ECE4893A: Electronics for Music Synthesis

Spring 2010

Homework #4

Due: Monday, April 19 at the start of class

This homework will be graded out of 100 points.

Ground rules: You are free to discuss approaches to
the problems with your fellow students, and talk
over issues when looking at schematics,
but your solutions should be your own. In particular, you should never
be looking
at another student’s solutions at the moment
you are putting pen to paper on your
own solution. That’s called “copying,” and it is lame.
Unpleasantness,
including referral to the Dean of Students for investigation,
may result from such behavior.
In particular, the use
of “backfiles” of solutions from homeworks and quizzes assigned in
previous offerings of this course is strictly prohibited.

Late penalty: If you show up really late, suggesting that you
were doing the homework during class, then I’ll take off up to 10
points based on my mood. Because we will have our quiz on Wednesday,
April 21, I plan to post solutions shortly after class on Monday,
so, in general, I will not accept late homeworks on this one. If there
is some extinuating circumstance, such as your car breaking down or
something, let me know as soon as possible.

Problem 1

In this problem we’ll
look at the
Oberheim OB-Mx.
Strangely, Tom Oberheim had nothing to
do with this synth; Gibson had bought the rights to the Oberheim name.
Don Buchla was called in to try to save the project, but it eventually
wound up released before it was really ready against Buchla’s wishes.

We’ll look at the schematic for
“Voice A” from one of the voice boards. (Each voice board has circuitry
for two voices; an OB-Mx chassis can hold up to six voice boards, for a total
of twelve voices.)

If you don’t see a specific unit on a capacitor, there’s usually an implied
“microfarads.”

a) The Moog transistor ladder VCF contains a cascade of four
one-pole lowpass filter sections. In class, I presented an analysis of a
hypothetical
“one-sided” latter
to get a feel for how this kind of circuit works. The analysis
of the actual “two-sided ladder” is a bit more complicated. We’ll rely on
the analysis in Tim Stinchcombe’s
Analysis
of the Moog Transistor Ladder and Derivative Filters, particularly
Equation 13 on page 11. Using this formula,
find the cutoff frequency (in Hertz) of
one of those sections in the OB-Mx’s transistor ladder
as a function of the control current
being pulled from the tied emitters of the transistor pair that feeds
the ladder.

(Note that when analyzing the Moog VCF, we don’t include a
resistive divider in the gain as we’ve done in OTA-C filter
cutoff computations;
there is typically a resistive divider right at
the first input, but it’s not important for our frequency analysis.)

b) Let’s do some DC analysis.
At DC, the caps are open circuits.
Supposing that the transistors draw negligible
current through the bases, what are the voltages
at the bases of the four stages of the
ladder? (Number the stages 1 through 4, from bottom to top).

Problem 2

In Session 22, we briefly
looked at the state variable filter in
the Oberheim SEM; see the schematics
here.

You should
be able to find the OTAs that are taking the place of resistors in the
variable gain integrators. You should also be able to find the capacitors
that the output currents of the OTAs are being sent into, as well as
the op amps that buffer the resulting voltage. Finally, you should be able
to look at the inputs of the OTA and find what resistor you will want to
call “Rbig” and what resistor you will want to call “Rsmall” to form the
Rsmall/Rbig gain factor that you will want to combine with the gain of
the OTA when computing the “critical frequency” f_0 in Hertz.
(In lecture
I sometimes used a subscript “0” and sometimes used a subscript “c”.)

Ignore D11, D12, R158, R159, C22, and R157; this network
provides some sort of
nonlinear shaping in the feedback path.

a) Find
f_0 as a function of the current fed to the control current inputs
of the OTAs. This should be a simple calculation once you find the component
values you need.

b) Consider PS16, the pot labeled “RES”. As the wiper of the pot is turned
toward ground, does the resonance “Q” go up or down? Briefly explain
your reasoning.

c) What is the output impedance of the HP, BP, and LP outputs?

