# ECE4893A: Electronics for Music Synthesis

## Spring 2008

## Homework #4

## Due: Tuesday, April 8 – turn into Logan between 12:05-1:25 in the

Senior Design lab

**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

may result from such behavior.

**Late policy:** 20 points off per day.

This isn’t to be mean – it’s

to encourage you to get it turned in and

get on with 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.

**If you are going to turn it in late, you will need to make arrangements
with Logan to get it to him.**

### Problem 1

In class, we look at second-order filters whose transfer functions had

denominators of the form

w_0 s^2 + ----- s + (w_0)^2 Q

Recall that to get unity gain at infinity, the highpass version of the

filter had a s^2 in the numerator; to get unity gain at 0,

the lowpass version of the filter had a (w_0)^2 in the numerator; and to

get a unity gain at w_0, the bandpass version had (w_0)/Q in the numerator. We

will use these conventions in this problem, where we further explore

the mathematical properties of second-order filters.

a) In class, we found the half-power frequencies

of the bandpass filter. Find

the half-power frequencies of the highpass and lowpass filters

as a function

of w_0 and Q. Simplify your expression as much as possible.

b) Find the quarter-power frequencies of the highpass and lowpass filters

as a

function of w_0 and Q. Simplify your expression as much as possible. What

does your expression simplify to for Q = 1/2?

c) For a fixed normalized frequency of w_0 = 1, make a plot showing how the

poles migrate as Q is increased from values near 0 to high values of Q.

You can probably do this by using MATLAB to make a vector of Q values,

and hand sketching a smooth curve connecting between the resulting poles.

Be sure to specifically label some of the poles with the value of Q

that made those poles (you need only label one of the pair, since the

poles are always symmetric.) Be sure to label the particularly interesting

values of 1/2 and 1/sqrt(2).

### Problem 2

Let’s check out

Ray Wilson’s

State Variable VCF 12dB/Octave With VC Resonance.

The schematic is drawn as a strange twisted psychopretzel, but 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 voltage. 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 w_0.

a) Are the variable-gain integrators inverting or non-inverting?

b) Find

w_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) What is the output impedance of the HP, BP, and LP outputs?

### Problem 3

The Mutron III is a state-variable filter that uses light-dependent

resistors to vary the cutoff frequency. The original Mutron III schematics

I’ve found on the web are difficult to read, so let’s take a look at

a modern clone called the Neutron. You can find the schematic

of the Neutron in

the

Neutron

Filter

construction guide.

a) Find the f_0 of the filter

for the following four conditions:

- Caps C5 and C7 switched “out”; LDRs = infinite ohm
- Caps C5 and C7 switched “out”; LDRs = 5 kohm
- Caps C5 and C7 switched “in”; LDRs = infinite ohm
- Caps C5 and C7 switched “in”; LDRs = 5 kohms

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

Aaron’s datasheet collection), what control current would

generate a 5 kohm LDR resistance? Use curve #4 on the graph (you’ll see

what I mean when you look at the datasheet). (Note I haven’t actually

analyzed the control circuit in detail, so I’m not sure such a current

could be produced by this circuit, but my intuition says it’s plausible.)

c) Consider the “Peak” 150K pot. As the wiper is moved to the left

on the schematic, does the Q increase or decrease? Explain your reasoning.

### Problem 4

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 I was able to find it on

Dave

Magnuson’s analog modular page.)

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 an f_0 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 w_0 of a Sallen-Key filter.

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 5

In class, we looked at the

Buchla 292C Lowpass Gate. We focused primarily on

the main Sallen-Key part of the filter. In this problem, we’ll look at

the circuit that creates the current for the vactrol LED.

Look in the upper left corner of the schematic. To simplify things, let’s

assume that the leftmost CMOS switch is “off,” and we will ignore C2 (treat

it as closed, i.e., close the cap). Also ignore D1 (treat it as open) –

as far as I can tell, when the circuit is operating normally, it doesn’t

come into play. Suppose the R8 pot is set to the middle (i.e. it forms

two 10K resistors).

a) Find the current through the vactrol diode as a function of the

control voltage input at jack 11 in the upper left hand corner of the

schematic. (Note:

This doesn’t match any standard op amp circuit I am aware of. I tackled it

it by writing two node-voltage equations and solving them.)

b) Find the voltage at the output terminal of op amp 9 as a function of

the control voltage input at jack 11. Assume that the vactrol LED has

a “diode drop” of 1.65 volts. I found this figure on the VTL5C3 datasheet.

(The answer to this question is less important than the answer to (a),

but it is useful since it tells you how far the output of the op amp

needs to be able to swing.)

<!–

### Problem 5

Spend some time browsing through the

Korg MS-20

Owner’s Manual and the

Korg

MS-20 Setting Examples.

Choose a patch setting example from the

documentation that uses at least one patch cable.

Set the knobs and connections on our MS-20 to match the settings on the

patch sheet, and take a photo of you smiling next to the MS-20 set up with

your patch. Your photo should also show that you have the MS-20 hooked to

speakers to prove you actually listened to it. ðŸ˜‰

Include a printout of the original patch sheet and your photo.

You should also just spend time time playing around with the MS-20.

To avoid too many people trying to use the MS-20 at once, try not wait

until the last minute to do this problem.

–>