In my limited review of data sheets, it seems that as we reduce the load on pentodes the 2nd harmonic is increased while the 3rd harmonic is reduced, but in power triodes both the 2nd and 3rd harmonic increase with reduced load.
https://frank.pocnet.net/sheets/127/2/2A3.pdf
https://frank.pocnet.net/sheets/127/4/45.pdf
https://frank.pocnet.net/sheets/127/6/6Y6G.pdf
Is this always true?
Is it due to tube construction, or mode of operation. That is, when we triode-strap a pendode will the 2nd and 3rd harmonic track together like in a triode?
https://frank.pocnet.net/sheets/127/2/2A3.pdf
https://frank.pocnet.net/sheets/127/4/45.pdf
https://frank.pocnet.net/sheets/127/6/6Y6G.pdf
Is this always true?
Is it due to tube construction, or mode of operation. That is, when we triode-strap a pendode will the 2nd and 3rd harmonic track together like in a triode?
A look at the curves helps. At small levels, even pentodes have mainly 2nd harmonics. There are some datasheets, which show that (I guess eg EL84). The more the curves are closer at one side in your load curve, the more 2nd harmonics you get. If at both of your load line are compressed, then you get in general more 3rd harmonics. So, when you look at small output levels, pentodes often show more 2nd harmonics. In the famous 6L6 the engineers stretched this area as much as possible, so this tube have even in higher levels mostly 2nd harmonics, til 3rd rise rapidly.
Conclusion. It depends on the tube construction, triode or pentode, output level and load. If you put a stage in front of the outputtube, which is nearly always the case, things gets more complicated....
Conclusion. It depends on the tube construction, triode or pentode, output level and load. If you put a stage in front of the outputtube, which is nearly always the case, things gets more complicated....
The Radio Designer's Handbook inadvertently acknowledges the phenomena I am struggling with. In Figures 13.26 and 13.30 the pentode characteristic of inversely correlated 2nd and 3rd harmonics is shown, and the text describes the need to avoid excessive loads and the resulting excessive 3rd harmonic. Later in fig 13.54 the triode characteristic of directly correlated 2nd and 3rd harmonics is shown.
But I find nothing which describes how a triode-strapped pentode behaves... with the inverse correlation of the pentode, or the direct correlation of the triode?
But I find nothing which describes how a triode-strapped pentode behaves... with the inverse correlation of the pentode, or the direct correlation of the triode?
Generalizations:
Single Ended: A driver that has 2nd harmonic distortion, and an output stage that has 2nd harmonic distortion will cause partial cancellation of 2nd harmonic at the output (the 2nd is in opposite direction for the two stages). But it can also increase the 3rd harmonic distortion (as when the driver nears clipping in one direction, and the output stage nears clipping in the other direction, again in opposite directions).
An amplifier is a system, involving all stages and the load, usually the loudspeaker. We are loading the amplifier with a loudspeaker, and it has different impedances at different frequencies. The resistor is a good load to start testing. It is the "standard" load. But after that, the amplifier has to drive a loudspeaker so we can listen. The ratio of 2nd versus 3rd harmonics from the amplifier can change as the loudspeaker changes impedance versus frequency.
The loudspeaker has its own 2nd harmonic distortion, which either is in the same direction as the amplifier (adding; increasing 2nd harmonic distortion); or it is in the opposite direction (subtracting; partially cancelling the 2nd harmonic distortion). But we do not know which way it is, with normal connection order. To change whether it is adding or subtracting, change the connection from the amp to the loudspeaker (+ amp to + loudspeaker and common to common); (or try + amp to loudspeaker common, and amp common to loudspeaker plus). Do this for both channels, so they are still in phase (left relative to right).
Then there is push pull, where the 2nd harmonic of a good output stage is mostly cancelled, with the 2nd harmonic depending more on the drivers and earlier stages. Full differential on all the stages cancels most of the 2nd all through the chain, and mostly only the 3rd harmonic is left.
It may seem like we need to be worried about all of this. But often, it just works pleasingly well, and sounds good.
Just sit back and listen.
