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Why is a tuning capacitor placed in series with a free piston stirling alternator rather than parallel with it?

I am accustomed to seeing power factor correction capacitors placed in parallel in school rather than in series, why would this application be different?

To be honest I have never seen an example of power factor correction being used on an AC source, only on AC loads so maybe that has something to do with it.

Also, it's called a tuning capacitor, so maybe it has something to do with controlling the resonance of the engine piston (RLC circuit)? I know that both the piston and displacer must have the correct resonant frequency in order for the engine to operate correctly.

free-piston stirling engine diagram FPSE model

EDIT: I just found some more info about about the multiple purposes of a tuning capacitor in "Tradeoff Between Magnet Volume and Tuning Capacitor in a Free Piston Stirling Engine Power Generation System" (https://doi.org/10.4271/929262) This paper doesn't really answer my question, though.

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    \$\begingroup\$ The paper you cite seems to explain it pretty well. What's not clear? \$\endgroup\$ – Spehro Pefhany Jun 6 at 18:35
  • \$\begingroup\$ The paper explains the purposes of the tuning capacitor, but I don't think it explained why it is placed in series rather than parallel with the alternator output. \$\endgroup\$ – D. Goodell Jun 6 at 18:39
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I can't seem to read the paper via your link, so this is a generic answer:

Series-tuned circuits have their minimum impedance at resonance, while parallel-tuned circuits have their maximum impedance at resonance.

It would seem that the idea here is to nullify the effects of the leakage inductance of the generator coil on power delivery, so minimum impedance is what you want.

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Fun Stuff!

I'm guessing you have a linear alternator, which can be roughly modeled just as shown in your diagram: a sinusoidal voltage source from the back emf of the alternator with an output impedance consisting of the inductance and resistance of the coil. The sinusoidal frequency will be the oscillation of the piston. The series inductance means that the output voltage would vary depending on load and frequency if the capacitor were not present.

At your operating frequency, the capacitor and inductance, if the capacitance is properly chosen, would make the output impedance purely resistive and equal to the coil's resistance and the capacitor's ESR. By designing a control system to supply the proper heat to maintain the frequency at a constant value, the system's output looks like an AC source with a resistive output impedance. You must maintain this osillation frequency; if the frequency changes from your resonant point the output impedance will become inductive or capacitive.

Good Luck!

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The total impedance of a series RLC circuit is R + j(Xl - Xc), which has a magnitude of R = \$\sqrt{R^2 + (X_L - X_C)^2}\$, so the reactance of the inductance can be cancelled out by resonating it with the capacitor (pick C such that \$\omega L = \frac{1}{\omega C} \$ so C= \$\frac{1}{\omega^2L}\$). That maximizes the magnitude of the current output.

However there are other considerations (potential demagnetization) that are covered in your linked paper.

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