I was doing some reading this weekend, and ran across a section about feedback, pentodes and speaker damping-specificially that the high plate resistance of a pentode can cause oscillations with the voice-coil of a speaker whose impedance varies with changing loads. The feedback "damps" the interaction between plate and speaker by reducing plate resistance.
Text also said the lower plate resistance of a triode is one of the reasons no negative feedback is needed.
So that got me to thinking...seems that pentodes will be more influenced by speakers whose impedance fluctuates. So how would I go about measuring the impedance of a speaker to see how far it fluctuates between stated and actual impedance?
Also, can anyone tell me of any speakers whose impedance stays relatively stable under a load?
Best,
mr. mojo
Text also said the lower plate resistance of a triode is one of the reasons no negative feedback is needed.
So that got me to thinking...seems that pentodes will be more influenced by speakers whose impedance fluctuates. So how would I go about measuring the impedance of a speaker to see how far it fluctuates between stated and actual impedance?
Also, can anyone tell me of any speakers whose impedance stays relatively stable under a load?
Best,
mr. mojo
Speaker impedances vary all over the place for 99.9% of speakers. They vary with level for 100.0% of speakers. For a typical 2 way mini, you might see impedance max of 25-30 ohms, impedance mins of 3-4 ohms, and of course, varying phase angle...
There's a lot of good hardware/software available for doing speaker impedance measurement. Speaker Workshop is very popular at the moment and it works well (if a bit fiddly about setup).
There's a lot of good hardware/software available for doing speaker impedance measurement. Speaker Workshop is very popular at the moment and it works well (if a bit fiddly about setup).
> how would I go about measuring the impedance of a speaker
Use a signal generator. Put the speaker and a 300 ohm resistor in series across the output. Sweep frequency while watching the voltage across the speaker.
Say the signal generator puts out 10V. And say we are not looking for 10% accuracy (we aren't). If the speaker is 3 ohms, the output voltage will be 10V*(3/300)= 0.1V. If the speaker is 30 ohms, the output voltage will be 10V*(30/300)= 1.0V. So you can very quickly sweep frequency and see the general trend and the outstanding peaks (and dips if any).
You can calibrate with good resistors and some math. But mostly there are two impedances that matter: the lowest midband impedance (which will suck the most power and heat in the amp) and the highest bass and treble peaks (because their ratio to the lowest impedance affects frequency response).
A typical 4-inch speaker in box will be 6Ω at DC and maybe at 20Hz, about 50Ω at 150Hz, about 8Ω at 500Hz, rising above 16Ω above 5KHz.
If the alignment is tuned flat for a zero-Ω source, and you use an 8Ω source (DF=1), then around 500Hz the response will be 8Ω/(8Ω+8Ω)= 1/2 = -6dB relative to the zero-Ω source, at 150Hz it will be 50Ω/(50Ω+8Ω)= 0.86 = -1.3dB relative to the zero-Ω source. In effect the low damping gives a 6dB-1.3dB= 4.7dB bass-bump relative to the zero-Ω source.
DF=1 is kinda like a triode. Most triode amps give DF=2 or 3, so the error is less, like 1dB-2dB. Naked Pentodes give DF=5 or 10 on paper, in practice sometimes limited to 3-5 by transformer losses. A naked pentode can show a BIG bass-boom on a speaker tuned for zero-Ω source. You can tune a speaker different for high-Ω source and get flat response; zero-Ω source design generally gives deeper bass in less box size.
> speakers whose impedance stays relatively stable under a load?
The "load" we care about is the air load. For a 4-inch speaker, this will reflect-back as about 10Ω above 2KHz, falling very fast at lower frequencies. We can hardly see that, because the bigger load is the cone+coil mass, which is infinite at DC but falls past 8Ω at 200Hz toward 0.8Ω at 2KHz. So the inside of a speaker is all slanty impedances BUT for low-efficiency (<5%) speakers, the "inside" is a low impedance over the whole working range except its bottom octave. So what we see at the terminals is mostly coil resistance and inductance (and inductance is typically selected for the speaker function).
