owen_vallis wrote:however, I'm confused about the Q value. I'm trying to recreate these circuits in a Digital system, and I need to figure out Q in terms of resonance [0...1]. Any thoughts?
Several, but few of them are printable..
Resonance calculations seem to be one of those "if you can't dazzle them with brilliance" things. They spend twenty pages talking about differential equations with complex coefficients, give you five theoretical models of the value, define Q in terms of bandwidth, bandwidth in terms of zeta, and zeta in terms of Q, then maybe if you're lucky they throw in a footnote with the parts that are actually useful.
To find the center frequency, you find the corner frequencies for the high-pass and low-pass parts, multiply them, and take the square root. Q is the ratio of the corner frequencies and the center frequency.
For the filter labeled F1, the high-pass part is R394 (2.2K) and C112 (.01u). The low-pass part is R407 (470k) and C113 (.01u) . The corner frequency is 1 / (2 * pi * R * C), so plugging and chugging gives us 7234 Hz for the high corner and 33.8 Hz for the low corner. The center frequency is sqrt( 7234 * 33.8 ) = 494.5, or about 500Hz. Q = (494.5 / 33.8 ) = (7234 / 494.5) = 14.6 . To get the resonance/attenuation you invert that and get 0.068 .
For the filter labeled F2 the values are: flo = 17.86 Hz, fhi = 2697 Hz, fc = 218.75 Hz, Q = 12.25, 1/Q = 0.081 .
For the filter labeled F3 the values are: flo = 72.05 Hz, fhi = 15392 Hz, fc = 1053 Hz, Q = 14.6, 1/Q = 0.068 .
I used way too many significant digits for those calculations, but it made the results come out cleanly. I'd guess the original design parameters were:
F1: fc = 500 Hz, Q = 15
F2: fc = 250 Hz, Q = 12.5
F3: fc = 1000 Hz, Q = 15
owen_vallis wrote:2) I'm also still working on the Kick Circuit. Assuming we're looking at the original Roland schematic... It takes in the 2ms trigger at Transistor Q8, then seems to LP filter through C5, and HP filter through C2. I'm not sure what R14 is doing, but I think it has to do with inducing a Voltage?
R14 is there to discharge C5 after Q8 shuts off. When Q8 opens, C5 charges more or less instantly. When Q8 closes, the only way for charge to leave C5 is through R14.
owen_vallis wrote:Then R7 and R15 are a Voltage divider that feed into the next section, which I think is a BP filter of some kind. R16 and C4 make up a LP filter into Q9, which then outputs through a HP of C3 and R8, feeding back into R16... So I imagine it has some resonance. So how do I calculate the values of the various filters (including any [0...1] resonances), and am I understanding the circuit correctly?
The tool you're looking for is the Bode plot. It allows you to break multistage filters into simple RC stages, plot simple graphs for each stage, then combine all the graphs into a single description of the whole system. You can make graphs for the effects each stage has on both magnitude and phase, and derive Q from things like the phase response (high Q gives you fast changes in phase).
Also, take a look at a simulator like LTSpice. Instead of trying to derive filter parameters from the component values, you just draw the circuit, plug in the values, and let the computer crank out the analysis. Simulation is no substitute for actually building a circuit, but it gives you a decent guess at the overall behavior.
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