Gas station without pumps

2012 December 26

Mic modeling lab too complicated

Filed under: Circuits course — gasstationwithoutpumps @ 23:00
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My son and I cycled up to campus today to turn off the computers in my office and in the lab (since the campus has a 2-day power shutdown starting tomorrow morning).

While we were on campus we checked out the latest version of his data logger code on the Windows machines there.  We found that the installation was incomplete, and my son fixed the driver installation (testing with both an Arduino Uno and an Arduino Duemilanove, as they need different Windows drivers), Timer1 library renaming, and the Path variable on 6 of the machines (benches 7–12).  These six are now all usable, except that the computer on bench 11 has only one USB port (the left port seems to be damaged). We did not update benches 1–6, but might go in next week to do it.

While my son was making sure that the drivers were installed and the other installation fixes, I checked out the function generator.  This was a bit hard, as the output is from a BNC connector, and I had to hunt through the whole lab to find one cable with BNC connector on one end and clip leads on the other.  I’m hoping that the cables are just in storage during break, because we need the function generator for the second lab.  There was no problem driving a loudspeaker from the function generator, and the sine waves are clearly picked up by the microphone.

I also did a bunch more measurements of the I-vs-V DC characteristics of the electret mic, for lower voltages.  This really changes my picture of the DC characteristics of the electret mic. Looking on a log-log plot, I now think we’ll need to piece together two very different models, a linear model for low drain-to-source voltages and a power-law fit for large drain-to-source voltages.  The two-part fit is a common modeling trick for FETs (the linear region and the saturation region), but the saturation region is usually modeled as constant current.

    Current vs. voltage curve for electret mic with more data points, showing that just making measurements from 1v to 10v was a bad idea.

Current vs. voltage curve for the electret mic with more data points than my previous plot, showing that just making measurements from 1v to 10v was a bad idea. The magenta curve (with the log dependence on voltage across the mic) was my previous model, based on data from 1v to 10v.  I don’t know what theory gives the appropriate slope to the saturation current—most of the models I’ve seen make that region constant current.

Unfortunately, I think that this 2-part modeling is too complicated for the bioengineering students to discover on their own and we don’t want to go into such complicated models for FETs, so part of the microphone lab is now too messy for students to do. I mean, I can have them make the measurements, and see that it is a mess, and they can certainly figure out what size bias resistor to use to get a given DC output voltage given their measurements, but I don’t think I can have them do the more complicated fitting and they won’t come away from the lab with a simple model of the mic that they can use for design.

The usual operating conditions for the mic (with 3V across it) are well into the saturation region—I wonder how the mic behaves if the FET is operated in the linear region instead.  Does this introduce a lot of distortion?  If we want to keep the mic in the saturation region (and not linear or sublinear), we have to have at least 0.4V across it, which does put some constraints on the load resistor for converting the current to a voltage.

I’ll have to give some thought to how I’ll modify this lab to make it useful without being overwhelming.




  1. Interesting results. I think you’re using the same electret mic I use, and I’ve never gotten any noticeable distortion that I’ve traced back to the mic. That doesn’t necessarily mean much — by the time that project rolls around, I’m so busy getting students to troubleshoot that I’m not much concerned with modelling the mic, so I haven’t tried to quantify the distortion. Do you have a way to measure harmonic distortion — maybe by feeding the signal into a sound card?

    What range of signal amplitude are you getting from the electret mic? If it’s biased at 3V, I can’t imagine that you’re in any danger of going into the linear region. You mention a load resistor — do you necessarily need one? If the signal will eventually be fed into a non-inverting op-amp (that presumably has megaohms of input impedance), then for the purpose of characterizing the mic, could you use the voltmeter (or scope) as the “load”?

    I know what you mean about not expecting students to come up with the two-part model. I don’t know of a model that accurately represents the slope of the “saturation” region either. I’ve always seen it described as “approximately constant current” but drawn with a slight positive slope, in that way that textbooks often gloss over their choices of abstractions. Would it make sense for students to characterize the mic in the frequency domain instead? My students often find it interesting to discover that “everything is a band-pass filter”, so that when we sweep an entire circuit, the loss of (say) high-frequency signals consists of contributions from every stage. A way to extend their sense-making is to ask, “If we wanted to use this circuit at higher frequencies, which stage would have to change first?”

    Comment by Mylène — 2012 December 28 @ 19:02 | Reply

    • I played with my amplifier circuit some more today. Almost all the distortion I was seeing was from either the input AC-coupling or the AC-coupling of the speaker. I could get rid of most of it by using huge (470µF) capacitors for the DC-blocking capacitors.

      There may be a little crossover distortion from not having a little too much separation between the bias voltages of the nFET and pFET, but I plan to stick in a trimpot and see whether trimming the bias resistor helps.

      The mic is definitely staying in saturation, but I’ll have to discuss that with the students more than I had originally planned, since the linear region is something to avoid here. I kind of like the idea of having them plot the i-vs-v curve, though, since it is not what they would expect (not having had any nonlinear models at the point in the course where they’ll be doing the plot).

      I also found out that the power amp based on a single op amp plus cMOS push-pull output stage was oscillating at around 4kHz,and I had to add a compensating capacitor between the op amp output and the negative input of the op amp. I believe that the problem is that the FETs and the bias network acted as a large capacitive (or RC) load on the op amp,resulting in enough phase change that the feedback signal was shifted. Now I’m wondering whether the power amp stage is too complicated for a first circuits class. I hope not, since I’ve already bought the FETs for the students and scheduled both threshold voltage measurement and the power amp lab.

      Comment by gasstationwithoutpumps — 2012 December 28 @ 20:53 | Reply

  2. […] Mic modeling lab too complicated, I complained about the following graph being too complicated for the 2nd week lab for the circuits […]

    Pingback by Mic modeling lab rethought « Gas station without pumps — 2012 December 30 @ 11:11 | Reply

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