# ACMS 2015 – Homework #5

ACMS 2015 – Homework #5

# ECE4893A: Electronics for Music Synthesis

## Due: Tuesday, April 14, by 7:30 PM

This homework will be graded out of 100 points.

Turn-in procedure:
We no longer have usual lectures.
If you happen see me, you can give it to me in person; otherwise, just slip
it under my Van Leer 431 office door. I will collect them from my
office around 7:30 PM on April 14.

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 bad.
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.

No late turn-ins accepted, since I will need to post solutions quickly
so you have a chance to look at them before Quiz 2, which will be on
Thursday, April 16.

## Problem 1

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_n, the natural frequency of the 2nd-order filter
in Hz, 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 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 natural frequency f_n. (I might have called
this f_n 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_n (the natural frequency in Hertz)
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’s ele4music.com site seems to no longer exist, but
the EFM VCF8E documentation
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 natural frequency (in Hertz), f_n, 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 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.)