I agree that the impedance between the cathode and plate is about 2/gm.
I also agree that the impedances at the plate and cathode are very different.
I have never heard SY or Morgan Jones opine anything other than that the ground-referenced plate and cathode impedances are both about 1/gm.
I also agree that the impedances at the plate and cathode are very different.
I have never heard SY or Morgan Jones opine anything other than that the ground-referenced plate and cathode impedances are both about 1/gm.
OK lets look at the application and follow the current.
any current that travels from plate to cathode has an output impedance of 2/gm and any current that completes its loop through ground has an output impedance of Rp if the source is the plate and 1/gm if the source is the cathode.
dave
any current that travels from plate to cathode has an output impedance of 2/gm and any current that completes its loop through ground has an output impedance of Rp if the source is the plate and 1/gm if the source is the cathode.
dave
CPaul, I know that many people are temperamentally opposed to parallel output tubes, even in push-pull, for musical reasons. I don't know if you are one. But there really isn't any good reason to be opposed to them in push pull provided you have a driver capable of handling them. Mosfet source followers certainly are. There are more fundamental musical problems with paralleling single ended output tubes because you lose the coherence of a single output tube.
In push-pull however you've already lost that single tube coherence. You actually gain musical smoothness in that case by going to PPP. That's because you have more statistical possibilities of matching the combined characteristics on both sides of the push-pull by swapping them around. The statistical possibility of matching only two output tubes in normal PP isn't that good. If you care enough then you get matched tubes. But it still isn't perfect. But if you care that much about matched performance then use the same standard and buy a matched foursome. Then use some testing instruments to best match the 2+2.
There is no statistical downside to going PPP. But I agree it wouldn't be smart to get an outsized tube meant for high drive voltages and then parallel it because you have limited drive capability. That would be a waste of efficiency and cost.
Dave, I'm not sure I follow you. I determine the impedance between two points by dividing the voltage between those two points by the current passing from one to the other.
May I ask your opinion as to the ground referenced impedances at the plate and cathode of a matched load cathodyne? These would take into account the effects of the triode and the cathode load at the cathode, and the plate and the plate load at the plate.
May I ask your opinion as to the ground referenced impedances at the plate and cathode of a matched load cathodyne? These would take into account the effects of the triode and the cathode load at the cathode, and the plate and the plate load at the plate.
Or I just use Thevenin, which the Institute of Electrical and Electronic Engineers says can be used between any two terminals of a linear circuit between which a voltage exists.
But there are those who disagree with the IEEE. They say that connection of a single ended test load to a matched load cathodyne (MLC) means you can't be measuring an MLC because the loads are no longer matched. (I disagree.)
Fortunately, the single ended impedance at the plate can be measured by a simple technique that alters no impedances, employs no test loads, and simply makes use of the plate power supply's noise.
But there are those who disagree with the IEEE. They say that connection of a single ended test load to a matched load cathodyne (MLC) means you can't be measuring an MLC because the loads are no longer matched. (I disagree.)
Fortunately, the single ended impedance at the plate can be measured by a simple technique that alters no impedances, employs no test loads, and simply makes use of the plate power supply's noise.
agreed. it doesn't matter if there is a ground connection anywhere between those two points since any current traveling through it will fall outside the scope of what you are trying to measure.
I think the ground referenced impedances are irrelevant for this discussion. Just because you can calculate them doesn't mean that they apply. Rather than measuring one independently from the other what happens when you measure them both at the same time with identical test setups?
dave
Sorta late to this discussion and maybe I haven't thought hard enough about this yet, but it seems intuitively obvious that Zout would be different at plate and cathode on a cathodyne. Just look at where the feedback is, what type of feedback it is, etc. and you can see that. (Serial applied voltage feedback) It will make cathode voltage strongly track grid voltage. If you imbalance the circuit by cutting cathode load in half, you will find that cathode voltage still strongly tracks grid voltage. If you return cathode load to what it was, and cut the anode load in half, cathode voltage will still strongly track grid voltage. That seems to indicate a lower Zout at the cathode to me.
