Difficulty

[microcare]

I was studying Diffrential Amplifiers when I came across this difficulty. Hence I thought of consulting to you for help.
Well,

This is regarding *common mode response
*There are two different views (Analysis) given regarding the above topic in two different books
Sedra/Smith and B.Razzahvi

If you c B.Razaavi on Pg. 118-119 under chapter Differential amplifiers, they have analyzed and concluded that :

_/*Finite output impedence of tail current source results in some common mode gain in a symmetric diffrential pair

*/_whereas if you go through the analysis in Sedra/Smith.,on Pg.700-701 unde the chapter Diffrential and Multi stage Amplifiers under sub topic Common mode gain and common mode rejection ratio,they have analyzed and concluded

_/*Even though Rss (tail current sourse impedence) is finite ,taking output diffrentially results in infinite CMRR.However this is true only when circuit is perfectly matched

*/_These two analysis seem to contradict each others .If we follow analysis given in B.Razzavi, there should be some finite common mode gain even when circuit is perfectly matched.But as seen in Sedra/Smith, we notice that the common mode gain becomes = 0 .

Kindly guide me over this
Regards
Nikhil

 

[DigiTan]

Sedra/Smith's example was assuming that the drain resistances Rd for both sides is perfectly matched. On the next page, it defines the differential gain, common gain and CMRR as:

Ad = (Vo2 - Vo1) / Vd
Acm = (Vo2 - Vo1) / Vcm
CMRR = |Ad| / |Acm|

Going back to the amplifier itself, split it into half-circuits so that both transistors have their own seperate Rss, Rd, and gm. This time, give one side the resistor Rd and the side resistor Rd + ΔRd. The output of both half-circuits are:

vo1 = - Vcm (Rd / 2Rss)
vo2 = - Vcm ((Rd + ΔRd) / (2Rss))

If you substitute those 2 lines into the "Acm" and equation I wrote above, the "Vcm" terms will cancel and you can simplify it into...

Acm = vo2 - vo1
Acm = [- ((Rd + ΔRd) / (2Rss)) + (Rd / 2Rss)]
Now the Rd terms cancel, leaving only ΔRd behind...
Acm = - ΔRd/2Rss

The Rd term can be reintroduced by multiplying that last equation by (Rd/Rd). This becomes helpful later.

Acm = - ΔRd/2Rss = (ΔRd/2Rss)*(Rd/Rd) = (ΔRd/Rd)*(-Rd/2Rss)

Since ΔRd is assumed to have an insignificant effect on differential gain "Ad," they leave the equation "Ad = -gm*Rd" unchanged from the previous page.

Finally, combine the new Acm equation with the original Ad equation...

CMRR = |Ad|/|Acm|
CMRR = gm*Rd / |Acm|
CMRR = gm*Rd / ((Rd/2Rss)*(ΔRd/Rd))
CMRR = 2gm*Rss / (ΔRd/Rd)

...so you can see from this final equation that any time ΔRd is zero, the CMRR would be infinite if the inputs were perfectly matched. This happens even when Rss is finite. When Sedra & Smith assumed ΔRd=0, this is where the infinity term came from. I haven't read the Razavvi book, but I would guess they always assumed a non-zero ΔRd.