HW 4

 

Text Box: Figure 4: M1=M2; M3=M4; M7=M9; M13=M14; M11=M9; M8=M6 The bulk of all transistors is connected to their source
Figure 4 shows an operational amplifier with differential input and single ended output. The relevant sizes of some transistors are shown. Further assume VDD=5, VSS=0, and assume that all transistors are sized so that VTn=-VTp=0.8V and (VGS - VT)n =-(VGS - VT)p=0.2V. You can also assume that M1, M2, M3, M4, M5, M7, M13 and M14 have a lambda=0.

 

A.    Calculate the maximum value of VB1 so that all transistors are in the active region.

Expression:

VB1-max =

Value:

VB1-max =

B.     Derive the minimum value of VB2 so that all transistors are in the active region.

Expression:

VB2-min =

Value:

VB2-min =


For all the following questions, assume the values of VB1 and VB2 that you calculated in A & B.

C.     Derive symbolically the gain of the amplifier for a differential input signal i.e. VOUT/VIN

Expression:

VOUT/VIN =

D.    Derive common mode input range so that all transistors remain in the active region. Indicate for each limit which transistor(s) go(es) out of active region first.

Transistor(s)

                        

--------------------------

 

Expression:

                         <= VIncommon-mode <=

Values:

                         <= VIncommon-mode <=

E.     Derive output range so that all transistors remain in the active region. Indicate for each limit which transistor(s) go(es) out of active region first.

Transistor(s)

                        

--------------------------

 

Expression:

                               <= VOUT <=

Values:

                               <= VOUT <=

F.      Now assume that the devices have a non-zero output conductance (i.e. lambda is not zero). Find an expression for the common mode gain. You can make approximations if necessary. Explain your reasoning and justify your assumptions.

G.    Find a expression for the CMRR i.e. (differential mode gain)/(common mode gain).