We used MicroSim PSpice to model our system. The following is the circuit used for analysis:
The 48 ohm resistor if the output impedance of the function generator. The 67 ohm resistor is the resistance of the inductor.
Using a sweep of the output's frequencies, PSpice found the resonant frequency (where the ratio of Vout/Vin is at a maximum) to be 138.7 kHz:
We proceeded with our PSpice modeling by setting the sourse frequency to the resonant frequency of 138.7 kHz. Then we varied the input voltage to observe the effects on the periodicity of the output.
The following is a plot, thanks to PSpice, of the output when the frequency of the input signal is the resonance frequency and the amplitude of the signal is 0.01V and the Fourier transform of that plot (there is a time delay of 500 us to avoid analysis of the transients):
The Fourier Analysis demonstrates that there is one dominant frequency (the resonant frequency) composing the output signal.
When the amplitude of the voltage is increased to 0.06 V, the output and its Fourier appear as:
This appears to be representative of period doubling. In the Fourier analysis, the peaks on either side of the dominant peak (corresponding to the resonant frequency) occur at a frequency difference (distance from the dominant peak) equal to one-half of the resonant frequency.
We could not reproduce other periodic outputs from higher voltage amplitudes. However, the output seems to be chaotic for inputs with amplitudes greater than 0.06 V. Some of the intervals between adjacent peaks are consistent, but the peaks have differing values with no apparent patter. For instance, here is a plot of the output from a 0.08 V input and its Fourier transform:
Notice how there is no reoccurring pattern between the amplitudes of the peaks in the plot. The Fourier also shows aberrations and no longer shows solely smooth peaks, but 'noise' between them. Here is the output when the input has an amplitude of 2 V, it's quite chaotic!
From this voltage peak on, there appears to be solely chaotic output. This leads to the conclusion that PSpice cannot reproduce other types of periodic output.