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2014 March 2

Colorimeter design—weird behavior

In Colorimeter design—almost working, I talked about the prototype colorimeter made out of foamcore, and the non-linear behavior of its phototransistor circuit. I suggested some possible reasons for the non-linearity, and I tried experiments this weekend to try to remove the problems.

The first thing I did was to remake the dilution series, with one drop of blue food dye in 10ml of distilled water for the highest concentration, then twofold serial dilution to get 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, and 1/128, each in its own cuvette.

The next thing I did was to make a transimpedance amplifier (current-to-voltage converter), so that I could have a constant voltage across the phototransistor, even as the current changed. I also made it so that I could swap out the phototransistor and use a photodiode instead, to see if that gave me more linear behavior.

LED circuits and transimpedance amplifiers for phototransistor and photodiode. The phototransistor amplifier has a gain of 100kΩ, and the photodiode one a gain of 22.4MΩ.  Only the 627nm LED has been tested so far. Both are intended for differential (E20–E21) analog-to-digital conversion.

LED circuits and transimpedance amplifiers for phototransistor and photodiode. The phototransistor amplifier has a gain of 100kΩ, and the photodiode one a gain of 22.4MΩ. Only the 627nm LED has been tested so far.
Both are intended for differential (E20–E21) analog-to-digital conversion.

I have not yet managed to get full-scale range with the phototransistor—the 1/64 and 1/128 dilutions often come out having lower absorbance than the blank! I did manage to get some decent series with the photodiode:

I began and ended with a blank (distilled water only) cuvette.  The difference between the beginning and the ending values is fairly large (an absorbance of about 0.02), and probably reflects changes in alignment of the optical components, which are not very rigidly held by the foamcore.

I began and ended with a blank (distilled water only) cuvette. The difference between the beginning and the ending values is fairly large (an absorbance of about 0.02), and probably reflects changes in alignment of the optical components, which are not very rigidly held by the foamcore.

The high gain on the photodiode transimpedance amplifier causes another problem: 60Hz pickup from capacitive coupling. I get a 60Hz signal that is quite large compared to the DC signal I’m interested in. Adding a 0.022µF capacitor in parallel with the 5.9MΩ resistor got rid of most of the 60Hz noise (a corner frequency of about 1.2Hz). It may be better to use 0.01µF, for a corner frequency of 2.7Hz—that seems to work fairly well also, and may give a bit better time-domain response to changing absorbance.

My first calculation of the desired capacitor size was way off (what I get for doing it in my head instead of with a calculator).  Using only a 100pF capacitor did not reduce the 60Hz noise.

My first calculation of the desired capacitor size was way off (what I get for doing it in my head instead of with a calculator). Using only a 100pF capacitor did not reduce the 60Hz noise.

Adding a 0.022µF capacitor in parallel with the 5.6MΩ resistor did clean up the 60Hz noise.

Adding a 0.022µF capacitor in parallel with the 5.6MΩ resistor did clean up the 60Hz noise.

The values from three runs (no capacitor, 100pF, and 0.022µF) were monotonic (except for one or two measurements of 1/64 and 1/128), fairly consistent, and substantially larger than the error in the re-reading of the blank cuvette, so I tried plotting them against the relative concentration:

 Three different sets of measurements with the photodiode colorimeter. Ideally , the measured absorbance should be linear with the concentration, but I am getting a relationship that looks more like the square root of concentration!

Three different sets of measurements with the photodiode colorimeter. Ideally , the measured absorbance should be linear with the concentration, but I am getting a relationship that looks more like the square root of concentration!

I’ve been getting pretty frustrated with this design, as I have no idea where the non-linearity is coming from.  I’ve checked that both Beer’s Law and the current from a photodiode refer to the same measure of light intensity (W/cm2).

The non-repeatability of the measurements (which is probably due to changes in the light path from movement of the LED and photodiode) also limits the usefulness of this colorimeter.  If I could figure out was going wrong with the light measurement and conversion to absorbance, I could probably fix the changing light path by making a new holder out of sturdier materials—drilling 3mm holes in wood or aluminum is pretty simple.

