High Gain Bootstap Audio Amplifier
You can bootstrap the collector load of a common emitter amplifier to get significant extra gain.
Also the emitter follower used for bootstrapping provides a low output impedance which is useful for driving long connecting cables with low hum and noise pickup.
Capacitor C1 feeds-back the output of emitter follower Q2 to resistor R3 making it look like R3 has been multiplied by many times to the collector of Q1.
A similar circuit, the low input impedance is due to current shunt feedback through the biasing resistor R1.
Adjustable Bias.
Adding an emitter resistor to Q1 does not reduce the gain very much,it does reduce distortion, increase input impedance and makes biasing easier. This is because the gain of the circuit is mainly limited by a number of other factors such as how near unity the gain of the emitter of Q2 is. You can also reduce distortion further by replacing R3 with a constant current source.
It is also possible to avoid the use of a feedback coupling capacitor using a emitter follower transistor of opposite polarity. R5 and R2 provide negative feedback to reduce distortion and also biasing. You could bias Q1 in a different way to get maximum gain.