Problem 3

Let’s take a look at

Tom Gamble’s EFM VCF8E circuit, which is somewhat based on
the Korg MS-20 (but notice the capacitor values are somewhat different).
(Tom appears to have taken down the schematic on his ele4music.com site,
but it was kindly archived by fonik).
It has two
separate filter circuits, but they look more or less the same to me.

a) When switched in the lowpass mode, find the OTA control current
that would
result in a critical frequency f_0
(in some lectures I called this f_c) of 2000 Hz.
(The 10K resistors to the negative supply at
the output of the buffers are just goo needed to make the built-in
Darlington buffers of the LM13700 work.) Remember you can fold the
R_small/R_big factor in with the gain of the OTA when using the formula
for the critical frequency of a Sallen-Key filter. Because the two capacitor
values are the same and the resistor values are the same, this is a
relatively simple calculation.

b) In the original Korg MS-20, resonance is controlled with a pot. Notice
how Tom has modified the circuit to make the resonance voltage controllable.
In class, we showed that for this “Bach” topology, a feedback of K < 2 is
needed, or else the filter will go unstable. What value of control current
for the resonance-controlling OTA would give a feedback of 2? (I conjecture
that
Tom has designed this so that isn't possible, but I haven't checked it
in detail.)

Problem 4

At the end of Session 24 (April 7th), we briefly looked at the
Buchla 292C Lowpass Gate. The lowpass gate is basically
a traditional Sallen-Key filter with vactrols (light-dependent resistors
packaged with LEDs) replacing the resistors. Buchla employs several other
tweaks; we will ignore many of these in an effort to simplify
the analysis.

In this particular circuit, a single LED drives two LDR elements, so
we can suppose that the resistors in the Sallen-Key have the same resistance.
Using the notation from Session 23,
C4 is the Sallen-Key “feedback cap,” Cf, and C5 is the Sallen-Key
“cap to ground,” Cg. We’ll ignore C3 (open the cap) and R26
(open the resistor). IC8 is being used as a unity gain noninverting
buffer (you can ignore R25; it’s probably just compensating for non-ideal
op amp effects.)

We will assume the circuit is switched into “lowpass filter” mode.
In this mode, the CMOS switch
IC2 with pins 1, 2, and 3 is switched “on” so that the feedback cap C4 is
included the circuit. Also, IC2 with pins 6, 7, and 8 is switched “off,” so
R16 isn’t connected to ground (i.e. is open), and IC1 with pins 1, 2, and 3
is switched “off,” so R15 isn’t connected to ground and IC7 operates as
a unity gain noninverting buffer.

If Buchla doesn’t list units on a cap, that usually means it is in microfarads.
If he wants picofarads, he will typically write “pf.”

a) What is the “Q” of the filter? You can find the needed formula
in your notes from the Session 23 lecture, or from one of the many
writeups you can find on the web, such as
this one.

b) We determined that a Q of 1/sqrt(2) was special, since for Q values
above that, the lowpass filter response exhibits a bump. How does your
value from (a) compare with this magical value of 1/sqrt(2)?

c) Now let’s focus on the circuit that creates the current for the vactrol
LED. Look in the upper left corner of the schematic.
To simplify things, let’s
assume that the leftmost CMOS switch is “off,” and we will ignore C2 (treat
it as closed, i.e., close the cap). Also ignore D1 (treat it as open) –
as far as I can tell, when the circuit is operating normally, it doesn’t
come into play. Suppose the R8 pot is set to the middle (i.e. it forms
two 10K resistors).

Find the current through the vactrol diode as a function of the
control voltage input at jack 11 in the upper left hand corner of the
schematic. (Note:
This doesn’t match any standard op amp circuit I am aware of. I tackled it
it by writing two node-voltage equations and solving them.)

d) As a continuation of the previous subpart,
find the voltage at the output terminal of op amp 9 as a function of
the control voltage input at jack 11. Assume that the vactrol LED has
a “diode drop” of 1.65 volts; I found this figure on the VTL5C3 datasheet.
(The answer to this question is less important than the answer to (a),
but it is useful since it tells you how far the output of the op amp
needs to be able to swing.)

e) What is the critical frequency f_0 (in Hertz; again, sometimes I called
this f_c) of the filter if the vactrol resistors
each have an effective resistance
of 10K? You can find the required formulas from the same sources listed in
part (a).

f) According to the VTL5C3/2 datasheet (which you can find in
Aaron’s
datasheet collection), what control current
through the LED would
generate this equivalent 10K resistance?
Use curve #4 on the graph (you’ll see
what I mean when you look at the datasheet).

Problem 5

Make a brief video demo (at least a minute, but longer is OK)
that consists of you making
interesting sounds on the MOTM system, and upload it to youtube.
Your demo should somehow include
the sounds of an oscillator (or oscillators) going through a filter, with
the parameters of the filter changing over time.

Experiment! Have fun!

I will create a “MOTM demo” topic on the Forums section on T-square.
Post link to your youtube videos there.

As with our previous youtube adventures, because of privacy concerns,
you do not need to show your face
if you do not want to, and you are not required to post under your real name.