http://sim.okawa-denshi.jp/en/OPseikiLowkeisan.htm
Design from the second calc gives two different resistor values for either damping ratio or quality factor selection.
As Wayne said to me privately:
Huh. What does it mean? I promised to bring the observations here for dissection by smarter people.If this is a unity gain SK filter why aren't the LPF resistors of equal value?
For a unity-gain SK LPF R=R. The FB cap is 2/d, the shunt cap, d/2.
So, backtracking and using the first calc, entering all values using one R value from this calc:
http://www.calculatoredge.com/electroni ... 20pass.htm
Gives a different cutoff and QF.
I then ran the numbers a couple of ways; identical R value, QF (0.707), and damping (1). I got the following results using C values of 0.1 and 0.047.
R1/2 (2)281R
8261hz cutoff
QF 0.729
Damping ratio 0.685
Osc freq 6014
Overshoot 1.05
R1/2 374R/226R
7985hz cutoff
QF 0.7067 (closest to Butterworth)
Damping ratio 0.7074
Osc freq 5643
Overshoot 1.04
R1/2 732R/115R
8001hz cutoff
QF 0.49 (closest to critically damped)
Damping ratio 1
Osc freq none
Overshoot none
I would guess for audio I am overreacting to the differences here, but am curious about their practical meaning, if any. I can only guess the uncredited source Z of the calculators plays a large part in the results. I also (shame, shame) haven't built up all three and had a close look and listen yet.
I started exploring my vast ignorance with books, google, and wikipedia, and found the following:
http://en.m.wikipedia.org/wiki/Sallen–K ... #section_5
A second-order Butterworth filter, which has maximally flat passband frequency response, has a Q of 1/?2 (0.707) Because there are two parameters and four unknowns, the design procedure typically fixes one resistor as a ratio of the other resistor and one capacitor as a ratio of the other capacitor.
http://en.m.wikipedia.org/wiki/Q_factor#section_4
http://en.m.wikipedia.org/wiki/Butterwo ... #section_6Quality factors of common systems
? A unity gain Sallen–Key filter topology with equivalent capacitors and equivalent resistors is critically damped (i.e., Q=1/2).
? A second order Butterworth filter (i.e., continuous-time filter with the flattest passband frequency response) has an underdamped Q=1/?2.
Q factor and damping
? A system with low quality factor (Q < ½) is said to be overdamped. Such a system doesn't oscillate at all, but when displaced from its equilibrium steady-state output it returns to it by exponential decay, approaching the steady state value asymptotically. A second-order low-pass filter with a very low quality factor has a nearly first-order step response; the system's output responds to a step input by slowly rising toward an asymptote.
? A system with high quality factor (Q > ½) is said to be underdamped. Underdamped systems combine oscillation at a specific frequency with a decay of the amplitude of the signal. Underdamped systems with a low quality factor (a little above Q = ½) may oscillate only once or a few times before dying out. As the quality factor increases, the relative amount of damping decreases. A high-quality bell rings with a single pure tone for a very long time after being struck. A purely oscillatory system, such as a bell that rings forever, has an infinite quality factor. More generally, the output of a second-order low-pass filter with a very high quality factor responds to a step input by quickly rising above, oscillating around, and eventually converging to a steady-state value.
? A system with an intermediate quality factor (Q = ½) is said to be critically damped. Like an overdamped system, the output does not oscillate, and does not overshoot its steady-state output (i.e., it approaches a steady-state asymptote). Like an underdamped response, the output of such a system responds quickly to a unit step input. Critical damping results in the fastest response (approach to the final value) possible without overshoot.
In negative feedback systems, the dominant closed-loop response is often well-modeled by a second-order system. The phase margin of the open-loop system sets the quality factor Q of the closed-loop system; as the phase margin decreases, the approximate second-order closed-loop system is made more oscillatory (i.e., has a higher quality factor).
I imagine someone can easily tell me why I am spending too much time on these differences, or that the calculator is wrong in it's assumptions, etc etc. Any insight appreciated.The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband. It is also referred to as a maximally flat magnitude filter.