Because if the effect of output impedance is the frequency response, then we already have that measured. Output Z from the filter is minimal at 1kHz, while at 20kHz it is high enough to cause the FR to dip a bit. Or even ring.
"This begs the question of why this filter has customarily been used if it isn't needed."
- Because it is customarily been needed. It still is needed today. Filterless class D have their own set of limitation, like generally not allowed to have long cables / being limited to the same enclosure as the driver.
Or maybe we think of it another way. The class D amp itself, without the filter, creates a ton of extra frequencies. We don't want that. Hence we add the filter, which has high impedance (seen from amplifier direction), to alter the frequency response to -9999dB. But at the same time a properly designed filter will also have 0dB insertion loss in the passband.
I appreciate your willingness to participate, but I'm afraid that you only managed to obfuscate some of the questions, including the main question. The main question is why it would not be important to measure and report the output impedance of low-cost class D amplifiers. I think you said that it doesn't need to be measured because it is always lower than it needs to be. Perhaps you were thinking only in terms of the affect on power available to the speaker. I'm not quite convinced that even in this respect we do not need to be concerned with the output impedance of low cost class D amplifiers. My casual observations have been that many of the low cost class D amps have output impedance on the order of 1 to 10 Ohms. But this particular concern, i.e., the power available to the speaker, is not the primary reason that the output impedance of a low cost class D amplifier is an important consideration.
The more important concern is with the affect on the frequency response of the speaker driven by the amplifier. With respect to frequency response, you wrote, "... we already have that measured." Yes, the frequency response of the amplifier itself has been measured, but it is almost silly to bother to do this with some of the low cost class D amplifiers. The reason is that the frequency response of the amplifier itself does not tell the whole story of how the frequency response of the speaker will be affected by the high output impedance of the amplifier. This has been discussed and explained numerous times in numerous places, but it is apparent that people who understand this do not make up the majority.
Together with the speaker impedance, the output impedance of the amplifier forms a voltage dividing network, i.e., two impedances in series. The distribution of the voltage between these two impedances follows the ratio of the two impedances. For example, in the case of two simple resistors in series and with the two resistance values in the ratio 2:1, 2/3 of the voltage will appear across the greater resistance and 1/3 of the voltage will appear across the lesser resistance. Even in the case of a hypothetical speaker that has constant impedance (with respect to frequency), the speaker's share of the voltage would decline steadily with increasing frequency, because the impedance of the low-pass filter will increase steadily with increasing frequency. But of course real speakers aren't like this. With any real speaker, the impedance will exhibit a pronounced peak at the driver resonance. If it is a ported speaker, there will be another impedance peak at the port tuning frequency. And driver impedance generally increases with increasing frequency once the frequency is high enough such that the reactance of the voice coil becomes significant in comparison the to the coil's DC resistance. If you consider just the impedance peak at the driver resonance (this frequency is altered by the enclosure, i.e., it is higher than the driver's Fs), it is apparent that the driver's share of the voltage will be significantly greater at this frequency compared to other frequencies. With many low cost class D amplifiers, the net effect is a conspicuous peak in the response in the upper bass, just barely low enough in frequency to be considered bass as opposed to lower midrange.
With the more conventional class A and class AB amplifiers, this is never a practical concern because of the very low output impedance; essentially all of the voltage appears across the speaker notwithstanding the frequency-dependent variation in the speaker's impedance. The variation in the speaker's impedance, when the speaker's impedance is taken as a percentage of the combined series impedance of the speaker and the amplifier's output impedance, is insignificant. The same is true for high quality, high cost class D amplifiers. The NCORE amplifiers from Hypex have output impedance less than .003 Ohm. And they are complete amplifiers (except for needing DC supply), in contrast with the class D chip amplifiers, which obviously do not have the low pass filter to remove the ultrasonic frequencies unless and until it is added by the manufacturer of the complete amplifier. The completed amplifiers that you can buy, which are based on any of the popular class D chips from TI and others, each have their own individual implementation of the low-pass filter that filters out the ultrasonics. My expectation is that this is an important basis by which these low cost class D amplifiers are distinguished from one another.
