To me, there are the three Thiele-Small parameters Qes, Qms, and Qts, and then there is the actual mechanical Q of the driver, mounted in its enclosure, and connected to an amplifier. The last one is not a Thiele-Small parameter, but simply the Q-factor of a damped mechanical harmonic oscillator, as outlined in a thousand basic physics textbooks.
I think we all agree that this actual mechanical Q is affected by several factors, including Qes and Qms, the speaker enclosure volume (if sealed) and air mass in the port (if vented).
There are two limiting values for this mechanical Q that I found helpful in understanding how speakers work. One is that, if the amp's output impedance is essentially zero, the unmounted drivers free-air Q is virtually equal to Qts.
The other is that, if the amp's output impedance is much greater than Re, the free-air Q is virtually equal to Qms.
-Gnobuddy
I understand what you're saying, but I think for the sake of clarity we should avoid calling it "mechanical Q", since Qms has that definition.
I quite like Qtc, ie, cabinet total Q.
With regards to output impedances, valve amps are usually a couple of ohms. I haven't heard of anything outside current drive where it's very much greater than Re, where, as you note, Qts (total Q of the speaker) would be Qms.
Chris
I quite like Qtc, ie, cabinet total Q.
With regards to output impedances, valve amps are usually a couple of ohms. I haven't heard of anything outside current drive where it's very much greater than Re, where, as you note, Qts (total Q of the speaker) would be Qms.
Chris
Qms is the mechanical Q due only to the speakers own suspension and moving mass - spider & surround compliance, cone and voice coil mass.
The "Q" I was talking about is the actual mechanical Q of the speaker, including all electrical damping, enclosure air compliance, et cetera, in addition to spider and surround.
I can see why that could be a little confusing, but the speaker is ultimately a mechanical device, and it has a mechanical Q. The only unusual part is that the speakers mechanical Q is also affected by the electrical things we connect to the voice coil!
Also, are we talking triode outputs with heavy negative feedback, or pentode outputs with no feedback? I don't see any way that the latter can be brought down to just a few ohms.
In response to my quick calculation (same one I showed here), someone else ran an LTSpice simulation, and also came up with output impedances in the hundreds of ohms. No negative feedback, pentode output, and, of course, results only as good as whatever LTSpice valve model he happened to use.
I've been too lazy to sit down and measure this, but I guess I should just do that and be done with it.
-Gnobuddy
The "Q" I was talking about is the actual mechanical Q of the speaker, including all electrical damping, enclosure air compliance, et cetera, in addition to spider and surround.
I can see why that could be a little confusing, but the speaker is ultimately a mechanical device, and it has a mechanical Q. The only unusual part is that the speakers mechanical Q is also affected by the electrical things we connect to the voice coil!
Got any references you can point me at?
Also, are we talking triode outputs with heavy negative feedback, or pentode outputs with no feedback? I don't see any way that the latter can be brought down to just a few ohms.
In response to my quick calculation (same one I showed here), someone else ran an LTSpice simulation, and also came up with output impedances in the hundreds of ohms. No negative feedback, pentode output, and, of course, results only as good as whatever LTSpice valve model he happened to use.
I've been too lazy to sit down and measure this, but I guess I should just do that and be done with it.
-Gnobuddy
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Sure, here's a little reading. Haven't heard of anything past 10ohm.
Typical output impedance for tube amps
Chris
Typical output impedance for tube amps
Chris
Thanks for the link!
The first post states in that thread states "...typical output impedance of a push-pull and a SET amp..", so he's talking about triode output stages.
I know nothing about the strange and bizarre world of triode audio power amps, so I Googled to find a valve used in them, and found a reference to a 2A3 triode. I then found a 2A3 datasheet that lists an 800 ohm anode resistance (ra, or rp if you prefer "plate"). The same datasheet also recommends a 2500 ohm load.
Let's re-do my quick calculation using ra=800, and a transformer that steps down the impedance from 2500 ohms to 8 ohms.
The transformer impedance ratio is (2500/8), or 312.5:1.
An 800 ohm anode resistance will therefore be stepped down to (800/312.5), or 2.56 ohms. So, without any negative feedback, we can expect a single-ended triode power amp using a 2A3 to have an output impedance in the ballpark of 3 ohms.
Applying 10 dB of negative feedback around the output stage would reduce that by a factor of roughly three, and you would end up with roughly one ohm. Exactly as Chris661 says.