Single Ended: A driver that has 2nd harmonic distortion, and an output stage that has 2nd harmonic distortion will cause partial cancellation of 2nd harmonic at the output (the 2nd is in opposite direction for the two stages). But it can also increase the 3rd harmonic distortion (as when the driver nears clipping in one direction, and the output stage nears clipping in the other direction, again in opposite directions).
An amplifier is a system, involving all stages and the load, usually the loudspeaker. We are loading the amplifier with a loudspeaker, and it has different impedances at different frequencies. The resistor is a good load to start testing. It is the "standard" load. But after that, the amplifier has to drive a loudspeaker so we can listen. The ratio of 2nd versus 3rd harmonics from the amplifier can change as the loudspeaker changes impedance versus frequency.
The loudspeaker has its own 2nd harmonic distortion, which either is in the same direction as the amplifier (adding; increasing 2nd harmonic distortion); or it is in the opposite direction (subtracting; partially cancelling the 2nd harmonic distortion). But we do not know which way it is, with normal connection order. To change whether it is adding or subtracting, change the connection from the amp to the loudspeaker (+ amp to + loudspeaker and common to common); (or try + amp to loudspeaker common, and amp common to loudspeaker plus). Do this for both channels, so they are still in phase (left relative to right).
Then there is push pull, where the 2nd harmonic of a good output stage is mostly cancelled, with the 2nd harmonic depending more on the drivers and earlier stages. Full differential on all the stages cancels most of the 2nd all through the chain, and mostly only the 3rd harmonic is left.
It may seem like we need to be worried about all of this. But often, it just works pleasingly well, and sounds good.
Just sit back and listen.
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As a general rule almost all single-ended active devices fed a small signal will have more 2nd than 3rd. A combination of trigonometry and algebra requires this.
As you increase the signal higher order nonlinearitiies come in too, but they can also add lower order distortion. For example, 4th order nonlinearity can create both 4th and 2nd order distortion; this added 2nd can add to or partially cancel the 2nd from 2nd order nonlinearity. As a general rule you don't want these higher orders to be significant, so if you are running a pentode in the bias/signal region when 3rd dominates over 2nd you may already be getting significant 4th too.
As you increase the signal higher order nonlinearitiies come in too, but they can also add lower order distortion. For example, 4th order nonlinearity can create both 4th and 2nd order distortion; this added 2nd can add to or partially cancel the 2nd from 2nd order nonlinearity. As a general rule you don't want these higher orders to be significant, so if you are running a pentode in the bias/signal region when 3rd dominates over 2nd you may already be getting significant 4th too.
Generalizations and food for thought:
The distortion of a vacuum tube that is not in a feedback loop follows certain ‘rules’.
Let us look at distortion products for a well behaved single vacuum tube at reasonable signal levels.
Generally and simply, that means we are not at clipping, or even near to clipping.
The “order’ of harmonic distortion means how many times the fundamental the distortion is.
2nd order is 2 X the fundamental, 3rd order is 3 X the fundamental, 4th order is 4 X the fundamental, and so on . . .
The increase of harmonic distortion products and increase of intermodulation distortion products will usually change at the same rates, as the signal level is increased. If one order of harmonic distortion goes up 2 X, the same order of intermodulation product will go up 2 X of the original distortion values, versus the new distortion values as the signal level is increased.
Clipping may be caused by drawing grid current.
Depending on the tube, grid current can happen during a signal that puts the grid voltage versus Either the direct heated filament “cathode” voltage, Or the indirect heated cathode voltage.
Just having the grid voltage very close to 0v, at 0V, or positive volts can cause this grid current. And the amount of grid current is not linear as the grid goes near, at, and beyond the cathode voltage.
The amount of this effect depends on the impedance that drives the grid.
Clipping can also be caused by increasing the signal level to the grid (versus the filament “cathode”, or cathode voltage).
When the grid goes enough negative, the tube is either near cut off, or at cutoff.
An increase of signal level by +3 dB, is 1.414 X the original voltage, and 2 X the power.
