Allen,
What will be your (real-world) source for that circuit?? Something with 1 milliohm output resistance?? 🙂
Dave.
Lol, you mean the circuit I posted. Never mind the numbers it was just easier than rigging an *.frd file for a speaker that measures 50k 😉
Well, what circuit did you think I was referring to???
Why did you post it if all the numbers are meaningless???
That's esoteric all right. 🙂
Dave.
Why did you post it if all the numbers are meaningless???
That's esoteric all right. 🙂
Dave.
Well, I guess someone must be the first to use low DF triode amps to drive the speakers and a Krell clone to drive the crossover... 😎
Sorry, I thought you were joking.
It is the topology that matters. They are equivalent to Zout=6ohms, Rseries1=600ohms, Rseries2=6kohms, RL=50kohms
So far I've only found the result of my calculations, rather than the calculations themselves. This circuit was for someone who wanted to mix a headphone signal to mono and to have an approximately second-order Linkwitz-Riley crossover while only using resistors and capacitors.
See also https://www.diyaudio.com/community/...db-line-level-calculation.320216/post-5375368
See also https://www.diyaudio.com/community/...db-line-level-calculation.320216/post-5375368
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I found the actual calculation in the attic.
What it boils down to, is that when you cascade two first-order RC low-pass filters with equal time constants, the first with a resistance R1 and the second with a resistance R2, you get a second-order roll-off with a quality factor
Q = 1/(2 + R1/R2)
while ideally, you would need Q = 1/2 for a Linkwitz-Riley filter.
For a given ratio R1/R2, you can improve the quality factor a little bit by making
R1C1 = sqrt(1 + R1/R2) * (1/(2 pi fc))
R2C2 = (1/sqrt(1 + R1/R2)) * (1/(2 pi fc))
where fc is the cross-over frequency. The same holds for the high pass.
The resulting Q is
Q = 1/(2 sqrt(1 + R1/R2))
which is only marginally better than the value with equal time constants when R1 << R2.
I intended to also look at the flatness of the sum of the high-pass and low-pass output signals when you allow unequal values of fc, but didn't manage to get a result out of that.
What it boils down to, is that when you cascade two first-order RC low-pass filters with equal time constants, the first with a resistance R1 and the second with a resistance R2, you get a second-order roll-off with a quality factor
Q = 1/(2 + R1/R2)
while ideally, you would need Q = 1/2 for a Linkwitz-Riley filter.
For a given ratio R1/R2, you can improve the quality factor a little bit by making
R1C1 = sqrt(1 + R1/R2) * (1/(2 pi fc))
R2C2 = (1/sqrt(1 + R1/R2)) * (1/(2 pi fc))
where fc is the cross-over frequency. The same holds for the high pass.
The resulting Q is
Q = 1/(2 sqrt(1 + R1/R2))
which is only marginally better than the value with equal time constants when R1 << R2.
I intended to also look at the flatness of the sum of the high-pass and low-pass output signals when you allow unequal values of fc, but didn't manage to get a result out of that.