# ECE4893A: Electronics for Music Synthesis

## Spring 2011

## Homework #4

## Due: Friday, April 22, by 3:00 PM

This homework will be graded out of 100 points.

**Turn-in procedure:**

We will not have our usual lecture, on either the 22nd or the 25th.

If you happen see me, you can give it to me in person; otherwise, just slip

it under my Van Leer 276 office door. I will collect them from my

office around 3:00ish PM on Friday. If you turn it in after that time, or

if you turn it in *before* that Friday, please e-mail me to let me know

so I can be sure to come in and collect it.

**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 turn it in late by

Monday, April 25, by 3:00 PM, I will still grade it, but 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.

## Problem 1

In this problem,

we’ll

look at the

VCF in the Minimoog (at least the

version linked here; the Minimoog went through several revisions). The

scan I am linking to was posted by someone calling themselves

Fantasy

Jack Palance; this FJP person has

posted

a

lot more info about it, including the story about how

they acquired their Minimoog.

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

“microfarads.”

a) The Moog transistor ladder VCF contains a cascade of four

one-pole lowpass filter sections. In class, I presented an analysis of a

hypothetical

“one-sided” latter

to get a feel for how this kind of circuit works. The analysis

of the actual “two-sided ladder” is a bit more complicated. We’ll rely on

the analysis in Tim Stinchcombe’s

Analysis

of the Moog Transistor Ladder and Derivative Filters, particularly

Equation 13 on page 11. Using this formula,

find the cutoff frequency (in Hertz) of

*one* of those sections in the Minimoog’s transistor ladder

as a function of the control current

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

the ladder.

(Note that when analyzing the Moog VCF, we don’t include a

resistive divider in the gain as we’ve done in OTA-C filter

cutoff computations;

there is typically a resistive divider right at

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

b) Let’s do some DC analysis.

At DC, the caps are open circuits.

For the purpose of this analysis, ignore R76 (the 330 ohm resistor) and

the R73 (the 1K regeneration calibration pot); treat them as “open” too.

Supposing that the transistors draw negligible

current through the bases, what are the voltages

at the bases of the four stages of the

ladder? (Number the stages 1 through 4, from bottom to top).

## Problem 2

Let’s check out the

ASM-1

State Variable VCF. For the purpose of this analysis, ignore (i.e. “open”)

the 30 pF caps C1 and C3.

You should

be able to find the OTAs that are taking the place of resistors in the

variable gain integrators.

You should also be able to find the capacitors

that the output currents of the OTAs are being sent into, as well as

the op amps that buffer the resulting voltages.

Finally, you should be able

to look at the inputs of the OTA and find what resistor you will want to

call “Rbig” and what resistor you will want to call “Rsmall” to form the

Rsmall/Rbig gain factor that you will want to combine with the gain of

the OTA when computing the critical frequency f_0. (I might have called

this f_c in lecture).

Real OTAs have some non-ideal offset; P2 and P3 are trim pots that can help

compensate for this offset. We will assume the OTAs are ideal so you can

assume the positive inputs of the OTAs are grounded.

a) Are the variable-gain integrators forming this SVF

inverting or non-inverting?

b) Find

f_0 as a function of the current fed to the control current inputs

of the OTAs. This should be a simple calculation once you find the component

values you need.

c) If R16 was increased, would the Q of this filter increase or decrease?

Briefly explain your reasoning.

## Problem 3

Let’s take a look at

Tom Gamble’s EFM VCF8E circuit, which is somewhat based on

the Korg MS-20 (but notice the capacitor values are somewhat different).

(Tom appears to have taken down the schematic on his ele4music.com site,

but it was kindly archived by fonik).

It has two

separate filter circuits, but they look more or less the same to me.

a) When switched in the lowpass mode, find the OTA control current

that would

result in a critical frequency f_0

(in some lectures I called this f_c) of 2500 Hz.

(The 10K resistors to the negative supply at

the output of the buffers are just goo needed to make the built-in

Darlington buffers of the LM13700 work.) Remember you can fold the

R_small/R_big factor in with the gain of the OTA when using the formula

for the critical frequency of a Sallen-Key filter. Because the two capacitor

values are the same and the resistor values are the same, this is a

relatively simple calculation.

b) In the original Korg MS-20, resonance is controlled with a pot. Notice

how Tom has modified the circuit to make the resonance voltage controllable.

In class, we showed that for this “Bach” topology, a feedback of K < 2 is

needed, or else the filter will go unstable. What value of control current

for the resonance-controlling OTA would give a feedback of 2? (I conjecture

that

Tom has designed this so that isn't possible, but I haven't checked it

in detail.)

## Problem 4

In class, we briefly looked at the

Buchla 292C Lowpass Gate. The lowpass gate is basically

a traditional Sallen-Key filter with vactrols (light-dependent resistors

packaged with LEDs) replacing the resistors. Buchla employs several other

tweaks; we will ignore many of these in an effort to simplify

the analysis.

In this particular circuit, a single LED drives two LDR elements, so

we can suppose that the resistors in the Sallen-Key have the same resistance.

Using the notation from Session 23,

C4 is the Sallen-Key “feedback cap,” Cf, and C5 is the Sallen-Key

“cap to ground,” Cg. We’ll ignore C3 (open the cap) and R26

(open the resistor). IC8 is being used as a unity gain noninverting

buffer (you can ignore R25; it’s probably just compensating for non-ideal

op amp effects.)

We will assume the circuit is switched into “lowpass filter” mode.

In this mode, the CMOS switch

IC2 with pins 1, 2, and 3 is switched “on” so that the feedback cap C4 is

included the circuit. Also, IC2 with pins 6, 7, and 8 is switched “off,” so

R16 isn’t connected to ground (i.e. is open), and IC1 with pins 1, 2, and 3

is switched “off,” so R15 isn’t connected to ground and IC7 operates as

a unity gain noninverting buffer.

If Buchla doesn’t list units on a cap, that usually means it is in microfarads.

If he wants picofarads, he will typically write “pf.”

a) What is the “Q” of the filter? You can find the needed formula

in your notes from class, or from one of the many

writeups you can find on the web, such as

this one (see

the equation for Q under equation (9) on page 4).

b) We determined that a Q of 1/sqrt(2) was special, since for Q values

above that, the lowpass filter response exhibits a bump. How does your

value from (a) compare with this magical value of 1/sqrt(2)?

e) What is the critical frequency f_0 (in Hertz; again, sometimes I called

this f_c) of the filter if the vactrol resistors

each have an effective resistance

of 10K? You can find the required formula from the same sources listed in

part (a).

f) According to the VTL5C3/2 datasheet (which you can find in

Aaron’s

datasheet collection), what control current

through the LED would

generate this equivalent 10K resistance?

Use curve #4 on the graph (you’ll see

what I mean when you look at the datasheet).

<!–

## Problem 5

Make a brief video demo (at least a minute, but longer is OK)

that consists of you making

interesting sounds on the MOTM system, and upload it to youtube.

Your demo should somehow include

the sounds of an oscillator (or oscillators) going through a filter, with

the parameters of the filter changing over time.

Experiment! Have fun!

I will create a “MOTM demo” topic on the Forums section on T-square.

Post link to your youtube videos there.

As with our previous youtube adventures, because of privacy concerns,

you do not need to show your face

if you do not want to, and you are not required to post under your real name.

–>