So it seems nothing is fundamentally wrong with my calculation method; we have now verified that it does in fact predict about the right output impedance for a triode output amp.
And now we also know that the same calculation method, applied to a 6V6 beam tetrode instead of a triode, estimates a 300 ohm output impedance with no negative feedback, and maybe 100 ohms with 10 dB of negative feedback. Output impedance is about a hundred times higher than for the triode.
A look back at the two datasheets shows there is no mystery about this: ra for the triode was specified in the data sheet at 800 ohms. ra for the 6V6 beam tetrode was specified at 77,000 ohms, very nearly one hundred times larger than for the triode. And, sure enough, my quick calculation estimated the pentode/beam tetrode amps output impedance at about a hundred times larger than the triode amp.
I think I have a better idea now why people are willing to put up with the high cost, abysmal efficiency and minuscule output power of triode power amps. It's the only way to get any sort of reasonable damping factor from a valve power amp!
But, going back to the "tube bass guitar amp" comment in this thread that triggered this tangent, I have never heard of a triode-output valve bass guitar amp, for obvious reasons. The few that became popular always used pentodes or beam tetrodes in the output, so we now have reason to believe that they were effectively driving their speakers from a constant current source (Zo of amp >> speaker voice coil resistance Re)
-Gnobuddy
a lot of classic tube push pull pentode output amps (Fender, Marshall, Traynor, Mesa), used a cathode coupled inverter with loop feedback from the secondary's tap to the cathode circuit of the inverter. For economy , reliability and simplicity, the 2nd plate load resistor was ~20% higher than the first for balance. (if a really 'long" tail were employed such as CCS, then the plate loads would be equal).
using 420v plate supply and 12at7, such an inverter should swing 50vrms with 150K grid resistors on the outputs. Mesa used a 12ax7 on their Strategy 400. (not bad in hifi application but I've only run it with Klipschorns - it's output Z might help with some overdamped stuff.
not a lot of nfb available with that scheme - guess that's good with avoiding oscillation. My SRW10 (made by Eminence) have qt ~0.23.
RE OHMS 4.33 FS HZ 52.22
LE MH .74 MMS GMS 25.60
QM 2.94 CMS mm/N .3622
QE .250 RMS NS/M 2.8583
QT .230 VAS LTRS 68.19
XMAX MM 3.00 SD SCM 366.10
BL TM 11.99 EBP 206.2
EFF % 3.70 SPL dB 97.7
these old tube amps had a more fluid midrange in general than the solid state amps of their times - how much of that were HF rolloffs and higher output Z = ?
YBA-3 power section
https://i.imgur.com/c4wCBeP.jpg
using 420v plate supply and 12at7, such an inverter should swing 50vrms with 150K grid resistors on the outputs. Mesa used a 12ax7 on their Strategy 400. (not bad in hifi application but I've only run it with Klipschorns - it's output Z might help with some overdamped stuff.
not a lot of nfb available with that scheme - guess that's good with avoiding oscillation. My SRW10 (made by Eminence) have qt ~0.23.
RE OHMS 4.33 FS HZ 52.22
LE MH .74 MMS GMS 25.60
QM 2.94 CMS mm/N .3622
QE .250 RMS NS/M 2.8583
QT .230 VAS LTRS 68.19
XMAX MM 3.00 SD SCM 366.10
BL TM 11.99 EBP 206.2
EFF % 3.70 SPL dB 97.7
these old tube amps had a more fluid midrange in general than the solid state amps of their times - how much of that were HF rolloffs and higher output Z = ?
YBA-3 power section
https://i.imgur.com/c4wCBeP.jpg
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here is a page dedicated to analysis of a typical simple push pull EL34 guitar amp with cathode - coupled inverter with negtive feedback to its cathode circuit from a tap on the output transformer's secondary and typical feedback resistors of ~5K in inverter's tail, 100K from the transformer's secondary.
the calculated output Z is from 4 to 5.2 ohm or so with 5K & 100K (depending upon secondary tap. This would drop further if there were another gain stage included in the feedback loop and more nfb applied.
Designing for Global Negative Feedback
the calculated output Z is from 4 to 5.2 ohm or so with 5K & 100K (depending upon secondary tap. This would drop further if there were another gain stage included in the feedback loop and more nfb applied.
