Essensially, the AM modulation is caused by a minute difference in the actual resonant frequency of each stage, and is not a desired function of the circuit.  This modulated frequency can range from a relatively high audio frequency to a very low audio frequency.  In designing a battery charger a high frequency is more desirable than a lower modulated frequency because, the power level will fluxuate between half of its maximum output, and the maximum output.  The changing output wattage can be so high that it's not practical to design the circuit that way.

   My aim is to provide you with the rules of thumb for building and designing a circuit that will preform as this one, and frequency ranges to use with this type of circuit, as well as how to design its chaotic equivalent.

   Above is a basic tank circuit, or parallel resonant LC resonant circuit showing the kind of readings you would see from an actual tank circuit in operation.

   Again, above is another parallel tank circuit and the kind of readings you would expect to find on an unloaded step up transformer.  Here is where everything changes because, transformers only sense a load on the secondary as a change in the value of inductance of the primary.  If you know your basic resonant circuit formula for tuned LC circuits, that would only change the value of L, in the equasion.  As a result this only changes the actual resonant frequency of the primary, and the capacitor in parallel with the primary coils windings.

   Taking these facts into mind about a parallel resonant tank circuit on the primary of a transformer knowing this has proven that an equally resonant state can be achieved with, or for a stable resistive load on the AC output.  The problem is that if a coil, or a capacitor is placed on the output, the actual impedance changes as either current flow reaches its peak through a coil, or as voltage reaches its peak in charging the capacitor.  Therefore, any component that changes its impedance over time in micro, milli, or seconds, changes too fast for an oscillator tuned to a single frequency to maintain LC resonance.  At the center frequency of resonance, the tank circuit uses the least amount of power, and produces the most but, if you change the impedance of the secondary, the change in inducance reflected on the primary will demand as much current as the change in current represented in watts.  This is true even if the output has increased in resistance, therefore, a change of 3 watts plus, or minus, will demand 3 watts from the oscillator as a result.  You might need to go breadboard a potentiometer on the output to check the results against my statement before you actually believe it.  So, whether you are or are not experianced, and doubt me then do that, and come back to this web page when you have finished.

   Now, that you've been there, or your own personal experiances with electronics have you in the know, I will continue.

   Now, reviewing the schematic above, the differences in the values of capacitors are the result of a resonance calculation based on a step up, step down tranformer configuration, and the difference in inductance presented by the secondary verses the primary circuit values because, they would only be resonant to the same frequency if, the charge time of the capacitor was differnt compared to the different value of inductance.  The reason for this being the choice circuit configuration is that my results produced so much more energy than the oscillator provided to the first stage.  Chaotic resonance of this circuit is produce by choosing a value of capacitor that is resonant to twice the frequency of the oscillator based upon whatever value of measured inducance that you have on the secondary compared to the primary.  This means you must know your LC resonance fomula to build this circuit, or the chaotic resonant version which is the result of a capacitor value that would make the secondary resonant to twice the frequency of the primary to the next stage which steps down that signal.  I know that you will expect an energy loss but, you will not find it, and there is power gain as a result.  Again, if you don't believe go work out fomula, breadboard the circuit as described, and once you are in the know, come back to this web page.

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