# ECE4803B – Homework #5

ECE4803B – Homework #5

# ECE4803B: Theory and Design of Music Synthesizers

## Homework #5

Due: Tues, Nov. 7 at the start of class (I want to send out solutions
to this right away, so just for once, everyone
get it in on Tuesday, OK? I won’t accept
it once solutions are posted. Last semester, everyone just turned in
everything in on time, so I assumed that was the norm for an advanced class.
I’m not sure what makes the Fall semester different.)

In the problems below, I use underscores to indicate
subscripts. In all the problems with OTAs, assume the standard voltage
temperature for room temperature, and assume the OTA is operating in the
linear region. Also, if you see “big” and “small” resistors being used
to divide down input voltages for the OTA, you may make the customary
R_small/R_big approximation we have often used in class and in other homeworks.

### 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
```

I started to blab about how the poles migrate, but realized on the fly
that it was just a little bit too complicated to sketch in real-time
on the board. So let’s look at it here.

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 them.
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

Read Problem 2 from HW #6 from the Spring 2006 offering, and read over
its solution.

Choose one of the three designs listed in that problem using the
scheme described in the problem.
Find the OTA control current that would
result in an f_0 = w_0/(2*pi)
(here I’m using the notation of problem 1; I now think using f_0 and
w_0 is less
ambiguous than calling it a “cutoff”) of 2000 Hz.

### Problem 3

Read Problem 1 from HW #6 from the Spring 2006 offering, and read over
its solution.

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 different). 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 2000 Hz. (The 10 K 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.)

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 assume
Tom has designed this so that isn't possible, but I haven't checked it
in detail.)

### Problem 4

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.