is there a connection between 0.707(critically damped sealed box Qtc) and 0.707 as in (sqroot of 2)/2?
im retarded… But it’s fun 😝
im retarded… But it’s fun 😝
They are the same. (sqroot of 2)/2 is just more accurate though you are never going to get close enough with your box volume to matter.
Have to be dropping grains of sand into that enclosure to get that fourth significant digit right.
Have to be dropping grains of sand into that enclosure to get that fourth significant digit right.
0.707 is not critically damped (0.5 is)
The significance of 0.707 is that it is the half-power point. 0.7V x 0.7A =0.5W
The significance of 0.707 is that it is the half-power point. 0.7V x 0.7A =0.5W
It's indeed not critically damped, but a second-order filter with Q = 0.5 √2 has a maximally flat magnitude response (also known as Butterworth).
That's also how I learned it, and the definition Wikipedia uses https://en.m.wikipedia.org/wiki/Damping
Booger - I see you as a math wiz - isnt it your physics thats failing you this morning 🙂
I suppose it has something to do with basic filter workings... that I dont know by heart...
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I suppose it has something to do with basic filter workings... that I dont know by heart...
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Let's see if I can remember from my first filters class, roughly 45 years ago. This is entirely from memory, so someone correct me if I am wrong. Everything mentioned refers to a 2nd-order lowpass filter:
Q = 0.5 is the highest Q at which both poles are purely real. Any Q > 0.5 produces complex poles.
Any Q <= 0.5 and the impulse response requires infinite time to return to zero.
Q = sqrt(2)/2 is Butterworth response. It is also the response in which the half-power frequency equals the resonant frequency. It is also the highest Q in which the frequency response has no peak, i.e., the frequency response never rises above 1.0 in magnitude.
I have seen both Q = 0.5 and Q = sqrt(2)/2 labeled as "critically damped". I don't remember which is correct.
Q = 0.5 is the highest Q at which both poles are purely real. Any Q > 0.5 produces complex poles.
Any Q <= 0.5 and the impulse response requires infinite time to return to zero.
Q = sqrt(2)/2 is Butterworth response. It is also the response in which the half-power frequency equals the resonant frequency. It is also the highest Q in which the frequency response has no peak, i.e., the frequency response never rises above 1.0 in magnitude.
I have seen both Q = 0.5 and Q = sqrt(2)/2 labeled as "critically damped". I don't remember which is correct.
According to my control systems book, critical damping is defined as "damping ratio = 1.0", where the poles (roots) are repeated and real. This corresponds to Q = 0.5, because 2*(damping ratio) = 1/Q.
The 0,707 is a resonant filter where the resonance still don't produce enough energy to surpass the level of the true passband - it just extends the FR downwards flat for a bit - but its still in resonance.
0,5 is perfection!? 🙂
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0,5 is perfection!? 🙂
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Some might argue that Bessel response [Q = 1/sqrt(3) -- maximally-flat delay] is superior. Depends upon circumstances.
I've seen it, but to me it seemed contrived because the only filter that is truly transient-perfect has a transfer function of "1".