The really cool thing about the cathodyne is that the Zout at plate and cathode don't have to be the same for you to get identical low-distortion outputs as long as you constrain the circuit so that Kirchhoff's current law works in your favor. In other words, if the plate and cathode loads are identical, the high negative feedback will work to linearize both the plate and cathode because net currents into and out of all nodes must equal zero. Of course, this applies to both capacitive and resistive loading.
So I think it is a bit of a distraction (as far as practical amp design goes) to get hung up on calculating Zout differences at plate and cathode when KCL analysis shows that when loads are equal (a condition we can easily meet in a push-pull output stage) there can be no imbalance, therefore the plate side will benefit from the feedback on the cathode side.
Also, it is often overlooked in the quest for the perfectly-balanced phase splitter that output tubes will have mismatches in gain. It may not be desirable from an overall system design point-of-view to have a perfect phase splitter. Many older amplifiers included an "AC balance" adjustment that was a trimmer resistor in one of the loads of the cathodyne phase splitter that allowed for imbalance to be introduced to compensate for output tube imbalance. My Fisher X-101-B owner's manual says to hook the amp to a distortion analyzer and adjust the pot for minimum distortion.
The really cool thing about the cathodyne is that the Zout at plate and cathode don't have to be the same for you to get identical low-distortion outputs as long as you constrain the circuit so that Kirchhoff's current law works in your favor. In other words, if the plate and cathode loads are identical, the high negative feedback will work to linearize both the plate and cathode because net currents into and out of all nodes must equal zero. Of course, this applies to both capacitive and resistive loading.
So I think it is a bit of a distraction (as far as practical amp design goes) to get hung up on calculating Zout differences at plate and cathode when KCL analysis shows that when loads are equal (a condition we can easily meet in a push-pull output stage) there can be no imbalance, therefore the plate side will benefit from the feedback on the cathode side.
Also, it is often overlooked in the quest for the perfectly-balanced phase splitter that output tubes will have mismatches in gain. It may not be desirable from an overall system design point-of-view to have a perfect phase splitter. Many older amplifiers included an "AC balance" adjustment that was a trimmer resistor in one of the loads of the cathodyne phase splitter that allowed for imbalance to be introduced to compensate for output tube imbalance. My Fisher X-101-B owner's manual says to hook the amp to a distortion analyzer and adjust the pot for minimum distortion.
Dave, they matter in at least one very practical way. The very high single ended impedance zpg looking into the plate means that there is virtually no rejection at the plate of power supply noise; practically the full plate supply noise comes booming through - quite typically, far more than 90% of it. Just set up a simple test circuit with supply noise that is visible on the 'scope. If the grid is adequately filtered so that it sees negligible noise, this > 90% result will be evident. The only way this could happen is if zpg were much greater than the plate load Rp - which it is.
For various reasons, there is much less supply noise at the cathode. This differential, non-common mode cathodyne output noise is amplified by the output stage.
At least if zpg were 1/gm as some claim, supply noise would be greatly attenuated because Rp >> 1/gm. Unfortunately, this is not the case.
For various reasons, there is much less supply noise at the cathode. This differential, non-common mode cathodyne output noise is amplified by the output stage.
At least if zpg were 1/gm as some claim, supply noise would be greatly attenuated because Rp >> 1/gm. Unfortunately, this is not the case.
SpreadSpectrum, I agree with practically everything you've said.
I would argue though that calculating impedances enhances understanding of how the circuit works and also explains the poor power supply noise rejection at the plate that I mentioned in post 1129 above.
I would argue though that calculating impedances enhances understanding of how the circuit works and also explains the poor power supply noise rejection at the plate that I mentioned in post 1129 above.