The main impedance "flaw", then, is the bass resonance. If we could use infinitely limp suspensions in infinite boxes, there would be no bass resonance: impedance would rise smoothly below about 100Hz. In fact we have lots of stiffness, usually selected to tune-up the soft corner of a no-stiffness speaker's response. If the suspension and box had zero losses, the impedance rise would be proportional to midband efficiency, roughly 100:1 or 8Ω for typical 1% efficient speakers. Zero losses never happens, and losses help muffle surround-flap and other incidental flaws, so the impedance peak tends to be 30Ω to 100Ω for 8Ω speakers. Adding loss at bass resonance reduces the impedance peak but also reduces bass output: impedance rise is a necessary part of an optimized speaker.
That's for a single driver. The sins of crossovers are complex. It is possible, with flat drivers, to design a 6dB/8ve crossover with dead-flat impedance through the crossover frequency. If the impedance rose at crossover, total response would dip because less power is being drawn at the higher impedance. In fact we are usually fighting driver droop, which suggests a crossover that dips in impedance to suck more power and compensate the driver droop. But we could go on for 9,999 pages about the complexity of crossovers.
Use a signal generator. Put the speaker and a 300 ohm resistor in series across the output. Sweep frequency while watching the voltage across the speaker.
Say the signal generator puts out 10V. And say we are not looking for 10% accuracy (we aren't). If the speaker is 3 ohms, the output voltage will be 10V*(3/300)= 0.1V. If the speaker is 30 ohms, the output voltage will be 10V*(30/300)= 1.0V. So you can very quickly sweep frequency and see the general trend and the outstanding peaks (and dips if any).
You can calibrate with good resistors and some math. But mostly there are two impedances that matter: the lowest midband impedance (which will suck the most power and heat in the amp) and the highest bass and treble peaks (because their ratio to the lowest impedance affects frequency response).
A typical 4-inch speaker in box will be 6Ω at DC and maybe at 20Hz, about 50Ω at 150Hz, about 8Ω at 500Hz, rising above 16Ω above 5KHz.
If the alignment is tuned flat for a zero-Ω source, and you use an 8Ω source (DF=1), then around 500Hz the response will be 8Ω/(8Ω+8Ω)= 1/2 = -6dB relative to the zero-Ω source, at 150Hz it will be 50Ω/(50Ω+8Ω)= 0.86 = -1.3dB relative to the zero-Ω source. In effect the low damping gives a 6dB-1.3dB= 4.7dB bass-bump relative to the zero-Ω source.
DF=1 is kinda like a triode. Most triode amps give DF=2 or 3, so the error is less, like 1dB-2dB. Naked Pentodes give DF=5 or 10 on paper, in practice sometimes limited to 3-5 by transformer losses. A naked pentode can show a BIG bass-boom on a speaker tuned for zero-Ω source. You can tune a speaker different for high-Ω source and get flat response; zero-Ω source design generally gives deeper bass in less box size.
> speakers whose impedance stays relatively stable under a load?
The "load" we care about is the air load. For a 4-inch speaker, this will reflect-back as about 10Ω above 2KHz, falling very fast at lower frequencies. We can hardly see that, because the bigger load is the cone+coil mass, which is infinite at DC but falls past 8Ω at 200Hz toward 0.8Ω at 2KHz. So the inside of a speaker is all slanty impedances BUT for low-efficiency (<5%) speakers, the "inside" is a low impedance over the whole working range except its bottom octave. So what we see at the terminals is mostly coil resistance and inductance (and inductance is typically selected for the speaker function).
The main impedance "flaw", then, is the bass resonance. If we could use infinitely limp suspensions in infinite boxes, there would be no bass resonance: impedance would rise smoothly below about 100Hz. In fact we have lots of stiffness, usually selected to tune-up the soft corner of a no-stiffness speaker's response. If the suspension and box had zero losses, the impedance rise would be proportional to midband efficiency, roughly 100:1 or 8Ω for typical 1% efficient speakers. Zero losses never happens, and losses help muffle surround-flap and other incidental flaws, so the impedance peak tends to be 30Ω to 100Ω for 8Ω speakers. Adding loss at bass resonance reduces the impedance peak but also reduces bass output: impedance rise is a necessary part of an optimized speaker.
