1. Operational Amplifier (2)
Chapter 9

2. Topics Two-Stage Op-Amps Gain-Boosting Input Rage Limitation Slew Rate
Power Supply Rejection
Noise

3. Simple Implementation of a Two-Stage Op-Amp

4. Two-Stage Op-Amp Employing Cascoding
(small voltage swings)
High gain stage

5. Two-Stage Op-Amp With Single-Ended Output

6. Gain-Boosting
Idea behind gain boosting: increase the output impedance without adding more cascode devices.

7. Increasing the Output Impedance by FeedbackIo
Io is sensed by ro1,
convert into voltage,
subtracted Vb.
Current-Voltage Feedback.
Loop gain
Increased by A1

8. Output Resistance of a Source Degenerated Transistor

9. Gain Boosting Using Feedback Analysis

10. Implementation
(Small signal gain)
Vout, min=VOD2+VGS3

11. Differential Implementation
Minimum voltage
at the drain of M3:

12. Folded Cascode Gain Boosting
(Minimum Vx)

13. Various Implementations of Gain Boosting

14. Input Range Limitations
(Vin is input limited, as opposed to output limited)

15. Extension of input CM Range
As Vin, cm →VDD, the PMOS input pair turns off.
As Vin, cm →0, the NMOS input pair turns off.

16. Slew Rate
“Linear settling” is only applicable to sufficiently small inputs.
With a large input step, the output displays a linear ramp with a constant slope. The slope of the ramp is called the slew rate.
While the small signal bandwidth of a circuit suggests a fast time-domain response, the large signal speed may be limited by the slew rate simply because the current available to charge the dominant capacitor is limited.

17. Response of a linear circuit to an input step
The slope of the step response is proportional to the final value of the output; if we apply a larger input step, the output rises more rapidly.

18. Response of a linear circuit to an input step

19. Linear Op-amp to Step Response

20. Linear Settling in Time Domain

21. Slewing in an Op-Amp Circuit

22. Slewing During Low to High Transition

23. Slewing During High to Low Transition

24. Slewing
Slewing is a nonlinear phenomenon. If the input doubles, the output level does not double at all points because the ramp exhibits a slope independent of the input!

25. Slewing in telescopic Op-Amp

26. Slewing in a Folded Cascode Op-Amp

27. Power Supply Rejection
Op-Amps are supplied from noisy lines, and must “reject” the noise adequately.
Power Supply Rejection Ratio (PSRR) is defined as the gain from input to the output divided by the gain from the supply to the output.

28. Example (1) If M3 and M4 carry the same amount current, then
VGS3=VGS4=VDS3=VDS4.
Therefore VX=Vout
At low frequencies, M3 carries ISS/2,
VGS3 is constant for a bias current
of ISS/2, therefore, noise from VDD
couples directly to VX. Since VX=Vout,
the VDD noise is coupled to Vout,
with a gain of unity.
The PSRR at low frequencies:

29. Example (2) Calculate the Low Frequency PSRR of the feedback circuit
(KCL)
(KVL)

30. Example (3) (PSRR) β=C1/(C1+C2), Vout/Vin=1/ β=1+C2/C1
(Low frequencies analysis, C1 and C2 do not draw any current)
(PSRR)
β=C1/(C1+C2), Vout/Vin=1/ β=1+C2/C1

31. Noise in a Telescopic Op-Amp
(Do not
contribute
much noise)

32. Noise in a Telescopic Op-Amp
Observation:
1. Low impedance path
to output via M3.
2. Divde Vout, M1 by Av2
(Flicker noise)
Account for M1 and M2

33. Rule of Thumb
Mentally change the gate voltage of each transistor by a small amount and predict the effect at the output.

34. Noise in a Folded Cascode Circuit
Do not contribute
much noise

35. Noise Analysis

36. Equivalent CS Stages

37. Noise due to M7

38. Noise-Voltage Swing Trade-Off
If the VOD of M9 and M10 is
Reduced to increase output swing,
the noise of M9 will increase.

39. Noise in a Two-Stage Op-Amp
Noise of stage 2 not
so significant

40. Summary (Telescopic) (Folded cascode, Only thermal noise is included)
(Two Stage Op-Amp)