I changed the load to 8 ohms so we can get 3 watts from a 12V supply.
problem: We need more current. The little output transistors can not with stand the heat and the current is very close to the max the part can with withstand. I chose 5A transistors not 600mA parts. These parts can connect to a heat sink to get rid of the heat.
Below is a graph of the old transistors. You can see the current gain is about 200 with current below 100mA. At 500mA the gain drops to 20. By choosing a bigger transistor there will be good gain at the desired current. So start at the load. Find what voltage, current and power you need. Choose transistors designed to work at that level.
To get 10x more current in the output you need (about) 10x the current in the bases. I changed the resistors to get about 10x more current through out the amplifier.
The goal is not clear to me. I think your teacher wants 10x more power out. So change the output transistors to parts that can work well at 10x the current.
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Another option: (every thing in this picture functions as one, very high gain transistor)
Increase the current and power capability of the output transistors AND (increase the current gain) so Q1 does not need to be changed. Q5= the old low current transistor. Q4= the new high current transistor.
Question: Why do I need two diodes? D3, D4
Question: What is Q5+Q6 called?