If an inductor and a capacitor are connected in parallel with each other, as illustrated in Figure 1, and then briefly energized by connection to a DC voltage source, oscillations will ensue as energy is exchanged from the capacitor to the inductor and vice versa.
These oscillations may be viewed with an oscilloscope connected in parallel with the inductor/capacitor circuit. Parallel inductor and capacitor circuits (LC circuits) are commonly known as tank circuits.
In this experiment, the power transformer is used simply as an inductor, with only one winding connected. The unused winding should be left open. A simple iron core, single-winding inductor (sometimes known as a choke) may also be used; however, such inductors are more difficult to obtain than power transformers.
Important note: I recommend NOT using a PC/sound card as an oscilloscope for this experiment because high voltages can be generated by the inductor when the battery is disconnected (inductive kickback). These high voltages will surely damage the sound card’s input and perhaps other portions of the computer as well.
Step 1: Build the parallel inductor-capacitor (LC) circuit illustrated by the schematic diagram of Figure 1 and the terminal strip implementation of Figure 2.
Step 2: Connect the oscilloscope probe to the high side of the LC circuit.
Step 3: Touch the battery supply to the parallel LC circuit to energize the circuit. Observe the output on the oscilloscope.
Step 4: A tank circuit’s natural frequency, called the resonant frequency, is determined by the size of the inductor and the size of the capacitor according to the following equation:
$$f_{resonance} = \frac{1}{2\pi \sqrt{LC}}$$
Many small power transformers have primary (120 V) winding inductances of approximately 1 H. Use this value as a rough estimate of inductance for your circuit to calculate the expected oscillation frequency. Compare your calculated frequency with what you observe on the oscilloscope.
Ideally, the oscillations produced by a tank circuit continue indefinitely. However, realistically, oscillations will decay in amplitude over the course of several cycles due to the resistive and magnetic losses of the inductor. Inductors with a high-quality factor, or Q rating, will produce longer-lasting oscillations than low-Q inductors.
Step 5: Try changing capacitor values and noting the effect on the oscillation frequency. You might notice changes in the duration of oscillations as well due to capacitor size.
Step 6: Since you know how to calculate the resonant frequency from inductance and capacitance, can you figure out a way to calculate inductor inductance from known values of circuit capacitance (as measured by a capacitance meter) and resonant frequency (as measured by an oscilloscope)?
Step 7: Resistance may be intentionally added to the circuit—either in series or parallel—for the express purpose of dampening oscillations. This effect of resistance-dampening tank circuit oscillation is known as an antiresonance. It is analogous to the action of a shock absorber in dampening the bouncing of a car after striking a bump in the road.
We can simulate the resonance of the LC tank circuit using the SPICE schematic and node numbers shown in Figure 3.
The resistance, R_{stray}, is placed in the circuit to dampen oscillations and produce a more realistic simulation. A lower R_{stray} value causes longer-lived oscillations because less energy is dissipated. Eliminating this resistor from the circuit results in endless oscillation.
Netlist (make a text file containing the following text, verbatim):
LC Tank Circuit with Resistive Loss l1 1 0 1 ic=0 rstray 1 2 1000 c1 2 0 0.1u ic=6 .tran 0.1m 20m uic .plot tran v(1,0) .end
Learn more about the fundamentals behind this project in the resources below.
Textbook:
Worksheets:
In Partnership with Future Electronics
by Aaron Carman
by Robert Keim
by Aaron Carman