Merlin: Since each of the Thevenin sources in series with their equivalent impedance gets referenced to the same ground, then the differential source impedance is twice 2/gm (in the low rp, high gm limit). Since you're driving a push pull amplifier, the poles are at the single (plate or cathode) source impedance times the single sided input capacitance, or the differential source impedance times half (series) the input capacitance. If a builder thinks that he'll get two different poles from the two different sides, which many do, disaster awaits.
Exactly. Phase splitter black box containing two Thevenin sources with identical (and low) source impedances driving identical loads.
DF96 wrote (#140): "I think the issue is that the doubters keep trying to sneak in unbalance by some means or other. As I said right back at the beginning, if you take the ports one at a time you get different impedances. How can you get two different impedance measurements/calculations at the same port? Easy: by changing the impedance at the other port you have changed the circuit you are measuring/calculating at this port, so it is not the same port at all!"
By exciting with a current source, infinitesimally if you like so any current-varying impedance remains constant, one is not changing the impedance at that port.
I reiterate: no one disagrees about how the Cathodyne preserves equality of output voltage magnitudes with equality of resistive loading. That's what makes it so effective in the typical applications. I used a sand-state complementary-pair-based version as a "phase splitter" in a product that needed, early in the signal chain, two identical magnitude opposite-polarity signals. And of course I had to assure that the variable loading of the passive networks that followed were the same for each output. It was effective, cheap, low noise, and one of the first powered speakers that was utterly immune to cellphone radiation without additional RF filtering/shielding. It shipped in the millions of units. The approach, for transitioning between simulated surround and stereo, was even patented.
It would seem that most of the disputations here are semantic, but they are no less important. We might wish to define a new sort of "impedance" for a machine with two complementary outputs that, part and parcel, require equal passive loading for such impedances, to be defined. We could call them the sY impedances.
What about a circuit on which we can both agree, where the outputs measured separately, or together, are exactly the same? Well, it's easy to conjure such: I propose the Yoyodyne. It consists of an ideal transconductance: differential voltage input, current generator output. Each output leg of the current generator is terminated in a resistor, and the resistors are of equal value, R, with their free ends grounded.
The output impedance at each resistor-generator junction is R, whether measured together or separately. What's not to like? We can use the circuit as a differential line driver and our differential line receiver can have perfect common-mode rejection. We can drive grids or whatever, even into forward conduction, and the horrendous distortion with a push-pull output stage will at least be odd-order.
Or even another take on such an approach, perhaps easier to realize but fraught with performance compromises: The Optodyne, where a photoconductor is used as a variable resistance, in place of the above current generator.
Just a thought. No kits are planned.
By exciting with a current source, infinitesimally if you like so any current-varying impedance remains constant, one is not changing the impedance at that port.
I reiterate: no one disagrees about how the Cathodyne preserves equality of output voltage magnitudes with equality of resistive loading. That's what makes it so effective in the typical applications. I used a sand-state complementary-pair-based version as a "phase splitter" in a product that needed, early in the signal chain, two identical magnitude opposite-polarity signals. And of course I had to assure that the variable loading of the passive networks that followed were the same for each output. It was effective, cheap, low noise, and one of the first powered speakers that was utterly immune to cellphone radiation without additional RF filtering/shielding. It shipped in the millions of units. The approach, for transitioning between simulated surround and stereo, was even patented.
It would seem that most of the disputations here are semantic, but they are no less important. We might wish to define a new sort of "impedance" for a machine with two complementary outputs that, part and parcel, require equal passive loading for such impedances, to be defined. We could call them the sY impedances.
What about a circuit on which we can both agree, where the outputs measured separately, or together, are exactly the same? Well, it's easy to conjure such: I propose the Yoyodyne. It consists of an ideal transconductance: differential voltage input, current generator output. Each output leg of the current generator is terminated in a resistor, and the resistors are of equal value, R, with their free ends grounded.
The output impedance at each resistor-generator junction is R, whether measured together or separately. What's not to like? We can use the circuit as a differential line driver and our differential line receiver can have perfect common-mode rejection. We can drive grids or whatever, even into forward conduction, and the horrendous distortion with a push-pull output stage will at least be odd-order.
