would be a little better presumeably. Lets see, 6W6 with 12 Watt rating gets 3.8 Watts output. Using that same ratio for the 6CU5 would give 7 (3.8/12) = 2.2 Watts out. But the 6CU5 is getting 2.3 Watts using 120 V. Hmm, so much for efficiency improvement with higher B+. I guess they picked the load better for the 6CU5.
One litte check. The 6CU5 at 7 Watts rating was using 120V B+. The 6W6 at 12 Watt rating was using 200V B+. For the same 65 mA DC max rating, one would expect the B+ to increase by 120 (12/7) = 205.7 V. So that checks reasonably. Similar scaled models.
Hmm, 200/205.7 x 2.3 Watts gives 2.2 Watts.
That probably explains that little discrepancy.
The 6L6GB data at 350V B+ shows 10.8 Watts out for a 19 Watt tube. Using that ratio for a 7 Watt tube: 7 (10.8/19) = 3.9 Watts out. Definitely seeing some efficiency gain there with the 350V B+, and probably some tube design factor as well.
I just noticed that I calc'd the 6L6GB k factor wrong last night above using 30 Watts rating instead of 19 Watts. Was getting too late last night.
Lets see: k SQRT(19)/110 = 4200 so k = 105990. I'm assuming the DC max current rating is still 110 mA for the GB version, haven't actually seen DC max data for the GB version, but the Htr ratings are the same as the GC version.
Well, the 6L6GB has nearly twice the k factor, so the 6CU5 is not looking like a scaled down 6L6GB. But 6CU5 is looking pretty close to the 6W6 as George suggested.
Conclusion: 6CU5 is a scaled down 6W6. (that still eats 1.2 Amps of Htr current)
Looking at the 6W6 datasheet, I see max DC current rated at 65 mA, using the same 1.2 Amp Htr at 6.3 V.
Putting that into the 6CU5 single tube class A model data:
k SQRT(7)/65 = 2500 we get k = 61419
I obviously messed up above with that earlier k =166823 estimate to get 89 mA.
Lets see what the 6W6 single tube class A model data gives using its 12 Watt rating:
k2 SQRT(12)/65 = 4000 we get k2 = 75055
Well, close enough I guess. The 6W6 model is using 200V B+ so efficiency would be a little better presumeably. Lets see, 6W6 with 12 Watt rating gets 3.8 Watts output. Using that same ratio for the 6CU5 would give 7 (3.8/12) = 2.2 Watts out. But the 6CU5 is getting 2.3 Watts using 120 V. Hmm, so much for efficiency improvement with higher B+. I guess they picked the load better for the 6CU5.
One litte check. The 6CU5 at 7 Watts rating was using 120V B+. The 6W6 at 12 Watt rating was using 200V B+. For the same 65 mA DC max rating, one would expect the B+ to increase by 120 (12/7) = 205.7 V. So that checks reasonably. Similar scaled models.
Hmm, 200/205.7 x 2.3 Watts gives 2.2 Watts.
That probably explains that little discrepancy.
The 6L6GB data at 350V B+ shows 10.8 Watts out for a 19 Watt tube. Using that ratio for a 7 Watt tube: 7 (10.8/19) = 3.9 Watts out. Definitely seeing some efficiency gain there with the 350V B+, and probably some tube design factor as well.
I just noticed that I calc'd the 6L6GB k factor wrong last night above using 30 Watts rating instead of 19 Watts. Was getting too late last night.
Lets see: k SQRT(19)/110 = 4200 so k = 105990. I'm assuming the DC max current rating is still 110 mA for the GB version, haven't actually seen DC max data for the GB version, but the Htr ratings are the same as the GC version.
Well, the 6L6GB has nearly twice the k factor, so the 6CU5 is not looking like a scaled down 6L6GB. But 6CU5 is looking pretty close to the 6W6 as George suggested.