Designing for Global Negative Feedback
note in Aiken's discussion of pentodes
Effective Output Impedance
Using the formula for output impedance, along with the originally calculated open-loop gain of 41, and assuming a feedback resistor, Rf, of 100k, and an input resistor, Ri, of 5K, and an internal output impedance of 16 ohms, the closed-loop effective output impedance would be:
Zout = ((Ri + Rf) * Ro) / (Ri + Rf + Ro + Ri*A)
= (5K + 100K) * 16 / (5K + 100K + 16 + 5K*41)
= 5.2 ohms
The Effect of Changes in Load Impedance
Note that in a tube amp, the load impedance greatly affects the open-loop gain, because the internal plate resistance of the typical pentodes is very high, so the effective output impedance would be rather large if you didn't have a load connected. The impedance seen looking into the output would be equal to the effective plate resistance of the tubes divided by the impedance ratio of the tubes. When a load is connected, it reflects back an impedance equal to its value multiplied by the impedance ratio of the transformer. This means that the effective internal output impedance is equal to the output load in parallel with the tube plate resistance reflected to the secondary. It is still fairly close to the load resistance, because the plate resistance of a typical pentode is quite large.
What this all means is that the open-loop gain is going to change when a different load impedance is connected to the same tap. This change in open-loop gain changes the effective output impedance and the overall closed-loop gain of the amplifier.
I think there a few tube amps running ultralinear such as one Sunn which was very close to Hafler's Dyna MK!!/III. That achieved good damping factor with nfb and the pendtode gain/ split load triode inverter (6an8, 7199). Audio Research's D90 pentode amp with regulated screen supply was listed as having a damping factor of "12".
Effective Output Impedance
Using the formula for output impedance, along with the originally calculated open-loop gain of 41, and assuming a feedback resistor, Rf, of 100k, and an input resistor, Ri, of 5K, and an internal output impedance of 16 ohms, the closed-loop effective output impedance would be:
Zout = ((Ri + Rf) * Ro) / (Ri + Rf + Ro + Ri*A)
= (5K + 100K) * 16 / (5K + 100K + 16 + 5K*41)
= 5.2 ohms
The Effect of Changes in Load Impedance
Note that in a tube amp, the load impedance greatly affects the open-loop gain, because the internal plate resistance of the typical pentodes is very high, so the effective output impedance would be rather large if you didn't have a load connected. The impedance seen looking into the output would be equal to the effective plate resistance of the tubes divided by the impedance ratio of the tubes. When a load is connected, it reflects back an impedance equal to its value multiplied by the impedance ratio of the transformer. This means that the effective internal output impedance is equal to the output load in parallel with the tube plate resistance reflected to the secondary. It is still fairly close to the load resistance, because the plate resistance of a typical pentode is quite large.
What this all means is that the open-loop gain is going to change when a different load impedance is connected to the same tap. This change in open-loop gain changes the effective output impedance and the overall closed-loop gain of the amplifier.
I think there a few tube amps running ultralinear such as one Sunn which was very close to Hafler's Dyna MK!!/III. That achieved good damping factor with nfb and the pendtode gain/ split load triode inverter (6an8, 7199). Audio Research's D90 pentode amp with regulated screen supply was listed as having a damping factor of "12".
Aiken's website was also where I got the 10 dB number, which he suggests is about the maximum amount of negative feedback found in valve guitar amps.
How does he arrive at the stated "internal output impedance of 16 ohms", do you know?
-Gnobuddy
I think the 16 ohm figure comes from the xformer's impedance ratio Amplifier Output Impedance
most of my bass guitar amps were tube - at least for the power section (Traynor - Peavey Alpha Bass)
most of my bass guitar amps were tube - at least for the power section (Traynor - Peavey Alpha Bass)
Thanks for the link! Let's start from this excerpt:
Half the windings equals one-quarter the impedance ratio for a transformer, so the actual transformer stepdown ratio seen by any one output device is only 1250 ohms : 8 ohms, or 156.25 times.
Using the 10k paralleled anode impedance they suggest, output impedance will then be (10,000 ohms / 156.25), or 64 ohms. Four times higher than the 16 ohms they calculated!
There is one thing in this calculation that I didn't realize before: they treat the anode resistance of a push-pull pair of valves as though they were paralleled, which would be the case if they were both operating simultaneously, in class A.
In my earlier calculations, I didn't do this, because I was thinking class B, where only one side of a push-pull pair works at a time.
