Class A Amplifier Circuit Doesn't Work

From the quiescent point perspective, yes. You would do better to bias the base to 1.5V and use a 18 ohm emitter resistor for 50 mA bias current. Then a collector resistor of 80 ohms. That would allow the output to swing close to 8Vpp.

You're still faced with the problem of driving a 8 ohm load with an 80 ohm output impedance. You would need a transformer.

The other approach would be to ask what voltage and current you need to drive an 8 ohm speaker. We can calculate that. Let's assume we expect 100 mW power. We need 0.9V rms (2.5 Vpp) swing at the collector. And we need 111 mA rms (314 mA p-p). Can your 2N2222 handle that much current? Not really.

But you can design the amp and then select a suitable transistor. Your amp needs to swing at least 2.5Vpp and have a load resistor of 2.5v/314mA=8 ohms. You would want something closer to a 3V 1/2A power supply. Design your amp for a quiescent point of 1.75 V @ 160 mA.

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