# ECE4893A: Analog Circuits for Music Synthesis

## Spring 2016

## Homework #3

## Due: Thursday, February 18 at the start of class

This homework will be graded out of 100 points.

**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.**

## Problem 1

In this problem, we will explore

the Advanced

VCO

of the

Bergfotron. The

Advanced VCO is, uhm, a more advanced version of the Complex VCO that

we looked at in class on Tuesday, February 11.

In particular, we will investigate a very small part of the

schematic of its waveshapers. There’s a lot of freaky stuff on

that schematic. We will concern ourselves with the op amp labeled IC2

in the middle of the page (the TL072 is a dual op amp; we will not worry

out the op amp in the upper right corner). This IC2, along with

some additional circuity, claims to produce a sawtooth wave,

labeled “SAW OUT,”

from the triangle wave produced by the Advanced VCO’s core.

Let’s denote the output signal labeled “TRIANGLE OUT,” which is produced

by half of IC9 (not to be confused with the IC9 in the upper left

corner of the page), as V_tri (where I am using the underscores to indicate

subscripts). Let’s denote “SAW OUT” as V_saw.

The square wave produced by the Advanced VCO’s core controls the 4066

CMOS switch; for this case, focus on the switch corresponding to pins

3, 4, and 5 (pin 5 is the control). The 11K resistor and 22p capacitor

in the feedback loop of IC2 seem to form a lowpass filter; however,

computing the cutoff of this filter yields a cutoff of 658 kHz. This

is far above the range of human hearing, so I presume the 22p capacitor

is there for stability and general gremlin-eating. So, let’s ignore

(i.e. open) that capacitor.

The 20K and 68K resistors attached to pin 2 of IC2, and the 4.7M, 13K,

and 24K resistors attached to to pin 3 of IC2, will all play a role in

this problem. The circle with a + in it connected to the 4.7M resistor

is the +15 volt power supply; the cirlce with the – in it connected

to the 68K resistor is the -15 volt power supply.

a) Find V_saw as a function of V_tri when the 4066 connected

to the 13K resistor is switched OFF. (Assume its OFF resistance is

infinite.)

b) Find V_saw as a function of V_tri when the 4066 connected

to the 13K resistor is switched ON. (Assume its ON resistance is zero).

## Problem 2

In class on Tuesday, Februrary 9,

we looked at exponential converters, particularly

a current “sink” that used a matched NPN pair. In this problem, we will look

at a current “source” that uses a matched PNP pair; the same sort of thinking

we used in class also applies to this variation.

J.G.N. Bergfors, the

creator of the Bergfotron,

conducted a

VCA

shootout

comparing various VCA designs. Let’s take a look at

CA3080

VCA 1. The exponential converter is at the top of the schematic, and

the main VCA is at the bottom part of the schematic.

The power supply voltages are not marked on the schematic or on the webpage,

but based on J.G.N.’s

<A HREF="http://hem.bredband.net/bersyn/psu.htm"power supply design,

let’s assume the VCA uses a +/- 15 V supply.

The exponential converter takes a control voltage “CV” (found in the

upper left of the schematic) and

generates a control current for the OTA of the

form I_{con} = I_{ref} exp(const*CV).

(a) What is I_{ref}?

(b) Assuming that the CV offset trim pot is set all the way to the

“right”

(i.e. at ground), what change in

CV will cause the control current to double? (Assume the PNP BJTs

draw insignificant current throught their bases).

(c) Assuming the OTA is operating in the linear region, give

an expression relating the audio

output voltage to the audio input voltage in

terms of the **current at the control input pin of the OTA.** (You

may ignore the offset trimming circuitry of the OTA. Assume

the positive input of the 3080 is grounded.)

(d) What is the input impedance of this VCA?

(e) What is the output impedance of this VCA? (It might be “0” –

remember we’re assuming ideal op amps.)

## Problem 3

This is a direct continuation of Problem 3 from Homework 2, continuing

to explore

Ray

Wilson’s 1V/Octave Voltage Controlled Oscillator.

(a) Let’s get some practice in reasoning with tempco resistors. In

the example exponential converter shown in class, the tempco resistor was

used in a resistive divider just before one of the bases of

the transistor pair.

Here, Ray decided instead to use the tempco resistor in the feedback loop

of an op amp.

Examining this

schematic, suppose

that R8, R10, R18, R23, R27 aren’t there, and we’ll focus just on the CV1

input through R15.

What is the output of U1-A (pin 1) as a function of voltage

CV1 if the tempco is at a temperature of 25 degrees celcius (the base

resistance is 2K for 25 degrees celcius)?

(b) Now suppose you’re using Ray’s VCO circuit to make sound for an art

installation at the Burning Man Project, which can get up to and above

100 degrees fahrenheit during the day. Redo problem (a), except use

temperature of 40 degrees celcius instead of 25 degrees celcius.