# EMS 2008 – Homework #2

EMS 2008 – Homework #2

# ECE4893A: Electronics for Music Synthesis

## Due: Thursday, Feb. 28 at the start of class

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
may result from such behavior.

Late policy: 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.
If you turn it in later that day, say before 6:00 PM
or so (that’s when my 2025 recitation ends –
you can find me in Van Leer 361 from 3 to 6).
After that, I’ll take off 20 per day.
This isn’t to be mean – it’s
to encourage you to get it turned in and
get on with whatever other work you have to
do in other classes, even if it’s not
perfect – but also to encourage you to
go ahead and do the work and turn it in
and learn some stuff and get some points, even if you’re past the deadline.

Suggested references: CA3080 and LM13700 datasheets (available from
Aaron’s
datasheet collection
)

## Problem 1

In class session 9, we looked at the triangle VCO core of the
Buchla 259.
That oscillator is designed to operate at audio rates. In this problem we
will look at a voltage-controlled VC “low frequency oscillator” (LFO), which
is a particular kind of VCO.
Although some LFOs can run at
it can run at lower audio frequencies, they’re typically not designed
with the rigorous requirements needed to play “in tune.” Instead, they’re
usually intended to provide control voltages to control other parameters
(such as the pitch of an audio VCO to create a police siren.)

Let’s look at
Ray Wilson’s VC-VCO.

The main triangle core is on the left half, midway between the
top and the bottom. C11 and U2-A form the integrator. (I’m not sure
why the R22 is there, so let’s ignore it in our analysis). Let’s call
the output of U2-A (pin 1)
V_tri (I’m using the underscore to indicate a subscript).

Notice that U4-A is not being used in a negative feedback configuration,
so the “golden op amp rules” do not apply. U4-A is being used as a comparator,
so the output of U4-A (pin 1) will try to snap to the
positive supply (+12 V)
if the voltage at pin
3 is greater than pin 2, and try to snap to the
negative supply (-12 V) otherwise. Now, in reality, the TL082 is not
a so-called “rail to rail” op amp. Take a look at simplified schematic
of the National TL082 datasheet on my
Datasheet Archive
you’ll see there’s
a NPN BJT between the output and the positive supply and a PNP BJT
between the output and the negative supply. Hence, we’d expect that the
output could swing to at most within a “diode drop” of the supply lines
(in this case, assuming a 0.7 V diode drop, -11.3 V to 11.3 V). Based on
the “output voltage swing” line on the datasheet, I’m guessing it’s closer to
something like to within 2 volts of the supply. So, let’s suppose that
the comparator outputs +10 V or -10 V.

Let’s suppose that the Tri Skew trim pot is set to the middle. Assume that
the diodes are either “off” (in which case no current flows through them) or
“on” (in which case we’ll assume a “diode drop” of 0.7 V).

Assume the OTA has infinite input impedance. Ignore the C10 cap in the
feedback loop of the comparator op amp (U4-A).

a) When the output of the comparator is +10 V, what is the
voltage at the positive
input terminal of U3-A
?

b) When the output of the comparator is +10 V,
using the nonlinear “tanh” model for OTA behavior, what is the output
current of the OTA as a function of the current control input (pin 1) of
the OTA. (Note that unlike the Buchla 259 VCO circuit we looked at in
class, the OTA here does not seem to be fully saturated.)

c) When the output of the comparator is +10 V, what voltage at the output
of the integrating op amp (pin 1 of U2-A) would cause 0 V to appear at the
positive terminal of the comparator op amp (pin 3 of U4-A). (Note that
this will tell you the maximum level of the triangle wave).

d) What is the frequency of the triangle wave as a function of the
current control input (pin 1) of the OTA?

e) Take a look at the TRI output in the middle of the page (pin 2 of R15).
What is the output impedance of the TRI output?

## Problem 2

In class session 8, we looked at exponential converters.

Jorgen Bergors, the
creator of the Bergfotron,
conducted a
VCA shootout
comparing various VCA designs. Let’s take a look at
CA3080
VCA 1
. The exponential converter is at the top of the schematic, and
the main VCA is at the bottom part of the schematic.
The power supply voltages are not marked on the schematic or on the webpage,
but based on Jorgen’s
<A HREF="http://hem.bredband.net/bersyn/psu.htm"power supply design,
let’s assume the VCA uses a +/- 15 V supply.