Or even another take on such an approach, perhaps easier to realize but fraught with performance compromises: The Optodyne, where a photoconductor is used as a variable resistance, in place of the above current generator.
Just a thought. No kits are planned.
Whilst goofing around with drawing an easier to understand
(not necessarily better performing) version of the feedback
reduction method for equal Z's , I discovered a math error.
The feedback should *NOT* be 1/Mu as I had said earlier.
Looks like Z's are equal when cathode feedback is 2/Mu...
Careful the levels you put into this thing, it has gain!
(not necessarily better performing) version of the feedback
reduction method for equal Z's , I discovered a math error.
The feedback should *NOT* be 1/Mu as I had said earlier.
Looks like Z's are equal when cathode feedback is 2/Mu...
Careful the levels you put into this thing, it has gain!
Attachments
True, but it is only a cathodyne with equal loads. Strictly, you should add an infinitesimal current source to the other output too.bcarso said:
SY, since it's evident that your understanding of Thevenin circuits is at odds with my understanding, and since I'm certain that my understanding lines up with the EE literature on the subject, there is no common ground upon which we can resolve our disagreement.
But to others that haven't yet made up their minds: if SY's equivalent circuit were correct, then it would predict the correct results both when the circuit is driving equal and opposite signal currents into equal loads and when it isn't. But, it can't and it doesn't.
SY and others here, evidently insist on combining Zp with the trans-impedance from cathode to plate and calling that combination Zp. In the standard EE literature, that's not acceptable. Zp, properly understood, cannot be a function of the cathode output current. The dependence of the plate voltage on the cathode output current is represented by a controlled source. Let me say that again for emphasis:
Zp, properly understood, is independent of the AC load attached to the cathode.
The AC voltage at the plate is a result of 3 independent terms: the input voltage, the cathode output current, and the plate output current. The dependence on the input voltage and cathode output current are represented by a controlled source (they must be since the controlling variables are not in the Thevenin plate circuit).
In the special case that the AC plate and cathode output currents are equal, it is possible to "fold" the trans-impedance into Zp in the Thevenin equivalent circuit and get the right answer for the plate voltage. This combination of Zp and the trans-impedance is what SY is measuring, not Zp. It also happens to be equal to the differential output impedance.
It's easy to see how this combination of Zp and the trans-impedance could be misinterpreted and I don't fault anyone for falling into that trap. However, a trap is what it is.
To summarize: the model I've outlined in the hand written notes I attached earlier will give the correct results regardless of whether the loads are balanced or not and further, the Zp and Zk and the trans-impedances remain constant regardless of the loading. In the special case of equal and opposite output currents, my model and SY's give the same results. In all other cases, my model will, SY's will not.
So, it's up to you. Take your pick.
But to others that haven't yet made up their minds: if SY's equivalent circuit were correct, then it would predict the correct results both when the circuit is driving equal and opposite signal currents into equal loads and when it isn't. But, it can't and it doesn't.
SY and others here, evidently insist on combining Zp with the trans-impedance from cathode to plate and calling that combination Zp. In the standard EE literature, that's not acceptable. Zp, properly understood, cannot be a function of the cathode output current. The dependence of the plate voltage on the cathode output current is represented by a controlled source. Let me say that again for emphasis:
Zp, properly understood, is independent of the AC load attached to the cathode.
The AC voltage at the plate is a result of 3 independent terms: the input voltage, the cathode output current, and the plate output current. The dependence on the input voltage and cathode output current are represented by a controlled source (they must be since the controlling variables are not in the Thevenin plate circuit).
In the special case that the AC plate and cathode output currents are equal, it is possible to "fold" the trans-impedance into Zp in the Thevenin equivalent circuit and get the right answer for the plate voltage. This combination of Zp and the trans-impedance is what SY is measuring, not Zp. It also happens to be equal to the differential output impedance.
It's easy to see how this combination of Zp and the trans-impedance could be misinterpreted and I don't fault anyone for falling into that trap. However, a trap is what it is.