That's for a single driver. The sins of crossovers are complex. It is possible, with flat drivers, to design a 6dB/8ve crossover with dead-flat impedance through the crossover frequency. If the impedance rose at crossover, total response would dip because less power is being drawn at the higher impedance. In fact we are usually fighting driver droop, which suggests a crossover that dips in impedance to suck more power and compensate the driver droop. But we could go on for 9,999 pages about the complexity of crossovers.
Yowza! Thanks guys-great info as always. This is THE best place on-line for DIY audio by far.
Sy,
Thanks for the tip on Speaker Workshop and the general info on impedance. Part of the reason for my curiosity is when my DIY amp is done I'm just gonna HAVE to get new speaks to go with it!
I've listened to MG1s on a 40wpc Scott 296 and got great sound and good volume so the MMGs are now on my short list, but when I read about their impedance dipping to @ 1.5 ohm I became a little hesitant.
PRR, I gotta say I always appreciate your incredibly detailed responses. I also gotta admit, as a graphic artist by trade I've got to read it over a few times before some of it starts to
sink in.
But by all means, if you continue to be so inclined, please keep it up-I surely do appreciate it.
Best,
mr. mojo
Sy,
Thanks for the tip on Speaker Workshop and the general info on impedance. Part of the reason for my curiosity is when my DIY amp is done I'm just gonna HAVE to get new speaks to go with it!
I've listened to MG1s on a 40wpc Scott 296 and got great sound and good volume so the MMGs are now on my short list, but when I read about their impedance dipping to @ 1.5 ohm I became a little hesitant.
PRR, I gotta say I always appreciate your incredibly detailed responses. I also gotta admit, as a graphic artist by trade I've got to read it over a few times before some of it starts to
sink in.
But by all means, if you continue to be so inclined, please keep it up-I surely do appreciate it.
Best,
mr. mojo
MG-1s have a much flatter impedance curve than normal, so that's a big help right there. I used a pair with some Dyna MkIII-based amps for many years (ultralinear connection) and was quite happy with the sound. I haven't tested MMGs. If they really do dip that low and it's in any part of the audio spectrum where you expect to need power, that suggests (I hate to say this) solid state might work better.
Or you could think about speakers which have a long and honorable reputation of being happy with tubes, like LS3/5a or BC-1.
Or you could think about speakers which have a long and honorable reputation of being happy with tubes, like LS3/5a or BC-1.
Sy,
That would explain a lot about the MG1s-the folks at the shop dropped their chins to their chests when they heard them sing on the 296-that, of course after they said I'd need at least 200wpc to really make them shine.
Before I paint myself into a corner, I should say I read somewhere that Magnepans can dip as low as 1.5ohm-no specific models listed, and with all things on-line it may be best taken with a large grain of salt.
I've been curious to try some of those LS3/5As. I've read so many conflicting opinions about them that if I have a chance I'll have to let my ears decide for myself.
Best,
mr. mojo
That would explain a lot about the MG1s-the folks at the shop dropped their chins to their chests when they heard them sing on the 296-that, of course after they said I'd need at least 200wpc to really make them shine.
Before I paint myself into a corner, I should say I read somewhere that Magnepans can dip as low as 1.5ohm-no specific models listed, and with all things on-line it may be best taken with a large grain of salt.
I've been curious to try some of those LS3/5As. I've read so many conflicting opinions about them that if I have a chance I'll have to let my ears decide for myself.
Best,
mr. mojo
The LS3/5as are not accurate, but they image like a champ, have pretty good detail, and can almost fool you into thinking they've got bass. All that assumes an amp that doesn't mind the highish impedance with a few funny phase angles through crossover. A good p-p 35 watter will do wonders with them.
I should throw one of the newer single-driver HE designs into the mix, too, but my experience there is pretty limited.
