Who can help me in designing an amplifier with the following characteristics?
Sorry but the characteristics you've mentioned make no sense - I'll go through themn and pick at them if it helps you.
1) Ability to amplify signals from DC to 3MHz
Is 3MHz the 3dB point?
2) Use minimum power (less than 25mV)
Power is measured in Watts not V.
Also are you talking about the input power output power?
What's the load impedance?
Impossible, no amplifier has completely no distortion.
4) Have some level of protection
What level of protection?
Short circuit?
Over voltage?
5) Use minimum passive component
What do you mean by minimum?
Passive components are resistors, capacitors and inductors, is there no limit on active components? Can you use 100 transistors but are limited to say three resistors?
6) Gain should be >100,000
That's a very high gain, is there a maximum gain?
Would it be fine if the gain was 1000,000, 000?
Good luck with achieving a gain of 100,000 at 3MHz.
7) Power supply (±12V @ ±9V @ ±5V)
No mention of current draw.
Besides that's a lot of power supplies, surely ±12V is enough.
What do you mean by that?
Is β the gain or negative feedback? Either way you've previously specified a gain of 100,000 which contradicts this.
9) Value of resistor less than 10kΩ
What resistor, don't you mean the input impedance?
I recommend you politely tell your lecturer that the specification he's given you is total rubbish.