Conclusion: 6CU5 is a scaled down 6W6. (that still eats 1.2 Amps of Htr current)
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Interesting tube "families" can now be mathematically quantified in a useful way other than the "Tube Lore" book. I could see an online calculator tool that uses this in reverse, put in a tube and it returns its nearest known (pre-seeded) family and the values.
Possibly, but tube datasheets are notably lacking in consistent usage data models, using inconsistent B+ voltages. Its more of an exercise trying to show related tubes are really related, despite the quirky ratings.
Strictly speaking, the 6CU5 is not really meeting the scaled model of a 6W6 since reduced Watts rating would normally mean reduced DC max current as well to get the same k factor. (which were a little different between these) The 6CU5 looks to be a 6W6 with its plate chopped down to fit into a smaller bottle. Like a 6GF5 is a chopped down 6GE5.
By the way, for 1.2 Amps of Htr current (6.3V), one can get 175 mA DC max with a 12GE5/12JN6 and 17.5 Watts Pdiss. (instead of just 65 mA with 6CU5 or 6W6) But they won't fit a 7 pin profile.
I should clarify the constant k "family" meaning. For a constant k family, the tube sizes are like geometric magnified images of each other. Twice the Watt rating would give 1.414 x V rating and 1.414 x the current rating and 1.414 x the physical size. (plate area then increasing by 1.414 squared, or 2x)
The 6CU5 / 6W6 on the other hand are related by V rating linearly prop. to Watt rating, and the current rating staying the same. A different kind of "family".
One discrepancy with the k rating family idea is that twice the plate area would also mean twice the cathode area for a magnified tube.
Strictly speaking, the 6CU5 is not really meeting the scaled model of a 6W6 since reduced Watts rating would normally mean reduced DC max current as well to get the same k factor. (which were a little different between these) The 6CU5 looks to be a 6W6 with its plate chopped down to fit into a smaller bottle. Like a 6GF5 is a chopped down 6GE5.
By the way, for 1.2 Amps of Htr current (6.3V), one can get 175 mA DC max with a 12GE5/12JN6 and 17.5 Watts Pdiss. (instead of just 65 mA with 6CU5 or 6W6) But they won't fit a 7 pin profile.
I should clarify the constant k "family" meaning. For a constant k family, the tube sizes are like geometric magnified images of each other. Twice the Watt rating would give 1.414 x V rating and 1.414 x the current rating and 1.414 x the physical size. (plate area then increasing by 1.414 squared, or 2x)
The 6CU5 / 6W6 on the other hand are related by V rating linearly prop. to Watt rating, and the current rating staying the same. A different kind of "family".
One discrepancy with the k rating family idea is that twice the plate area would also mean twice the cathode area for a magnified tube.
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The 6GF5 IS a 6GE5, but the wings on the plate got clipped to fit in the skinny glass. I get 50 WPC from a pair in a push pull version of the UNSET, 80 watts per pair for short periods of time (up to a minute before plate glow).
Both are 6DQ6's stuffed into a different bottle.
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If the V rating and I rating both increase with SQRT(Watts) at the same rate, then the k factor would be expected to stay constant, and load Z to stay constant.
But with the cathode area increasing at the same rate as the plate area (ie Watts), one would expect the k factor to be increasing with bigger Watt tubes for the above formula, EXCEPT the Zload is decreasing to compensate:
k = Zload Idc /SQRT(W)
Zload = V/I and V is prop. to SQRT(W)
so k = V/I times Idc/SQRT(W) = V/I times I/V = a constant
So looks like the k factor formula is OK still, k still likes to be constant.
My geometric model just needs amending so that V goes up as SQRT of Watts, and I goes up as Watts, leading to lower load impedances.
Of course some transmitting tubes keep the cathode small and increase the cathode to plate distance instead, leading to lower current and higher V.
I guess the k factor can be looked at as an indicator of which model the tube is nearer.