I should throw one of the newer single-driver HE designs into the mix, too, but my experience there is pretty limited.
> their impedance dipping to @ 1.5 ohm
From what?
If it wobbles from, say, 1.5 to 5, with an odd peak to 20, just tap your transformer to 2 ohms. If you roll your own, you can wind ANY low impedance you like. Just do the math. It may come out a little awkward for arbitrarily low loads: you can't have less than one (maybe one-half) turn which works out about 0.001Ω which suggests strap-copper.... but speakers with cable-terminals would never be wound to a milliOhm. If the load works on the other end of a few feet of wire, you can wind an audio transformer to suit.
If you don't have an iron-spinner: You could try tricks. 10K:4Ω used at 5K gives about 2Ω output. But the DCR is still around 0.4Ω, which starts to be a lot for 2Ω or 1.5V loads.
What are we talking about? Flat-diaphragm "loud"speakers? Get real. A JBL D-130 is "only" 5Ω DC but won't even touch 9Ω over the audio band, and a good 5% of that is actual air. It's a little shy above 4KHz; that's what the JBL bullet tweeter is for. Accurate? Maybe not, but more than many things I've heard. And you don't need any 200 watts to shine-up a D-130 in a living room. 2 watts will break your lease.
From what?
If it wobbles from, say, 1.5 to 5, with an odd peak to 20, just tap your transformer to 2 ohms. If you roll your own, you can wind ANY low impedance you like. Just do the math. It may come out a little awkward for arbitrarily low loads: you can't have less than one (maybe one-half) turn which works out about 0.001Ω which suggests strap-copper.... but speakers with cable-terminals would never be wound to a milliOhm. If the load works on the other end of a few feet of wire, you can wind an audio transformer to suit.
If you don't have an iron-spinner: You could try tricks. 10K:4Ω used at 5K gives about 2Ω output. But the DCR is still around 0.4Ω, which starts to be a lot for 2Ω or 1.5V loads.
What are we talking about? Flat-diaphragm "loud"speakers? Get real. A JBL D-130 is "only" 5Ω DC but won't even touch 9Ω over the audio band, and a good 5% of that is actual air. It's a little shy above 4KHz; that's what the JBL bullet tweeter is for. Accurate? Maybe not, but more than many things I've heard. And you don't need any 200 watts to shine-up a D-130 in a living room. 2 watts will break your lease.
Good post as usual, PRR.
My bit on flat impedance (well, taking a lot of poetic licence on "flat"): One can get a reasonably useful impedance with most driver combinations by using the right compensating (conjugating) networks. One can also get a real horror show using ordinary off-the-shelf networks that appear to have been designed round resistive values (the 2xC - 2xL types for a single cross-over). It must be remembered that at a cross-over frequency of say 2.5 KHz, 8 ohm drivers are hardly 8 ohm, apart from having a healthy phase angle. Get this wrong, and one is in for a 10 dB peak at 2 KHz with a 15 dB dip at 2.6 KHz (actual example). I have never been able to get an acceptable impedance performance with fewer than 5 components for a single cross-over. (Acceptable like amplitude between 4 and 8 ohm; phase angle not exceeding +/- 25 degrees.)
The point I wish to make is that the impedance/frequency characteristic of a number of commercial loudspeakers can be improved by using the right reactive/resistive (additional) components. Purists are likely to go Texas on me, but it is often a case where the corrected loudspeaker giving a reasonable impedance to the amplifier to work with, comes out still better than a grand low-component loudspeaker but presenting such a lousy load to the poor amplifier that the end result is worse. I am no more a fan of cross-overs than any other person, but where the options are limited, I prefer some impedance correction to some of the "difficult-to-drive" models on the market.
