## Common-mode operation Assignment Help

Assignment Help: >> Differential Mode and Common Mode Gains - Common-mode operation

Common-mode operation:

In order to derive an expression for the common-mode gain Ac = voc/vc, we view REE in Figure as formed of two resistors, each of value 2REE, in parallel. The resulting circuit is the half circuit model for common-mode operation and is illustrated in Figure

Analysis follows through inspection as follows :

vc  = vπ + ve

v e  = [(v π/ r π  )+ gm v π]2REE

= 2 REE [(1/r π) + gm] vπ

voc  =- gm vπ RC

A  = voc / vc

AC  = - gm RC/1 + 2 REE (1+ gm rπ )/ rπ

Since β = gm rπ >> 1, this simplifies to

Ac  = - gm RC / (1 + 2 gm REE )

Therefore, by using the value of Ad and definition of CMRR, we get

CMRR = 1 + 2 gm REE

Since 2 gm >> 1 and gm = IC / VT =  I EE /2VT , at last we get

CMRR ≅ I EE REE / VT

As CMRR must be as large as possible, IEE may not be increased indefinitely, neither can we use a very large REE. Besides needing a corresponding high voltage power supply for VEE, a large resistor may not be fabricated by IC technology. Usually This problem is solved by replacing REE by a current source, which has a very large output resistance. 