The First Picowatt

The first femptowatt is even more important,...,


Why?


System theory defines a linear system as any system with the property:
For any x with System(x) output,
For any y wity System(y) output
x+y has an output of System(x+y)=System(x)+System(y)
ie the response to the sum of input signals is equal to the sum of the responses of each signal fed individually. Principle of superposition.


So the response to any signal can be predicted by Fourier transforming the input signal to its infinite components, find the response of each component, adding the responses...


It follows that the non distorting system with be the one that has flat frequency response. In the case of music production, flat frequency response from producer's brain to listener's brain. (Expanding from the [Lowe, Morgan] paper.)


It can be proved mathematically that linear systems have also the property that no matter how small the signal above superposition relation holds.


Nothing in nature is linear but it can be approximately linear if excusions around an operating point are small enough. For example walking around a point on our elliptical shaped earth. At small walks surface is flat.


Similarly to class A amplifiers (electrons flowing all the time). The transfer curve is bent at extremes but near the 0 operating point the curve is linear. (See also [Hamm]. In fact the smaller the excursions or closer to the operating point the more linear it is. In fact as signal tends to 0 the limit of distortion is 0. Distortion tends to 0 too. So the system can be assumed to be linear on analogue systems.


Class A operation means electrons flowing all the time. Riding on the signal is analogous to seagulls flying over the flow of a river and modulating their velocity so that some times they run faster or slower than the flow. Or seagulls riding on the stream of air. This is what electrons do in a class A amplifier while the music signal (electrons dancing to the music signal) simultaneously ride on the steady DC quiescent electron flow. More on class A amplifiers [Gray].


On digital systems distortion on the other hand tests to infinity as the signal tends to 0. So they are not linear. [Tsakiris] Therfore the superposition principle does not hold. Therefore even if the bandwidth were infinite still a trumpet would not sound like a trumpet.


One of the problems (or perhaps reliefs for a marketing department) in sound reproduction is that most listeners do not have a live reference [BBC]. Anyone in their right mind who have pressed gently the real key of a piano may then find the reproduction of a piano from a digital chain sounding like a joke.


Where has this led to?


Possibly to music, almost free like tap water [Eno], but not sounding like music.


References:


Engineer Circuit Analysis - Hayt, Jr., Kemmerly - McGraw Hill


Tubes vs Transistors (vs op amps), Is there an audible difference? - Russel O. Hamm - JAES


Applied Electronics - Gray - MIT


Design and Investigation of a Triode Single Ended Audio Frequency Amplifier with no Negative Feedback - Y. N. Tsakiris - final year BEng thesis project - Department Of Engineering - Engineering Electronics - University of Warwick - 1993


Acoustics in the BBC - Research Department - report No B-068 (1958/29) - Loudspeakers - page 22


Dick Flash interview - Brian Eno - YouTube


Further reading : Linear Systems Analysis etc