My bit on flat impedance (well, taking a lot of poetic licence on "flat"): One can get a reasonably useful impedance with most driver combinations by using the right compensating (conjugating) networks. One can also get a real horror show using ordinary off-the-shelf networks that appear to have been designed round resistive values (the 2xC - 2xL types for a single cross-over). It must be remembered that at a cross-over frequency of say 2.5 KHz, 8 ohm drivers are hardly 8 ohm, apart from having a healthy phase angle. Get this wrong, and one is in for a 10 dB peak at 2 KHz with a 15 dB dip at 2.6 KHz (actual example). I have never been able to get an acceptable impedance performance with fewer than 5 components for a single cross-over. (Acceptable like amplitude between 4 and 8 ohm; phase angle not exceeding +/- 25 degrees.)
The point I wish to make is that the impedance/frequency characteristic of a number of commercial loudspeakers can be improved by using the right reactive/resistive (additional) components. Purists are likely to go Texas on me, but it is often a case where the corrected loudspeaker giving a reasonable impedance to the amplifier to work with, comes out still better than a grand low-component loudspeaker but presenting such a lousy load to the poor amplifier that the end result is worse. I am no more a fan of cross-overs than any other person, but where the options are limited, I prefer some impedance correction to some of the "difficult-to-drive" models on the market.
> a speaker whose impedance varies with changing loads.
Wait a minute. What "changing loads"? The air-load is essentially constant. You can shift it a little in the bass with corner placement, or box venting, or horn loading. But corner placement effects are small at the amplifier, and effective horn-loading is a completely different design.
SY> Speaker impedances ... vary with level
Yes, when the coil starts to come out of the magnet gap (huge excursions) or when the copper gets so hot its resistance rises (high average power). When the coil does start to come out of the gap, back-EMF and impedance drops; but not lower than the midband impedance. If the coil actually comes out of the gap and bounces back, huge oscillations are possible, but this is speaker abuse, more than amp-abuse. If a speaker is designed to work to the edge of the gap and beyond, as in competition car-sound woofers, the designer will balance a bunch of factors, including the ready availability of cheap (transistor) amplifiers. A tube amp may not be the wisest pick for throwing a woofer that far; but few tube amps have the power to really get crazy that way.
So I don't know what mojo's quote means.
The commonest impedance variation is with frequency. I took dave's plot of a very typical full-range speaker, assumed it was flat with a modern zero-Z amplifier, and plotted for several non-zero-Z sources for DF of 8 to 0.25.
You see that a speaker with perfectly flat voltage response but a bumpy impedance response will have "errors" with a non-zero source. (OTOH, you can design a speaker to be flat with a hi-Z source, and it will be bumpy with a zero-Z source. Most "good" speakers before the mid 1950s were tuned for significant source impedance, and sound blah on a zero-Z source. As an extreme, Nelson Pass is working/playing with high-Z drive and selecting and tuning the speaker to suit that condition.)
Since you have a VOLume knob and will trim any amp to a "reasonable" sound level, I have corrected for average output.
DF=Infinite is the modern standard, and I've assumed it is "flat".
DF=8 would be a transistor amp with long thin wires (typical BestBuys stuff) or a light-feedback tube amp. It gives +/-0.5Db errors.
DF=2 approximates a naked triode. Errors are OTOO +/-1.5dB. The bass-bump and top-rise may be pleasing.
DF=0.5 seems to be about right for UltraLinear without other NFB. DF=0.25 is getting into naked pentode territory. Both of these give an obviously boomy one-note bass for a speaker designed for large DF. However this and the top-rise may compliment the limits of a single-driver full-range system, by boosting where it starts to fall.
Wait a minute. What "changing loads"? The air-load is essentially constant. You can shift it a little in the bass with corner placement, or box venting, or horn loading. But corner placement effects are small at the amplifier, and effective horn-loading is a completely different design.
SY> Speaker impedances ... vary with level
Yes, when the coil starts to come out of the magnet gap (huge excursions) or when the copper gets so hot its resistance rises (high average power). When the coil does start to come out of the gap, back-EMF and impedance drops; but not lower than the midband impedance. If the coil actually comes out of the gap and bounces back, huge oscillations are possible, but this is speaker abuse, more than amp-abuse. If a speaker is designed to work to the edge of the gap and beyond, as in competition car-sound woofers, the designer will balance a bunch of factors, including the ready availability of cheap (transistor) amplifiers. A tube amp may not be the wisest pick for throwing a woofer that far; but few tube amps have the power to really get crazy that way.
