Nuts and Volts - June 2014

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

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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