ECE4803B – Homework #3

ECE4803B – Homework #3

ECE4803B: Theory and Design of Music Synthesizers

Fall 2006

Homework #3

Due: Tuesday, Oct. 10 at the start of class


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, you should listen to
by Charles Cohen,
who performs live exclusively using a Music
Easel. (He collaborates with other musicians, so not everything you’re hearing
is the Easel.)

Problem 1

On 9/28, we looked at the
“timbre” nonlinearity implemented in the
Buchla 259 Programmable Complex Waveform Generator
, and also briefly
looked at a similar timbre generator circuit is used in the Music Easel (the
“B2080-9A Oscillator 3/3 link on
Buchla page
Last Spring, I had students analyze the Music Easel circuit. This Fall, let’s
look at the Buchla 259 circuit.
You’ll see five of those “Buchla diodeless deadband” circuits. From top to
bottom, let’s number them 1 through 5. Pick one based on your birthday;
Jan. or Feb. pick #1; March, April, or May pick #2; June or July pick #3;
Aug., Sept., or Oct. pick #4; Nov. or Dec. pick #5.

a) For your particular deadband circuit,
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 of op amp 29.
You may adapt the
formula we derived in lecture on 9/28; you don’t have to
do it from scratch.

b) The final summing amp has a 100 pf capacitor and a 1.2 megaohm resistor
in the feedback loop. This forms a one-pole lowpass filter, which is
designed to make the sound less harsh and strident. What is
the cutoff frequency (in Hertz) of this filter?

Important warnings:

  • 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.

  • Pay attention to the supply voltages the CA3160s are given; also remember
    the CA3160 offers “rail-to-rail” operation.

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

Problem 2

In class on 9/26, we looked at a nonlinear circuit used in
Ken Stone’s
Cat Girl Synth Wave Multiplier. To find the schematic, go to,
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 3

I meant to put a problem with an opamp-BJT linear current source or sink
on the last homework,
but forgot about it, so I’ll put one on this homework instead. It took
me a while to find a circuit that used this basic structure that was also
reasonably understandable.

Let’s look at the VCA of the PAiA FatMan. To find the FatMan schematic,
go to the
PAiA website, click on FatMan synth under
the (under the “Kits” menu in the upper left), and scroll down to the
“Schematic, Parts list, Design analysis” link. The VCA is in the lower
right corner of the diagram.

Pin “1” (IC1) of IC18 is the current control input of the LM13600 OTA
that forms
the gain control element of the VCA. IC13:C and Q12 form a linear current
source for the OTA.

That’s a complex little circuit. Let’s make some simplifying assumptions.
According to the documentation,
“Adding D9 to the circuit clamps the output of IC13:c and
keeps it from going negative and C24 provides frequency
compensation for the high loop-gain state that exists at
near-zero control voltages.” For the purposes of an easy analysis,
ignore C24 and D9; i.e. open them up (as you would a cap at DC). For
Q12 to be “on,” it seems that D9 would need to be “off,” so I think
that’s a safe assumption for the values I assume below.

Let’s suppose that the wiper of
R104, which controls the amount that keyboard velocity
effects the VCA, is set all the way “down” (i.e., at ground).
Let’s also suppose that the wiper of R102, which controls the amount that
the ADSR envelope, is set all the way to the “left” (i.e. it connects
directly to the output of IC12:D).

Let’s suppose that the
output of IC12:D (pin 14), (AA) on the schematic, is at +5 volts (I haven’t
analyzed the rest of the circuit, so I don’t know if +5 volts is a
resonable value for that; I’m just picking it to have a number to
work the problem with.

The negative voltage supply, V-, is -12 volts.

What current is flowing into pin 1 of IC18? (You may assume that
Q12 has negligible base current, so the emitter and collector currents
are approximately the same.)