But with the cathode area increasing at the same rate as the plate area (ie Watts), one would expect the k factor to be increasing with bigger Watt tubes for the above formula, EXCEPT the Zload is decreasing to compensate:
k = Zload Idc /SQRT(W)
Zload = V/I and V is prop. to SQRT(W)
so k = V/I times Idc/SQRT(W) = V/I times I/V = a constant
So looks like the k factor formula is OK still, k still likes to be constant.
My geometric model just needs amending so that V goes up as SQRT of Watts, and I goes up as Watts, leading to lower load impedances.
Of course some transmitting tubes keep the cathode small and increase the cathode to plate distance instead, leading to lower current and higher V.
I guess the k factor can be looked at as an indicator of which model the tube is nearer.
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Actually NOT. The Zload adjusts to the new V/I ratio for a transmitting type tube, and k still stays constant.
Well, looks like k might really BE a constant, at least for the same Watts out versus Watts rating ratio.
For example, the 6L6GC class AB1 data has the tubes idling at roughly 1/4 Imax DC, and reaching roughly 2x the Imax DC at peaks. This is a conservative design, since peak current rating is usually more like 3.3 x Imax DC.
Now George likes to run things up to more like peak current rating or until the plate just starts to glow. (usually using cheap tubes...)
The only user variable parameter in the k factor formula is Zload though.
k = Zload Idc /SQRT(W)
And one can make that higher with higher B+, or lower, with higher current and lower B+. So actual k value doesn't seem to be telling us much except when the load Z is in the nominal middle range for a tube.
It IS useful though for taking a known working conservative tube setup over to a new un-characterized tube to determine a nominal Load Z OT.
I think the k formula still needs some actual B+ and actual Ipeak factors added to it to null out these B+ effects. Have to fiddle with it some more. Work in progress.
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No, it's not. It is single-ended. Yes, 30+ Watts SE from 75W Pdiss.
Miracle tube design formula for class AB1 Beam Pentodes
Two-tube output is 315 Watts. (A little more than a 6L6....)
https://bms.isjtr.ro/sheets/114/h/HK257B.pdf
It seems they take "Class A" as meaning "entire cycle", not "near-constant supply current". As opposed to their B and C ratings (not shown here) which do not preserve an entire cycle.
https://bms.isjtr.ro/sheets/114/h/HK257B.pdf
It seems they take "Class A" as meaning "entire cycle", not "near-constant supply current". As opposed to their B and C ratings (not shown here) which do not preserve an entire cycle.
Attachments
Triode curves in posts #6 and #8 :
4E27A monster se amp??
But don't tell anybody.
All good fortune,
Chris
4E27A monster se amp??
But don't tell anybody.
All good fortune,
Chris
Single ended ehh, 30 Watts
Using the 6L6GC data for single ended:
k = Z Idc_max / SQRT(W)
so k = 4200 110 / SQRT(30) = 84349 giving 10.8 Watts output
K scaling the 6L6GC up to 75 Watts would give 27 Watts output,
at 350V x SQRT(75/30) = 553 V for B+.
(this scaling up using the k stuff is not the same as 2.5 tubes in parallel by the way, Idc only increases here by SQRT(75/30) )
And Zload = 84349 SQRT(75/30) / ( SQRT(75/30) x 110) = 766.8 Ohms
Not quite 30 Watts, but it is running without positive grid V for that.
With 3x 6L6GC actually in parallel (now Imax DC at 330 mA), for 90 Watts Pdiss, we would see 32.4 Watts output using a 443 Ohm OT and 350V B+ .
But we've already seen that the 4E27/HK257 likes k around 100416 to get near the correct Zload results on its datasheet.
The big difference I see is that the 4E27/HK257 is using class A2 with +/- 47V or +/- 27V drive signal, so the modeling is not quite apples to apples here. So I'm not too surprised the k factors are somewhat different, k = 100416 versus 84349 (and different load Zs, and the I max DC increase to 174 mA with k scaling).
Just checked Ebay and 4E27 is listed at $33 to $59 used, working. $210 new.
