The Schroedinger picture and Heisenberg picture are different formulations, not different models. The two are mathematically equivalent. Similarly, some problems are easier to solve in the time domain while others are in the frequency domain. You can freely move between the different representations confident that the underlying mathematics are exactly equivalent.
But our models are prima facie mathematically inequivalent. For example, in your model, the open-circuit output impedances are equal while in mine, they aren't. This fact is evident by inspection, no fancy algebra required. Since the open-circuit output impedances cannot be equal and not equal at the same time and in the same respect, our models are inequivalent. Both cannot be correct.
Newton vs. Einstein ? Boundary conditions determine if both work, or if only one of them will work.
And indeed, when the same initial conditions (equal loads) are used, the network model and the two-Thevenin-source model give the same answer.
I'd slightly disagree- Einstein's model is more exact and correct, but far more complex than one needs for solving baseball dynamics.
Newtonian mechanics gives approximately correct results for a wide variety of initial conditions. It is, to make an analogy with AC analysis, the "small-signal" approximation of the full relativistic dynamics.
Your model, on the other hand, agrees with experiment in only one exceptional, idealized case. And its agreement with experiment is coincidental, i.e., the result is correct but for the wrong reason.
If Newtonian mechanics were like your model, it would predict the baseball's dynamics for only one particular set of initial conditions and no other. Sure, as long as the particular initial conditions are met, such a model would predict the correct dynamics.
Imagine someone came up with an equation for kinetic energy that is correct at only one speed. He then makes the claim that, as long as his "boundary conditions" hold, i.e., as long as the baseball's speed is that speed and no other, his equation gives the correct answer for the kinetic energy. And then he further claims that no experimental result that respects his "boundary conditions" has come forth falsifying his equation.
Imagine that when it is pointed out that another equation exists that gives the correct KE at that speed as well as all others, he claims that the more correct, more complex equation is needlessly so and that his equation is simpler and more convenient for the "boundary conditions". He points out that he's only concerned with the energy at that speed and no other so it's irrelevant if his equation doesn't work for other speeds.
Imagine that, despite your sincere attempts to reason with this person, his response is to repeatedly challenge you to show that the kinetic energy, at that speed, is different from what his equation "predicts".
Your model, on the other hand, agrees with experiment in only one exceptional, idealized case. And its agreement with experiment is coincidental, i.e., the result is correct but for the wrong reason.
If Newtonian mechanics were like your model, it would predict the baseball's dynamics for only one particular set of initial conditions and no other. Sure, as long as the particular initial conditions are met, such a model would predict the correct dynamics.
Imagine someone came up with an equation for kinetic energy that is correct at only one speed. He then makes the claim that, as long as his "boundary conditions" hold, i.e., as long as the baseball's speed is that speed and no other, his equation gives the correct answer for the kinetic energy. And then he further claims that no experimental result that respects his "boundary conditions" has come forth falsifying his equation.
Imagine that when it is pointed out that another equation exists that gives the correct KE at that speed as well as all others, he claims that the more correct, more complex equation is needlessly so and that his equation is simpler and more convenient for the "boundary conditions". He points out that he's only concerned with the energy at that speed and no other so it's irrelevant if his equation doesn't work for other speeds.
Imagine that, despite your sincere attempts to reason with this person, his response is to repeatedly challenge you to show that the kinetic energy, at that speed, is different from what his equation "predicts".
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One case, yes, that's what we mean by "boundary conditions." Exceptional, no. Cathodynes are almost universally used to drive matched loads. My "one case" covers 99% of applications. Given that context, I don't get your analogy at all- it doesn't matter what the tube is, what the signals are, what the loads are, as long as the loads are matched, the model works.
A better analogy is that the Baseball Equation works for all speeds, all spins, all directions, all temperatures, all wind directions. It's just restricted to round balls. In that case, given the universal applicability for the intended purpose, one might think that there's some real physical meaning behind it and, since it is universally predictive with no exceptions being brought forth, one might wonder at it being dismissed as "incorrect." 😀
edit: tightened analogy
edit: tightened analogy
But the loads aren't matched when grid current is drawn. What then? We shouldn't ignore that important 1%.
Indeed, and no one uses an unbuffered cathodyne to drive big class B triodes. Source Z is the least of your problems there, swing is. Cathodynes have restricted swing. And the baseball equation doesn't work for Frisbees, but does quite well for soccer, tennis, lacrosse, basketball, racquetball, handball, stickball...
No one? So because you say no one does, you are justified in ignoring the situation?
And pentodes don't draw grid current?
And pentodes don't draw grid current?
Chris, I suspect SY is getting quite a kick out of all this attention and I suspect the rest of the forum has lost interest. I'm calling it a night on this one.
Cheers y'all!
Cheers y'all!
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I'm not sure I'd put it quite that way, Alfred. But everyone else has gotten awful quiet! Have a good night's rest for a good day's work!
Not particularly. But it's important for amp designers to know how to use simple circuit elements and to avoid the mistakes of others when they hear about high plate impedances from cathodynes.
In fact of reality, it's important for them to recognize that, when taking the output differentially AKA the "boundary conditions", they should use the differential output impedance, not the single-ended output impedances.
It would be, what did you call it, disastrous to do otherwise.
And, with that; good night SY, Chris, Dave and whoever else may be lurking.
It's been fun. Thanks!