Operational Amplifier (2)

Chapter 9

Topics

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

Simple Implementation of a Two-Stage Op-Amp

Stage 1

Two-Stage Op-Amp Employing Cascoding

High gain stage

(small voltage swings)

Two-Stage Op-Amp With Single-Ended Output

Gain-Boosting

• Idea behind gain boosting: increase the output impedance without adding more cascode devices.

Increasing the Output Impedance by Feedback

Io

Io is sensed by ro1,convert into voltage, subtracted Vb.

Current-Voltage Feedback.

Loop gain Increased by A1

Output Resistance of a Source Degenerated Transistor

Gain Boosting Using Feedback Analysis

Implementation

(Small signal gain)

Vout, min=VOD2+VGS3

Differential Implementation

Minimum voltageat the drain of M3:

Folded Cascode Gain Boosting

(Minimum Vx)

Various Implementations of Gain Boosting

Input Range Limitations

(Vin is input limited, as opposed to output limited)

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.

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.

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.

Response of a linear circuit to an input step

Linear Op-amp to Step Response

Linear Settling in Time Domain

Slewing in an Op-Amp Circuit

Slewing During Low to High Transition

Slewing During High to Low Transition

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!

Slewing in telescopic Op-Amp

Slewing in a Folded Cascode Op-Amp

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.

Example (1)

If M3 and M4 carry the sameamount 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 VDDcouples directly to VX. Since VX=Vout, the VDD noise is coupled to Vout, with a gain of unity.

The PSRR at low frequencies:

Example (2)

• Calculate the Low Frequency PSRR of the feedback circuit

(KVL)(KCL)

Example (3)

(Low frequencies analysis, C1 and C2 do not draw any current)

β=C1/(C1+C2), Vout/Vin=1/ β=1+C2/C1

(PSRR)

Noise in a Telescopic Op-Amp

(Do not contributemuch noise)

Noise in a Telescopic Op-Amp

Observation:1. Low impedance pathto output via M3.2. Divde Vout, M1 by Av

2

Account for M1 and M2(Flicker noise)

Rule of Thumb

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

Noise in a Folded Cascode Circuit

Do not contributemuch noise

Noise Analysis

Equivalent CS Stages

Noise due to M7

Noise-Voltage Swing Trade-Off

If the VOD of M9 and M10 isReduced to increase output swing, the noise of M9 will increase.

Noise in a Two-Stage Op-Amp

Noise of stage 2 notso significant

Summary

(Folded cascode, Only thermal noise is included)

(Telescopic)

(Two Stage Op-Amp)