JohnRoberts said:
Balijon said:
Could we agree that, if there are time delay and/or phase effects in a circuit, it will not null to silence when subtracting original source signal?
Theo
Of course... That's why we always need to review the null product and not read too much into errors associated with HP and LP skirts. The errors and failure to null that I predict are not at frequency extremes but in band and specifically at the crossover transition frequency.
JR
I have attached an article on active crossover designs and their crossover behavior in summing and phase / time delay behavior.
The most clean solution is a Linkwitz-Riley crossover design:
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1. In-phase outputs (0° between outputs) at all frequencies (not just at the crossover frequency as popularly believed by some).
2. Constant voltage (the outputs sum to unity at all frequencies).
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however:
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A Linkwitz-Riley crossover alignment is not linear phase: meaning that the amount of phase shift is a function of frequency. Or, put into time domain terms, the amount of time delay through the filter is not constant for all frequencies, which means that some frequencies are delayed more than others. (In technical terms, the network has a frequency-dependent group delay, but with a gradually changing characteristic.)
Is this a problem? Specifically, is this an audible “problem?” In a word, no.
Much research has been done on this question with approximately the same conclusions: given a slowly changing non-linear phase system, the audible results are so minimal as to be nonexistent.
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Transient response:
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We also refer to the step response as the transient response of the circuit. The transient response of the summed out- puts is perfect since their sum is perfectly equal to one.
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Where the Linkwitz-Riley result in power-drop of -3db at the crossover frequency in a loudspeaker system, they sum on a line-level perfectly as they are constant voltage.
Due to the non-constant input / output phase behavior, summing with subtracting the original source signal will never null completely to silence. (also relevant and more dominant for Butterworth based filters).
Theo