only pin 13 sets the count at 16369, yielding a time delay
of 5.856 s.
At the lower right is U4 — the VT integrator that
is started and stopped by relay K12. Switch S4 selects
resistive feedback through R31 for simply amplification,
or capacitive feedback through C31 for integration. In
integration mode, the U4 output ramps up at a rate
proportional to the voltage input. Button B3 shorts the
capacitor and resets the output to zero.
I designed the circuit using parts available in my shop,
but if you buy it all, the total will be about $60 plus the
PCB. The PCB and its layout files are available with the
My motor was harvested from a defunct CD drive.
I turned up the brass cylinder on my mini-lathe. Suitable
disks in brass (~$20) or steel (~$5) are available from
McMaster Carr. To run the experiment, you’ll also need
a ±15V DC power supply, a digital voltmeter, and a
frequency counter or oscilloscope.
The circuit of Figures 5 and
6 has five modes of
operation: four calibration modes and one run mode. In
mode 1, we’ll calibrate integrating amplifier
U4 by applying a 10.00V reference voltage
input for a precise time and then adjust the
gain so that Vout equals exactly 0.1VT. The 10V
reference voltage and Vout are both measured
with our voltage standard: an Agilent 34420
In mode 2, we calibrate the motor voltage
by correcting out the component of motor
voltage caused by the motor resistance. With
25 mA applied to the motor, we prevent the
motor from spinning so that the motor voltage
is I Rm where Rm is the resistance of the motor.
Trimpot VR30 is then adjusted to subtract
the voltage I Rm from the input to the integrator.
This ensures that the part of the motor
voltage associated with resistive loss is excluded from the
Figure 7. Motor current as a function of motor voltage.
Figure 6. The schematic of the PCB in Figure 5
80 September/October 2018