So I don't know what mojo's quote means.
The commonest impedance variation is with frequency. I took dave's plot of a very typical full-range speaker, assumed it was flat with a modern zero-Z amplifier, and plotted for several non-zero-Z sources for DF of 8 to 0.25.
An externally hosted image should be here but it was not working when we last tested it.
You see that a speaker with perfectly flat voltage response but a bumpy impedance response will have "errors" with a non-zero source. (OTOH, you can design a speaker to be flat with a hi-Z source, and it will be bumpy with a zero-Z source. Most "good" speakers before the mid 1950s were tuned for significant source impedance, and sound blah on a zero-Z source. As an extreme, Nelson Pass is working/playing with high-Z drive and selecting and tuning the speaker to suit that condition.)
Since you have a VOLume knob and will trim any amp to a "reasonable" sound level, I have corrected for average output.
DF=Infinite is the modern standard, and I've assumed it is "flat".
DF=8 would be a transistor amp with long thin wires (typical BestBuys stuff) or a light-feedback tube amp. It gives +/-0.5Db errors.
DF=2 approximates a naked triode. Errors are OTOO +/-1.5dB. The bass-bump and top-rise may be pleasing.
DF=0.5 seems to be about right for UltraLinear without other NFB. DF=0.25 is getting into naked pentode territory. Both of these give an obviously boomy one-note bass for a speaker designed for large DF. However this and the top-rise may compliment the limits of a single-driver full-range system, by boosting where it starts to fall.
Does DF scale linearly with number of output devices? I.E., if single triode out DF=2, two triodes DF = 4, times 3 DF =6, etc.. The previous assumes all triodes share the bias and standing current as the the single triode case, what if current is reduced as tubes are added? I just ordered a metric boatload of Russian EL84 equivs to play with and one consideration is triple or higer PSE.
rdf said:
Yes and no. Normally, when you parallel output devices, you reduce the plate to plate load proportionately, so DF becomes a wash.
FWIW, naked pentodes can have a somewhat higher source impedance than even the gloomy estimates from PRR- removing the feedback loop from a pentode-connected ST70 (EL34s, 400V on screens and as B+ feed for the output transformer), I saw source impedances over 100 ohms.
Thx Sy. In this case the prime consideration is to increase the anode load and try for higher linearity, increasing power out is secondary. The transformer's a 5 kohm primary capable of sinking about three times a normal EL84 bias. I want to play around with the load/power out balance as a learning experience. The tubes are cheap like borscht for experimentation, if something good comes out of it the circuit can be adapted to something better.
In this particular case then am I correct in thinking that driving a 5000 ohm primary with multiple tubes results in a DF increase over a single similar tube of about equivalent DC operating condition?
In this particular case then am I correct in thinking that driving a 5000 ohm primary with multiple tubes results in a DF increase over a single similar tube of about equivalent DC operating condition?
PRR,
Yet again relief from me that someone has pointed out that DFs above 10 don't amount to much. When I suggested under another thread that the popular definition of damping factor is electrically in error I got blasted for daring to do so; I will not resurrect that.
A small comment regarding your guestimates for some DFs (I accept that it was ball-park). But triodes would be nearer the 4 mark - I find that the Ra for the KT66 is only 1.2K as triode under normal conditions. Then, the UL use of a pentode for the few examples given shows an Ra about 80% of that for the equivalent triode connection. (Folks often seem to think that UL operation is close to pentode; it is actually closer to triode except for output.) For the KT66 this is about 2.5K compared to the pentode Ra of 22K, so the "naked" DF there for UL would be nearer 1.5.
But please, not to be pedantic or diminish your contribution. Just thought I would mention. UL data is actually hard to come by.
Yet again relief from me that someone has pointed out that DFs above 10 don't amount to much. When I suggested under another thread that the popular definition of damping factor is electrically in error I got blasted for daring to do so; I will not resurrect that.