The exponential converter takes a control voltage “CV” (found in the
upper left of the schematic) and
generates a control current for the OTA of the
form I_{con} = I_{ref} exp(const*CV).

(a) What is I_{ref}?

(b) Assuming that the CV offset trim pot is set all the way to the
“right”
(i.e. at ground), what change in
CV will cause the control current to double? (Assume the PNP BJTs
draw insignificant current throught their bases).

(c) Assuming the OTA is operating in the linear region, give
an expression relating the audio
output voltage to the audio input voltage in
terms of the current at the control input pin of the OTA. (You
may ignore the offset trimming circuitry of the OTA. Assume
the positive input of the 3080 is grounded.)

(d) What is the input impedance of this VCA?

(e) What is the output impedance of this VCA? (It might be “0” –
remember we’re assuming ideal op amps.)

## Problem 3

In class session 7, we looked at sawtooth VCO core designs. Let’s look at
Ray
Wilson’s 1V/Octave Voltage Controlled Oscillator
.
This is a very complicated circuit, so we’ll rely on Ray’s thorough
description.

Check out the LM394 in the schematic; this forms the core of the exponential
converter (note Ray recently found the SSM2210 works better). Call the current
flowing into pin 1 of the LM394 “I_{freq}.” (Hint: you may use Ray’s
“1.1 volt” figure.)

(a) Given Ray’s description of the circuit operation, find the frequency of
the oscillator in Hertz in terms of I_freq. (To make things easy, assume
the reset time is finite.)

(b) Given you result in part (a),
what value of I_{freq} would generate a 440 Hz tone?

(c) Now let’s get some practice in reasoning with tempco resistors (see
class session 8 if you need help). Suppose
that R8, R10, R18, R23, R27 aren’t there, and we’ll focus just on the CV1
input through R15. What is the output of U1-A (pin 1) as a function of voltage
CV1 if the tempco is at a temperature of 25 degrees celcius (the base
resistance is 2K for 25 degrees celcius)?

(d) Now suppose you’re using Ray’s VCO circuit to make sound for an art
installation at the Burning Man Project, which can get up to and above
100 degrees fahrenheit during the day. Redo problem (c), except use a
temperature of 38 degrees celcius instead of 25 degrees celcius.

## Problem 4

In class session 11, we looked at a nonlinear circuit used in
Ken Stone’s
Cat Girl Synth Wave Multiplier. To find the schematic, go to
http://www.cgs.synth.net,
click on “Modules,” and click on “Wave Multiplier” (be sure it just
says “Wave Multiplier” by itself; don’t click on the “Saw Pitch Shifter/Wave
Multiplier”), and then click on “Grinder and Folder Schematics.” The
folding nonlinearities are at the bottom of the page. Note that Ken uses
four in series (unlike the six in series like the Serge Wave Multiplier
uses). The last one has some additional diode clipping action, but we’ll
ignore that.

Let’s consider one of the first three stages. Use your favorite implementation
of SPICE to run a
simulation of
one of the stages (10K resistors from input to each of the op amp terminals,
10K resistor in negative feedback configuration, and two 1N4148 diodes, facing
different directions, in parallel from the positive terminal to ground). Be
sure to use a 1N4148 model (if one isn’t built into your SPICE, let me know)
and not some sort of “idealized” diode.
Make a plot of the output voltage vs. the input voltage for input voltages
ranging from -1.5 to 1.5 volts. Does the nonlinearity exhibit a sharp
corner, as my handwaving analysis in class suggested, or does it have a
more rounded corner?

Be sure to provide some sort of printout “showing your work,” i.e.
a SPICE schematic or netlist (if you’re into typing your own netlists
by hand).

## Problem 5

The

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.
In class session 11, we looked at the
“timbre” nonlinearity implemented in the
Buchla 259 Programmable Complex Waveform Generator
.
A similar timbre generator circuit is used in the Music Easel.
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 second one for the top, which consists of an op amp and
R28, R32, R29, and R33.
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 formula we derived in class session 11; you don’t have to
do it 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 ECE3050 guru and have reason to pick different output