A Folded Pendulum seismometer Electronics package 
David H. Youden 
dyouden at ipass dot net 
March 12, 2003


General description

The folded pendulum seismometer uses a differential capacitance displacement sensor to sense the movement of the pendulum carriage. The signal from the sensor is demodulated, filtered, and amplified, and is then used to close a proportional position, or force-balance, loop. The actuator is comprised of a coil that is mounted on the pendulum carriage, and a rare-earth magnet mounted on the frame of the instrument. The current through the actuator coil is proportional, for small displacements, to the force required to maintain the carriage in a fixed position with respect to the instrument frame, and, as force is proportional to acceleration, the current through the coil is proportional to the acceleration of the earth beneath the seismometer. A voltage proportional to the coil current is generated across a resistor in series with the coil, and applied to a series of filters, amplifiers, and an integrator, which converts the acceleration signal into a velocity signal. The velocity signal is then sent to an analog-to-digital converter, which is connected to a personal computer. The personal computer, collects, stores, and displays the data for review or further analysis.

Capacitance Sensor

The capacitance sensor is made up of three aluminum plates spaced approximately .010 inches apart. The active area of these plates is 3.0 square inches and so the theoretical capacitance can be calculated to be about 67 pf. As actually built, the measured capacitance is closer to 30 pf, due to lack of parallelism between the plates, and a slightly larger gap than intended. The center plate of the sensor is connected to ground, and the two outside plates provide the differential signal to the detection circuitry. The bridge is excited by a 50 Khz. sine wave with a P-V amplitude of 7 volts. The upper two arms of the bridge are comprised of 100K resistors, which have about the same impedance as the capacitors, thus maximizing the sensitivity of the bridge.

Figure 1: The schematic diagrams of the two boards used to implement the capacitance displacement transducer.

Electronics Overview

There are four circuit boards that make up the electronics package for the seismometer. The Oscillator/Phase Shifter board provides the 50Khz. bridge excitation, and also provides the reference signal to the demodulator. The Amplifier/Demodulator board accepts the signal from the capacitance bridge, synchronously demodulates it, and then filters it with a two pole 35 Hz low pass filter. The Coil driver board accepts the demodulated and filtered position signal and passes it through a phase lead network and a power amplifier to provide the signal to the motor that controls the pendulum carriage. The current passing through the coil of the motor is converted to a voltage proportional to the force required to hold the carriage in position, and this voltage signal is the input to the filter board, which provides the final signal processing.

Oscillator /Phase Shifter

The oscillator that provides the 50 Khz signal to the capacitance bridge is a phase shifting design which uses four op-amps each of which shifts the phase of the signal by 45 degrees. The design of the oscillator is described in the August 2000 issue of the Texas Instruments Analog Applications Journal in an article entitled "Design of Phase Shift Oscillators" by Ron Mancini pp 33-37. I have altered the original design by adding the two diodes and their series resistor to control the P-P amplitude of the sine wave so as to improve its linearity. The output from the oscillator passes through a decoupling stage and is then delivered to the capacitance bridge. this same signal is also applied to the phase shifter circuit, which provides an adjustable phase lead of up to nearly 90 degrees. The phase-shifted signal is applied to an LM393 comparator which has its other input held just slightly (50mv) above ground. It was found that by doing this the jitter on the output square wave was significantly reduced. The output of the LM393 is a phase-adjustable square wave. This signal is applied to the synchronous demodulator.


The signal from the capacitance bridge is applied to the inputs of an INA121 instrumentation amplifier. The gain of this amplifier is set to 100 by the 500 ohm resistor connected between pins 1 and 8 of the DIP package. The output of the instrumentation amplifier is inverted by op-amp U7A. A MAX319 analog switch demodulates the inverted, and the non-inverted signals. The signal from the demodulator has a fair amount of noise from the switching transients. This noise is removed by the two-pole 35 Hz low pass filter that completes this section of the circuit. Note that the oscillator/phase shifter and the amplifier/demodulator form what is commonly known as a lock-in amplifier. Refer to Linear Technology application note 87,pp 87-89 for another approach to this problem.

Figure 2: The coil driver board schematic diagram. The alternate outputs are not used.

Coil Driver

The coil driver board is the simplest of the four boards. It contains only the OPA551 based amplifier that provides the signal to the coil of the motor. The OPA551 is a high-power op-amp that is definitely overkill for this application. It can source up to 200 ma into its load. The amplifier is preceded by a phase lead network that extends the bandwidth of the servo by providing a phase lead that increases with frequency (up to a point). The components that form this network, i.e, the 100k and 15k resistors, and the .047 mfd capacitor should be considered to be tuning components and should be located so that they can be adjusted to suit the particular application. Two alternate outputs were included on this board so that the coil of the motor could have one end tied to ground, if the additional connection was not available. In this configuration the signal to the filter could be taken directly from the amplifier output. Note that it might be wise to replace the 3.3k resistor that is in series with the motor with a potentiometer so that the signal level to the filter can be controlled.


