Coupled Oscillators: Part A (Square Wave Input)
By: S. A. Dodds
Physics Department
Rice University
Houston, TX
Our first exercise will be to pulse the circuits and watch the
energy slosh back and forth between the two capacitors. The method
is similar to what you used in studying transients in a single RLC
circuit.
Wire up the circuit shown below. The variable capacitor has a
range of 250 - 650 pF so it can vary the oscillation frequency for
the first RLC circuit in a range centered on that of the second.
The 3.3ohm resistor is used to reduce the impedance of the function
generator. Otherwise the 50ohm internal impedance would introduce
too much damping in our first oscillator. Channel 1 measures the
charge on Ca (approximately) and Channel 2 measures the charge on
Cb. Begin with Cc at an intermediate value, say 0.01 uF.
Set the function generator to produce a maximum-amplitude square
wave at 200-300 Hz. Adjust the time base and vertical sensitivity
of the scope so that you can see the transients that occur each
time the square wave reverses polarity. You will probably find it
convenient to use the TTL output as an external trigger for the
scope.
Vary the tunable capacitor and observe the qualitative behavior
of the signals. Find the capacitor setting that gives the slowest
beat frequency on Cb. By minimizing wex in this way we
achieve the condition Ca = Cb assumed in our previous analysis.
Using this setting, sketch the two waveforms and identify the relevant
features on your sketch. You should be able to recognize the decay
of the signal due to the finite resistance in the circuit and the
expected cos*wext and sin*wext dependencies
of the qa and qb envelopes. Be sure to get a good estimate of the
modulation frequency wex for comparison with later measurements.
Don't forget that the minima in the modulation envelope occur at
intervals of 2*pi/2wex, not 2*pi/wex.
After doing the detailed sketches for Cc = 0.01 uF, describe the
changes when you use a 0.0047 uF and a 0.047 uF coupling capacitor.
As before, adjust the variable capacitor setting to obtain the slowest
beat.
Using your mouse, click on the instrument controls to adjust them.
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