I did try to do some debugging—the problem is not in the Freedom board or the software, as the voltages reported by the Freedom board are consistent with ones measured with a multimeter, and calculating absorbance from the multimeter measurements gives me the same numbers as the program on the Freedom board (within measurement errors).  The dilution series looks good—if I stack cuvettes,  1/2+1/4+1/8 is almost as dark as 1/1 (and similarly for other combinations).  That leaves only my understanding of how photodiode currents are generated and how transimpedance amplifiers convert current to voltage as potential failures (unless I’m missing something obvious).

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2014 February 26

Colorimeter design—almost working

Filed under: freshman design seminar — gasstationwithoutpumps @ 00:34
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Since my freshman design students did not show much interest in designing their own colorimeters, and my son has just gotten to the colorimetry labs in his online AP chemistry class, I decided to prototype my own colorimeter design.  (His AP lab relies on eyeballing the light through two columns of fluid and adjusting the length of the light path through one until the intensities seem to match—that’s a very low tech approach, but it seems rather tedious.)

I had made a prototype colorimeter out of black foamcore,which I mentioned in Seventh day of freshman design seminar. I’d meant to blog about it earlier, but I got a bad virus infection of some sort and was out of action for a while.  The prototype I’d made earlier was not very functional—it fit the cuvette tightly, but did not provide an easy way to remove the cuvette from the colorimeter.  I went through two more prototypes today that would allow me to remove the cuvette, but they looked like they would have bad light leaks.  I finally settled on a 4th design, that uses a separate lid, rather than trying to make a hinged lid.  I’ve included a PDF file that has the design for this version: Colorimeter-draft4.

I constructed the colorimeter by spray-gluing the pattern I made to the black foam core, then carefully cutting it out with a razor knife.  The dashed lines are cut only through the top layer of paper and part way through the foam—bending the foam core then snaps the rest of the foam and leaves the paper on the back as a hinge.  I used black electrical tape to hold the colorimeter together, and to block light from coming through the backs of the phototransistor and the LED.

Top view of the colorimeter with the lid in place.

Top view of the colorimeter with the lid in place.

Top view of the colorimeter with the lid off and the wings open to allow grasping the sides of the cuvette.

Top view of the colorimeter with the lid off and the wings open to allow grasping the sides of the cuvette.

I connected the LED through a current-limiting resistor to the 3.3v supply on the Freedom KL25Z board, and the phototransistor with a current-to-voltage resistor to E22. I actually ended up doing two different circuits, using different LEDs:

    I started with the circuit on the left, using a deep red LED that has a peak wavelength of 700nm. Later I switched to a different LED, with a peak wavelength of 627nm. In both cases, I picked the current-to-voltage resistor so that I got near full-scale readings on a blank cuvette.

I started with the circuit on the left, using a deep red LED that has a peak wavelength of 700nm. Later I switched to a different LED, with a peak wavelength of 627nm. In both cases, I picked the current-to-voltage resistor so that I got near full-scale readings on a blank cuvette.

When the KL25Z is reset, the analog-to-digital measurement on E20 is recorded as the intensity for the blank cuvette.  Then the transmittance (measurement/blank) and absorbance (–log10(transmittance)) are reported 10 times a second on the USB serial line.

With the 700nm LED, I could measure from A=0 to A=1.8 (with an opaque piece of foam core blocking the light). Light leakage around the cuvette and from the outside prevented me from measuring higher absorbancy.

The first thing we tried measuring was a solution of blue food coloring (blue dye #1). My son made a stock solution of 1 drop in 10 ml, and we measured the absorbance (with the 700nm LED) at about 0.0028, which seemed rather low to us. He then made a very concentrated solution with 5 drops in 5ml, which looked almost black to us, and the colorimeter reported it as having an absorbance of 0.157, which seemed absurd—that’s almost clear! We tried looking at the sky through the solution and noticed that the sky looked deep red through the blue. This lead me to suspect that the dye was transparent in the near IR where much of the light from the LED was concentrated.