With signal levels applied to a single vacuum tube that are in the well behaved regions:
An increase of +3 dB (1.414 X voltage) causes causes the 2nd order distortion products to go up by +6 dB (2 X voltage).
But since the original signal went up by +3 dB, and the distortion product goes up by + 6dB,
the net change is +3 dB more distortion relative to the signal (1.414 X the distortion).
If the signal increased by +3 dB, and the distortion was 1%, it is now 1.414% at the increased signal level.
An increase of +3 dB causes causes the 3rd order distortion products to go up by +9 dB.
But since the original signal went up by +3 dB, and the distortion product goes up by + 9dB,
the net change is +6 dB more distortion relative to the signal (2 X the distortion).
If the signal increased by +3 dB, and the distortion was 1%, it is now 2% at the increased signal level.
The higher the order of the distortion (4th, 5th, 6th, 7th, 8th, 9th, . . .) the faster the distortion product increases versus the original +3 dB increase of signal level.
But fortunately, the higher the order of the distortion, the lower the original level of that distortion product versus the original level of the fundamental signal/tone we started out with.
This means that we see a falloff of the higher order (higher frequency) harmonics.
Symmetrical clipping causes the Odd harmonics to increase, with full clipping (a square wave),
that is the 3rd, 5th, 7th, 9th, . . . harmonics. As the order goes up, the amplitude of that order falls off. If the fundamental signal, c, is 1, the 3rd is -9.5dBc, the 5th is -14 dBc, the 7th is -16.9 dBc, the 9th is -19dBc, . . .
Clipping that is asymmetrical clipping, a square wave with more time at one extreme than the other extreme, causes Even harmonics to increase, 2nd, 4th, 6th, 8th, 10th, . . .
But the curious thing is that All of those harmonics are at the same level (-dBc versus the fundamental). The -dBc value is dependent on the asymmetry (time of one extreme versus time of the opposite extreme).
But asymmetrical clipping still has those odd order harmonics too (3rd, 5th, 7th, 9th, . . .).
But as the odds fall off at high frequency, eventually at some order of harmonic, the even harmonics are stronger than the odd harmonics.
How about the sound of a single ended guitar amp that is clipping asymmetrically, versus the sound of a push pull guitar amp that is symmetrically clipping?
Of course, we (I) usually do not listen to our (my) playback amplifiers in square wave clipping mode.
Fortunately, these wonderful single vacuum tubes in their well behaved region at reasonable signal levels do not have much higher order distortion.
A triode in the well behaved signal levels, typically has 2nd and 3rd order distortion, and not much else of a significant level.
But adding negative feedback causes higher order distortion products to occur.
The 2nd harmonic that is feedback becomes 2 X 2nd = 4th; 2 X 3rd = 6th,
and 3 x 3rd = 9th. . .
The lower level 4th, 5th, 6th, 7th, and 8th, from the triode are at a lower level, but they also are distorted by the dominant 2nd and 3rd order distortion of the triode (or pentode, or beam power tube).
These new products, as they are fed back also become higher order products.
Fortunately, their amplitude is lower each time they come around again (are fed back).
Remember, if you look for dirt under the rug, you will find dirt.
Just listen, and do not worry too much about what is "buried" under your amplifier's rug.
And do not worry too much about what is "buried" under your loudspeaker's rug.
A reasonably good amplifier and reasonably good loudspeaker can provide hours and years of musical enjoyment.
The distortion of a vacuum tube that is not in a feedback loop follows certain ‘rules’.
Let us look at distortion products for a well behaved single vacuum tube at reasonable signal levels.
Generally and simply, that means we are not at clipping, or even near to clipping.
The “order’ of harmonic distortion means how many times the fundamental the distortion is.
2nd order is 2 X the fundamental, 3rd order is 3 X the fundamental, 4th order is 4 X the fundamental, and so on . . .
The increase of harmonic distortion products and increase of intermodulation distortion products will usually change at the same rates, as the signal level is increased. If one order of harmonic distortion goes up 2 X, the same order of intermodulation product will go up 2 X of the original distortion values, versus the new distortion values as the signal level is increased.
Clipping may be caused by drawing grid current.
