Some friends have pointed out to me that some aspects of my
previous post are described too “hermetically”.
One of the aspects on which I struggled the most in providing explanations is that relating to the sentence where I affirm that "the amount of distortion digitally injected is that actually audible only at a certain level of listening", set as a parameter in the model. Therefore, even the listening tests are only valid for this listening level.
To better explain this point, it is necessary to spend few words on how a preamp, or the preamplication section of an integrated amplifier, "arrives" at the output signal with the desired level, based on the volume control.
In short, the amount of the amplification of the input signal applied by the preamp stage is always the same: it is the one reported in the technical characteristics under the item Gain (G below). For a preamp it is typically between 10dB and 20dB. For example, if we have a sinusoidal signal with a peak-to-peak voltage value V
in = 1V in input to an amplifier with G = 20dB, we will have at output the same sinusoid with V
out = 10V. Since this value determines also the listening level, it must be controlled by the user. This naturally happens with the volume knob, which attenuates the signal. Based on the point of the preamp circuit where this attenuation is performed we can distinguish two design approaches:
1. Attenuation is performed on the input signal and then amplified.
2. The input signal is first amplified and then attenuated at the output.
In my previous sentence I was implicitly referring to the first approach, which is by far the most used. Let's briefly see both below, in relation to the static nonlinear distortion model described previously. In the following, please remember that the
masking effect of our ear:
- It is higher for frequencies close to the fundamental; in particular it is more extended towards frequencies with a higher value than the fundamental.
- It is higher when the level of the fundamental is higher. In other words, at low volumes the masking effect is much more modest, for intensity and extension.
Type 1: Input Attenuation + Amplification
For the first type of preamp the signal management is outlined in the following figure.
Figure 1 - Input attenuation + Amplification
Basically, the input signal
x(
t), which we assume of fixed intensity V
in for simplicity of exposure, is attenuated by a certain amount controlled by the volume knob, before being subjected to the fixed amplification part of G value. The volume control then determines the portion of
f(
x) curve (responsible for the distortion) around the origin that is actually used and therefore the maximum extension to avoid clipping. From the point of view of output distortion this implies that:
- Given that the deviation of the linearity of f(x) increases with the rise of the value of x, then the distortion will also follow the same trend: low (in dB) at low volumes and higher at higher ones. Considering the masking effect of our ear, if the distortion is more concentrated on low orders, this behaviour is a positive aspect.
- If the linearity deviation of f(x) is already present in the neighborhood of 0, such as crossover distortion (actually, unlikely for a preamp stage) then we will have high distortion even at low volumes and, given the harmonics of high order generated for this situation, and listening will likely be unpleasant. As the volume increases, these distortions decreases in dB and the masking effect makes it less perceptible.
For this type of preamp the digital distortion simulation is valid only for a certain volume level. On the simulator it is possible to configure how much of the
f(
x) curve to use, and therefore how much distortion to inject, which cannot then be modified once the distorted digital signal has been generated, as happens by modifying the volume of the real amplifier.
What has been described can also be applied to power amplifiers, as the gain G is fixed: it is the preamp that determines the part of
f(
x) that is used via V
in.
Type 2: Amplification + Output Attenuation
For the second type, used less frequently, the signal management is outlined in the following figure.
Figure 2 - Amplification + output attenuation
Here the input signal
x(
t) is amplified first and then attenuated before the output to the desired level. In this case, a much wider part of the curve than the previous type is used. The amount (in dB) of the output distortion is practically independent of the set volume. In theory, amplifiers with crossover distortion could benefit from this design, since this is then attenuated at the output and can first be “covered up” by distortions due to the more distant parts of the curve.
For this type of preamp the digital simulation of distortions is correct for any volume level, since the amount of curve
f(
x) to be used in the simulation is always the same, like for the real amplifier, regardless of the volume.
Final remarks
To understand which of the two types of situations we are in, it is necessary to measure harmonic distortion for different volume settings. Assuming crossover distortion is absent, if the distortions (in dB) are practically independent of the volume then we have the second type; if the dB values increase as the volume increases, we have the first type. What about the differences in sound? In my limited experience, changing the position of the potentiometer, at input or output, on the same preamps in class A you have a greater characterization (in terms of warm or dynamic contrast) of the sound in the second case; in the first you have a feeling of greater neutrality.