When I switched to a 627nm LED, I had to use a larger current-to-voltage conversion resistor, as the phototransistor is less sensitive to those wavelengths. This meant that the noise level from light level was increased, and so an opaque object read as absorbance around 1. The stock solution read as 1, as did a 2-fold and 4-fold dilution. We went to a 40-fold dilution (so equivalent to 1 drop in 40ml) and got a reading of 0.637. From there, we started 2-fold dilutions:

dilution Absorbance at 627nm
1/40 0.637
1/80 0.407
1/160 0.230
1/320 0.139
1/640 0.0679
water 0.0040
1/1280 0.0380

I was worried that cuvette was stained by the dye, but putting in distilled water after the 1/640 dilution showed that any residual staining could only be contributing a small error.

Here is a plot of one run of the colorimeter:

The colorimeter is reset with a blank cuvette (filled with distilled water).  After a few seconds the blank is removed and the test cuvette is inserted.  After waiting about 20 seconds, it is removed and the blank re-inserted.  The absorbance is fit on the flat part in the middle.  Note that the colorimeter did not return exactly to 0 on this run.

The colorimeter is reset with a blank cuvette (filled with distilled water). After a few seconds the blank is removed and the test cuvette is inserted. After waiting about 20 seconds, it is removed and the blank re-inserted. The absorbance is fit on the flat part in the middle. Note that the colorimeter did not return exactly to 0 on this run.

The data from the run did not fit the straight line of Beer's Law.  It did fit a power-law curve, but the exponent is too low.

The data from the run did not fit the straight line of Beer’s Law. It did fit a power-law curve, but the exponent is too low.

I’m now trying to figure out why we did not get a good fit for Beer’s Law. Here are some possibilities:

  • The dilutions were not done accurately.  That would explain random fluctuations, but seems unlikely to give such a clean, consistent deviation from theory.
  • Beer’s Law doesn’t apply to this example.  That seems really, really unlikely, since this is the canonical experiment done by 1000s of students a year.
  • The colorimeter is not linear.  I’m relying on the phototransistor providing a current proportional to light intensity, even though the voltage across the phototransistor varies.  I think that this is likely to be the problem.  To check it, we’d have to redo the experiment with a different circuit—probably a transimpedance amplifier to do the current-to-voltage conversion.

Unfortunately, my son did not keep all the serial dilutions, so to test a different colorimeter circuit I’d have to make a new series.  I might do that this weekend if I have time.  At least I know what stock concentration to start with—about one drop of food color in 25ml of distilled water.

I’m also interested in trying the colorimeter design with an RGB LED, so that we could try different wavelengths—perhaps doing a Beer’s Law test with yellow food coloring.

2014 February 11

Ninth day of freshman design seminar

Filed under: freshman design seminar — gasstationwithoutpumps @ 17:10
Tags: , , , , ,

The astute reader of this blog may notice that there was no “eighth day of freshman design seminar” post.  I was sick last Wednesday and unable to attend class, so I had the group tutor (a senior in bioengineering) take the class and have them discuss possible projects to take on.  I asked them to turn in proposals yesterday, but forgot to collect them—I’ll collect them tomorrow.  We’re about halfway through the course, so it is time for students to start on their projects.

I returned two homeworks yesterday: the colorimeter design and the RGB LED resistor sizing.

The colorimeter designs were not very good, lacking necessary details, but were somewhat better than previous spectrometer attempts. I think I’ll try reversing the order of those assignments in future, as the colorimeter is a simpler device. The biggest problem with the designs is that most of them were pieced together from web pages, with no citations.  Two of them were blatantly copied from Science Buddies, which has a decent design, but the students did not cite the source. I yelled “Cite your sources!” at the class, and explained that I could have flunked several of them out for plagiarism, and that in an upper-division course I would have. I hope they get the message, so that they don’t fail out later on. I decided not to prosecute academic integrity cases in this 2-unit, optional course, though I am making the science-buddy copyists redo the assignment.

