# ECE4893A: Electronics for Music Synthesis

## Spring 2011

## Homework #3

## Due: Friday, March 18 at the start of class

This homework will be graded out of 100 points.

**Background music**: 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. 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 *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. If you turn it in on Monday, March 21, by noon

(since this will be during Spring break, we won’t have class, but you

can slip it under the door to my Van Leer 276 office; please e-mail me

to let me know if/when you do this),

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

Monday

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.)

## Problem 1

In class, we looked at a nonlinear “folding” 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 “Click Here for the Schematic.”

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 (OrCAD, Multisim, LTspice, whatever…) 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 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
deadband**

(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 ECE3050 guru and have reason to pick different output**

voltage swing range, please go ahead and use

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

Now let’s look at the triangle-to-sine waveshaper in the Buchla Music

Easel. Once again, check out

Magnus’s

Buchla page, and search for the

search for the “B2080-8A” “Complex Oscillator 2/3” link. The

waveshper consists of R37, R36, R38, R39, D1, D2, and Q1. Don’t worry about R40

and all the other associated “sine adjust” circuitry. The input to the

waveshaper is at the “top” of the shaper, at the junction of R37, D1, and R39.

The output of the waveshaper is the the junction of Q1 and R38.

I don’t have a good understanding of how this circuit works; in such cases I

often turn to SPICE.

Use your favorite SPICE implementation to plot the output of the waveshaper,

sweeping the input linearly over a symmetric voltage range

(i.e from some -V to some +V).

Experiment with the input range until you find something that looks like half

of a sine wave. To small of a range will make the output look like a line;

to large of an range will make the the peaks of the output sine wave look

too wide.

(You can “eyeball” this; there’s no single perfect right answer.

It’s a judgement call.) Include an input/output voltage

plot of this specific case.

The diodes are 1N457s, and the transistor is a 2N4339. If you don’t have

1N457s in your SPICE library, try a 1N4148 or 1N914, and if you don’t have

those, try some other silicon diode model. If you don’t have a 2N4339 in your

SPICE library, try any other N-channel JFET.

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 4

Check out

Ray Wilson’s Voltage Controlled Low Pass Filter (Four Pole 24db/Oct):

The input and feedback resistors are 100K; it looks like the divider is

made with a 1K to ground. (I find it interesting that he chooses to use

TL084 op amps as buffers instead of the buffers built in to the LM13700.

Maybe this is to avoid

having to deal with the weird 1.4 V drop you get from the LM13700 buffers?

The TL084 also are probably better quality than just the simple Darlington

pair in the LM13700.)

In parts (a) and (b), we will consider the gain of just

**one** of the filter stages,

either the second, third, or fourth (they are all the same; I’m not

including the first one so we can avoid talking about

the effect of the resistor coupling

in the resonant feedback loop while working (a) and

(b)).

a) Assume that the transductance gain

of the OTA is 19.2**I_con*, where *I_con*

is the current flowing into the

control pin of the OTA.

What is the cutoff frequency of

the filter block in terms of (*I_con*) in Hertz?

(Remember that the transconductance gain just takes the place of

1/R in the usual single-pole cutoff freuqency calculation, and for convenience

we include the scaling of the resistive divider as part of the transconducance

gain. You may use the various approximations that I used in class to reduce

the resistive divider to a R_small/R_big type of multiplier. I want

to emphasize that you don’t need to rederive anything; you can feel free

to use the final results from lecture.)

b) Given the result in (a), what value *I_con* would be needed for the

cutoff frequency of one stage to be 1000 Hz?

c) Now let’s consider the full four-pole cascade with feedback level

denoted as K, as in lecture. Let the

cutoff frequency of a single stage be 1000 Hz. Using MATLAB, Mathematica,

Maple, or some similar tool, on the same plot, show the

magnitude of the frequency response (with the horizontal axis in Hertz),

from DC to some value that you think best shows off the curves, for four

cases: K=0, K just big enough so that you can just barely see a resonance

“bump” in the curve, K close to 4 (but not so big that it swamps your other

curves), and a K somewhere between the last two cases that you think is

interesting. **Make sure the value at DC corresponds with the results computer
by the simple formula derived in lecture.**