But valve-amp reality is class AB...so it's class A for small signal excursions, moving into class B for large ones. Oye ve! I don't even want to think about what that does to the output impedance, which now varies over each half-cycle of the guitar signal!
Now let's look at a quartet of EL34 to see what we can estimate:
El34 datasheet plate resistance: 15 kilo ohms (much lower than 77 kilo ohms for 6V6).
Datasheet push-pull transformer: 3.5k anode-to-anode; that's 875 ohms from centre-tap to one end.
Transformer impedance ratio (each El34): (875 ohms / 8 ohms) = 109 times.
Anode resistance of 15k seen "through" impedance stepdown of 109 times: (15000 ohms/109) = 137 ohms.
Since this particular amp uses a quad of EL34, there are two EL34 in parallel at all times in class B, so we can halve the 137 ohms to 68 ohms. If we consider small-signal operation when all four valves are working at the same time (class A), then we can halve that again, to 34 ohms. (I still can't get to 16 ohms.)
But I think the big picture is starting to emerge. With pentode and beam-tetrode output stages, before feedback is applied, it looks like output impedance of typical amps varies from maybe 35 ohms for a quad of big bottles to maybe 150 ohms for a pair of 6V6s. With feedback, that might go as low as 10 ohms, best case, for the big quad-valve amp.
The interesting part of this is that even the lowest no-feedback number - 35 ohms - is still five or six times greater than the DC speaker resistance of typical 8 ohm guitar speakers (DCR is usually around 6 ohms). This means that a single speaker connected to an amp like this will have almost zero electrical damping (due to voltage induced in the voice coil by cone movement), and it's mechanical Q will rise to nearly Qms.
With negative feedback, the big amp might drop to 10 - 12 ohms, but that is still about twice the DCR of an 8 ohm speaker. There is still very little electrical damping, and there will still be a big woofy bass peak near speaker resonance.
Things will get more complicated in a 4x10 or 4x12 cab, since there are now some speakers in parallel with others, and damping electrical currents from one speaker can flow through it's parallel companion(s).
-Gnobuddy
I don't think this is correct, because they used the entire 5000 ohm anode-to-anode impedance of the output transformer, but no single output valve ever sees that full primary, only one-half of it.
Half the windings equals one-quarter the impedance ratio for a transformer, so the actual transformer stepdown ratio seen by any one output device is only 1250 ohms : 8 ohms, or 156.25 times.
Using the 10k paralleled anode impedance they suggest, output impedance will then be (10,000 ohms / 156.25), or 64 ohms. Four times higher than the 16 ohms they calculated!
There is one thing in this calculation that I didn't realize before: they treat the anode resistance of a push-pull pair of valves as though they were paralleled, which would be the case if they were both operating simultaneously, in class A.
In my earlier calculations, I didn't do this, because I was thinking class B, where only one side of a push-pull pair works at a time.
But valve-amp reality is class AB...so it's class A for small signal excursions, moving into class B for large ones. Oye ve! I don't even want to think about what that does to the output impedance, which now varies over each half-cycle of the guitar signal!
Now let's look at a quartet of EL34 to see what we can estimate:
El34 datasheet plate resistance: 15 kilo ohms (much lower than 77 kilo ohms for 6V6).
Datasheet push-pull transformer: 3.5k anode-to-anode; that's 875 ohms from centre-tap to one end.
Transformer impedance ratio (each El34): (875 ohms / 8 ohms) = 109 times.
Anode resistance of 15k seen "through" impedance stepdown of 109 times: (15000 ohms/109) = 137 ohms.
Since this particular amp uses a quad of EL34, there are two EL34 in parallel at all times in class B, so we can halve the 137 ohms to 68 ohms. If we consider small-signal operation when all four valves are working at the same time (class A), then we can halve that again, to 34 ohms. (I still can't get to 16 ohms.)
But I think the big picture is starting to emerge. With pentode and beam-tetrode output stages, before feedback is applied, it looks like output impedance of typical amps varies from maybe 35 ohms for a quad of big bottles to maybe 150 ohms for a pair of 6V6s. With feedback, that might go as low as 10 ohms, best case, for the big quad-valve amp.
The interesting part of this is that even the lowest no-feedback number - 35 ohms - is still five or six times greater than the DC speaker resistance of typical 8 ohm guitar speakers (DCR is usually around 6 ohms). This means that a single speaker connected to an amp like this will have almost zero electrical damping (due to voltage induced in the voice coil by cone movement), and it's mechanical Q will rise to nearly Qms.
