EMS 2010 – Homework #2

EMS 2010 – Homework #2

ECE4893A: Electronics for Music Synthesis

Spring 2010

Homework #2

Due: Friday, Feb. 26 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.
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. If you turn it in on Monday, March 1
at the start of class,
I will take off 30
points. This isn’t to be mean – it’s to encourage you to get it turned in and
move on to 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. I won’t accept it after class on
since I will send out solutions shortly after. (If you have some severe
extenuating circumstance, i.e., family emergency, major health issues,
date, etc.,
e-mail me and we will work something out. On the other hand, if
you know ahead of time that you won’t be able to come to class
because of something like a job interview,
please plan to work in advance and get your homework to me ahead of time.)

Suggested references: CA3080 and LM13700 datasheets (available from
datasheet collection

Problem 1

In class session 12, 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 sessions 10 and 11, we looked at exponential converters, particularly
a current “sink” that used a matched NPN pair. In this problem, we will look
at a current “source” that uses a matched PNP pair; the same sort of thinking
we used in class also applies to this variation.

Jorgen Bergors, the
creator of the Bergfotron,
conducted a
VCA shootout
comparing various VCA designs. Let’s take a look at
. 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
(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 9, we looked at sawtooth VCO core designs. Let’s look at
Wilson’s 1V/Octave Voltage Controlled Oscillator
This is a very complicated circuit, so we’ll rely on Ray’s thorough

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

For this problem, we will provide a Korg MS-20 for your use (location to
be determined.)

A large amount of documentation on the Korg MS-20 may be found here:
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 give me instructions on how
to find your video(s).

You have many options for recording video. If you don’t already own a
dedicated video recorder, like the flip cam I have been using to record
the lectures, you will find that many “still” digital cameras have the
ability to record brief snippets of video, as do some cell phone. 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)