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Velocity response	flat from 0.02 Hz to 30 Hz
Output channels	high gain, low gain, internal temperature, and centering force
Coil Forcing Constant, Gn	9.3 Newtons / Ampere
Coil / Magnet	41.0 ohms, 542 turns 34AWG / N45 magnet
Generator Constant (Ag)	336.2 Volts / meter / sec
Ag High gain output, (Ag HI)	33,599 Volts / meter / sec
Ag Low gain output, (Ag LOW diff)	1,344 Volts / meter / sec
Boom free period	2.3 seconds
Boom moment, M0	87.5 g
ADC board input impedance	38 kOhm
ADC divider ratio	17.0
ADC reference voltage	2.5V
ADC input full scale range, gain=2	+/- 1.25V (-VREF/2 to +VREF/2), Vcm = 2.5V
ADC board full scale range, gain=2	+/- 10.625 V (for -VREF/2 to +VREF/2)
ADC Quantization	2.53 uV/Count (24 bits)
ADC gain flatness	-0.2 dB at 20 Hz
Quantization (HI)	0.0753 nm/s/count. (unfiltered ADC noise: 9 nm/sec pp)
Quantization (LOW diff)	1.88 nm/s/count. (unfiltered ADC noise: 225 nm/sec pp)
Clipping level (HI)	632 um/s
Clipping level (LOW diff)	1.58 cm/s

Measured by U1272A @ 22.2C

The coil constant, Gn, was measured two ways. Unfortunately there's some discrepancy in the two results, but I think this is due to my reconfiguration of the magnet and pole piece, and some slight misalignments.

First, the magnet/coil assembly was tested separately, by placing magnet assembly on a scale, suspending the coil above from an aluminum bar. Inject known current (+/-50mA) into coil and measure change in weight.

Gn =  Δ Weight * 9.81 / current
Less than +/- 3mA, coil constant: 10.5 +/- 1.0 N/A
From +/- 50 mA, coil constant: 9.62 +/- 0.48 N/A.
(These values had been measured with a slight misalignment of the coil.)

542 turns, AWG34, N45 magnet, Rc=43.7 ohms.
Gn = 9.6 +/- 0.5 N/A

GN can be measured with the instrument assembled and operating normally. First record the coil resistance, Rc, and the measured value of Ri. Attach an accurate voltmeter to the"CENT FORCE" output, pin 6, and turn on the seismometer. Balance the boom if necessary and after it stabilizes, record the voltage, VCF . Then place a 500mg weight on the top of the boom at the same distance from the pivot as the center of the coil. If necessary, any approximately 500mg non-magnetic object whose weight is accurately known, such as a #6 brass washer, may be used instead of a 500mg standard weight. After the output on pin 6 settles, record the new voltage. The coil constant Gn = W/ δVCF * 0.00981* (Ri+Rc) N/A, where W is the test weight value in grams..

Using the second method, on a fully assembled instrument, remeasure Gn by using CF output and known mass on boom, at coil mount:

Ri = 14.985K. Rc = 41.0 ohms.
Measured CF = -0.5622 V
Add 500mg calibration weight.  Allow to stabilize 5 minus. CF= -8.513V

delta V = 7.9508 V
delta I = 7.9508 V / (14985+41 ohms) = 5.2914e-4 Amps
delta F = 500e-3/1000 * 9.81 = 4.905e-3 N
Gn = F / I = 4.905e-3 N / 5.2914e-4 A

Gn = 9.27 N/A

First, the instrument may be assembled without the spring and the effective boom weight measured by means of a sensitive scale, arranged to support the beam so that it is level, at a point which is the same distance from the pivot as the center of the coil/magnet. That gives M0. When using particularly flexible (Kapton) flexures, watch to be sure that without the spring, they aren't flexing downward too much during the measurement.

Spring: 4.7g
Boom w/o spring or weights (including vertical brass threaded rod): 165.1g
Boom with weights: 210.3g
Hanging support: 10.5g + 0.5g nut = 11.0 g
Measured weight at nominal position: 98.5g

Net boom mass, M0 = 87.5g
M1 is difficult to measure. Estimated 110 g

Free period was measured by disconnecting the coil, selecting GAIN=1 by removing JP1, and measuring POSN_ERR output while generating an impulse with a canner air duster. This was repeated several times. The measurement was made 7.5 seconds after the impulse to try to capture the small signal reponse. Period was measured on the scope to be 2.3 +/- 0.1 sec. An FFT of the data indicated a period of 2.26 sec. Zeta was determined to be 0.15, by fitting the data to a damped harmonic oscillator.

  

To measure the sensor gain, remove jumpers JP1 and JP2 and unplug the connection to the forcing coil. Arrange for the boom to seek its upper stop, either by installing and adjusting the spring or by means of an external spring such as a rubber band gently lifting the boom. Mount a micrometer or micrometer head to press down on the boom at the same distance from the pivot as the center of the coil. Mount the micrometer so that it can move the boom over its vertical range. Starting with the boom approximately centered, connect a meter to the 'POS ERR' output, pin 7 and turn on the electronics. After the voltage stabilizes, using the micrometer, move the boom in steps in both directions from center over about half its range, approximately ±0.4mm or ±0.015", while recording the micrometer readings and corresponding output voltages. The slope of the data curve at its zero-volt point (change in voltage/change in position in mm) should be approximately 12.5V/mm, which, multiplied by R6/R29 (nominally 1/10), will give the value of rsensor

Since I didn't have a micrometer head, I chose to do this measurement on my mill. Rubber bands provided upward tension on the boom. A pointed tip in the chuck pressed down on the boom at the coil mount screw. The Z-axis DRO measured position as I recorded POSN_ERR output voltage.