I then explained to students the mistake I had made in the photodiode explanations (see Lying to my students) and corrected the understanding of the “open-circuit voltage” spec from the photodiode datasheets. I think that the students are a little more comfortable about finding things on datasheets now—I hope that lasts for them.

We then went over one of the RGB LED datasheets and did the resistor sizing for it.  About a third of the class had done a decent job on that assignment, and I cleared up the common mistakes:

  • If a battery is used in a schematic, both ends need to be connected.  Other options are to use +5v and Gnd port symbols, or a +5V DC voltage source symbol.
  • The LED diode must be forward biased (with a large current flow), and the triangular shape of the diode symbol shows which way conventional current flows.
  • The voltage needed for determining the resistance is the voltage across the resistor, not the voltage across the diode, so it is 5v–VF, not VF.

I think I managed to get these points across—I relied fairly heavily on asking the students to do each step, so I’m pretty sure that at least half the class can now size a resistor for an LED.

Finally we could get to some new material. I wanted to show them how to program an Arduino, so we built up the standard blinking-LED first example for an Arduino.  To make it a little more interesting, I started with a true statement—I did not know whether the LED on pin 13 was hooked up with the anode or the cathode connected to pin 13.  We looked at the two possible circuits and how they would behave differently when the pin was high and when it was low.  I then explained “void setup()”, “void loop()”, and “pinMode(13,OUTPUT);”.  I had the students come up with the body of loop, feeding them the important constructs (digitalWrite and delay) only once they had expressed the action they wanted.  We ended up with a loop that help pin 13 high for a second and low for ¼ second.  After I typed in the program we had written, I showed them how to select the appropriate board type and download it to the Arduino.  The light blinked, and the students were able to figure out from the pattern of on and off that the LED was connected between pin 13 and GND (with a series resistor), with the anode towards pin 13.

I ran out of time and material at about the same time (a first for this quarter), and assigned the students to read about Arduino programming from the Arduino reference website, with particular attention to “if”, “while”, “pinMode”, “digitalWrite”, “digitalRead”, “analogRead”, and the timer functions.  I expect to go over some analogRead stuff in class tomorrow, and assign a small programming assignment over the weekend, probably using “Serial”.

2014 February 3

Seventh day of freshman design seminar

Today we continued looking at photodiodes, phototransistors, and LEDs, in the context of the colorimeter I had asked them to design.  I think that next year I may go to the colorimeter first, and then to the more complex photospectrometer.  Since the students weren’t familiar with spectrometry, starting with it was of no help, and all the other concepts (absorbance, irradiance, linearity of phototransistors, …) are more than enough to start with.

I started the class by collecting the work I had asked them to do on fleshing out the design of the colorimeter, which I have not read yet. I’ll have to grade their colorimeter designs before Wednesday, but I hope we can start learning some Arduino programming by then (probably just setup, loop, analogRead, Serial.print, and delay), rather than going over the homework.

After reading what they turned in for photospectrometer and photodiode assignment, I’m not setting my expectations very high for the colorimeters.  I think (hope?) that the students are getting something out of the class, if not quite as quickly as I would like. I guess it takes some time for them to turn around habits of a lifetime and start generating new answers and new questions to answer, rather than just coughing back what the teacher said.

I wanted to get to Arduino programming today, but we didn’t get that far. I started with going over the homework, which was to find the resistor values for the following circuit:

Simple circuits for measuring light with an Arduino.

Simple circuits for measuring light with an Arduino. Update 2014 Feb 6: Q1 is intended to be an NPN phototransistor, not PNP as shown here!

