Harmonic roll-off rates for assessing crossover distortion
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the same applies as above but this time at 100Hz.
For both frequencies the NS harmonic roll off rate looks to be around 65 or so dB per decade.
Is there some analytical approach or method of inspection which can be used on closed loop results to derive a simple first order figure of merit?
Thanks ian
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Unfortunately, my Linear Audio article in
Vol.4 on harmonic weighting is behind a paywall, but I briefly cover it's application in my free
Supplement on p17, mentioned in Post 10. The key point:
Why is the harmonic roll-off rate an important parameter? Our hearing sensitivity curves roll-up at
approximately +40 to+50dB/dec in the 1kHz to 3kHz range when multiple tones do not cause
masking. This means we want any harmonics from crossover distortion to roll-off faster than
-50dB/decade so harmonic distortion from crossover distortion cannot be heard.
Standard Class-B amplifiers have difficulty reducing the level of the higher order harmonics from crossover distortion due to:
1) Our ear boosts the higher order harmonics at about the same rate as they reduce so all are nearly equally apparent, and
2) The negative feedback factor of most Class-B power amplifiers rolls-off at 20dB/decade in the same frequency range where our ear boosts the higher order harmonics and this makes it hard to suppress crossover distortion and make it inaudible...
After writing my Vol.4 article I realised that the rate of roll-off of harmonics in -
xdB/decade is an easier way when doing simulations to assess whether high order harmonics like from crossover distortion than adding a special weighting filter. You can do it by placing a ruler on the FFT plot and slide the ruler to say 0dB and start of a decade and read off the dB drop at the next decade. Easy as.
If you read anything less than -50dB/decade then crossover distortion will most likely be the dominant distortion in the sound of the amp -- then you need to check if the weighted THD is below about 1%, eg by using the double differentiator I used in Post 10 and RMS add all harmonics to the 100th with a 100Hz fundamental; the ErrorLog THD using ".four {freq} 100 V(D2) ". You probably want a 20dB safetey margin, that's a target of ~0.1% for D2 100 harmonics with 100Hz to be safe enough to say any HD will be inaudible at this power level. Note a double differentiator is +40dB/decade not the +50dB/decade of our hearing so it under estimates what we can hear, but this is partly offset by taking harmonics to 10kHz (rather than 3kHz where our hearing sensitivity to falls).
Effectively the double differentiator magnifies all the higher harmonics so they can appear on a FFT plot of V(D2) at the same
relative audibility as the lower order harmonics. And when D2 is displayed on an o'scope IF you can see any harmonic distortion then it's most likely you can hear it as well from your amp.
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The two plots you gave with 100Hz, the first with NS and about -60dB/decade harmonic roll-off is very good. Also the first low order harmonics are -120dB below fundamental, so low that they would be hard to measure let alone hear.
The second without NS has about -30dB/decade, but with the first low order harmonics at -120dB below fundamental you have a safety margin of +80dB (below 1% needed for audibility). So even if you weighted the higher harmonics they are unlikely to get to -40dB to become audible (at least at the output level used here).
You can conclude that 1) NS does in fact reduce high order distortion, and 2) that the distortion even without the NS is not likely to be audible.
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Regarding the Blomley approach, which uses 1) current drive of the splitters, and 2) non-switching in the power stage. The use of current drive of the splitters increases the amount of high order distortion compared to ordinary voltage drive splitting. Current drive of the splitters causes a faster transition through the zero-cross and a doubling of the rate when weighted with say +40dB/decade (double differentiator) gives 4 times the level of higher harmonics, that's a net increase of +20dB/decade. So unless current drive of the splitters can reduce the level of higher harmonics by -20dB/decade at the same time then you are not getting ahead by using current drive of the splitters.
An exception might be in the extreme case where the switching rate at the zero crossing is so fast that the majority of the higher harmonics are pushed above 20kHz where they don't affect the audible range (assuming there's not much other nonlinearites to created demodulation into the audio band by intermodulation). Antoinel's Class-aP (Post 5) would seem to fit into this category if the switching rate is fast enough. I'd be interested to see FFT plots and some D2 values for any of Antoinel's Class-aP amps.
Cheers