# ECE4803B: Theory and Design of Music Synthesizers

Fall 2006

Homework #1

Due: Thursday, Sept. 14 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.

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 four 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 just one of the inputs and specify which 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.

4) Find an instance of a inverting single-pole lowpass filter (voltage in

through a resistor to negative terminal, feedback resistor and capacitor

in parallel from negative terminal to output, positive terminal to ground).

Print out the schematic, circle the instance, and compute its 1/2 power

cutoff frequency (in Hertz) and its gain (at DC).

A few words of warning: In an inverting configuration, sometimes you’ll see

resistor between the positive terminal and ground. These resistors are designed

to compensate for non-ideal op amp effects and may be ignored in your analysis.

## 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;

there are twelve semitones per octave).

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 an infinite input impedance; you also do not

need

worry about input and output protection (assume nobody will be abusing

your module). For this part

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.