  • For Monday, 2014 Jan 27, as individuals (not groups), find a data sheet for the phototransistor WP3DP3BT. Also, select a cheap photodiode that is available in the same size and shape of package as the WP3DP3BT phototransistor and look up its data sheet.For the photodiode and the phototransistor, report the dark current, the voltage drop across the device (that would be collector-emitter saturation voltage for a phototransistor and the open-circuit voltage for a photodiode), and the sensitivity (current at 1mW/cm2 at λ=940nm, which is the wavelength where silicon photodiodes and phototransistors are most sensitive).Find a plot of the spectral sensitivity of a silicon photodiode or phototransistor (it need not be from the data sheets you found—all the silicon photodiodes and phototransistors have similar properties, unless the packaging they are in filters the light).

    We want to make a circuit so that the full-scale (5v) reading on the Arduino corresponds to an irradiance of 204.8μW/cm2 at 940nm, so that each of the 1024 steps corresponds to an increment of 0.2μW/cm2. Remember that 1000μW=1mW. (We may not be able to use the full range, as the circuit should saturate at a somewhat lower value, depending on the saturation voltage or open-circuit voltage of the photodetector.)

    For the circuits above, figure out what values of R1 and R2 to use to get the desired voltage range at A1 or A2. Look up what standard resistance values are available with 2% tolerance, and pick the nearest one. (Hint: Google is your friend for finding tables of information.)

    In class on Monday, we’ll try building this circuit and seeing how it works with the Arduino Data Logger.

  • By Wed 2014 Jan 29, redo the homework originally due on Monday, and turn it in on paper, typed, with the questions echoed and answered in full sentences. If you have any questions, discuss them on the class e-mail list. (I don’t want “I don’t know” to come up for the first time in class—you should have been asking for help over the weekend!)

The first thing I did in class was to go over that homework, giving them useful advice for adapting to college courses:

  • No one computed R2 correctly. It didn’t bother me (much) that no one knew how to do it, but it did bother me that no one asked for help. I tried to impress on them that asking for explanation is not a sign of weakness, and that it should not be their goal to hide from view when they are confused about something. I don’t know whether this rant got through to them, but maybe if they hear it enough they’ll start asking questions in class or on the e-mail list.
  • Only one person cited a source for the plot of spectral sensitivity for silicon photodiodes, and that more by accident than by design (the URL was printed by the browser). I explained the notion of plagiarism to them, how it was the most serious of academic sins, and how other engineering faculty (and me in other courses) might fail them for the course if they continued to claim other people’s work as their own (which is what an uncited figure is).
  • I told them that they had to get very comfortable with the metric prefixes (only femto, pico, nano, micro, milli, kilo, mega, giga—they mostly won’t have much use for the smaller and larger ones) and their single-letter abbreviations.  This is clearly something they need to work on, as one of the common problems in the homework was off-by-a-factor-of-1000 errors, as students changed µW to mW without scaling the numbers.
  • I also impressed on them the importance of typing part numbers accurately—several had mistyped the part numbers for the photodiode they were specifying, and it took me a little detective work to figure out what they had really meant.  Some had not provided part numbers at all, and I could not check whether their numbers were right (those students still got the computations wrong).
  • Only three students found photodiodes that matched the specs: “a cheap photodiode that is available in the same size and shape of package as the WP3DP3BT phototransistor ” and that was sensitive to visible light.  That meant finding a 3mm diameter, through-hole package.
  • Several students found photodiodes in black packages that block visible light, which was not useful for this application.  I explained why such parts exist (listening to IR emitters like in remote controls, without being swamped by ordinary light).
  • Many students, having found photodiodes, could not accurately specify the sensitivity of the photodiode.  Most just reported a current, without specifying the irradiance that caused that current. We went over the notion of linearity and that what we were interested in was the slope of the line, and that units were µA/(mW/cm^2). I mentioned that some spec sheets specified responsivity in A/W, but that had to be divided by the sensor area to get the more useful unit. I then had them compute the current at the specified maximum irradiance and the resistance that would be needed to get that current with 5v across the resistor.  It took them a very long time (algebra skills are much lower than I would have expected for college freshmen—I have more sympathy now for the teachers of freshman physics), but they did eventually get the right answers for both the current and the resistance.
  • I spent a fair amount of time letting students know that units were their friends, and that they should carry the units throughout the computation.  I don’t know if the message got through, but I hope for their sakes that it will eventually.

