small signal model of differential amp in ALLEN BOOK

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Recently I study differential amp in Allen book

when I convert differential amp into small signal equivalent circuit, I wonder that why does allen book ignore M5 TR, just connected ground.

when I just differential amp convert into small signal model, I know that conversion process so easy, but I can't anything derive from small signal model, like Rout, Av.

why does Allen ignore M5, just connected ground?

thanks
 

You mean the channel length modulation resistor for M5? To ignore it is an approximation. I tried solving this by including it once. The expression is really huge, doesn't give you much insight.
 

Because the drain of M5 is virtual ground.
 

hi ..
what NXING is correct.
this is true only for fully differential in & differential out opamp.
this may not be 100% true for differential in & single end out opamp.
if you want more explanation you can read razavi book.

--
kamal.
 

M5 can only be a perfect virtual ground if the tail current source is ideal otherwise it is not a perfect virtual ground. So when we make the tail current through a transistor like shown, the accurate small signal equivalent model will be when we represent the channel length modulation resistance. But it is normally neglected for simplicity of calculations. Even if you include it and derive the whole expression you will see that neglecting it is a good approximation.
 

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