12 November 2004

"The Amateur Scientist" Classics:

Measuring Micrograms

Shawn Carlson

I regret only one thing about moving from San Diego to Rhode Island four years ago. I miss my friends. There are perhaps six people on earth whom I consider to be my close friends, and none of them happen to live here in Rhode Island.

I met two of my dearest friends, Greg Schmidt and George Schmermund, because they decided to rescue me from myself shortly after I started writing for Scientific American. When they found out that the new writer of "The Amateur Scientist" lived in their town and ran his non-profit group as a virtual shut-in, they invited me to join their ad hoc hiking club. My columns had convinced them we were all kindred spirits. And they turned out to be so very right.

George and Greg suffered from the same serious personality defect that I do, a pathological hatred of being told what to do—the "maverick gene" as we used to call it—and that condition made it impossible for any of us to ever be happy employees. It's what drove us out of academe and turned us into citizen scientists. That particular pathology made life pretty hard. Each of us had suffered through long periods when we were barely able to feed our families. But it also had one wonderful benefit—absolute freedom of a kind no 9-to-5er could ever know.

We took full advantage. Every Friday George, Greg and I (and sometimes a few other odd-fellows) would head out into the San Diego County badlands to revel in our independence, in our mutual love of all things science and in the quiet solitude of the countryside. At least once each trip when we reached a beautiful lookout over a distant cityscape, George would point out how right at that moment millions of our fellow San Diegans were working hard to pay the taxes that kept these wild spaces open on weekdays when only we seemed to be able to enjoy them. We stood there imagining them all sitting at their desks, working for us, and we felt like Kings.

I was the academic of the group, the Berkeley-trained nuclear physicist, but I learned so much more from each of them than either ever learned from me. In fact, I never felt more the student than when they would start talking about instrumentation and the methods they had invented to make difficult measurements easy. How wasted they made my time in graduate school seem. I had been forced to live amongst the penumbras of physics, spending years mastering abstruse theoretical abstractions that I knew I would never use again. But these two incredibly gifted citizen scientists lived where the scientific rubber met the experimental road. Their vast experimental knowledge and experience enabled them to develop practical inventions that made it possible for more people to do more measurements than ever before. Over and over again their genius simply astounded me. And I was quite proud to be able to share some of their inventiveness with the rest of the world's citizen scientists through my monthly column.

In the four years since I moved to Rhode Island, not a Friday has gone by when I have not thought about them out there on the San Diego trails, still feeling like Kings. Not a Friday has gone by when I have not longed to stand there along side them. So just as soon as this year's National Citizen Scientist conference in Las Vegas was over, I was planning to head back to San Diego to enjoy one more hike with my gang.

I was therefore totally unprepared when George called just days ago to give me the news. Greg Schmidt had just died—quietly and quite unexpectedly in his sleep from an undiagnosed problem with his heart. The loss terribly diminishes our small community of citizen scientists. Worse than that, he leaves behind a wife, three beautiful children, and a small cadre of close friends who all miss him terribly.

So in tribute to those magical days on the trail, and in fondest memory of my dear friend, I present two projects that came into being somewhere in the San Diego outback when three Kings took on the challenge of measuring micrograms on a shoestring.

Homemade Microgram Electrobalances

Shawn Carlson, "The Amateur Scientist," Scientific American, June 1996.

Expanded November 2004.

Microgram balances are clever devices that can measure fantastically tiny masses. Top-of-the-line models employ an ingenious combination of mechanical isolation, thermal insulation and electronic wizardry to produce repeatable measurements down to one tenth of a millionth of one gram. With their elaborate glass enclosures and polished gold-plated fixtures, these balances look more like works of art than scientific instruments. New models can cost more than $10,000 and often require a master's touch to coax reliable data from background noise.

But for all their cost and outward complexity, these devices are in essence quite simple. One common type uses a magnetic coil to provide a torque that delicately balances a specimen at the end of a lever arm. Increasing the electric current in the coil increases the torque. The current required to offset the weight of the specimen is therefore a direct measure of its mass. The coils in commercial balances ride on pivots of polished blue sapphire. Sapphires are used because their extreme hardness (only diamonds are harder) keeps the pivots from wearing. Sophisticated sensing devices and circuitry control the current in the coil, which is why microgram electrobalances are so pricey.

Believe it or not, all that is good news for amateur scientists. If you are willing to substitute your eyes for the sensors and your hands for the control circuits, you can build a delicate electrobalance for less than $30.

