# ECE4803B – Homework #1

ECE4803B – Homework #1

# ECE4803B: Theory and Design of Music Synthesizers

Spring 2006

Homework #1

Due: Monday, Jan 30 at the start of class

Suggested references:
National
Semiconductor Application Note 31

(or pretty much any textbook that has op amp circuits in it)

## Analysis

The main goal of this problem is to get you looking through some
synthesizer schematics. Since each solution will be different, grading
will be less boring for me.

Do some google searching for synth schematics. They could be commercial
or “homemade” designs; you’ll find a large community of
Synthesizer Do-It-Yourself enthusiasts.
(Some early synths, such as the Buchla 100 series and early Moog Modules and
EMS Synthi, are made entirely with discrete transistors. Those are extremely
difficult to analyze; I’d recommend staying away from them for now.)

Make sure each “subcircuit” you are asked to find is being fed by a
low-impedance output (for instance, another op amp; also you may assume
that any input to a module is coming from a module with a low-impedance
output). For variety, use a circuit by a different manufacturer or
DIY designer for each of the three problems below
.

1) Find an instance of a simple voltage follower (one without resistors;
output directly tied to negative terminal.) Print out the schematic and
locate the instance.

2) Find an instance of an inverting amplifier (voltage in through a
resistor to negative terminal, feedback resistor from negative terminal
to output, positive terminal to ground). Print out the schematic, circle
the instance, and compute its gain. If it’s an inverting adder
with multiple inputs,
compute the gain for each input.

3) Find an instance of a noninverting amplifier (a resistor from negative
terminal to ground, feedback resistor from negative terminal to output,
input direct to positive terminal). Print out the schematic, locate
the instance, and compute its gain.

## Design

Moog (east coast) and Buchla (west coat) developed their ideas about
voltage controlled synthesizers independently. Moog used a pitch control
standof of 1 volt/octave, which works out to 0.08333… volts/semitone
(the pitch difference between to adjacent notes on the piano is a semitone).
Buchla preferred to use 0.1 volts/semitone, which works out to
1.2 volts/octave.

Hence, if to try to directly drive
a Moog oscillator from a Buchla pitch control source, or vice-versa,
everything will be horribly out of tune.

1) Design an op-amp circuit that will covert pitch control voltages from
the
Moog standard to the Buchla standard. You may assume that your conversion
module is given an input from a voltage source with zero output impedance
and is being fed to a module with zero input impedance; you also need
worry about input and output protection (assume nobody will be abusing
of the exercise, assume you have perfect “zero-tolerance” resistors.

2) Off-the-shelf resistors never exactly match their listed values.
Let’s do a “worst case” analysis for the case where your circuit is given
a one volt input. If you use 10% resistors, assuming the true resistance
is uniformly distributed, what is the highest voltage you might get out?
What is the lowest voltage? How many semitones above and below the desired
value are these voltages in the Buchla pitch standard?

3) Repeat the above analysis for 5% and 1% resistors.