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Calculate Envelope times from Schematic

by owen_vallis on Sat Dec 01, 2012 1:52 am

Hello,

I am hoping someone can point me in the right direction. I've been trying to calculate the time constants for the 909 envelopes from the schematic. I know the trigger is a 2ms, 5V pulse, and I've been getting good results for some of the simpler envelopes... however, there is an envelope that I can't seem to understand. Its ENV1 in the kick Drum. It seems like C8 charges super fast, holds for the remainder of the 2ms pulse, and then discharges through VR5 and R58. The trouble is, I don't know how R35 affects the attack charge time, R36/R22 seem confusing to me. Any thoughts?

The schematic can be found here

http://www.kolumbus.fi/janne.husu/specs/909va.gif

Any thoughts or advice would be helpful.

Cheers
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Re: Calculate Envelope times from Schematic

by adafruit_support_mike on Sat Dec 01, 2012 9:33 pm

Hmm.. lots of moving pieces there, so it's easier to break it down into parts.

First of all, let's ignore everything but R35 and C8.. that's the path through which C8 charges. The time constant is the product of those values (1.8k resistance and .33uF capacitance), or about 600 microseconds. A 2ms pulse is about 3.5 time constants, which is long enough for C8 to reach 'full charge'. That's far from the whole story, but the part to take away is "R35 charges C8, C8 is at full charge by the end of the control pulse."

D9 only allows current to flow from R35 to C8 when the control pulse is HIGH, but also isolates C8 from a voltage limiter made from D8, R36, and R22.

If we ignore everything but R36 and R22, we have a voltage divider whose center voltage is roughly Vcc/6. Adding R35 and D8 back in, nothing happens when the control signal is LOW.. IMO, R36 is only there to guarantee D8 is reverse-biased when the control signal is LOW, eliminating any parasitic effects D8-R22 might have.

When the control signal is HIGH, we get R35-D8 in parallel with R36. R36 is about 26 times as large as R35, so R35 will dominate. That means we have a voltage divider with a diode in the middle: R35-D8-R22. The voltage across D8 will be about .65v, and the remaining 4.35v will be divided between R35 and R22. Crunching the numbers, the voltage at the top of R22 will be about 3.5v.

Now here's the nifty part: D8 and D9 are in parallel, and the voltage across both will be roughly the same. The voltage at the bottom of D9 will match the voltage at the bottom of D8: about 3.5v. That means C8 charges to about 3.5v by the end of the control pulse.

C8 discharges through VR5 and R58. R58 sets the minimum discharge time constant (about 16ms), VR5 allows you to raise that to about a third of a second.

The signal at the top of C8 goes through R54 to the base of Q12. Q12's emitter is tied to the negative input of op amp IC11a, which is set up as a current-to-voltage converter. IC11a's positive input is tied to GND and the negative feedback through VR4 means the negative input will also stay nailed to GND. That means we have to take Q12's Vbe into account.

To make things simple, let's just declare Vbe to be .5v. Below that, Q12 is off. Above that, Q12 is on, and the current through it is proportional to the voltage across R54.. roughly VC8 - .5v.

When the control pulse goes HIGH, there will be a short delay while VC8 rises to .5v. The delay will be well less than one R35-C8 time constant, since VC8 will be around 2.3v by the end of the first time constant. The math involves fractions and logarithms, but the actual delay will be about 100 microseconds. Therefore the current through Q12 will rise sharply after 100us.

When the control pulse goes LOW, C8 starts to discharge. It will take about two VR5-R58-C8 time constants to fall below .5v and the current through Q12 will match that discharge curve.

Now, it's possible that R54 overdrives Q12.. if the current through Q12 maxes out when VC8 reaches 2.3v (C8's value at the end of the first R35-C8 time constant), we can basically chop the top off the envelope described above. The current will max out in one charging time constant, and will stay maxed out for about 40% of the first discharge time constant. That would match the curve drawn next to the ENV1 flag in the diagram.
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Re: Calculate Envelope times from Schematic

by owen_vallis on Sun Dec 02, 2012 4:28 am

Wow! I can't thank you enough. I actually managed to mock up a software version of the circuit, and I was able to discern that R36/R22 was some kind of voltage limiter... but I was pretty lost about how everything exactly fit together. Thanks for taking the time to explain the circuit in such detail. Your reply has answered so many questions for me its crazy.

Thank you, thank you, thank you.
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Re: Calculate Envelope times from Schematic

by adafruit_support_mike on Mon Dec 03, 2012 4:26 pm

Glad it helped.

I keenly remember staring at ciruit diagrams and wishing I knew what they meant, so ferreting out signals is a minor obsession for me. Getting me to shut up once I start is a challenge no one has yet mastered. ;-)
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Re: Calculate Envelope times from Schematic

by owen_vallis on Thu Jan 10, 2013 4:42 pm

I was wondering if you could help with understanding two other sections of the circuit?

1) I found a bunch of T-Bridge BP filters in the circuit (Like the Rim Shot), and although I think I figured out how to calculate the center freq... 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?

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? 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?

Thanks again for the help in understanding this stuff better.
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Re: Calculate Envelope times from Schematic

by adafruit_support_mike on Fri Jan 11, 2013 10:53 pm

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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