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Well, from my old days (no you can ask but no you won't get an answer to that) the SINAD - in order to work, needed no power, its power was from the amplifiers ability to develop power into a load (the resistors) so it can determine the amps ability to remain faithful (Fidelity) to the original signal. I'm wondering about your amplifier for the VU meter - unless the VU meter is a specific application. Like perhaps a Galvanometer. Otherwise - many of them that we used were small signal - 600 ohmic d'Arsonval movements measuring mA on down to uA for the purposes of simple distortion that we may not hear due to our sensory overload the brain simply interprets it as something else.
I remember reading tons of articles in mags, like Radio Electronics, Popular Electronics and Stereo Review - about the SINAD functions in a test bench. At least I had to, being in such a competitive market - you had to know and sometimes re-create some of the test conditions they showed in their articles - for one of them was to question a validity of a test was to show if it can be duplicated.
So I am surprised that you have to amplify a signal to obtain distortion - when the amp you use for the signal gain, can introduce such artifacts on it's own. How do you protect it from itselt?
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