Analyzing an Oscillator Circuit: Voltage and Current Dynamics

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tburke2
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I have the following circuit that I need to calculate the voltage across the capacitor as a function of time. Standard variables for the component values, voltage drops, currents, ect.

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You'll notice that the voltage (at the top right corner) oscillates at a frequency dependent on the capacitor value and the inductance of the transformer (what i found when physically testing the circuit). When the resistor is large enough it doesn't allow enough current through to activate the transistor when current is flowing through the transistor, turning it off and allowing current to flow back to the base. This is why I cannot use conventional circuit analysis, we assume that changes in the circuit are instantaneous while this circuit depends on the finite speed of the current.

Thanks for any assistance.
T. Burke
 
on Phys.org
tburke2 said:
This is why I cannot use conventional circuit analysis, we assume that changes in the circuit are instantaneous while this circuit depends on the finite speed of the current.
I think what you say here could not possibly be correct.

The first thing you should do is mark the dots on the transformer windings.

Next, find a reference that tells you how this circuit operates. Does operation hinge on non-linear characteristics of the transformer, or can you assume a linear model?
 
Sorry, the transformer coils are oppositely wound so a dot should be on top of the left coil and on the bottom of the right coil. The circuit is dependent on the non-linear characteristics of the transistor. Can Kirchoffs laws be used to find the voltage across the cap?