George Schmermund of Vista, California, is the quiet genius who, so far as I know, is the first citizen scientist to do so. For more than 20 years, Schmermund has run a small company called Science Resources, which buys, repairs and customizes scientific equipment. Although he may be an austere professional to his clients, I know him to be quite the free spirit who spends time in the business world only so he can make enough money to indulge his true passion--amateur science.

Schmermund owns four expensive commercial microgram balances. But in the interest of advancing amateur science, he decided to see how well he could do on the cheap. His ingenious ploy was to combine a cheese board and an old galvanometer, an old-fashioned dial-type device that measures current. The result was an electrobalance that can determine weights from about 10 micrograms all the way up to 500,000 micrograms (0.5 gram).

The precision of the measurements is quite impressive. I personally confirmed that his design can measure to 1 percent masses exceeding one milligram. Furthermore, it can distinguish between masses in the 100-microgram range that differ by as little as two micrograms. And calculations suggest that the instrument can measure single masses as slight as 10 micrograms (I didn't have a weight this small to test).

The crucial component, the galvanometer, is easy to come by. These devices are the centerpieces of most old analog electric meters--the kind that use a needle mounted on a coil. Current flowing through the coil creates a magnetic field that deflects the needle. Schmermund's design calls for the needle, mounted in the vertical plane, to act as the lever arm: specimens hang from the needle's tip.

Electronic surplus stores will probably have several analog galvanometers on hand. A good way to judge the quality is to shake the meter gently from side to side. If the needle stays in place, you're holding a suitable coil. Beyond this test, a strange sense of aesthetics guides me in selecting a good meter. It is frustratingly difficult to describe this sense, but if I'm moved to say, "Now this is a beautiful meter!" when I look it over, I buy it. There is a practical benefit to this aesthetic fuzziness. Finely crafted and carefully designed meters usually house exquisite coils that are every bit as good as the coils used in fine electrobalances, sapphire bearings and all. But, since most dealers in electronic surplus think of these extraordinary devices as just one step above junk, you can buy them for just a few dollars at any such outlet.

To build the balance, gently liberate the coil from the meter housing, being careful not to damage the needle. Mount the coil on a scrap sheet of aluminum as shown in Fig. 1. If you can't use aluminum sheet metal, mount the coil inside a plastic project box. To isolate the balance from air currents, secure the entire assembly in a glass-covered cheese board, with the aluminum sheet standing upright so that the needle moves up and down. The two heavy guard wires cannibalized from the meter are mounted on the aluminum support to constrain the needle's range of motion.

Epoxy a small bolt to the aluminum support, just behind the needle's tip. The needle should cross just in front of the bolt without touching. Cover the bolt with a small piece of construction paper, and then draw a thin horizontal line across the center of the paper. This line defines the zero position of the scale.

The specimen tray that hangs from the needle is merely a small frame that is home-fashioned by bending a short length of non-insulated wire. The exact diameter of the wire is not critical, but keep it thin; 28-gauge wire works well. A tiny circle of aluminum foil rests at the base of the wire frame and serves as the tray pan. To avoid contamination with body oils, never touch the tray (or the specimen) with your fingers. Instead, always use a pair of tweezers. To energize the galvanometer coil, you'll need a circuit such as the one in Fig. 2 that supplies a stable five volts. Do not substitute an AC-to-DC adapter for the batteries unless you are willing to add filters that can suppress low-frequency voltage fluctuations.

The device uses two precision, 100-kilohm, 10-turn, variable resistors (also called potentiometers or rheostats), the first to adjust the voltage across the coil and the second to provide a zero reference. A 20-microfarad capacitor buffers the coil against any jerkiness in the resistors' response and helps in making any delicate adjustments to the needle's position. To measure the voltage across the coil, you'll need a digital voltmeter that reads down to 0.1 millivolt. Radio Shack sells handheld versions for less than $80. Using a five-volt power supply, Schmermund's scale can lift 150 milligrams. For larger weights, replace the type 7805 voltage-regulator chip with a 7812 chip. It will produce a stable 12 volts and will lift objects weighing nearly half a gram.

To calibrate the scale, you'll need a set of known microgram weights. A single standard high-precision calibrated weight between one and 100 micrograms typically costs $75, and you'll need at least two. There is, however, a cheaper way. One doesn't need to have weights of standard mass (like 10.0 or 100.0 micrograms). All that is necessary is to have weights of precisely known mass. The simplest way to do this is to purchase a small length of platinum wire and to cut it into at three different lengths of one, five and ten easy to define units. (Platinum is used because it is chemically stable. Most other types of wire will oxidize over time and the chemical reaction will ultimately lead to a measurable change in mass. Just Google "platinum wire" to find suppliers.)

