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Proper Capacitor for 555 Circuit with Simple NPN Amplifier

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As I understand it, in the classic 555 with a speaker circuit, the capacitor that is in series with the speaker is there to prevent DC from flowing through the speaker:

And this capacitor, C1, is usually around 100 uf. If the output of the 555 is amplified by a single NPN transistor 2N3904:

Should there still be a capacitor somewhere in the speaker circuit? An actual circuit based on this schematic does work (and the volume of the speaker is indeed louder), but the transistor gets warm. Could the transistor operate at a lower temperature and could the same speaker produce a louder volume by the introduction of a capacitor? If so, where? Would it be between the junction of R1 and Q1 and ground? And because the impedance seen by such a capacitor would be more heavily influenced by R1 than by Q1, and thus close to 330 ohms, would it be reasonable that its value would be significantly lower than the 100uf in the circuit without the amplifier (where the impedance is around 8 ohms)?
Asked: 10:41 01/03/2017

Proper Capacitor for 555 Circuit with Simple NPN Amplifier

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