The Pump Oscillator
The pump oscillator schematic in Figure 6 employs
the CMOS ICM7555 timer chip. The circuit is configured
to provide a square wave frequency given as:
R should be on the order of 2. 4 megohms for a
pump frequency of about 3 Hz, and C fixed at 0.1 µFd. R
is made up of a standard 2. 2 megohm resistor in series
with a 500K ohm potentiometer to trim the frequency.
The circuit is simple, so the pump oscillator was
constructed on perfboard with point-to-point wiring and
mounted in the lower half of the case where the battery
compartment is located. Leave long leads to connect to
the relay actuator to allow access to the oscillator trim
pot for adjustment of the correct frequency.
The bandwidth, Dƒ, at the half power point or
sharpness of resonance is defined as:
The Q factor can be measured by releasing the
pendulum at a given angle and recording the time, t,
for the angle to decay to about one-third its initial value.
The Q factor is then calculated from the relationship:
The factor Q of the pendulum is on the order of 150,
so the pump oscillator frequency is quite critical and
must be set at exactly twice the pendulum frequency.
The pendulum period can be easily obtained with a
stopwatch by measuring, say, 10 full cycles and dividing
the elapsed time by 10 to obtain one period. Alternately,
an optical tachometer could be used to measure the
period of the pendulum, and a frequency counter to set
the pump oscillator frequency.
I have used a small silicon photovoltaic cell taped on
the table directly below the pendulum and connected to
a sensitive oscilloscope. The photocell is illuminated from
above the pendulum with a bright flashlight, so a voltage
pulse from the pendulum shadow is cast every time the
pendulum swings over the photocell. There will be two
shadow pulses generated for every swing of the
pendulum because the pendulum has two zero crossings
per cycle of a sine wave. The pump oscillator trimpot R2
is then set, so the complete time of one cycle of the
pump oscillator is equal to the time between any two
shadow times of the pendulum.
This completes the construction of the parametric
amplifier model. It’s called an amplifier rather than an
oscillator because the pendulum must first be excited
with a signal (such as a large push) to start it swinging. A
large perturbation will allow the pendulum to continue to
oscillate long enough for the phase to slip into sync and
execute a swing of about ± 2”.
Now you know how it works, but to your friends it
will be magic. NV
40 June 2014
0.722 f = RC
Q = pft