The units you choose will depend on the thickness of your wire and the sensitivity of your electrobalance. Platinum's density is 21.45 grams per cubic centimeter. Platinum wires come in standard diameters starting as thin as 0.025 millimeters. Such a wire, if a pure alloy and perfectly constructed, would have a mass per unit length of 105.3 micrograms per centimeter. So a one-millimeter length of this wire would have a mass of about 10.5 micrograms. (You can easily do the math for other thicknesses yourself.)

If you cut the lengths precisely, you can calibrate your scale at the low end at seven different points corresponding to the seven different ways in which these three weights can be combined. The fact that platinum wire of a given gauge has a known mass per unit length makes it easy to estimate (and I mean only estimate) the mass of each length of wire.

Keep in mind that it is always safer to interpolate—that is, to calculate the mass in between two calibrated points—than it is to extrapolate to values outside the calibrated range. After all, at some point for voltages high or low enough, the system simply must fail to be linear. So going too far outside the range in which the instrument's response is known can trap you in experimental quicksand in a hurry. That means that you can't really be sure of your measurements until you calibrate your device at both the high and low ends of the range.

I tried to construct a high-mass calibration weight by making a standard platinum wire that weighed precisely 500 unit wires by making my unit length exactly 2.0 millimeters and the high-mass length 1.00 meters. Unfortunately, the results were disappointing, because getting an accurate length required the wire to be pulled so taught along the meter stick that the wire stretched. So I resorted to making a much shorter length of smaller gauge (thicker) platinum wire, and estimating its mass using its published mass per unit length. Not ideal to be sure, this solution is functional for many applications. (BTW: If you know of some easy-to-obtain object that has a precisely and accurately known mass in the range of 100-500 milligrams, please email me, and I will share it the rest of the community.)

While it's natural to think about measuring masses in terms of the standard CGS units, keep in mind that many applications don't require it. Sometimes, all you need to know is relative mass—that is, how your much your sample weighs compared to your calibration masses. Using the instrument you can easily know precisely and accurately how many unit platinum wire lengths your sample weighs, and you can calculate roughly the CGS weight of your unit platinum wire. If that's good enough for what you do, you're done. However, if you need to know precisely the accurate CGS weight of your samples, then you need to calibrate your scale against something with a weight that is accurately known in CGS units.

The simplest way I know to get that information is to have your standard platinum wires precisely and accurately weighed on CGS-calibrated microgram scale. For that, I suggest the chemistry department of your local college. Since it only takes a few minutes, it's usually possible to find someone at the university who will be willing to receive your samples, weight them at a convenient time, secure them individually in small sealed envelopes that you supply and return them to you in a larger self-addressed stamped envelop. If you can justify your request as being necessary for a science fair project, you should have no trouble finding a Good Samaritan.

Schmermund's balance is extremely linear above 10 milligrams. The slope of the calibration line decreased by only 4 percent at 500 micrograms, the smallest calibrated weight we had available. Nevertheless, I strongly suggest that you calibrate your balance every time you use it and always compare your specimens directly with your calibrated weights.

To make a measurement, begin with the scale pan empty. Cover the device with the glass enclosure. Choke down the electric current by setting the first resistor to its highest value. Next, adjust the second resistor until the voltage reads as close to zero as possible. Write down this voltage and don't touch this resistor until you have finished all your measurements. Now turn up the first resistor until the needle sinks down to the lower stop, and then turn it back so that the needle returns to the zero mark. Note the voltage reading again. Use the average of three voltage measurements to define the zero point of the scale.

Next, increase the resistance until the needle comes to rest on the lower wire support. Place a weight in the tray and reduce the resistance until the armature once more obscures the line. Record the voltage. Again, repeat the measurement three times and take the average. The difference between these two average voltages is a direct measure of the specimen's weight.

Once you have measured the calibrated weights, plot the mass lifted against the voltage applied. The data should fall on a straight line. The mass corresponding to any intermediate voltage can then be read straight off the curve.

Down Among the Micrograms

Shawn Carlson, "The Amateur Scientist," Scientific American, October 2000.

Expanded November 2004.

I LIVE FOR FRIDAYS. That's because I usually spend that day hiking through the San Diego badlands with an eclectic assembly of iconoclasts, including several brilliant technologists and some of my dearest friends. We connect through our love of instrumentation and our shared passion for developing inexpensive solutions to various experimental challenges. This common interest leads to friendly rivalries, the results of which often feed this column.

