Take the grid currents in example #55.
Here we have 17.5mA concertina current to drive those grids into A2.
And we have equal impedance due to cathode feedback reduction to 1//Mu.
This should "theoretically" fix all the challenges that grid current presents
to a concertina, but it doesn't...
It gets pushed completely off its nominal operating points by the more
severe problem of coupling caps charging due to output grid current!
This remains unsolved. You still need a Buffer that can conduct down
to DC. And if you still must add such a buffer, what was the point of
the impedance equalization?
Not sure such a concertina is useful for anything other than driving big
MOSFETs with a ton of non-linear capacitance, but no grid current.
Here we have 17.5mA concertina current to drive those grids into A2.
And we have equal impedance due to cathode feedback reduction to 1//Mu.
This should "theoretically" fix all the challenges that grid current presents
to a concertina, but it doesn't...
It gets pushed completely off its nominal operating points by the more
severe problem of coupling caps charging due to output grid current!
This remains unsolved. You still need a Buffer that can conduct down
to DC. And if you still must add such a buffer, what was the point of
the impedance equalization?
Not sure such a concertina is useful for anything other than driving big
MOSFETs with a ton of non-linear capacitance, but no grid current.
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Respectfully, you are avoiding the issue. Your circuit cannot test the P-Gnd or K-Gnd impedances because no current flows through ground during the test.
Regarding rise and fall times, equal rise times do not imply equal impedances. This is simple to show. Start with your balanced, R-C loaded Cathodyne. Double the plate load impedance by doubling the resistance and halving the capacitance (note the time constant remains unchanged.)
Since the plate load is now double the cathode load, the plate voltage is now exactly the negative of twice the cathode voltage. The plate voltage rises twice as far, but also twice as fast. The rise time doesn't change. Simulate or bench test this yourself to prove it. Equal rise times, but unequal impedances. Equal rise times do not imply equal impedances. QED.
Regarding rise and fall times, equal rise times do not imply equal impedances. This is simple to show. Start with your balanced, R-C loaded Cathodyne. Double the plate load impedance by doubling the resistance and halving the capacitance (note the time constant remains unchanged.)
Since the plate load is now double the cathode load, the plate voltage is now exactly the negative of twice the cathode voltage. The plate voltage rises twice as far, but also twice as fast. The rise time doesn't change. Simulate or bench test this yourself to prove it. Equal rise times, but unequal impedances. Equal rise times do not imply equal impedances. QED.
Equal rise times into equal capacitive loads absolutely imply equal Thevenin impedances.
...you have now violated the boundary conditions.
Your statement
For equal anode and cathode loads:
Zout(anode and cathode) = RL.ra/RL(u+2)assumes what is in dispute. How did you arrive at this expression? Please advise.
In Zout(cathode) = (RL+ra)/(u+2) + ra/RL, the units don’t match. Ra/RL is unitless. It should have units of ohms.
In Zout(anode) = RL x RL(u+1) + RL.ra / RL(u+2)+ra, RL x RL(u+1) has units of ohms squared when it should have units of ohms.
The spice modeling you have seen needs to be reviewed for what is being modeled. I have seen many claims that certain tests measure certain impedances when they actually don’t. Can you describe how you believe these impedances should be measured or derived?
I don’t understand how people who claim that the impedances of a balanced Cathodyne are equal can also cite Preisman and Jones. I quote from their articles:
Preisman (see eqs. (1) and (2) and the subsequent text): (the cathode impedance) …. is much less than rp, and (the plate impedance) is greater than rp…. In spite of this, the regulation of both portions of the circuit are the same as long as Zk = ZL.Jones, second paragraph: The cathode impedance… is low. At the plate terminal… the source impedance is high.Your beliefs contradict what they clearly assert. They also contradict similar conclusions reached in the Radiotron Designer's Handbook 4th edition, equations (30) and (31), p. 330, again showing that Zp > Zk. Can you comment?
For equal anode and cathode loads:
Zout(anode and cathode) = RL.ra/RL(u+2)assumes what is in dispute. How did you arrive at this expression? Please advise.
In Zout(cathode) = (RL+ra)/(u+2) + ra/RL, the units don’t match. Ra/RL is unitless. It should have units of ohms.