Good point. That makes me think of the phase splitter in the X-101-B that I mentioned above. It also had a resistor from B+ to the cathode of the phase splitter. I remember being confused as to why they would do that and someone pointed out to me that it looked like an attempt to inject some PS ripple into the cathode side (presumably so that it would be better cancelled in the output stage). I'm not sure how well that worked, but it looks like they thought it worked well enough to justify the expense of an extra resistor.
I do not claim that zpg is 1/gm and accept the whole power supply noise example however I still consider that outside the scope of the discussion at hand.
Lets say we want to calculate the bandwidth of our cathodyne phase splitter based on the input capacitance of the following stage. Do we use zag and zkg and come up with different frequency response for each or do we use zak and end up with matched hf behavior?
As I asked before, if we also use a conventional method to measure Z-out of both the anode and the cathode at the same time, what values do we end up with?
dave
If you look at page 110, post 1094 in this thread, you'll see I have treated this question already, taking into consideration the noise contribution from the voltage gain stage driving the cathodyne.
But that solution inserted cancellation at the cathode of the voltage gain stage, which had a cathode resistor much smaller than that of the cathodyne. It required a rather large coupling capacitor in series with a resistor from the supply.
I'm betting that inserting the signal at the cathodyne cathode would accommodate a much smaller capacitor if one were needed at all.
Thanks for mentioning it. I'll take a look at this and post my conclusions.
But that solution inserted cancellation at the cathode of the voltage gain stage, which had a cathode resistor much smaller than that of the cathodyne. It required a rather large coupling capacitor in series with a resistor from the supply.
I'm betting that inserting the signal at the cathodyne cathode would accommodate a much smaller capacitor if one were needed at all.
Thanks for mentioning it. I'll take a look at this and post my conclusions.
Dave, I'm not sure how the bounds of our discussions get set. Isn't that something we agree on mutually? If I make an implicit assumption with which you disagree, shouldn't you bring it up?
Regarding the bandwidth of the Cathodyne in your question in the second paragraph, as SpreadSpectrum points out, this is the beauty of the Cathodyne. Since all of the electrons flowing into the cathode flow out of the plate, as long as the resistive plus capacitive portions of the plate and cathode loads are identical, by Ohm's Law the same AC voltages will appear at the plate and cathode and therefor, the bandwidths will be the same. (Actually, the triode parasitic capacitances to its grid disturb this pretty picture somewhat, but typically not until rather high frequencies.)
I know of no "conventional method" to measure the impedances between more than two nodes in the same circuit at the same time. Typically, if a load or a signal source is applied to nodes A and B, the other nodes in the circuit will be affected, and this will confuse attempts to measure impedances of node pairs other than A and B. If you know of such a method, please describe how it applies to linear circuits in general, not just the Cathodyne specifically. Every statement of Thevenin, for instance, that I can find is a two node theorem. Just two nodes are involved - any two -but no more.
Regarding the bandwidth of the Cathodyne in your question in the second paragraph, as SpreadSpectrum points out, this is the beauty of the Cathodyne. Since all of the electrons flowing into the cathode flow out of the plate, as long as the resistive plus capacitive portions of the plate and cathode loads are identical, by Ohm's Law the same AC voltages will appear at the plate and cathode and therefor, the bandwidths will be the same. (Actually, the triode parasitic capacitances to its grid disturb this pretty picture somewhat, but typically not until rather high frequencies.)
I know of no "conventional method" to measure the impedances between more than two nodes in the same circuit at the same time. Typically, if a load or a signal source is applied to nodes A and B, the other nodes in the circuit will be affected, and this will confuse attempts to measure impedances of node pairs other than A and B. If you know of such a method, please describe how it applies to linear circuits in general, not just the Cathodyne specifically. Every statement of Thevenin, for instance, that I can find is a two node theorem. Just two nodes are involved - any two -but no more.
