ECE4893A: Analog Circuits for Music Synthesis

Spring 2016

Homework #5

Due: Friday, March 18 at 3:30 PM

This homework will be graded out of 100 points.
Please turn it in to my VL431 office.
Of course, you may turn it in ahead of time if you wish.

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 bad.
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.

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.
Using
Equation 13 on page 12 of
Tim Stinchcombe’s
Analysis
of the Moog Transistor Ladder and Derivative Filters (which
is the same as the result I hand-wavingly derived in class),
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 class on March 8, we briefly
looked at the state variable filter in
the Oberheim SEM; see the schematics
here
(look in the upper right corner).

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 natural frequency f_n in Hertz.

Ignore D11, D12, R156 through R159, and C22;
this network
provides some sort of
nonlinear shaping in the feedback path.

a) Find
f_n 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’s original website where he posted the schematic
no longer exists,
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 natural frequency f_n
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 natural frequency of a Sallen-Key filter (basically you
can replace the resistances in the standard formulas
like in Equation 9 of this document
with the reciprocals of transconductances). 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

For this problem, we will provide a Korg MS-20 for your use. It will generally
live under the workbench in the back left corner of the senior design lab.
If the classroom next to the senior design lab is empty, you may use it there
to avoid bothering people in the senior design lab. If that classroom is
in use, go ahead
and bother the people in the senior design lab. DO NOT TAKE IT ELSEWHERE,
and BE SURE TO ALWAYS RETURN IT TO THAT SPOT UNDER THE WORKBENCH.

A large amount of documentation on the Korg MS-20 may be found here:
Korg
MS Monophonic Synthesizers. Click on “Owner’s Manuals,” and then
click on “MS-20 synthesizer setting examples.” Under “Patch Settings,”
you will see links for “Musical instruments,” “Synthe sounds,” and
“Sound effects,” which list various patches.

Choose one “Musical instrument” patch, one “Synthe sound” patch, and
one “Sound effect” patch.

Create three brief (say, 30 seconds)
videos demonstrating each of your three patches,
explaining interesting
features about it, and upload them to youtube. (Alternatively, you can
edit together a single video demonstrating all three in succession; but
don’t spend a lot of time on the editing. This isn’t a video production
class, which is why I’m giving you the option of just uploading three
separate snippets.)

On your homework, for this problem, simply post the links to your
videos in reply to the post titled
“Post links to your HW 5 MS-20 videos here”
on our piazza
site.

You have many options for recording video. If you don’t already own a
dedicated video recorder,
you will find that many “still” digital cameras have the
ability to record brief snippets of video, as do some cell phones. You might
also be able to record video using your laptop, if it has a built in camera.
You might also be able to borrow one of these items from a friend. If none
of this works out, you can also check out video cameras from the library.

For privacy reasons, you do not need to show your face if you’d prefer not
to; similarly, you do not need to post the video under your real name.

(You might enjoy watching demos of the MS-20 that are already on youtube;
in particular, I recommend this series of tutorials:
part 1,
part 2,
part 3)