In Zout(anode) = RL x RL(u+1) + RL.ra / RL(u+2)+ra, RL x RL(u+1) has units of ohms squared when it should have units of ohms.
The spice modeling you have seen needs to be reviewed for what is being modeled. I have seen many claims that certain tests measure certain impedances when they actually don’t. Can you describe how you believe these impedances should be measured or derived?
I don’t understand how people who claim that the impedances of a balanced Cathodyne are equal can also cite Preisman and Jones. I quote from their articles:
Preisman (see eqs. (1) and (2) and the subsequent text): (the cathode impedance) …. is much less than rp, and (the plate impedance) is greater than rp…. In spite of this, the regulation of both portions of the circuit are the same as long as Zk = ZL.Jones, second paragraph: The cathode impedance… is low. At the plate terminal… the source impedance is high.Your beliefs contradict what they clearly assert. They also contradict similar conclusions reached in the Radiotron Designer's Handbook 4th edition, equations (30) and (31), p. 330, again showing that Zp > Zk. Can you comment?
Doesn't matter. I have proven that equal rise times do not imply equal impedances, which is what you claimed "proved" that the impedances were equal. Clearly, equal rise times do not imply equal impedances in the general case.
Will you now claim that equal rise times imply equal impedances in circuits where the boundary conditions are met because the impedances are equal? That would be circular reasoning.
May I assume that you now agree that your first circuit is not measuring P-Gnd and K-Gnd impedances?
Will you now claim that equal rise times imply equal impedances in circuits where the boundary conditions are met because the impedances are equal? That would be circular reasoning.
May I assume that you now agree that your first circuit is not measuring P-Gnd and K-Gnd impedances?
Jones fully agrees with my analysis and does not understand your objections, so I probably wouldn't cite him in this context if I were you. I don't know Preisman or whether he's still around. As I said before, his analysis is another way to model, albeit a much more complex (and IMO, contorted) way.
Were he alive, Dr. Thevenin would be quite surprised at that.
Ie. you agree that all depends on conditions. Concertina that drives equal linear networks is always balanced, but when it drives tube grids directly, through coupling capacitors, loads are no more equal and linear, so the whole system is not balanced.
I feel like all disagreements are caused by real experience with concertina splitter driving real tubes, and attempt to explain disbalance by concertina only, which is wrong. Concertina itself is balanced, while the same current flows through anode and cathode loads that are in series with each other and have equal impedances. But in real life it is very rare the case; even driving grids with negative only swing we hit grid non-linearities due to crest-factor in real musical signals.
For tubes that draw significant grid current, yes- but they should always have a buffer or possibly be transformer driven. For the tubes commonly used in amps with cathodynes (6L6, 6550, EL84, KT88...), the loads are quite equal and linear. Measurements of, for example, the Red Light District and the Bevois Valley confirm this.
You should be able to defend yourself against critiques of your reasoning. If I am wrong, you should be able to find the flaw in my reasoning. You should not have to depend on Jones.
If you are referring to George Ellis Jones, perhaps you or he can explain the disconnect between his agreement with you and the statement from his 1951 paper that I quoted. And Preisman said what he said, and clearly so, whether or not he is gone.
The fact that someone who is not involved in this conversation agrees with you is not an effective rebuke of the problems I pointed out with the analyses you presented.
Perhaps you would like to present what I wrote to Mr. Jones and ask him for a reply that you could share here? It might be even better if Mr. Jones himself cared to join the conversation.
For now, it seems that grounding the plate and cathode to measure short circuit current does not lead to a measurement of P-Gnd or K-Gnd impedance, because no current flows into ground. And since equal rise times do not in general imply equal impedances, the fact that a circuit exhibits equal rise times cannot be used to conclude that its impedances are equal.
I don't see any case left standing at the moment for equal cathodyne plate and cathode impedances.
If you are referring to George Ellis Jones, perhaps you or he can explain the disconnect between his agreement with you and the statement from his 1951 paper that I quoted. And Preisman said what he said, and clearly so, whether or not he is gone.
The fact that someone who is not involved in this conversation agrees with you is not an effective rebuke of the problems I pointed out with the analyses you presented.
Perhaps you would like to present what I wrote to Mr. Jones and ask him for a reply that you could share here? It might be even better if Mr. Jones himself cared to join the conversation.