Depending on the tube, grid current can happen during a signal that puts the grid voltage versus Either the direct heated filament “cathode” voltage, Or the indirect heated cathode voltage.
Just having the grid voltage very close to 0v, at 0V, or positive volts can cause this grid current. And the amount of grid current is not linear as the grid goes near, at, and beyond the cathode voltage.
The amount of this effect depends on the impedance that drives the grid.
Clipping can also be caused by increasing the signal level to the grid (versus the filament “cathode”, or cathode voltage).
When the grid goes enough negative, the tube is either near cut off, or at cutoff.
An increase of signal level by +3 dB, is 1.414 X the original voltage, and 2 X the power.
With signal levels applied to a single vacuum tube that are in the well behaved regions:
An increase of +3 dB (1.414 X voltage) causes causes the 2nd order distortion products to go up by +6 dB (2 X voltage).
But since the original signal went up by +3 dB, and the distortion product goes up by + 6dB,
the net change is +3 dB more distortion relative to the signal (1.414 X the distortion).
If the signal increased by +3 dB, and the distortion was 1%, it is now 1.414% at the increased signal level.
An increase of +3 dB causes causes the 3rd order distortion products to go up by +9 dB.
But since the original signal went up by +3 dB, and the distortion product goes up by + 9dB,
the net change is +6 dB more distortion relative to the signal (2 X the distortion).
If the signal increased by +3 dB, and the distortion was 1%, it is now 2% at the increased signal level.
The higher the order of the distortion (4th, 5th, 6th, 7th, 8th, 9th, . . .) the faster the distortion product increases versus the original +3 dB increase of signal level.
But fortunately, the higher the order of the distortion, the lower the original level of that distortion product versus the original level of the fundamental signal/tone we started out with.
This means that we see a falloff of the higher order (higher frequency) harmonics.
Symmetrical clipping causes the Odd harmonics to increase, with full clipping (a square wave),
that is the 3rd, 5th, 7th, 9th, . . . harmonics. As the order goes up, the amplitude of that order falls off. If the fundamental signal, c, is 1, the 3rd is -9.5dBc, the 5th is -14 dBc, the 7th is -16.9 dBc, the 9th is -19dBc, . . .
Clipping that is asymmetrical clipping, a square wave with more time at one extreme than the other extreme, causes Even harmonics to increase, 2nd, 4th, 6th, 8th, 10th, . . .
But the curious thing is that All of those harmonics are at the same level (-dBc versus the fundamental). The -dBc value is dependent on the asymmetry (time of one extreme versus time of the opposite extreme).
But asymmetrical clipping still has those odd order harmonics too (3rd, 5th, 7th, 9th, . . .).
But as the odds fall off at high frequency, eventually at some order of harmonic, the even harmonics are stronger than the odd harmonics.
How about the sound of a single ended guitar amp that is clipping asymmetrically, versus the sound of a push pull guitar amp that is symmetrically clipping?
Of course, we (I) usually do not listen to our (my) playback amplifiers in square wave clipping mode.
Fortunately, these wonderful single vacuum tubes in their well behaved region at reasonable signal levels do not have much higher order distortion.
A triode in the well behaved signal levels, typically has 2nd and 3rd order distortion, and not much else of a significant level.
But adding negative feedback causes higher order distortion products to occur.
The 2nd harmonic that is feedback becomes 2 X 2nd = 4th; 2 X 3rd = 6th,
and 3 x 3rd = 9th. . .
The lower level 4th, 5th, 6th, 7th, and 8th, from the triode are at a lower level, but they also are distorted by the dominant 2nd and 3rd order distortion of the triode (or pentode, or beam power tube).
These new products, as they are fed back also become higher order products.
Fortunately, their amplitude is lower each time they come around again (are fed back).
Remember, if you look for dirt under the rug, you will find dirt.
Just listen, and do not worry too much about what is "buried" under your amplifier's rug.
And do not worry too much about what is "buried" under your loudspeaker's rug.
A reasonably good amplifier and reasonably good loudspeaker can provide hours and years of musical enjoyment.
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