Finally we could get to some new material. I asked them about monochromatic light sources for the colorimeter.  Some thought of LEDs, but one student mentioned that he had seen incandescent bulbs as much cheaper than LEDs. It took me a second to figure out where this confusion came from—at the power levels used for room lighting, incandescents are indeed cheap and LEDs expensive.  But we don’t need 5–20W of power—we’re not trying to cook what is in the cuvette.  I pointed out that the maximum light level expected for the phototransistor was only 20mW/cm^2, so we needed only mW of power from the light, and at that light level, LEDs were much cheaper than incandescent bulbs.

I showed them the data sheet for a red LED,  and explained some of the concepts. One concept was the difference between peak and dominant wavelength—the peak is where the light has the highest intensity, and the dominant is where it shifts to when multiplied by human visual sensitivity.  I also explained what the “spectral line half bandwidth” was, though I did not go into the difference between half amplitude and half power—it was not important at the moment.

I then went over the symbol for a diode, how I remember that electrons move from the cathode to the anode (bring up vacuum tubes and cathode rays), and showing them a rough sketch of a diode current-vs-voltage curve.  I showed them where various parameters were on the data sheet, though the particular LED data sheet I was using did not include the threshold voltage, just the forward voltage at high current.

The students brought up the notion of having multiple LEDs to get multiple colors, so I introduced them to  RGB LEDs, showing both the common-anode and common-cathode circuits. They figured out, with a lot of prompting, which way round power had to be connected (the mnemonic device I used was that producing light required power, and power is voltage times current, so there had to be current flowing through the diode).

It doesn’t help that photodiodes are used backwards—the photodiode is reverse biased, and current flows only when light produces electron-hole pairs at the back-biased junction.  I carefully did not talk about that while we were looking at the LEDs, as I’m sure it would have confused them.

By this point we were almost out of time, so I assigned a homework:

For Wed 2014 Feb 5, find a through-hole (not surface mount) RGB LED that is common-cathode, and design a circuit to power it from a +5V power supply. Make each color be as bright as possible without exceeding maximum current (you can leave a safety margin of up to 25%). Explain your design and how you sized the resistors for it.

I recommend using Digi-key’s search feature (looking for RGB LED) to see what parameters are usually most important to designers. I recommend using Digi-key’s free web tool SchemeIt for drawing a circuit diagram. They don’t have an RGB LED symbol, but you can make one out of 3 LED symbols (I’d use variant 1 for that).

Bonus: find an RGB LED that is common-anode, and do the same design exercise with it. (If Digi-Key’s search doesn’t turn up a part, try using Google.)

I did show them the prototype colorimeter I made over the weekend out of black foamcore, but did not have time to demo it. I was also going to demonstrate the use of vernier calipers to measure the cuvettes, but again ran out of time.  I’ll probably do a blog post about my first colorimeter prototype later this week, but I’ll need to get to bed early tonight, as I’m grading an elementary school science fair early tomorrow, and I’ve got a bad cold that is leaving me exhausted.  (I’ll have another science fair to judge Thursday morning, so this is not a good week for me to have a cold.)

2014 January 27

Sixth day of freshman design seminar

Today I went into class with a long list of things to get done, but didn’t quite get to all of them:

  • Feedback on first homework.
  • Look at data sheets together.
  • Get class consensus on resistor values from homework due today.
  • Demo the Arduino Data Logger with the phototransistor and photodiode.
  • Discuss next homework (designing a colorimeter).
  • Start talking about Arduino programming.

