Operational Amplifier (2)
Chapter 9
Topics
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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
(small voltage swings)
High gain stage
Two-Stage Op-Amp With SingleEnded 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 voltage
at 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 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:
Example (2)
• Calculate the Low Frequency PSRR of
the feedback circuit
(KCL)
(KVL)
Example (3)
(Low frequencies analysis, C1 and C2 do not draw any current)
(PSRR)
β=C1/(C1+C2), Vout/Vin=1/ β=1+C2/C1
Noise in a Telescopic Op-Amp
(Do not
contribute
much noise)
Noise in a Telescopic Op-Amp
Observation:
1. Low impedance path
to output via M3.
2. Divde Vout, M1 by Av2
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 contribute
much noise
Noise Analysis
Equivalent CS Stages
Noise due to M7
Noise-Voltage Swing Trade-Off
If the VOD of M9 and M10 is
Reduced to increase output swing,
the noise of M9 will increase.
Noise in a Two-Stage Op-Amp
Noise of stage 2 not
so significant
Summary
(Telescopic)
(Folded cascode,
Only thermal noise is included)
(Two Stage Op-Amp)