# ECE4803B: Theory and Design of Music Synthesizers

## Spring 2006

## Homework #6

Due: Wednesday, April 5th at the start of class

**Ground rules on this homework:** You may *verbally*

discuss approaches to the

problems with each other *while looking at the schematics*, and

are encouraged to do so; but you

may not *look* at each other’s written

solutions or ask “what did you get on

part XYZ of problem ABC.” (In future homeworks, I will allow

varying degrees of

explicit collaboration on certain problems.)

Below, I will use underscores to indicate subscripting.

### Problem 1

What is the “cutoff” frequency (i.e. the omega_c from lecture)

of Rene

Schmitz’s MS-20 clone as a function of the current

at the control pin of the CA3080s? (You should be able to do this

by just using the formula for omega_c for the Sallen-Key in terms of

the gains and capacitors; just include the gain of the resistive

divider at the input of the OTA together with the gain of the OTA.)

### Problem 2

Pick one of the state-variable VCF schematics below based on on the

second-to-last

digit of your GTID number.

a) Are the variable-gain integrator stages inverting or non-inverting?

(Be sure to consider the *combined*

effect of both the OTA and the op-amp,

*if* an op-amp is being used as an integrator.)

b) What is the “cutoff” frequency as a function of the current at the

control pins of the OTAs? (Again, just include the gain of the resistive

divider at the input of the OTAs together with the gain of the OTA and you

should be all set.)

0-3)

Oberheim SEM VCF – you want to look at the page that says “VCF.”

4-6)

ASM-1 VCF – ignore the 30 pF caps.

7-9) PAiA

9730 VCF – either Filter A or Filter B (they have

the same integrator structure.)

### Problem 3

Choose a schematic below based on the second-to-last digit of your GTID number.

The patented Moog transistor ladder VCF contains a cascade of four

one-pole lowpass filter sections. Find the cutoff frequency of

*one* of those sections as a function of the control current

being pulled from the tied emitters of the transistor pair that feeds

the ladder. Two things to note: 1) Notice that when analyzing the Moog

VCF, we don’t include a

resistive divider in the gain as we’ve done in other VCF cutoff computations;

there is a resistive divider right at

the first input, but it’s not important for our frequency analysis. 2)

I wrote expressions on the board for a one-sided ladder; for a real

Moog two-sided ladder, the control current gets split between the two

halves of the ladder, so you get a transconductance gain from each

transistor pair that’s like that of an OTA, and the formula for the

cutoff is basically the same as for the OTA-C filters we looked at

earlier (except we leave out the resistive divider).

If you don’t see a specific unit on a capacitor, there’s usually an implied

“microfarads.”

0) Monowave

VCF – The Monowave was designed by

Paul Maddox,

a synth DIYer who hand-built

and sold 25 as a limited edition; he’s now declared

the project “hardware open source.” See the whole thing

here!

1) Oberheim OB-Mx

– Strangely, Tom Oberheim had nothing to

do with this synth; Gibson had bought the rights to the Oberheim name.

Don Buchla was called in to try to save the project, but it eventually

wound up released before it was really ready against Buchla’s wishes.)

2) Minimoog VCF

3) Moog Modular 904A VCF – assume the “Range 1” capacitor

is switched in (notice the ladder is drawn “sideways,” at the bottom of

the page)

4) Moog Modular 904A VCF – assume the “Range 2” capacitor

is switched in

5) Moog Modular 904A VCF – assume the “Range 3” capacitor

is switched in

6) Moog Rogue (see last page for schematic)

7) Moog Prodigy (see last page for schematic)

8) Moog

Source

9) Memorymoog (this is a reduced snippet

of a much larger scan, Sheet1.tif, found

here).