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:

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.)