The feedback on the homework went pretty much as planned.  I told them that the homework was not graded, but that I had both individual and general feedback on it.  Here is a summary of the general feedback:

  • College homework should be typed.  Professors expect it, even if they never say so.  The one exception is math homework, and I recommend to students that they learn LaTeX and typeset even their math.
  • Homework should always be stapled, not loose sheets, which get separated and lost.
  • Hand-drawn pictures are ok for this class (and many other classes), but I strongly recommend learning to use a drawing tool.  Adobe Illustrator is a popular one for those who have money, but Inkscape is an adequate tool for 2D diagrams and is free, though its user interface is rather clunky.  For more professional engineering drawings, I believe that AutoCAD has a free (or very low-cost) version for students. Sketchup and Blender are popular free tools for 3D modeling.  For schematic capture, I now use DigiKey’s SchemeIt, which I demoed briefly for the students (after having some trouble with the wireless connection in the room—I’ll have to check to see whether there is a live DHCP port by the projector cable in the room).
  • Most students added little to what we did in class. I pointed out that K–12 teachers mainly wanted them to spit back what they had been told, but that college professors were usually looking for added value—stuff from reading outside class or from original design.
  • I pointed out the importance of vocabulary (“diffraction” vs. “refraction”, “focus” vs. “collimate”) and of getting the right physical phenomena (Bragg’s Law for diffraction gratings, Snell’s Law and optical dispersion for prisms).  I told them to read the Wikipedia article on optical dispersion, so that they could understand the complexity of determining the wavelength-to-refraction-angle transformation, which is highly dependent on the material the prism is made of.
  • I also suggested that just dumping factoids (like the Bragg’s Law formula) on the paper without explaining the connection to the design didn’t really buy them much.
  • I pointed out the difficult design problem I had given them (300nm–700nm) with a diffraction grating would result in the second diffraction of 350nm at the same location as the first diffraction spot for 700nm—to handle both one would need two optical filters: one for the long wavelength, one for the short.  Even if we limit the range we’re interested in (say to 400nm–700nm), we’d still need a filter, since the sensor would still detect the 2nd-order 350nm spot, even though we weren’t interested in it.
  • I showed a couple of designs for a collimator (a lens and a slit, or a pair of slits on either end of a black tube) and explained why collimation was needed for a spectrometer (none of them had included a collimator).

The feedback took about the amount of time I expected, and I think I managed to communicate the problems without crushing anyone’s egos.  I was careful to tell them that I was not grading them on the homework, but providing feedback for them to do better later on things that would count—particularly that other faculty would often have these expectations of them without ever articulating them.  This freshman class is intended in part to help the students adapt to the college culture in a low-stakes environment.

Simple circuits for measuring light with an Arduino.

Simple circuits for measuring light with an Arduino. Update 2014 Feb 6: Q1 is intended to be an NPN phototransistor, not PNP as shown here!

We then looked at the WP3DP3BT phototransistor data sheet together.  First, I explained the mechanical drawing (dimensions in mm, the diameter sign , the two different ways that the case indicates which lead is which—both the flat and the shorter lead indicating the collector). This prompted a question about the naming of the collector and emitter (since it seemed strange to them that the collector went to the power lead and the emitter to the resistor), so I briefly explained that it was a NPN transistor, that the N’s stood for negative doping resulting in an excess of electrons as charge carriers, and that the emitter emitted the electrons and the collector collected them. I don’t know if that helped anyone.

I then asked the students what they needed help understanding for the numeric part of the data sheet. We ended up talking about 5 of the 7 parameters provided, covering a lot of different things (like that nA stood for nanoamps, not “not available”—a confusion I had not anticipated). I briefly went over milli-, micro-, nano- and explained that engineers preferred using those prefixes to expressing powers of 10, so that the prefer to express the dark current as 100nA, rather than 10-7A. Some scientific calculators provide engineering notation, in which only multiples of 3 are used as the power of 10, and the numbers are between 1 and 999.999999… .

