(2) (25 pts) Given the Op-amp circuit below: ive the expression for the output v
ID: 1766237 • Letter: #
Question
(2) (25 pts) Given the Op-amp circuit below: ive the expression for the output voltage in terms of the input voltages Vi and V and resistors R1, R2, R3, R4. ) Give the differential gain (Adiff =vo r) for this difference amplifier with Resistor values as shown. By definition, taff-½-V R1 R R2 2*R IDEAL -a Vout R3 R -o c. (5)The Common Mode Gain should be zero volts/volts provided exact values of the resistors. However, if R3-0.98 R and R4-2.02*R it will not be zero. Calculate the Common =Yout CM d. (5) Using the differential voltage Gain calculated from (b) and the common mode gain 20 logolAun Acml calculated in (c) calculate the Common Mode Rejection Ratio: CMRRExplanation / Answer
For the above given op-amp circuit,it is looking like differential amplifier
(a).Non invertng output for above circuit=Vnon=(1+(Rf/Ri))Vi. Here in the given op- amp Rf=R4,Ri=R3 and vi=v2 consider the resistors connected to + ve terminal.Vnon=(1+(R2/R1))(R4/(R3+R4)V2
inverting output=-(Rf/Ri)vi ...From the figure resistors connected to -ve terminal are Rf=R2,Ri=R1 and Vi=V1.
Vinv=-(R2/R1)v1.
Finally Total output=Vout=(1+(R2/R1)(R4/(R3+R4))V2-(R2/R1)V1).
Here from the figure R2/R1=R4/R3.So,it can also write as Vout=R2/R1(V2-V1)=R4/R3(V2-V1).
(b). Differential gain =Adiff=Vout/Vdiff. From the figure,changed resistor values are R1=R3=R and R2=R4=2R.
From the figure v1=vcm-(1/2)vdiff.
V2=vcm+(1/2)vdiff. Vdiff=v2-v1=vdiff.
Finally =Adiff=Vout/Vdiff=2R/R(V2-V1)/(V2-V1)=2.
(c) Common mode gain Acm=Vout/(Vcm)
If R3=0.98R and R4=2.02R. Now,R4/R3 not equal to R2/R1.So,common gain not equal to Zero.
Now,Vout=-(2)V1+(2.02/3)(1+2)V2=2.02V2-2V1.Here already we know that for common mode V1=V2=Vcm.
Now,Vout=0.02V1=0.02V2=0.02Vcm.
Common mode gain =Acm=Vout/(Vcm)=0.02Vcm/Vcm=0.02.
(d) .From the above calculations,Adiff=2 and Acm=0.02.
Common mode rejection ratio(CMMR)=20log10(Adiff/Acm)
=20log10(20.02)=20log10(100)=20log10102=40log1010=40.
Finally CMRR=40.
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