Subj: Sensor calibration
Date: 7/13/2004 3:35:28 PM Eastern Daylight Time
From: bob mcclure
Sensor calibration seems to be the topic du jour. Calibration is a tedious but recommended procedure for the serious amateur.
I wrote the following note on my calibration method to the PSN List on 07/19/2003. At this time, I am adding a dissertation on how to use current applied to the sensor coil and measurement of the resulting force exerted by the coil to achieve calibration. Be reminded of the fact that these calibration methods only determine the sensitivity of the sensor for frequencies greater than the natural resonant frequency of the sensor. Sensor response falls very rapidly at frequencies less than the natural frequency.
Locust Valley, NY
PSN Station REM
APPLIED MOTION METHOD:
1. Set up limit stops on the pendulum so that it can be displaced over a known and fixed number of millimeters at its radius of gyration.
2. Connect the sensor directly to the A/D, and log data as you move the pendulum gently back-and forth a few times between the stops. Record at a rate that gives a reasonable number of samples for the time taken to move between stops. Do not move so fast that you exceed the voltage range of the A/D, otherwise you won't get valid data, and you might even blow out the A/D. Also, verify that the resistance of the sensor coil is low compared to the input impedance of the A/D.
3. Make a WinQuake event file out of the data.
4. Use WinQuake to integrate the data. You should see the actual displacement versus time, measured in counts. Measure the peak-to-peak displacement in counts, using the mouse readout when it is positioned on the trailing edge of one peak to the leading edge of the following peak (which is opposite in sign).
5. Scale the count measurement to what you would have obtained for one centimeter of motion. If you used 5mm of displacement, for example, you would multiply your count estimate by two.
6. Multiply the scaled counts by the voltage gain setting of the amplifier you normally use.
7. Take the inverse of the number obtained in step 6. This is the number you should enter for "Sensitivity:" in the Sensor Information Dialog box.
APPLIED CURRENT METHOD:
Recall the following from your physics textbook:
Generator Law: Volts= B*L*(dx/dt), where
B= magnetic field in Teslas,
L= total length of wire in meters cutting flux lines,
(dx/dt)= velocity of coil motion in meters per second.
Motor Law: Force=B*L*I where F= force in newtons, B in Teslas, L in meters.
Combining the two laws, we obtain V/(dx/dt) = F/I
so, if we measure F/I we know V/(dx/dt), the sensor output in volt-seconds per meter. We don't need to know anything about magnetic field strength or coil configuration.
One newton is the force required to accelerate one kilogram mass at one meter per second. In grams, it is 1000/9.8 = 102.04.
Suppose we apply a current of 5 milliamperes to the coil and measure a force of 40 grams.
I=.005 amperes, F= 40/102.04= .392, F/I= 78.4 volt-seconds per meter.
The equation is simple, but execution of the measurement is not. If you use a countertop digital scale, you have to figure out how to transmit the force from the sensor to the scale. This ususually would require rigging up levers and pushrods. I did this measurement, but using only the component parts -- the magnet and the coil. My coil is a flat pancake, positioned in a 4-pole Nd magnet assembly. What I did was to place the magnet on edge on the scale, and make up a rig to hold the coil in place from the counter top. I then measured the apparent change in the weight of the magnet as current was applied in either direction to the coil. If you use a heavy magnet, you will probably have to secure the coil to the scale, and the magnet to the counter top. Estimate coil current by dividing the applied DC voltage by the coil resistance in ohms.
If you have a sensitive spring scale, that's great. You can probably use it on an assembled sensor. Just be sure that you pull the boom back to its normal rest position when the scale is being pulled upon by the current being applied to the coil. Measure how far from the boom pivot you took the force reading, and estimate the radius of gyration of the pendulum.
By whatever means you measure force, you will have to figure out what the force actually would be at the radius of gyration, which is not usually at the center of the coil. You will have to make lever arm corrections to convert the measured force at the point of measurement to the force at the radius of gyration, which in most cases is very near the center of the extra mass added to the boom.
After you have made the F/I measurement, make the lever arm correction to find the equivalent value at the center of gyration. Divide this F/I by 100 to get volt-seconds per centimeter, and multiply that result by your amplifier's voltage gain. Next, divide your A/D's full scale volts by the full scale digital word value. Usually, you will be dividing 10 by 32,768, yielding 0.000305176 volts per bit. Divide the result by the amplified F/I to get the number to be entered for sensitivity in WinQuake.
You also have the option of letting WinQuake do the calculations for you. Just enter the sensor output (volt-seconds per centimeter) in the "Output Voltage:" box, the amplifier voltage gain in the "Amp Gain:" box, the A/D full scale voltage in the "A/D Voltage:" box, and the A/D bit number in the "A/D Bits:" box, and then click on the "Calc Sens" box. (Note to Dataq users: Always enter 16 for A/D bits, even though the actual number is less. Dataq always scales 10 volts to digital value 32,768, regardless of the number of active bits in the device.)
If you use shunt resistance across the coil to provide damping, you may have to reduce your measured sensor output calibration value. The reduction factor is (Rshunt/(Rshunt + Rcoil). The value of Rshunt must also include the contribution of the amplifier input impedance: 1/Rshunt = 1/Rexternal + 1/Ramplifier. If you leave the shunt in place while making calibration measurements, you do not need to use a reduction factor in your calculations.
I recommend the use of shunt damping whenever possible because it permits easy measurement of natural period (with the shunt removed) and precise control of the degree of damping (amount of shunt conductance applied). It is easiest to use if your sensor has high output combined with low pendulum mass and low coil resistance. The conventional massive Lehman design may not have such properties, however. My own horizontal sensors are at the other extreme. They have a coil resistance of only 340 ohms, a pendulum mass of around 100 grams, and an output of 0.8 volt-sec/cm. Critical damping requires only 30K of shunt resistance. My amplifier input impedance is 100K, and so I add another 90K across that to get proper damping. My vertical sensor is more like a Lehman, with much more mass and much more coil resistance. Even so, I use shunt damping on it, at the loss of some sensitivity.
If you are building a sensor, consider the use of multiple magnets. If you place a horseshoe magnet on one side of the coil, place another with poles reversed on the opposite side. You will get twice the output, and much better linearity. My own preference is a 4-pole magnet assembly using powerful Nd block magnets, a narrow gap, and a pancake coil.
There is another test you can do for vertical sensors, called the "weight lift" test. It can yield both the spectral response and the sensor calibration. See John Lahr's description of that on "AS1 Calibration". I can envision other tests that you could do on either vertical or horizontal sensors, called "tap" tests. I have not worked out the dirty details as yet. For either weight lift or tap tests, you need to know the angular moment of inertia and radius of gyration of the pendulum.
If you can use shunt damping, measuring the damping versus total shunt resistance (coil plus the parallel combination of shunt and amplifier input resistance) can yield the sensor calibration.
The formula is E2 = 2hMwoRd , where
E is the output in volt-seconds/meter,
h is the damping coefficient (0.5/Q),
M is the effective pendulum mass in kilograms,
wo is the natural frequency of the pendulum in radians/sec, and
Rd is the total shunt resistance.
This technique is best applied to geophones, where the output is high and the motion is linear. The formula has to be modified somewhat for pendulums, where the mass and radius of gyration are not usually at the same radius as the coil. Damping is estimated by jarring the pendulum (I use a small capacitor discharged across the coil) and observing the decay of the resulting response. Use the calculator found at
for calculating the damping. Make measurements at various values of shunt resistance to verify that you get a consistent result.