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Chip Amps Amplifiers based on integrated circuits 

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14th September 2007, 07:17 AM  #1 
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Join Date: Jan 2004
Location: AUDIO

worst CMRR?

14th September 2007, 05:52 PM  #2 
diyAudio Member

You just calculate the worst error it produces at the both borders of the resistor´s tolerance. They should be identical, but when the + side has a bit higher gain than the  side you get the CM error. Plus add CMMR of the opamp if not ideal.

15th September 2007, 07:46 AM  #3 
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Join Date: Jul 2004
Location: Scottish Borders

Hi,
would someone be good enough to show us the calculation or at least the equations?
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15th September 2007, 06:50 PM  #4 
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sorry, I don't have the equations at hand and actually I'm too lazy to do the math myself
That's the approach I would try: set V1=V2=Vi calculate the voltages at opampinputs V3 as a subject of Vi, R1, Rf, Vout V4 as a subject of Vi, R2, Rg  assume V3=V4 and use this to get a large equation for Vout with Vi, R1, R2, Rg, Rf  set Vi to 1 and the resistors to 1,05 resp. 0,95 for worst mismatch  calculate Vout, this is now equivalent to commonmode amplification  use logarithms to get to the cmmr Have fun! 
16th September 2007, 09:25 PM  #5 
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Join Date: Dec 2001
Location: SIUE, Illinois, USA

this sounds like a homework question (someone concerned with CMRR would have chosen 1% parts).
in anycase, this problem is simple because of the linear nature, which will place the minimum CMRR at a worst case resistance value. step 1. break the system up using superposition. this gives a positive gain circuit and a negative gain circuit. for equal resistors the gains are: (Rg/(Rg+R2))*((Rf+R1)/R1) = 1 and Rf/R1 = 1 Giving a total gain of (Rg/(Rg+R2))*(Rf/(Rf+R1)) + Rf/R1 = 1  1 = 0 Normally, to find the worst case would mean finding the global maximum of the above on the surface of interest, which would mean taking partial derivitives. But in this case we're pretty confident that the worst case will occur at a corner. step 2. Slove (Rg/(Rg+R2))*((Rf+R1)/Rf) + Rf/R1 for the 16 cases of interest, eg, there are 16 combinations of Rg,R1,R2,and Rf with each being either 1.05R or 0.95R. Step 3. This will give the common mode gain for all cases. note that the common mode gain will be 0 in the cases where all resistors are equal. Find the maximum absolute common mode gain, eg the maximum of x. CMRR will be 1/x Solution: I get 4.9875, which is around +14dB
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21st September 2007, 05:58 AM  #6 
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Join Date: Jan 2004
Location: AUDIO

firstly, ya this is a homework, but it could also be a useful info for those opamps
CMRR is defined as Ad/Acm, where Ad is the differential gain Acm is the common mode gain R3=0.95R, R3'=1.05R, R4=1.05R, R4'=0.95R or R3=1.05R, R3'=0.95R, R4=0.95R, R4'=1.05R could the value be negative, since there is a decrease in CMRR? 
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