With negative feedback, the big amp might drop to 10 - 12 ohms, but that is still about twice the DCR of an 8 ohm speaker. There is still very little electrical damping, and there will still be a big woofy bass peak near speaker resonance.
Things will get more complicated in a 4x10 or 4x12 cab, since there are now some speakers in parallel with others, and damping electrical currents from one speaker can flow through it's parallel companion(s).
-Gnobuddy
hi Gnobuddy - look at Menno van der Veen's AES paper on a universal transformer for guitar tube amp duty and comments (especially subjective)
Z-out for circuit #10 = 53 ohm
https://mennovanderveen.nl/nl/download/download_3.pdf
with hi-fi tube amps and more nfb, Audio Research quotes a DF or 14 ref to 8 ohms for their D76.
partial schematic of D76A
https://i.imgur.com/ZKpXYFL.jpg
did the soft screen supplies of many guitar/bass amps lend some nice sounding compression? D76, like a lot of Audio Research amps, had a Zener - referenced 6550 cathode-follower for a screen supply.
Z-out for circuit #10 = 53 ohm
https://mennovanderveen.nl/nl/download/download_3.pdf
with hi-fi tube amps and more nfb, Audio Research quotes a DF or 14 ref to 8 ohms for their D76.
partial schematic of D76A
https://i.imgur.com/ZKpXYFL.jpg
did the soft screen supplies of many guitar/bass amps lend some nice sounding compression? D76, like a lot of Audio Research amps, had a Zener - referenced 6550 cathode-follower for a screen supply.
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Alright, here it is more specifically:
The free air values for Qes, Qms, and Qts (the s indicating driver system without a box)
become when in a closed box: Qec, Qmc, Qtc, the c indicating CLOSED box.
Your estimate on output impedance for a tube amp is off, as others
have pointed out.
You can download the T&S papers here: Read Research - Articles
Sorry, we're still talking in circles; I have been discussing NO BOX all along, only the effect of electrical damping (due to amplifier output impedance) on the mechanical Q of the driver. With NO BOX.
Are you disagreeing with the statement that mechanical Q of a driver rises to Qms when it is driven from a current source (with NO BOX)?
Or are you disagreeing with the statement that mechanical Q of a driver falls to Qts when it is driven from a voltage source (with NO BOX)?
Exactly the opposite, the number I calculated for a triode matched Chris661's stated values, and I found one error in one of Aiken's references, due to their using the entire transformer primary winding instead of the correct one-half of it.
Thank you, they are not new to me.
-Gnobuddy
The above statement is what you are confused about but you are so difficult to talk to such
that I've pointed you to the answer and rather than comprehend it you suggest that I am wrong,
I'm going to let you figure it out for yourself - someday.
One more hint, try using Unibox or any simulation program that allows you to set the source
impedance. There are two ways to compute the response, one is to assume that the response of
the driver does not change and to cascade the frequency response of the voltage divider formed
by the source impedance and the freq dependent load, the other is to modify Qe and use an effective
Qec that makes the driver behave as if the source impedance were part of the driver.
Chris suggested this very early on.
ST-70 output impedance, as just one of thousands of examples:
from: Dynaco Stereo 70 II power amplifier Measurements | Stereophile.com
"Its output impedance from the 8 ohm tap was 0.7 ohm from 20Hz to 1kHz, falling to 0.46 ohm at 20kHz. From the 4 ohm tap, these values were reduced to 0.5 ohm from 20Hz to 1kHz, falling at 20kHz to 0.4 ohm. Using the 16 ohm tap, the output impedance rose to about 1.37 ohms between 20Hz and 1kHz, and dropped to 0.99 ohm at 20kHz, with some load dependence noticeable."
from: Dynaco Stereo 70 II power amplifier Measurements | Stereophile.com
"Its output impedance from the 8 ohm tap was 0.7 ohm from 20Hz to 1kHz, falling to 0.46 ohm at 20kHz. From the 4 ohm tap, these values were reduced to 0.5 ohm from 20Hz to 1kHz, falling at 20kHz to 0.4 ohm. Using the 16 ohm tap, the output impedance rose to about 1.37 ohms between 20Hz and 1kHz, and dropped to 0.99 ohm at 20kHz, with some load dependence noticeable."
Hi, I think so, but have not looked into it in any detail.
Silver face Fender Twin Reverb was ultralinear by the way.
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