For now, it seems that grounding the plate and cathode to measure short circuit current does not lead to a measurement of P-Gnd or K-Gnd impedance, because no current flows into ground. And since equal rise times do not in general imply equal impedances, the fact that a circuit exhibits equal rise times cannot be used to conclude that its impedances are equal.
I don't see any case left standing at the moment for equal cathodyne plate and cathode impedances.
You brought him up ("I don’t understand how people who claim that the impedances of a balanced Cathodyne are equal can also cite Preisman and Jones."). His text also says explicitly that the impedances are equal under the equal-loads boundary condition- you're quoting him out of context. For a variety of reasons, he cannot post here at present, although he has been a valued contributor and moderator in the past. However, we are in frequent contact and he has read your objection and comes to the same conclusion I have- my analysis is correct, your issue is that you don't like or just don't understand the boundary conditions.
Now please connect your amps to speakers with less sensitivity in bigger rooms and confirm opposite...
Can't, because it isn't.
Actually, someone earlier in this thread brought up Jones.
Make the case that I am quoting him out of context. I see no such evidence. Please point out exactly where he says explicilty that impedances are equal under the equal loss boundary condition.
I don't doubt he said to you what he told you, but it's hearsay. I can't discuss it with him, and I can't even examine his arguments. I can only discuss this with you.
I say again, you should be able to find the flaws in my critique of what you're saying and argue against them. I have detailed and explained the flaws I have found. Why can't you prove me wrong?
Saying
Frankly, you are choosing to ignore the issues I raised, which are unrelated to the existence or non-existence of boundary conditions.
Please address the issues I raised!
Make the case that I am quoting him out of context. I see no such evidence. Please point out exactly where he says explicilty that impedances are equal under the equal loss boundary condition.
I don't doubt he said to you what he told you, but it's hearsay. I can't discuss it with him, and I can't even examine his arguments. I can only discuss this with you.
I say again, you should be able to find the flaws in my critique of what you're saying and argue against them. I have detailed and explained the flaws I have found. Why can't you prove me wrong?
Saying
in no way addresses the criticisms I made of your analyses. I did not violate boundary conditions in the discussion of your first circuit. I said that there is no ground current and therefore ground cannot be involved in the impedances you are measuring. I have given an example of where equal rise times occur without equal impedances, proving that the former as a condition cannot in general be used to imply the latter. If you then say that that was for a case of unequal boundary conditions, I will agree, but you would then be forced into the circular argument that equal rise times imply equal impedances when the impedances are equal.
Frankly, you are choosing to ignore the issues I raised, which are unrelated to the existence or non-existence of boundary conditions.
Please address the issues I raised!
Equal load, not equal loss. Valve Amplifiers, 3rd edition, p406:
His analysis may be found on the preceding three pages, you needn't rely on "hearsay." He was incorrect about class B loading for reasons detailed in Linear Audio, which will be corrected in the 4th edition.
Consider this circuit as a driver for balanced lines. At the end of the line terminate in a differential line receiver. Should work fine, right? We are told that the impedances (to some common point) are equal, which is of course the requirement for balanced. The fact that the signal voltages are equal and opposite is fine, but not essential.
Now subject the overall system to some common-mode disturbance. Perhaps it can be current generators, two equal ones connected to each line. Or couple to each line with capacitors if you like, driven from the same voltage signal. What do you see now as a differential signal?
If the impedances at plate and cathode are equal, the current sources should produce equal voltages, and the differential line receiver should reject them. But it does not. The induced voltage at the cathode is relatively small. The induced voltage at the anode is larger and the current induced at the cathode ADDS to this!
So the Cathodyne makes a very lousy balanced line driver. Draw your own conclusions about its output impedances.
Brad Wood
Now subject the overall system to some common-mode disturbance. Perhaps it can be current generators, two equal ones connected to each line. Or couple to each line with capacitors if you like, driven from the same voltage signal. What do you see now as a differential signal?
If the impedances at plate and cathode are equal, the current sources should produce equal voltages, and the differential line receiver should reject them. But it does not. The induced voltage at the cathode is relatively small. The induced voltage at the anode is larger and the current induced at the cathode ADDS to this!
So the Cathodyne makes a very lousy balanced line driver. Draw your own conclusions about its output impedances.