Comparable with 3x 6L6GC for $90. Or 3x 36MC6 for $60. Or 3x 31LZ6 for $30. Or 4x 21LG6A for $16.
Suggest using UnSET circuitry to get 211 type curves at Amperes if you want triode curves too.
Using the 6L6GC data for single ended:
k = Z Idc_max / SQRT(W)
so k = 4200 110 / SQRT(30) = 84349 giving 10.8 Watts output
K scaling the 6L6GC up to 75 Watts would give 27 Watts output,
at 350V x SQRT(75/30) = 553 V for B+.
(this scaling up using the k stuff is not the same as 2.5 tubes in parallel by the way, Idc only increases here by SQRT(75/30) )
And Zload = 84349 SQRT(75/30) / ( SQRT(75/30) x 110) = 766.8 Ohms
Not quite 30 Watts, but it is running without positive grid V for that.
With 3x 6L6GC actually in parallel (now Imax DC at 330 mA), for 90 Watts Pdiss, we would see 32.4 Watts output using a 443 Ohm OT and 350V B+ .
But we've already seen that the 4E27/HK257 likes k around 100416 to get near the correct Zload results on its datasheet.
The big difference I see is that the 4E27/HK257 is using class A2 with +/- 47V or +/- 27V drive signal, so the modeling is not quite apples to apples here. So I'm not too surprised the k factors are somewhat different, k = 100416 versus 84349 (and different load Zs, and the I max DC increase to 174 mA with k scaling).
Just checked Ebay and 4E27 is listed at $33 to $59 used, working. $210 new.
Comparable with 3x 6L6GC for $90. Or 3x 36MC6 for $60. Or 3x 31LZ6 for $30. Or 4x 21LG6A for $16.
Suggest using UnSET circuitry to get 211 type curves at Amperes if you want triode curves too.
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I'm sure it is not in grid current. If it were, HK would have specced the drive requirement.
BTW, if wondering why such a big class A amp: TV was new. Video is like audio except it goes past 1MHz, so you can't easily use transformer coupling. At least one early (RCA?) TV transmitter used four HK257 parallel to cathode-modulate the video RF final. Class A both for cleanliness, and because the situation suited it.
Yes, but hardly-at-all for pentodes with Vg2 near Va, because bottoming voltage tends to be a fraction of Vg2. I spent much time slaving over a hot 6550 to confirm this. Even running Vg2 at half of a very high Va does not gain enough efficiency to be worth the added power supply troubles.
Overall I think you have re-derived Ohm's Law. Pick a supply voltage. Divide into dissipation, you have a max current. Divide voltage by current you have a nominal load impedance. Since voltage appears twice it is reasonable to find a square in some form.
Now adjust. A Pentode may be lower THD with load 10% lower than nominal. For a Triode you have to deduct rp because it is "a load" even if not useful output.
Yes, in a way. It's derivation starts out that way for sure. But designers generally de-rate some from the max limits for safe operation and for distortion reasons. Hence the fudge factor k is stuck in there. The de-rating also allows some wiggle room for different B+ selection.
The exercise was conceived to see if the k values would converge sufficiently from known design examples to be helpful for a new tube without a class AB design case given.
The main problem is that designers are still free to pick a B+, within limits, which directly affects the load Z derived. So the magnified tube model was dreamed up [ setting new B+ at old B+ times SQRT(Watts' / Watts) ] The Z equation makes a further compensation for Idc_max change in computing the Zload, which needs to be incorporated into the B+ selection yet. But this is really just a suggested B+, to hopefully stay in the middle of the allowed/preferred range, the average used, in previous designs.
The Z equation really still needs an additional term to allow for actual B+ used. Especially for DIY, where B+ may depend on what xfmr is sitting on the shelf. And B+ selection accounts for most of the variation in k found in the existing designs, as listed. So a little more equation fix-up is in order I think. Getting the k factors to converge better from the existing designs would indicate success.
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