The filter circuit is the same circuit that Larry Cochrane published on the Public Seismic Network web site. I have made only insignificant changes to it to suit my purpose. The first stage of amplification drives a bi-colored LED that displays the DC level in the motor coil. This serves as an aid when leveling the instrument. The leveling should be adjusted so that the LED is out. I have found that the presence of this indicator is a great convenience. The .016 Hz high-pass filter, (U1B) eliminates any DC offset from being passed along to the integrator. The integrator integrates the acceleration signal thus turning it into a velocity signal. The components of the integrator might be subject to some minor modification, but those values shown seem to work well for me. The next stage is an adjustable gain amplifier that compensates for the losses in the filters. A second high-pass filter removes any DC offset from the preceding stages, and a two-pole, 5 Hz high-pass filter defines the frequency range of interest. The final stage of amplification compensates for the capacitive effects of a length of shielded cable (about 60 feet in my application.), and allows the introduction of a small amount of zero offset, in the event that it should be required.

Construction Technique

Over the years I have developed a technique for producing small circuit boards using Radio Shack perforated boards. I usually use the Radio Shack Universal component PC board, part number 276-168. The boards are laid out using a CAD system (Cadkey, in my case). I cut the foil traces where required with a razor blade. After the foil cuts are made, and verified with an ohm meter, the IC sockets are soldered in place. With the sockets in position, the jumpers bent, inserted, and soldered in place. With the jumpers in place, the passive components are inserted and soldered in position. At this stage, the circuit is rung out using an ohm meter and the power busses are verified. Last of all, the ICs are placed in their sockets, completing the assembly. The photo below, figure 4, shows the complete electronics package for the folded pendulum seismometer. The top board is the oscillator/phase shifter. Next, below it is the amplifier/demodulator, the coil driver, and, on the bottom, the filter. The components in flea clips are parts of the phase lead network on the coil driver board. The stack of boards is housed in a plastic case from Radio Shack. Note that this construction technique is applicable to perhaps one to five copies of a given circuit, but for more than that, a printed circuit is probably more cost and time effective.

Figure 3: The schematic of the filter board. This is nearly identical to a similar circuit by Larry Cochrane. Decoupling Capacitors

Decoupling capacitors and resistors are not shown on the oscillator/phase shifter and amplifier/ demodulator circuits. Please note that these components are used at each and every chip. In addition, I usually include 10 to 47 Mfd electrolytic filter capacitors on every board.

Figure 4: The stack of four circuit boards that comprise the entire circuit.


When the electronics have successfully completed the smoke test, turn all pots to their minimum settings and connect the circuit to the seismometer. Place non-conducting shims in the gaps of the capacitance sensor and turn the power on. Check for the presence of the 50 Khz excitation signal on the two outer capacitor plates. Verify that the reference square wave signal is present on at the demodulator. Remove the shims from the capacitors. Turn up the gain on the coil driver board. If Murphy is alive and well, the coil windings will be reversed and the carriage will begin to oscillate. Shut things off and reverse the coil connections and try again. This time the tilt LED will probably light indicating an out of level condition. Carefully level the instrument, extinguishing the LED. Look at the capacitor plates. The center plate will probably not be centered between the two stationary plates. Adjust the phase lead potentiometer on the oscillator/phase shifter board, and the leveling screw so that the LED is out and the center capacitor plate is midway between the outer two plates. Now increase the coil driver gain until the system is unstable, then back it off to regain stability. If you have included a level adjustment at the input to the filter, set it to the minimum needed to get the desired output with the filter gain set at midpoint. I feel that, if I can see the roughly 0.2 Hz micro-seismic noise that seems to be everywhere, then I have enough gain. Finally, adjust the offset pot to center the signal around zero volts.


As a mechanical engineer, electronics are not one of my major strengths, and, because of that, I have probably made errors in judgment, theory, and execution. I will be more than happy to entertain suggestions for alterations and improvements to this bit of work.


The TI Analog applications journal can be found at: http://www.ti.com/sc/docs/apps/msp/journal/aug2000/aug_07.pdf 

The Linear Technology Application Note can be found at: http://www.linear.com/pub/document.html?pub_type=app&document=89 

For a classic paper on the design and application of capacitance gauges obtain a copy of:

Jones, R. V. & Richards, J. C. S. The Design and some Applications of Sensitive Capacitance Micrometers Journal of Physics E: Scientific Instruments, Vol 6, 1973, pp589-600