Take for instance the problem of measuring extremely tiny masses. George Schmermund developed a fantastic approach, which I described in these pages in June 1996 (see above). George extracted the coil and armature from a discarded galvanometer and mounted them upright, so that the needle of the meter moved in a vertical plane as shown in Fig. 1. He then connected the coil to a variable voltage and adjusted it until the needle was exactly horizontal. A tiny mass of known weight placed at the end of the needle pulled it downward. George then increased the voltage until the arm returned to its starting position. Because a heavier mass required a proportionally larger increase in voltage to balance it, the change in voltage indicated the weight of a sample. George's electrobalance was able to weigh masses as small as 10 micrograms (that is, 10 millionths of a gram).

That achievement was stunning enough for me, but recently the organizer of our weekly outings, Greg Schmidt, realized that even this amazing performance could be improved on. Greg's design eliminates the need to adjust the needle manually. The balance automatically zeros (or "tares") and levels itself, and it can continuously track how an object changes in mass--the rate at which a single ant loses water through respiration, for instance. The result is an extremely versatile electrobalance with microgram sensitivity that can be built for less than $100.

Here's how it works. Greg took George's basic design and added an inexpensive microcontroller (a small computer with its central processing unit and memory all on a single chip), instructing it to send 2,000 weak current pulses through the coil each second. The inertia of the armature and needle prevents them from responding to each short pulse, so the deflection reflects the average current in the coil. The individual pulses do, however, seem to be large enough to vibrate the bearings of Greg's galvanometer. He believes that this slight jitter reduces "stiction," the tendency of a bearing to lock in place when it is not moving. This effect seems to account for why an inexpensive meter like his can respond to the tug of such tiny masses.

Greg didn't design his circuit to reduce stiction, though. This feature turned out to be an unforeseen benefit of using "pulse width modulation" to control the average current sent through the coil. With this scheme, the time between successive pulses is kept the same, but the microcontroller varies the duty cycle-the fraction of the cycle during which the current remains on. Pulse trains with short duty cycles energize the coil for only a smidgen of the total time and so can lift only the smallest weights, whereas pulse trains with longer duty cycles can hoist heavier loads. Greg's microprocessor can generate 1,024 different values for the duty cycle. That number sets the dynamic range of the balance. If the maximum current is set so that the apparatus can lift up to one milligram, for example, the smallest detectable mass will be about one microgram.

Such sensitivity is pretty impressive. Yet the microcomputer that runs the show need not be anything special. Indeed, one has a dizzying array of choices to pick from. But if you haven't a clue how to go about selecting and programming a microprocessor, don't worry: Greg developed his instrument with the novice in mind. He used the Atmel AT 89/90

Series flash Microcontroller evaluation kit, which includes a fully functional and extremely versatile microcomputer, one that linked directly to a personal computer. Atmel has since upgraded this unit with something called the AVR-Starter Kit (model STK-500). The Starter Kit includes everything you need to get going and costs $79 (see Atmel Corporation's Web site for a list of suppliers).

Atmel assures me that this system can be programmed by both the IBM and Macintosh computers. And you don't have to program everything from scratch, because Greg developed all the software needed to run his electrobalance, including instructions that show the weight in real time on a small liquid-crystal display (catalog number 73-1058-ND from Digi-Key; 800-344-4539). You can download his code in PDF format by clicking here. Although I haven't tested this myself, the Atmel's technical folks assure me that Greg's code will run perfectly well on the AVR microprocessor.

As with George's original design, almost any galvanometer plucked from a surplus bin will work. Just make sure that it measures small currents and that its needle tends to stay in place when the unit is rocked rapidly from side to side. Whereas George's prototype required the operator to squint at the needle, Greg's electrobalance senses the position of the needle electronically using a phototransistor and a light-emitting diode. These devices are called either a "slotted optical switch" or a "photo interruptor." You can also purchase these devices from Digi-Key (see catalogue number 365-1008-ND as one possibility). If you decide to go model shopping yourself, keep in mind that Greg's assumes the sensor is a phototransistor, and not a photodiode. Pierce a small piece of aluminum foil with a pin and center the hole on the phototransistor, as shown in Fig. 1. With the foil covering most of the phototransistor, the signal will go from full on to full off very rapidly when the needle interrupts the light from the diode. Attach a sliver of balsa wood as shown to stop the needle exactly at that point.

If too little current is in the coil, the needle will rest on the bottom piece of balsa and block the light. Too much current lifts the needle completely out of the light path. Greg's software uses a sophisticated algorithm to keep the needle balanced between these two states. After the device has been properly calibrated and tared, this pulse width reflects the mass of the sample.