To summarize: the model I've outlined in the hand written notes I attached earlier will give the correct results regardless of whether the loads are balanced or not and further, the Zp and Zk and the trans-impedances remain constant regardless of the loading. In the special case of equal and opposite output currents, my model and SY's give the same results. In all other cases, my model will, SY's will not.
So, it's up to you. Take your pick.
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SY
Thanks, I'm slow...
In thinking of the balanced splitter as a floating source and equivalent impedance I had trouble understanding the jump to identical sources and impedances (I could ratio resistive values and sources). It wasn't until I added capacitance that I saw the problem and understood how I violated the balanced condition in my ratio'ing.
edit: Alfred, much appreciation for your clear and explanations and insight. You've certainly helped me at least for now accept this as mostly a semantics issue with a model for an independent "Zp" but maintaining the balancing controlling source.
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No, but that changes the load, violating the basic boundary condition. See my LTE at the Linear Audio site.
edit: I see that Dave made the same point already.
Although truth is not a matter of an opinion poll (though one wouldn't know it to read a lot of exchanges these days), in case it isn't obvious, I'm with Centauri and Paul on this.
Brad Wood
It helps to see the original article where I drew this out explicitly- figures 2 and 3. Sorry all of this is out of context, Chris was apparently unhappy that Jan wouldn't publish any further letters where he showed that violating the boundary conditions of the model causes the model not to work, so decided to take it up here. 😀 Burkhardt Vogel's recently-posted letter goes through all of this in excruciating detail and mathematical rigor, so may be worth a read.
I hope we've all learned something from this - 'd be a shame to have been in vain!
One take-away lesson is that, because differential-mode and common-mode output impedances differ, the addition of a "build-out" or output impedance padding resistor is needed in applications where differential level balance is less important than common-mode source impedance balance. The classic case might be a long-line driver that expects to see a differential input on the far end and significant common mode noise on the way there. This is similar to the "impedance balanced" output stages of prosumer performance and recording gear. Although a pair of buffers would be even better...
Thanks,
Chris
One take-away lesson is that, because differential-mode and common-mode output impedances differ, the addition of a "build-out" or output impedance padding resistor is needed in applications where differential level balance is less important than common-mode source impedance balance. The classic case might be a long-line driver that expects to see a differential input on the far end and significant common mode noise on the way there. This is similar to the "impedance balanced" output stages of prosumer performance and recording gear. Although a pair of buffers would be even better...
Thanks,
Chris
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Indeed, the private comm to which I alluded had the original author saying that, at the least, he would add emitter followers. But again, as you point out, this is important for noise rejection in line driving, not usually for getting a inch or two over to the output tube sockets inside a power amp (although as Chris Paul details, overloading the grids will also invoke mischief).
This brings up a mostly off-topic story, if you will indulge me. Others can stop reading here without fear of missing anything germane. I was called in to see if I could solve a problem of synchronization of bitstreams and "digital" power amps for a 600-channel Huygens-wavefront synthesis sound system. The nice person in charge explained the issues, which amounted to a random delay upon powerup of the Cirrus 8 channel amps another consultant had designed with. The different delay, unnoticeable in an 8 channel home system, utterly demolished the wavefront synthesis. I looked into it and proposed two approaches. The first required a quite elaborate inspection of the outputs and a correction loop in the hybrid-signal domain, to as it were "right" the system upon powerup. The other, which I recommended, was to replace the Cirrus parts with some higher-performance conventional class D amps, prefaced by some good fully deterministic DACs. A look of horror passed over her face when she grasped the implications: ANALOG????? I said, well only for a few inches 😀
FWIW, Marshall Leach developed an ingenious Norton representation looking into the collector/drain of a BJT/FET. It more or less just occurred to me how easy it would to extend his work to vacuum tubes.
I may make that the subject of an entirely new post. It would interesting to see if, using the Norton circuit, any additional insights pop-up re the Cathodyne circuit.
I may make that the subject of an entirely new post. It would interesting to see if, using the Norton circuit, any additional insights pop-up re the Cathodyne circuit.
Cant quite believe that a circuit containing ONLY THREE COMPONENTS should have 277 posts over 28 PAGES and STILL no Agreements!
Sheesh!
Sheesh!
and this is just for the concertina, wonder if and when the issues about long tail pair splitters come up.....