Notice how the zero crossing is not in the symmetrical part of the curve. I suspect the boom is not planar with the PCB at zero position, possibly due to flexture sag or machining errors.  The flexture gap was set to 10 mil with a feeler gauge. Accounting for the -10X gain of the POSN_ERR output stage:

Rsensor:     1118 V/m

The centering force output was measured to be delta -7.951V with an additional 500 mg calibration weight on the boom, at the coil mount point.
CF = -7.9508/500e-6 = 15902 V/kg

Centering Force sensitivity = -15.9 Volt / gram, where negative means additional force supplied by the coil.

You really can use two balance weights, one horizontal and one vertical, though just one can be used if you accept a somewhat more complicated adjustment procedure. A properly balanced boom will have its center of mass lying in the same plane as the pivots. This means that its sensitivity to horizontal motion is minimized; or stated another way, its sensitive axis is close to vertical. Then the boom mass and the horizontal location of its COM will need to balance the spring when its length has been adjusted to get 3-seconds or so, free period. The spring adjustment sets the free period; the mass is just trimmed horizontally for balance. If you used two balance weights, you could make them adjust the x and y coordinates of the COM somewhat independently. Initially the COM will be located below the level of the pivots, mainly because the coil mass is fairly significant and is below the pivot plane. To balance, with the spring removed, but everything else on the boom in place, hang the boom coil down. If the pivot gap isn't too much over 0.010", the flexures should work fine in compression. The vertical trim weights are adjusted until the boom hangs straight down. Horizontal balancing is done at the time you are first adjusting the free period. Fine trimming can be done with a thumb nut or two on an horizontal brass screw, mounted as you observed below. With minimal horizontal trim weight, start shortening the spring until the boom balances and check the oscillation period. It will be less than 3 sec. Shorten the spring by a couple of thousandths (of an inch), temporarily add a bit of weight near the coil for balance (small brass washer or nut?), and check the period. Shorten more and rebalance, etc., etc. When you get up to something around 3 seconds, you can permanently attach equivalent weights (on the coil screw?) and then make final balance adjustments with the horizontal thumb screw(s).

Download the balancing spreadsheet: Tilt_test_357.xls

The vertical axis of the instrument is aligned within 0.26 deg of true. Horizontal sensitivity is 0.44% of vertical sensitivity. This is a pretty good result.

Since the sensitivity angle is negative, the vertical trim weight is slightly too low.
The centering force error is -22 milligrams, so the horizontal trim weight is slightly too close to the pivot.

Confirmed polarity of coil matches schematic - positive voltage moves boom upwards. The loop polarity spreadsheet has been recently updated to account for the Yuma2 circuitry.

Computed from Loop8Y.xls:

As you can see later, this matches the SPICE simulation within 2%.

Transfer function computation, using Loop8Y:

Poles:

Note: The pole at 33.4 Hz is estimated based on LTSpice simulation.


Zeros:

The instrument response to ground velocity is calculated using Brett's Loop8Y.xls spreadsheet, using measured values for electrical and mechanical parameters, and the Rev 4.0 schematic. M1 has been estimated at 155 g.

Using the loop test board, I measured the gain and phase of the feedback loop.  The loop was broken and a signal generator was inserted to inject a signal into the fedback loop. By measuring voltage and phase shift, several things about the feedback loop are characterized. The crossover frequency, where loop gain drops to unity, and phase margin at the crossover frequency are important metrics to assess loop stability and compare against expected values. 

Surprisingly, the crossover frequency was much higher than expected.  It was measured at 58 Hz, with 48 degrees phase margin. This is sufficient for stability, but a crossover frequency closer to 30 Hz was expected based on the Loop8 spreadsheet.

I ran some Spice simulations to investigate the discrepancy. See the Simulation section below for details.

Over 5 days, the Centering Force output (inverted), was compared against the internal temperature sensor, over a narrow range of temperatures. The sensor is mounted on the PCB, while the CF is primarily affected by the temperature of the spring. CF is a -1X output from the integrator, so the integrator has a +31 mV / C coefficient. This is exactly one tenth the value measured by another builder. I'm not sure what the source of this discrepancy is. 
 
Using the coil force constant, and the value of Ri, this represents a force difference of 2 mg / C.  Using M0 measured above, this is 23.1 ppm / C.
dF/dt = 0.267 V/degC / 14985 ohms * 9.6 N/A / (0.0875 kg * 9.81m/s^2) * 1e6 = 206 ppm/degC

The spring constant is expected be about 250ppm/C.

(On the plot there is an inadvertent gap of several hours when the data recording was interrupted.)

Displacement sensor is assumed to be linear.
Spring TempCo not included.
Simulations tested: transient, AC, noise.