1. Differential Amplifiers

2. Outline

3. Single-Ended Versus Differential Operation
The transitions disturb
the differential by
equal amounts, leaving
the difference in tact.

4. Immunity to Supply Noise
If VDD changes by
∆V, Vout changes by
the same amount.
Noise in VDD affects VX and VY,
but not Vx-Vy

5. Reduction of Coupled Noise
Noise coupled from L3 to L1 and L2 to L1 cancel each other.

6. Sensitivity to the Common mode level
Excessive low
Vin,CM turns off
Devices.

7. Basic Differential Pair

8. Schematic of Differential Amplifier

9. Input/Output Characteristics
Minimum Slope
Independent of Vin,cm
Maximum Slope
Thus maximum Gain

10. Range of Vin,cm Lower bound of Vin,cm:
VP should be sufficiently high in order for M3 to act
as a current source.
Upper bound of Vin, cm
M1 and M2 need to remain in saturation.

11. Sensitivity to Vin, cm M3 in the linear region is modeled
as a resistor
M1=M2
=On
M1=M2
=Off
M1=M2
=On
M1=M2
=Off
M1=M2
=On
M1=M2
=Off
M3=Linear
M3=Linear
M3=Linear

12. Small signal Gain as a function of Vin, CM

13. Maximum Allowable Output Swing
The higher the input CM level, the smaller
the allowable output swings.

14. Transconductance
∆Vin1Represents the maximum differential signal a differential
pair can handle.

15. Linearity
W/L increases
ISS Constant
Constant W/L
ISS increases

16. Determinations of Small Signal Gain
CS with resistive source degeneration
Thevenin Resistance
Cascode
Superposition Principle

17. CS with resistive source degeneration
Interpretation: The resistance at the drain
Divided by the resistance in the source path

18. Treat M1 as a CS stage with resistive source degeneration to find VX/Vin

19. Replace M1 by its Thevenin Equivalent Circuit
If RS is sufficiently large, then the small signal gain of the amplifier
can be obtained using thevenin’s equivalent circuit (see hand out)

20. Gain of CG

21. Replace M1 by its Thevenin Equivalent Circuit

22. Small Signal Gain

23. Half-Circuit Concept

24. Conversion of Arbitrary inputs to Differential and Common-Mode Components

25. Superposition Principle

26. Schematic of Differential Amplifier

27. Simulation
Vin,m=1 mV
Vout,m=8.735 mV
Av=-8.735
Calculations:
Gm=1mS
ro=30.53 KOhm
RL=12 Kohm
Av=-Gm(ro||RL)=-8.615

28. Common-Mode Response Sensitivity of Vout,CM due to Vin,CM
In the presence of resistor mismatch
In the presence of transistor mismatch
Common Mood Rejection Ratio (CMRR)

29. Sensitivity of Vout,CM due to Vin,CM
Vin,CM ↑, VP ↑, I(RSS) ↑,VX,V↓

30. Output CM Sensitivity due to Vin, CM
Vout,m
=0.285 mV
Vin,cm
=1 mV
RL=12 K
Gm=1.043 mS
Gds3=58.29 uS
Av, CM(Analytical)=0.343
Av, CM(Simulation)=0.285
(Excluding gmb, ro)

31. Common-Mode to Differential Conversion at High Frequencies
Even if the output resistance of the current source is high,
the common-mode to differential conversion becomes significant
at high frequencies.

32. Resistor Mismatch
(from CS with resistive source degeneration)

33. Common Mode to Differential Mode Conversion

34. Voutp-Voutn
Differential Mode signal at the output: uV

35. Effect of CM Noise in the Presence of Resistor Mismatch
Common Mode to Differential Conversion

36. Transistor Mismatch

37. Supply Noise Sensitivity

38. CMRR

39. Diode Connected Load
Problem: Difficult to decrease (W/L)P without dropping the
common mode voltage of Vout.

40. Addition of Current Source to Increase Voltage Gain
Reduce gm by reducing current rather than the aspect ratio.
Reduce I(M3) and I(M4).

41. Variable Gain Amplifier