It is obvious that in an LRC circuit, there must be some sort of inductance, resistance and capacitance.  In the circuit used in this experiment, the inductance comes from an actual inductor, the resistance comes from the intrinsic resistances off all the components, and the capacitance comes from the diode.

    How can a diode have a capacitance you might ask?  Well, when a diode is forward biased (which is the same as conducting), it acts as a constant source of voltage: 

where V = applied voltage

vd = the diode voltage

 In it's reversed bias position, however, it acts just like a capacitor:

vd = the diode voltage

C = the reverse capacitance

    Interestingly enough, when the there is a time associated with how long it takes the diode to switch from its forward bias mode to its reverse bias mode.  To get the diode to constantly switch back and forth, an AC signal (from a function generator) is applied.  The more current sent through the diode, the longer it takes for the diode to return to the equilibrium of one of its bias states.

    By examining the resonance area of the circuit and varying the voltage, these effects can be observed in the form of period doubling, period quadrupling, period times eight, and finally chaos.

    Chaos in the circuit occurs because of uncombined charges which cross the diode's p-n junction while it is in the forward bias mode.  When the diode switches to the reverse bias mode, these charges diffuse back over some amount of time which means that the diode is conducting for some time after it switches from forward to reverse biasing.  If this time is significant relative to the input signal's period, then chaotic behavior may occur.

    As we switch between the conducting and non-conducting mode, as as the amplitude is increased, we should see period doubling, etc., until we see chaos!

    Below is a picture of a bifurcation diagram.  It's useful in visualizing what is going on in the LRC circuit.  Later, in the results section, the characteristic bifurcation diagram for this specific circuit will be created.

Bifurcation Diagram:

Periodicity:

        1                    2            4                    8           CHAOS            8                4                2                1