Until a
circuit diagram, of the Axign Class-D Audio Amplifier PWM Controller Demonstration Board, can be located/posted, to discuss....
A suggestion, for discussion....
Gm Metric (Geddes and Lee Metric)…. Article/Paper No1, Auditory Perception of Nonlinear Distortion - Theory
Gm Metric (Geddes and Lee Metric)/Article/Paper No1.pdf
Historically…. distortion has been measured using specific signals sent through a system and quantified by the degree to which the signal is modified by the system. The human hearing system has not been taken into account in these metrics. Combining nonlinear systems theory with the theory of hearing, a new paradigm for quantifying
distortion is proposed.
Audio has viewed distortion metrics in the context of the nonlinear systems response to a sinusoid or sometimes, two or more sinusoids - basically a signal based metric. The current metrics that are used for distortion are THD, IM/IMD, Multi-tone inter-modulation, etc, which are all usually expressed as a percentage or number (the ratio of the distortion by-products to the total system output. In an absolute sense this view of distortion is satisfactory. If our goal were to eliminate all distortion then clearly any measure of its level is adequate. It is neither reasonable nor desirable to set as our goal the complete elimination of all distortion. From a cost effective standpoint, reducing distortion below perceivable levels is a complete waste of time and money. It may also be that we might want a scale by which to compare two levels of distortion in order to make tradeoff decisions. In this context, we will show that the signal-based metrics fall far short of the mark, for they fail to correlate with, or even consider, subjective impression. Therefore, it seems intuitively obvious to question the belief that a distortion measurement which is based purely on the mathematical difference between specific input and output waveforms, without any regard for the human hearing system, would yield a reliable metric? We think not!, but the need for a reliable distortion metric is obvious!
To be useful the metric must be consistent and reliable. The same number must mean the same thing in every context and there must be a close correlation between the metric and the response that it is intended to scale which is where the signal-based distortion metrics fail. For example, 01% THD of one type of nonlinear system can be perceived as unacceptable, while 10% THD in another type of nonlinear system is perceived as inaudible. Even one of these simple examples is sufficient to invalidate THD as a viable/relyable metric for discussion of the perception of distortion. Furthermore, 1% THD is not at all the same as 1% IM, but this article we will show that neither correlates with subjective perception, thus falling short of what of what is necessary/required.
Hearing Mechanism/Ears…. is not linear and taken as a System is also quite complex. The attribute of hearing that will overwhelmingly dominate the perception of distortion is masking. Masking is also the principal effect used in the creation of all modern techniques of perceptual coders (MP3, AAC, etc.). Masking has no analog in linear systems theory, and it is not very intuitive since it does not occur in systems other than the ear. Masking is predominately upward toward higher frequencies although masking does occur in both directions. The masking effect increases, masking occurs further away from the masker, at a substantial rate with excitation level.
- The masking effect of the human ear will tend to make higher order nonlinearitys more audible than lower order ones.
- Nonlinear by-products that increase with level can be completely masked if the order of the nonlinearity is low.
- Nonlinearitys that occur at low signal levels will be more audible than those that occur at higher signal levels.
Metric…. is a value (or it could be a function or multi-valued but a single value is usually desirable) which is given as an attribute of a relationship to indicate its scaling in some predefined context. For instance, temperature can be a metric in the context of human perception heat content. We can describe the perception of temperature in words like hot, warm, cool, or cold and since temperature also has an exact scientific scaling (conveniently), it is a simple matter to map from the subjective metric to the physical one. We must always remember however, that the subjective terms are relative and a precise mapping is often difficult to obtain. Whenever human perception is involved, metrics can only ever be statistically relevant.
Background…. a system that does not pass a signal through to its output that is indistinguishable from the input signal is said to distort it. Some signal modifications are desirable, like equalization and frequency response changes to improve the sound quality, but some Distortion is undesirable, like most Speaker resonances or the Nonlinear distortion of a signal. A system is said to be nonlinear if its input and output are not linearly related in a mathematical sense. Such systems do not obey the principle of superposition and can have frequency responses that are signal dependent. In fact, even the concept of frequency response is a linear one and its application to a nonlinear system must be done with care.
A single tone input to such a system does not produce a single tone at its output, but a multiplicity of tones. Nonlinear systems cannot be analysed with classical linear systems theory and as such they pose a significant impediment to systems analysis. Even though, in a good audio system linearity is usually one of the design goals, there are very real situations where one might want the system to be nonlinear, but and nonetheless, the Intent/Desire of Focus/Application is and will be, restricted to those systems where linearity and low distortion is a goal/focus, noteing that there are a multitude of mechanisms that can create distortion.
Consider, for consideration, in the Digital domain, the received Digital Signal could simply be made larger (via digital DSP and/or equivalent) then transcoded/transmuted/translated (digitally enlarged) then passed/delivered to a nonAmplifying/Unity Gain Analogue Power/Buffer (for PWM, carrier removed then passed/delivered directly to the output Power/Buffer section) which passes/delivers it to the Speakers (with very, very low output impedance). This is essentially being done/attempted/performed via the AX5689 chip but with PWM amplifycation, (still) very Novel.
Gm Metric…. the article proposes a metric that is based on the shape of the nonlinearity curve that has the following features….
- It should be more sensitive to higher order nonlinearitys than lower order ones. To meet this objective they propose useing the second derivative of the nonlinear transfer function since this function increases in value according to the square of the order. To alleviate a sign problem with this value we propose squaring this term. This function also addresses the third requirement above.
- It should be weighted towards greater values for nonlinearitys at lower signal levels. To meet this requirement they propose using a cosine-squared function which is unity for small values of the signal and zero for the largest ones.
- It must be immune to changes in offset and gain (first order slope) since these are inaudible effects. To meet this requirement they propose integrating this function to yield a single number which will be call Gm (Geddes/Lee metric), a proposed metric for distortion which is based in the general theory of nonlinear systems and takes into account the characteristics of human hearing.
- Pg6/7, this exact equation represents the central hypothesis. It is important to note that Eq.(5) is actually a property of the system, not of a signal sent through the system. It is completely independent of the actual input signal sent through the subject system and is thus valid for any signal. They suggest the Equation is to be applied, in the form shown, requires a knowledge of the shape of the nonlinear transfer function T(x), as defined in Eq.(1). As shown it is basically a frequency independent measure. There is no ambiguity in performing the calculations at a particular frequency, but in a real system T(x) can be a frequency dependent, i.e. T(x, f), in which case G m(f) will also be frequency dependent. Firstly it is a new approach to evaluating a nonlinear system, formulated to be consistent with the psychoacoustic criteria that the classical measures do not account for. Secondly the article shows the results of clinical tests which use each of these metrics on simulated nonlinear systems.
This is Geddes and Lee Article/Paper No1 and Article/Paper No2 shows the relationship of the signal based metrics to subjective impression is virtually nonexistent. It is our hope that the audio community will give the outdated notion of THD, IM/IMD, signal types, etc. (signal-based concepts) as these are all just symptoms of the real problem – nonlinearity.
. NAD only started using MOSFETS in amps more than a decade later.
