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What is M3 and M16 purpose.
Is it necessary to have a diode connected M16 to provides vgs to M14 and M15 cant it be a simple current mirror
What is the advantage of providing a high impedance to the sources of M14 , M15 and M 16
Yes. You can't ensure a fix Vds, but at least you can ensure a stable Vgs by M16. So resistance variation of M14 and M15 will be lower, but obviously the resistance will change with input differential voltage. If you don't want this use normal resistors. Most straightforward solution, doesn't require huge area, extra biasing circuit and very linear.If the drain terminals of M14 and M15 are changing due to the change in gate voltage of differential pair then the resistance of source degenerated MOS will vary. Will this M16 help in adjusting the resistance.
Not the high impedance is the point here, I think. If you don't use M3 all current of the M17 has to flow through M16 and M14,M15. If you pull DC current through M14,M15 it will increase the resistance of them which is quite uncontrollable. With higher DC current M14 and M15 will leave the deep triode region, even they can leave triode region and step into saturation region where they act as a current source, not as a resistor.What is the advantage of providing a high impedance to the sources of M14 , M15 and M 16
I am asking for source degeneration MOS.
Source degenerated MOS is different I have heard this for the first time that they are different. Can you also explain the difference?
How? As explained by frankrose and erikl in post #2 and #3, you need a circuit to generate the gate-source voltage for M14 and M15. Effectively at least an additional transistor in combination with a current source respectively two current sources. If you have a specific circuit topology in mind, please clarify.My question was can M14 and M15 be biased by simple current mirrors?
Diode connected M16 provides a reasonable Vgs ≈ Vth for M14 & M15, to set them to the required impedance for degeneration of the active differential pair MM1/M1 & MM2/M2.