Greg's algorithm uses a wonderful technique called "proportional-integral-derivative" or PID control. In general, PID control is a way of generating a feedback signal that helps regulate the behavior of some complicated system. Lots of things in daily life have feedback. A pothole, for instance, collects water that creates mud under the pavement. When a car drives over the hole, the tire splashes some mud out of the hole. This makes the hole deeper. The deeper holds water better than before. Moreover, when the next car comes along its wheel will fall a litter further downward, causing a harder splash and greater expulsion. As a result, the deeper the pothole gets, the faster it gets dug out and that explains why a minor thumper on your morning commute can grow into a jarring frame rattler in just a day or so. This is an example of positive feedback. In general, a system experiences positive feedback if doing whatever it normally does causes it to want to do even more of it. Positive feedback accelerates systems and can make them very difficult to control.

By contrast, negative back puts on the breaks. A system experiences negative feedback if the farther a system goes in one direction, that harder it is for it to continue going in that direction. A pendulum is an example. The father it gets from its equilibrium point, the greater is the force that pushes it back. That's why pendulums are stable and quite easy to control. Unless you drive them just right, pendulums will happily oscillate about their equilibrium positions forever.

PID control is a way to introduce feedback into a system to rapidly take it from some arbitrary starting state to its stable operating condition. Basically, a computer takes input whatever sensor it is monitoring and measures what's going on. Then it calculates a value for a feedback signal that it feeds into the control input of whatever it is controlling. The equation that the computer uses to calculate that value has three terms, one that is proportional to the size of the sensor's signal at that moment (the "proportional" term), one that is proportional to the rate at which that signal is changing (the "derivative" term), and one that is proportional to the aggregate of the signal over some period of time (the "integral" term). It turns out that no matter what is being controlled, just about everything that one needs to know about where the control signal is compared to where it needs to be can discovered by looking at those three quantities.

By mathematically weighting the importance of these three quantities (P, I and D) in the right way, the feedback can be made to rapidly drive the system towards its stable operating system no matter where it starts. If the system starts out far from where it needs to be, the equation generates a large positive number that the computer converts to a large voltage that drives the system hard in the direction that it needs to go. But when the system gets close to where it needs, the equation gives a negative number that causes the computer to put on the breaks with negative feedback so as to quickly settle in to stable operation. Greg's program does exactly this to rapidly adjust his microgram balance to a new weight, and to track the value of that weight stably over time. (Anyone interested in using microprocessors to control things really needs to understand this powerful technique. It is a deep subject. Fortunately, there are lots of excellent references on the Web. Just Goggle "PID control" and enjoy.)

The control circuit that helps accomplish Greg's magic is shown in Fig. 2. You will need to adjust the value of R1 to set the maximum current to something your meter can handle. The full-scale current might be indicated on the meter. Otherwise, use a variable resistor, a nine-volt battery and a current meter to measure it. Because Greg's galvanometer topped out at five milliamperes, he programmed the microcontroller to create a five-milliampere current by delivering a five-volt pulse across a one-kilohm resistor.

That current is not, however, directed through the coil. Rather it flows through a circuit called a current mirror, which forces an identical current to pass into the coil. This trick dramatically improves the long-term stability of the balance. Why? Because the resistance of the coil depends on its temperature, which rises whenever electrical energy is dissipated inside it. But the mirror circuit keeps the current constant no matter what the temperature of the coil is.

Of course, the resistance of R1 will itself vary somewhat with temperature, which could cause the calibration to drift. So you'll want to use a component with a low temperature coefficient. A 1 percent tolerance metal-film resistor, for instance, typically shifts a mere 50 parts per million for each degree Celsius. You will also need to keep the two transistors in the current mirror at the same temperature to prevent that circuit from drifting. It's best to use a set of matched transistors on a single silicon chip, like the LM194 or LM384 Supermatch transistor pair (part no. LM394CH-ND costs about $6 from Digi-Key). Otherwise, wire two identical NPN switching transistors together with their casings touching as shown.

A delightful demonstration of the sensitivity that his apparatus achieves is shown in Fig. 3. Greg soaked a centimeter of fine thread in water. He then monitored its weight as the water slowly evaporated. Next, he soaked a thread in wine. A mathematical analysis of the resultant curve shown in that graph reveals that the mass curve is actually the sum of two decaying exponentials. The slower one tracks the evaporation of water. The faster one tracks the evaporation of alcohol, which is the more volatile liquid. From this information alone one could calculate the ratio of water to alcohol in a single drop of Greg's wine.

Remarkable.