SpreadSpectrum, let's consider the simple design consisting of a power amp with a single input gain stage driving a cathodyne. If the gain stage is a pentode, the impedance zpg looking into its plate is generally larger than its plate load resistor. And so more than half the supply noise appears at that stage's plate. On the other hand, if the gain stage is a triode, good design practice for gain and linearity says that the plate load is larger than zpg, meaning that less than half the supply voltage appears on that stage's plate.
Consider that the cathodyne, which with no supply noise on its grid, has almost the full supply noise on its plate and very little of that on its cathode. The situation is reversed if the full supply noise appears on the grid.
So for a pentode gain stage, the connection of an impedance Z between the cathodyne cathode and B+ would tend to drive that circuit's plate and cathode supply noise voltages to better, more equal levels. But it would make matters worse if the gain stage were a well-designed triode amplifier. And of course, for the cathode components, Rk || Z would still have to equal Rp. What are the values of these components in the design you refer to?
Does the amplifier you are referring to have a pentode gain stage? such designs are more difficult to compensate an null out supply noise.
Consider that the cathodyne, which with no supply noise on its grid, has almost the full supply noise on its plate and very little of that on its cathode. The situation is reversed if the full supply noise appears on the grid.
So for a pentode gain stage, the connection of an impedance Z between the cathodyne cathode and B+ would tend to drive that circuit's plate and cathode supply noise voltages to better, more equal levels. But it would make matters worse if the gain stage were a well-designed triode amplifier. And of course, for the cathode components, Rk || Z would still have to equal Rp. What are the values of these components in the design you refer to?
Does the amplifier you are referring to have a pentode gain stage? such designs are more difficult to compensate an null out supply noise.
It is a 12AX7 gain stage followed by a cathodyne made from the other half of the 12AX7. See here for the schematic with specific values.
Like I said above, I'm not sure how well it works.
Edit: It looks like many of the Fisher amps used that 330k resistor to the cathode of a 12AX7 cathodyne.
Like I said above, I'm not sure how well it works.
Edit: It looks like many of the Fisher amps used that 330k resistor to the cathode of a 12AX7 cathodyne.
Last edited:
Wrong question, as you have erected a false dichotomy. As this phase splitter must have identical loads at cathode and anode you need to apply the capacitance at both and then calculate the frequency response. Capacitance just applied to one will affect the frequency response at the other.dave slagle said:
Questions about the output impedance at one output only make sense when you intend using this stage for some purpose other than a balanced phase splitter. In engineering, context is everything.
this is exactly my point. Cpaul does make a good point about the PSRR of the plate vs. cathode but any noise at the plate that doesn't exist at the cathode is simply an unbalanced load and logically sees the SE anode impedance.
dave
Noise is not an impedance; it is a signal. Noise at the plate which is not at the cathode is an unbalanced signal, not an unbalanced load.
To calculate the frequency response I would calculate stage gain to both outputs as a function of frequency with Za at the anode and Zk at the cathode. Then set Za=Zk=R||C to get the final result. Having got the result, people can then argue (if they wish) about 'output impedances'.
Yes. The noise across the anode load will equal the noise across the cathode load, if these two loads are equal (as they should be). Unfortunately the signal ground reference for the anode output is the same as the signal ground reference for the cathode output so the anode output will have more noise than the cathode. Thus, unlike the LTP phase splitter, supply rail noise gets fed through to the output stage as a differential mode signal.Cpaul said:
To calculate the frequency response I would calculate stage gain to both outputs as a function of frequency with Za at the anode and Zk at the cathode. Then set Za=Zk=R||C to get the final result. Having got the result, people can then argue (if they wish) about 'output impedances'.
SpreadSpectrum, I woke at 4 in the morning to realize that my analysis was not quite right. In the case of the pentode gain stage, a load between the cathode and the supply will make matters worse. The only solution in that case (and it is a poor one) is to add a signal from the supply to the pentode grid. But the amount added will generally interact with the impedance of the circuit driving the pentode grid. Not a good plan overall.