A small comment regarding your guestimates for some DFs (I accept that it was ball-park). But triodes would be nearer the 4 mark - I find that the Ra for the KT66 is only 1.2K as triode under normal conditions. Then, the UL use of a pentode for the few examples given shows an Ra about 80% of that for the equivalent triode connection. (Folks often seem to think that UL operation is close to pentode; it is actually closer to triode except for output.) For the KT66 this is about 2.5K compared to the pentode Ra of 22K, so the "naked" DF there for UL would be nearer 1.5.
But please, not to be pedantic or diminish your contribution. Just thought I would mention. UL data is actually hard to come by.
> Does DF scale linearly with number of output devices?
If you (perversely) kept the same transformer ratio: it would, except that transformer resistance sets a lower limit on DF even for infinite tubes.
But for any commercial design (not a borscht-cheap experimenter's toy) you would scale the load in rough proportion (so increased power justifies the increased price), so (as SY said) it washes out.
> driving a 5000 ohm primary with multiple tubes
Yes, though (again thinking rational commercial design) the increased idle current will demand a bigger hunk of output iron. That can actually reduce DCR, though the reduction with size is slow, and the increase in cost can be large, so the DCR may not fall much across the range of Standard Transformers.
Still, if bottles and heater-power is cheap, parallel away.
Looking for low transformer resistance to improve DF is one place where choke-feed makes sense. Getting the DC current out of the transformer allows a much lower DCR design. The choke's DCR will be high, but is not in series with the load, so does not degrade DF, just wastes DC power. Of course choke-feed generally implies a capacitor, which gives a very complicated output impedance. If you make the cap too small it interacts with speaker impedance; if too big it tends to give a big subsonic rise and resonance.
> if you keep the load constant but double the number of tubes (along with doubling idle current)
That scales linearly. If OTOH you add tubes but keep the total current the same (less current per tube), you still get some improvement, but much less. Roughly square-root of number of tubes. 800Ω Rp into 5K load is DF=6 (ignoring transformer resistance). Four such tubes at the same total current will be near DF= 12, twice as high (not always twice as good). The square-root factor is not exact, but gives a general idea where you are headed. The very-linear tubes like 300B may not show even this much improvement.
If you (perversely) kept the same transformer ratio: it would, except that transformer resistance sets a lower limit on DF even for infinite tubes.
But for any commercial design (not a borscht-cheap experimenter's toy) you would scale the load in rough proportion (so increased power justifies the increased price), so (as SY said) it washes out.
> driving a 5000 ohm primary with multiple tubes
Yes, though (again thinking rational commercial design) the increased idle current will demand a bigger hunk of output iron. That can actually reduce DCR, though the reduction with size is slow, and the increase in cost can be large, so the DCR may not fall much across the range of Standard Transformers.
Still, if bottles and heater-power is cheap, parallel away.
Looking for low transformer resistance to improve DF is one place where choke-feed makes sense. Getting the DC current out of the transformer allows a much lower DCR design. The choke's DCR will be high, but is not in series with the load, so does not degrade DF, just wastes DC power. Of course choke-feed generally implies a capacitor, which gives a very complicated output impedance. If you make the cap too small it interacts with speaker impedance; if too big it tends to give a big subsonic rise and resonance.
> if you keep the load constant but double the number of tubes (along with doubling idle current)
That scales linearly. If OTOH you add tubes but keep the total current the same (less current per tube), you still get some improvement, but much less. Roughly square-root of number of tubes. 800Ω Rp into 5K load is DF=6 (ignoring transformer resistance). Four such tubes at the same total current will be near DF= 12, twice as high (not always twice as good). The square-root factor is not exact, but gives a general idea where you are headed. The very-linear tubes like 300B may not show even this much improvement.
Thanks to both for the explanations. The iron is really (at this point) intended for a triode connected 813 so it'll take a lot of abuse from EL84s. It's an opportunity to play with some contentious concepts like PSE and driving like-with-like. Most EL84's I've tried are too microphonic or have a curious glassy-crackling noise to be seriously considered for a front end tube.
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