I had to explain the difference between collector-to-emitter and emitter-to-collector voltages, and show the current vs. VCE curve with the two breakdowns. We talked a bit about the saturation voltage (0.8V with an irradiance of 20mW/cm2 and a current of 2mA). I’m not sure I understand that specification that well myself—it mainly tells me that we want to stay well below a 2mA current.

I asked the students for their resistance values from their homework, expecting some fairly random values that would reveal different misunderstandings. What I had not expected is that most of the class had nothing—not even a guess—at the resistance. I would have expected them to ask questions on the class e-mail list if they didn’t understand, but the notion of asking each other (or a faculty member) for help still seems completely foreign to them.

So we spent some time going over how to interpret the on-state collector current: 0.2 nA at an irradiance of 1mW/cm2 of 940nm light. I then had the look for more information that was given in the question, which no one had in front of them:

For Monday, 2014 Jan 27, as individuals (not groups), find a data sheet for the phototransistor WP3DP3BT. Also, select a cheap photodiode that is available in the same size and shape of package as the WP3DP3BT phototransistor and look up its data sheet. For the photodiode and the phototransistor, report the dark current, the voltage drop across the device (that would be collector-emitter saturation voltage for a phototransistor and the open-circuit voltage for a photodiode), and the sensitivity (current at 1mW/cm2 at λ=940nm, which is the wavelength where silicon photodiodes and phototransistors are most sensitive). Find a plot of the spectral sensitivity of a silicon photodiode or phototransistor (it need not be from the data sheets you found—all the silicon photodiodes and phototransistors have similar properties, unless the packaging they are in filters the light). We want to make a circuit so that the full-scale (5v) reading on the Arduino corresponds to an irradiance of 204.8μW/cm2 at 940nm, so that each of the 1024 steps corresponds to an increment of 0.2μW/cm2.

Eventually someone figured out that we wanted a 5v output to correspond to 204.8μW/cm2. I asked what current that irradiance produced. Note that this is a simple linear scaling of the 0.2 nA at an irradiance of 1mW/cm2. It took several minutes for them to do this on their calculators, and several tries before the class agreed on a value (luckily the right one). Now that they had a voltage and a current, I asked them for the resistance that was needed. One student quickly mentioned Ohm’s law, and they set about doing the division. It took them a couple of minutes to do this division on their calculators, and then most of them got it wrong (getting values in the µΩ range!).  Eventually they managed to converge to 122.1kΩ, after almost settling on 12.2kΩ, but what I had expected to be a 30–60-second computation for computing the resistance had taken 10–15 minutes.  The arithmetic and algebra skills of college freshmen are even lower than I had feared.

I showed them a chart of standard resistance values and helped them round to 120kΩ.  I showed them a 120kΩ resistor and measured it with a multimeter to make sure I had the right resistor.  I passed around an Arduino board and a breadboard and explained the point of ther breadboard. I hooked the resistor up in series with the phototransistor (on a pre-prepared breadboard) and used the Arduino data logger to show them the voltage changing as I covered and uncovered the phototransistor. (Next year I should probably reduce the sensitivity they are requested to match to 0.1µW/cm2 per step, as the classroom light was bright enough to move the voltage almost full scale.)

Class had been over officially by 10 minutes at this point (the first time I looked at my watch), so I gave each student a cuvette and asked them to look up what a colorimeter was and design one around the cuvette.

We still need to discuss the photodiode resistance value (I’ll see if anyone figures it out by Wednesday, when I’ve asked them to turn in the homework for real).  We have lab tours on Wednesday, though, so there won’t be time to discuss colorimeters before they design them.  I hope they have the sense to read about them on Wikipedia or the many web sites that give high school labs using them. The actual assignment was

By Mon 2014 Feb 3, design a colorimeter around the cuvette you picked up in class. Your design report should describe the function of the device, explain how it works, have a detailed drawing (with dimensions) of it, have a materials list of what is needed to build it, and give instructions for using it. If there are any computer components, an outline of the needed software should be included also.

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