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In Reply to: There's gotta be a bug somewhere posted by Ralph on January 19, 2015 at 10:05:05:
"Did you read the article at the link? There is a reason why someone would want to design an amplifier that has a higher output impedance like this- oddly, its because you can get less coloration- quite the opposite of the 'accepted wisdom'. This is because of how the human brain processes sound, which ultimately is the final arbiter."Yes, I read the article you linked. It seems to me there are several distinct questions here. Some of them, such as the voltage paradigm vs the power paradigm, can be discussed even within the conventional model of an amplifier output stage as a perfect voltage source in series with an internal impedance R.
What is certainly true is that if the output impedance R is tiny, such as with a typical solid state amplifier, then for a given signal level the power delivered into a typical loudspeaker load impedance Z falls approximately inversely with Z. On the other hand, if the output impedance R is comparable with the typical loudspeaker impedance Z, then one is "sitting on the top of the curve" in the plot of power dissipated into the load as a function of Z. Thus, to a good approximation, moderate variations in Z around the value Z=R will then not cause the power into the load to change by too much. This is illustrated in the first plot here, of power into the load Z, as a function of Z, for the case of output impedance R=8 Ohms. (x-axis is Z, y-axis is power into load Z.)
By contrast, in the case of a very low output impedance amplifier, the power into Z=16 Ohms would be one quarter of the power into Z=4 Ohms, as can be seen in this second plot (normalised to the same power at Z=8 ohms):
In other words, you don't need to invoke any non-standard definition of "output impedance" in order to make your point about the power paradigm vs the voltage paradigm. It is already visible, just with the usual definition, and the usual model of an output device. If the output impedance is tiny, then for a load impedance Z in the range between 4 and 16 ohms, the power lies in a large range, with Pmin being 25% of Pmax. On the other hand, if the output impedance is 8 ohms then for the same range of load impedances the power lies in a relatively small range, with Pmin almost 89% of Pmax.
Another rather different question is whether the usual model of an amplifier output stage as a perfect voltage source in series with an internal resistance R is a good one or not. I tried various experiments in the past with my OTL amplifiers, and it seemed to me that the model worked reasonably well. Now, in all of my amplifiers there is quite a lot of negative feedback. I am interested now to experiment a bit more, in particular with how well the idealised model works if I turn off the negative feedback. I suppose my expectation would be that the model would still be reasonable, but now the value of R would be a lot larger. But I will keep an open mind until I have done the experiments.
Concerning the non-achievability of the "perfect" zero impedance voltage source, yes, of course I agree with you it cannot literally be realised in practice. But that doesn't mean it isn't a useful concept in circuit analysis. As long as its "actual" output impedance is very small compared to that of the internal resistance R that one adds in the model of the output stage, then the imperfection of the "perfect" source is insignificant. I still feel that if a definition of "output impedance" gives a radically wrong answer when tested on the conventional model of an output device, then there is reason to question the validity of that definition. But then, as I said above, I don't think you even need your non-standard definition of output impedance in order to make your point about the power vs voltage paradigms.
Anyway, I shall try to carry out some further experiments soon.
Chris
Edits: 01/21/15 01/21/15 01/21/15 01/21/15 01/21/15
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Follow Ups
- RE: There's gotta be a bug somewhere - cpotl 05:33:40 01/21/15 (1)
- Sounds/looks like we are on the same page here - Ralph 08:28:21 01/21/15 (0)
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