# ACMS 2015 – Homework #3

ACMS 2015 – Homework #3

# ECE4893A: Analog Circuits for Music Synthesis

## Due: Tuesday, February 24 at the start of class

This homework will be graded out of 100 points.

Background music: The original
Buchla Music Easel,
which consists of a Buchla 208 Programmable Sound Source and a
Buchla 218 Model Keyboard together in a single case, is one of the rarest
and most coveted of the Buchla designs.
(It has recently been re-released.)
To put yourself in the right frame
of mind for this homework, watch this
video
featuring Charles Cohen,
who performs live exclusively using a Music
Easel.

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.

Sorry, no late turn-ins accepted on this one: Since we’ll have Quiz 1 on
Thursday, February 26, I want to be able to get solutions up quickly.

## Problem 1

In this problem, we will explore
VCO

of the
Bergfotron.
In particular, we will investigate a very small part of the

schematic of its waveshapers
. There’s a lot of freaky stuff on
that schematic. We will concern ourselves with the op amp labeled IC2
in the middle of the page (the TL072 is a dual op amp; we will not worry
out the op amp in the upper right corner). This IC2, along with
some additional circuity, claims to produce a sawtooth wave,
labeled “SAW OUT,”
from the triangle wave produced by the Advanced VCO’s core.

Let’s denote the output signal labeled “TRIANGLE OUT,” which is produced
by half of IC9 (not to be confused with the IC9 in the upper left
corner of the page), as V_tri (where I am using the underscores to indicate
subscripts). Let’s denote “SAW OUT” as V_saw.

The square wave produced by the Advanced VCO’s core controls the 4066
CMOS switch; for this case, focus on the switch corresponding to pins
3, 4, and 5 (pin 5 is the control). The 11K resistor and 22p capacitor
in the feedback loop of IC2 seem to form a lowpass filter; however,
computing the cutoff of this filter yields a cutoff of 658 kHz. This
is far above the range of human hearing, so I presume the 22p capacitor
is there for stability and general gremlin-eating. So, let’s ignore
(i.e. open) that capacitor.

The 20K and 68K resistors attached to pin 2 of IC2, and the 4.7M, 13K,
and 24K resistors attached to to pin 3 of IC3, will all play a role in
this problem. The circle with a + in it connected to the 4.7M resistor
is the +15 volt power supply; the cirlce with the – in it connected
to the 68K resistor is the -15 volt power supply.

a) Find V_saw as a function of V_tri when the 4066 connected
to the 13K resistor is switched OFF. (Assume its OFF resistance is
infinite.)

b) Find V_saw as a function of V_tri when the 4066 connected
to the 13K resistor is switched ON. (Assume its ON resistance is zero).

## Problem 2

In class, we looked at the
“timbre” nonlinearity implemented in the
Buchla 259 Programmable Complex Waveform Generator
.
A similar timbre generator circuit is used in the Buchla Music Easel described
above.
You can print out
the schematic from
Magnus’s
Buchla page
;
search for the “B2080-9A” “Complex Oscillator 3/3” link.
You’ll see five of those “Buchla diodeless deadband” circuits.

Let’s analyze the third one from the top,
which consists of an op amp and
R31, R34, and R35.
Calculate the positive edge of the

(i.e., what is the largest input voltage for which the output stays
zero?), and
calculate the slope of the output/input curve past that point.
As in lecture, let’s define the “output” as the voltage at the negative input
of the op amp forming the deadband circuit,
and the “input” as the voltage at the output at the op amp
just above resistor R20 on the schematic. You may
adapt the formulas we derived in class; you don’t have to
do them from scratch.

Important warnings:

• Buchla sometimes has two kinds of grounds, denoted Q (quiet, for audio
signal paths) and N (noisy, for digital logic, etc.)

• Remember in Buchlaese, that when two lines cross without a dot, they
don’t electrically connect; when two lines meet at a T-intersection without
a dot, they do electrically connect.

• The Buchla 259 used CA3160 op amps, which enjoy “rail to rail” output
swings due to their CMOS output stage, run with “voltage starved” supplies of
6 V and -6 V. The Easel appears to use RC4136’s
instead, and although the power supplies are not explicitly marked, I’m
told they run off Buchla’s
usual +15 V and -15 V. With the exception of one JFET,
the rest of the circuit for the RC4136 shown on
the
datasheet
seems to be all bipolar,
so I doubt it can do the “rail to rail” business that the CA3160 can.
Elsewhere on the sheet, I see that the “maximum peak output voltage swing”
is listed as being “minimum +/- 12 V” and “typical +/- 14 V” for a 10K
load. The resistors I see on the sheet are all higher than 10K,
suspect they’re running more towards what’s listed as “typical”. Looking at
the schematic on the
datasheet, I see that the output is sandwitched between two BJT’s between
the supply rails, so there’s at least a diode drop there from the possible
output to the rails. So… let’s use -14 V and 14 V as the output voltage
limits (as opposed to the -6 V and -6 V volts we saw in the case of the
259). If you’re an ECE3400 guru and have reason to pick different output
it and tell me your reasonsing!

• Notice a few of the “resistors” are actually a couple resistors in
parallel. (Do you get the impression that Buchla might have started with
a basic design, and then tweaked it by throwing in a few more resistors
here and there?)

Interestingly, the 259 had both “timbre” (amplitude of sinewave going in)
and “symmetry” (DC offset on sinewave going in) controls; the Easel appears
to just have a timbre control.

## Problem 3

The
Korg
PS-3100
and

PS-3300

voltage-controlled resonator circuits that were basically a parallel
bank of three second-order bandpass filters that could be individually
tuned, and their outputs summed.
(Juergen
Haible
, who sadly passed away a few years ago,
built a

Korg PS series clone
from scratch!)

So far,
we’ve been focusing entirely on using OTAs to replace resistors. Some
circuits, such as that used in the Korg resonators, instead used
a combination of LDR (light dependent resistor) coupled together with
an LED; changing the current through the LED changes the amount of
light on the LDR, and hence the resistance. (Modern clones of
the Korg resonator,
such as the
MOTM-410
and the
Cyndustries
Triple Resonant Filter

typically use Vactrols, which are commercial
prepackagings of LEDs with LDRs. You can hear examples of what
the resonator sounds like on those pages. Try the “3 Zombie Tenors”
sample on the MOTM-410 page!)

Here’s the
schematic
of the resonators
.
On the right part of the diagram, you’ll see the three filters, which
are each formed from a 1458 op amp, two capacitors, and two LDRs.
The LDRs are driven identically, and hence each have the same
resistance.

Let’s analyze one of these filters. Call the capacitor feeding back from
the output of the op amp to the negative terminal of the op amp C2
(corresponding to C108 through C110 on the schematic);
let’s call the other capacitor C1 (corresponding to C105 through C107
on the schematic). Let’s suppose both LDRs have
the same resistance R.
Find the Laplace-domain transfer function describing the voltage
at the output of the op amp in relation to the input voltage
at the left terminal of C1 as parameterized by C1, C2, and R.

Ignore R105, R106, and the rest of
the circuitry on the left; assume that C1 is fed with an ideal voltage
source.
(This is basically an ECE2040 problem).

An aside: I’ve looked up and down trying to find this exact filter
configuration in the literature, and haven’t been able to find it!
One web author called it a bandpass Sallen-Key, but that’s clearly
incorrect. It looks kind of like a multiple feedback topology,
but it has four passive elements instead of five, and the caps and
resistors are switched from the way they’re usually presented in
a MFB bandpass circuit. So I’m not sure what to call it! Has anyone
seen this before?

## 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
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
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 your

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)