Brad Wood
Yes, that's an issue I addressed in my article. Common-mode disturbances represent an unbalanced load. Thus, the cathodyne has imperfect CMR. The other nonideality, which Chris correctly pointed out in a letter to the editor in AudioXpress, is that the PSR between the two nodes in unequal.
As a practical matter, the prototype of ImPasse preamp, which used a cathodyne as a line driver, happily drove 10 feet of cable in a noisy facility with no discernible noise.
As a practical matter, the prototype of ImPasse preamp, which used a cathodyne as a line driver, happily drove 10 feet of cable in a noisy facility with no discernible noise.
Are you talking about Morgan Jones or George Ellis Jones? The earlier reference was to George Ellis Jones and his 1951 Audio paper, "Analysis of the Split Load Phase Inverter".
Ah, Morgan Jones. I was hoping we would get to this. Was it he who set you on this path?
You would agree that his conclusions are predicated on his assertion on page 405 that "The (cathodyne) feedback acts to reduce anode output resistance", right?
It is easy to show that this is false.
Mr. Jones almost does it for us. On page 404, he correctly states, "ra` = (u + 1) *Rk + rp". Now, the linear approximation of the equation for triode operation is ip = (vgrid - vk)*gm. In the cathodyne, there is no feedback connection to the grid, so the only opportunity for feedback is through vk, created by ip*Rk. If we cap bypass Rk, we short out the ac voltage signal across Rk, so there is no ac component left in vk, and we eliminate ac feedback in the circuit. From an ac point of view, vk = 0, ip = gm*vgrid, and the bypased Rk looks like a short. The ac version of ra' becomes ra` = (1 + u) *0 + ra = ra. We have eliminated feedback, and we have reduced ra', the plate impedance. If we remove the cap, feedback and the ac portions of Rk and vk return along with an increase in the value of ra' back to (u + 1) *Rk + ra.
Cathodyne feedback increases plate resistance - it doesn't reduce it.
With the failure of that assertion, Mr. Jones' case for equal impedances falls apart. He cannot justly conclude that Za = Zk.
However, the frequency responses of the cathodyne plate and cathode are equal, but for a very simple reason which is true regardless of the plate and cathode impedances. Plate and cathode currents are equal and opposite in any triode with no grid current. With identical plate and cathode loads, ohm's law establishes equal and opposite voltages, which implies equal frequency responses.
Please see where we are now. I have pointed out flaws in every case made for equal Cathodyne impedances that I know of. Can you or anyone find any flaws in any of these analyses?
Ah, Morgan Jones. I was hoping we would get to this. Was it he who set you on this path?
You would agree that his conclusions are predicated on his assertion on page 405 that "The (cathodyne) feedback acts to reduce anode output resistance", right?
It is easy to show that this is false.
Mr. Jones almost does it for us. On page 404, he correctly states, "ra` = (u + 1) *Rk + rp". Now, the linear approximation of the equation for triode operation is ip = (vgrid - vk)*gm. In the cathodyne, there is no feedback connection to the grid, so the only opportunity for feedback is through vk, created by ip*Rk. If we cap bypass Rk, we short out the ac voltage signal across Rk, so there is no ac component left in vk, and we eliminate ac feedback in the circuit. From an ac point of view, vk = 0, ip = gm*vgrid, and the bypased Rk looks like a short. The ac version of ra' becomes ra` = (1 + u) *0 + ra = ra. We have eliminated feedback, and we have reduced ra', the plate impedance. If we remove the cap, feedback and the ac portions of Rk and vk return along with an increase in the value of ra' back to (u + 1) *Rk + ra.
Cathodyne feedback increases plate resistance - it doesn't reduce it.
With the failure of that assertion, Mr. Jones' case for equal impedances falls apart. He cannot justly conclude that Za = Zk.
However, the frequency responses of the cathodyne plate and cathode are equal, but for a very simple reason which is true regardless of the plate and cathode impedances. Plate and cathode currents are equal and opposite in any triode with no grid current. With identical plate and cathode loads, ohm's law establishes equal and opposite voltages, which implies equal frequency responses.
Please see where we are now. I have pointed out flaws in every case made for equal Cathodyne impedances that I know of. Can you or anyone find any flaws in any of these analyses?
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