One distinguishing characteristic of a simple
parametric amplifier is that the energy is pumped at
twice the resonate frequency, as opposed to a driven
oscillator where the drive frequency is equal to the
resonate frequency. The phase of the pump frequency
and the oscillation is also very critical, so that the mass of
the pendulum is lowered at the extremes of the swing
and raised at the center so the motion is in the form of a
figure eight.
The term “parametric amplifier” comes from the time
varying coefficients of the mathematical equations that
describe the motion. A generalized treatment was first
given by Lord Rayleigh in the late 1800s, and since then
many papers have been written to describe the
complexity of the phenomenon and its many variations.
In the early days of radar development, it was
necessary to design very low noise microwave receivers
at a time when very few devices could even work at
microwave frequencies. Parametric amplifiers provided a
very attractive solution to this problem since they could
be built with a simple varactor diode (voltage controlled
capacitor) to pump a resonate cavity and provide gain.
Both in theory and in practice, the parametric amplifiers
could also provide very low noise.
Theoretically, a parametric amplifier can produce
zero noise since the modulating unit is an energy storage
device, or completely reactive in which the voltage and
currents are 90 degrees out of phase. This is opposed to
a conventional amplifier in which the modulating device
is resistive and inherently adds noise because the
voltages and current are in phase. In reality, the
parametric amplifier adds some noise because the
phasing of the pump frequency and the desired resonate
frequencies are not exactly known. In addition, the
energy storage devices are not perfect and produce
losses.
We can build a mechanical model of a parametric
amplifier in the form of a simple pendulum that
continues to swing like perpetual motion as illustrated in
Figure 1. The pendulum could be referred to as a
degenerative parametric amplifier because the pump
frequency is twice the resonate frequency of the
pendulum, and the pump phase is critical. Fortunately,
the phase of the pendulum is free when excited and will
drift into phase lock with the pump oscillator, and build
up the swing.
There are also non-degenerative parametric
amplifiers that employ a third frequency to eliminate the
rigid restraints on the phase relationship.
The Actuator Relay
The model employs a modified relay to pull the string
to modulate the potential energy of the pendulum. A
Panasonic JQ1A-9V relay was purchased from Mouser
Electronics and is one of the few that is not hermetically
sealed. It has a nine volt coil and runs about 23 milliamps
when energized. Other relays can be used, especially the
June 2014 37
ITEM/DESCRIPTION COST
Mechanical Parts:
1/8" OD x 0.014" wall x about 8" long brass tubing $1.80/ft
3/32" OD x 0.014" wall x about 8" long brass tubing $1.80/ft
0.040" OD x 0.010" wall x about 8" long Teflon tubing $3.00/2 ft
0.010" OD x about 14" long Spiderwire EZ fluoro fishing line $7.99/200 yds
Hobby Lobby 211201, 3/4" OD wood ball $1.99/nine balls
Electronic Parts:
K1 Panasonic JQ1A-9V relay $3.52
U1 ICM7555 CMOS DIP timer IC $0.88
R1 2. 2 megohm, 1/4 watt resistor $0.03
R2 500K ohm 25-turn trimpot $3.50
C1, C2 0.1 µF, 50V, ceramic $0.10
C3 10 µF, 25V, electrolytic $0.25
D1 1N4148 diode $0.10
B1 9V battery $1.70
9V battery connector $0.45
LMB Heeger 502 plastic case $9.36
Miscellaneous:
Perfboard (or RadioShack PCB #276-159) $2.60
Eight-pin DIP socket $0.15
Scrap 1" x 1/2" x 1/16" thick fiberglass or plastic base
Double-sided foam adhesive mounting tape about 1" x 1/2" (try Magic Mount 3701) $8.00/16 strips
Five minute epoxy adhesive $6.00
Crazy Glue $3.00
Several #4 x 1/4" self-tapping mounting screws $0.50
PARTS
LIST