ECE4803B – Homework #1

ECE4803B – Homework #1

ECE4803B: Theory and Design of Music Synthesizers

Spring 2006

Homework #2

Due: Wednesday, Feb 8 at the start of class

Suggested references: CA3080 and LM13700 datasheets (available from
datasheet collection

Problem 1

Links to ten OTA-based voltage controlled amplifier (VCA) schematics
are listed
below. Choose a schematic based on the last digit of your GTID number.
Throughout this problem, treat all OTAs and op amps as ideal. (Although
you may have high-level discussions with people working on a different
schematic than you, you may not dicuss your problem with anyone who is
working on the same schematic as you. This way I can get independent
interpretations of the circuits.)

a) Assuming that the OTA is operating in a nicely linear region, give
an expression relating the output voltage to the input voltage in
terms of the current at the control input pin of the OTA. Treat
the OTAs and op amps as ideal. (You’ll
see a substantial amount of circuitry devoted to creating about that current.
Don’t worry about that now; we’ll look at that sort of stuff
in another week or so.)

0) VCA
from, attributed to Mikko Helin

Polyfusion 2010 VCA
(see also
– There’s several places to trim offsets that we’ll ignore;
basically, set the + terminals on the 3080 and the TL081 to ground.
Set the gain trim pot wherever you feel like it. Let’s see what else…
Oh, notice the clever current mode
filter (probably designed to dump out noise) between the 3080 and
the TL081 – really high frequencies get dumped to ground. You may
ignore that in your analysis.

2) Serge
Lin/Log VCA
– Ignore the audio DC input; just ground the – terminal
on the 3080. The cap at the audio AC input is just blocking DC, just
short it in your analysis. Ignore the audio trimming circuitry.
The 33K running from the + terminal on
the TL071 to ground is just compensating for nonideal input currents,
you may ignore it. You may also neglect the capacitor in the feedback
loop of the TL071; open it, it’s just there to cut out noise.

3) Aaron
Cram’s Apache VCA
– Let’s just ground the
inverting input, and look the “input” to “signal out” relation.

Bergfotron CA3080 VCA 1

Don’t worry about the offset trim; just ground the + terminal of the
3080. (Am I imagining things, or does does this VCA invert the signal?)

Bergfotron CA3080 VCA 2

Don’t worry about the offset triml just ground the + terminal of the
3080. (Am I imagining things, or does does this VCA invert the signal?)

Ray Wilson’s Dual Voltage Controlled Amplifier
– you can analyze
either VCA-1 or VCA-2; the basic OTA/Op-Amp follower core of each VCA
is the same. You may ignore (open) the cap in the feedback loop.

7) Dirk Lindhof’s Exponential VCA – ignore the caps at
the inputs; they just block DC. This module has two inputs; it looks
like IN2 gives you the option of bypassing the DC blocking cap on that
channel. Anyway, just do the analysis for one input. Ignore the trimming
circuitry, i.e. just ground the + input on the 3080.

– This one has inverting and non-inverting inputs; let’s
focus on the “+ Input,” so ground the + terminal on the 3080. You may
ignore (open) the feedback cap on the TL082 in your analysis.

9) PAiA 9710 VCA – Take a look
at the bottom part of the diagram; you’ll find the LM13600. You may ignore the
op amp’s feedback cap; you may also ignore the trimming ladder
on the + terminal of the LM13600 and just ground that + terminal.

b) What is the input impedance of this VCA?

c) What is the output impedance of this VCA? (It might be “0” –
remember we’re assuming ideal op amps.)

d) What input voltage to the VCA corresponds to 10 mV at the main
signal input pin
of the OTA? (In class, we used 10 mV as a rough figure for where the
OTA starts to become nonlinear; but you shouldn’t consider this number
etched in
stone. For instance, the LM13700 has special diodes that can be used
to give you a wider linear range. We’re just using 10 mV in this subpart
to keep things simple).

Problem 2

In the set of VCA schematics given above,
find an example of an op amp with a
feedback impedance consisting of
a resistor and a capacitor in parallel; this will act as a
single-pole lowpass filter. Circle the example.
The op amp may be taking a current
input (say, from an OTA), or it may be taking a voltage input through a
resistor from the input to virtual ground. Find the cutoff frequency
of the filter (recall that’s 1/(2*pi*RC)).

You may readily find such an example in the VCA-based OTA circuit you
analyzed above; if not, look around at some of the other examples in that
list until
you find one.

Problem 3

This question concerns DC blocking capacitors.

a) Let’s look at the AC input
of the Serge VCA linked to above. The input capacitor
and the two resistors form a single-pole highpass filter.
Find its cutoff frequency. (Note the resistor in series with the cap gives
this configuration a non-unity gain.)

b) Check out
this link. What kinds of capacitors
does the author recommend for use
as DC blocking (i.e. “audio coupling”) capcitors?