Hints and answers for exercise 5
Problem 6.1.
1. Use the data given in the problem.
2. Determine the output current (IOut) as a function of the input voltage (Vin), the Op-Amp is
ideal (V+=V-); Answer: IOut =Vin/R.
Problem 6.4
1. Use the data given in the problem.
2. Draw the circuit schematic and assign voltages to all nodes (the ones not already named);
Answer:
3. Set up the equations for all the node voltages; Hint: Express V3 as a function of Vout, express
VY as a function of V1 (the voltage division of R1 and R2) and finally use the expression for V3
and VY to find expression for VX (eq. 1); Answer: VX= VY-V3= (R2/(R1+R1))V1-(Vout/a)
4. Set up the equation for the currents in node VX (Eq. 2); Hint: The current flowing from V2 to
VX is equal to the current flowing from VX to Vout. Assume no current flows in to the Op-Amp;
Answer: (V2-VX)/R1 = (VX-Vout)/R2.
5. Solve the system by substituting eq. 1 into eq. 2 and solve for the transfer function;
Answer: AV= Vout/Vin=Vout/(V2-V1)=(-R2/R1)/(1+(1/a)(1+(R2/R1)))
6. Calculate how much Op-Amp gain (a) is needed if the transfer function has changed by 0.1%,
if the Op-Amp gain has decreased by 25%; Hint: Use ΔAV≥1 (0.1% of 1000). Set up an
expression for the difference in the transfer function (ΔAV=AV((3/4)·a)-AV(a))
Answer: a≥3.3·103.
Problem 6.5
1. Use the data given in the problem.
2. Use eq. 6.48 to find the CMRR; Answer: CMRR≥72dB
Problem 6.10
1.
2.
3.
4.
5.
6.
Use the data given in the problem.
Find the voltage gain of the circuit (Adm=AV); Answer: AV=-gm(R//ro)= -gm·((R·ro)/(R+ro))
Calculate the transfer function from VDD to Vo (A+=Vo/VDD); Answer: A+=ro/(ro+R)
Use eq 6.51 to find the PSRR+; Answer: PSRR+=-1/(gmR).
Calculate the transfer function from Vss to Vo (A-=Vo/Vss); Answer: A-=(gm+1/ro)((R·ro)/(R+ro))
Use eq 6.51 to find the PSRR-; Answer: the PSRR-=-(1+(1/(gmR))).
Problem 6.12
1. Use the data given in the problem.
a)
1. Use eq. 6.56 to find the voltage gain (AV); Answer: AV =-gm,1(ro,2//ro,4)·gm,6(ro,6//ro,7).
b)
1. Find the output swing; Hint: VD,7≤Vo≤VD,6; Answer: Vov,7-Vss-≤ Vo ≤VDD-ӀVov,6Ӏ
c)
1. If eq. 6.66 is satisfied, use eq 6.67 and eq. 6.68 to find the systematic offset (Vos(sys));
Answer: Vo=VDD-VSD,6=VDD-VSG,3=VDD+Vt,3+Vov,3→Vos(sys)=(VDD+Vt,3+Vov,3-((VDD-VSS)/2)) /AV
d)
1. Use eq. 7.71 to find the CMRR; Answer: CMRR≈(2·gm·ro,5)·gm(ro,2//ro,4); Note: ro,5=rtail
e)
1. Find the CM input range (Vic) , M5 is kept in the active region; Answer: Vic ≥Vov,5+Vt,1+Vov,1-VSS
2. Find the CM input range (Vic), M1 is kept in the active region (VGD,1<Vt,1);
Answer: Vic<VDD+Vt,1+Vt,3+Vov,3
3. Write the CM input range (Vic) , so M1 and M5 are kept in the active region;
Answer: Vov,5+Vt,1+Vov,1-VSS ≤Vic<VDD+Vt,1+Vt,3+Vov,3
Problem 6.18
1. Use the data given in the problem.
2. Find the CM input range (Vic) , M5 is kept in the active region; Answer: Vic ≤VDD+Vt,1+Vov,1+Vov,5
3. Find the CM input range (Vic), M1 is kept in the active region (VGD,1>Vt,1);
Answer: Vic>-VSS+Vt,1+Vov,11
4. Write the CM input range (Vic) , so M1 and M5 are kept in the active region;
Answer: -VSS+Vt,1+Vov,11<Vic≤VDD+Vt,1+Vov,1+Vov,5
5. Calculate the CM input range (Vic); Answer: -VSS-0.6<Vic≤VDD-1.2