eece488: analog cmos integrated circuit design set 7...
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1SMEECE488 Set 7 - Opamp Design
EECE488: Analog CMOS Integrated Circuit Design
Set 7
Opamp DesignReferences: “Analog Integrated Circuit Design” by D. Johns and K. Martin
and “Design of Analog CMOS Integrated Circuits” by B . Razavi
All figures in this set of slides are taken from the above books
Shahriar MirabbasiDepartment of Electrical and Computer Engineering
University of British Columbiashahriar@ece.ubc.ca
2SMEECE488 Set 7 - Opamp Design
General Considerations
• Gain
• Small-signal bandwidth
• Large-signal performance
• Output swing
• Input common-mode range
• Linearity
• Noise/offset
• Supply rejection
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3SMEECE488 Set 7 - Opamp Design
One-Stage Op Amps
4SMEECE488 Set 7 - Opamp Design
One-Stage Op Amp in Unity Gain Configuration
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5SMEECE488 Set 7 - Opamp Design
Cascode Op Amps
6SMEECE488 Set 7 - Opamp Design
Unity Gain One Stage Cascode
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7SMEECE488 Set 7 - Opamp Design
Folded Cascode Op Amps
8SMEECE488 Set 7 - Opamp Design
Folded Cascode Stages
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9SMEECE488 Set 7 - Opamp Design
Folded Cascode (cont.)
10SMEECE488 Set 7 - Opamp Design
Folded Cascode (cont.)
| Av |≈ gm1{[( gm3 + gmb3)ro3(ro1 ||ro5)] ||[( gm7 + gmb 7)ro7ro9 ]}
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11SMEECE488 Set 7 - Opamp Design
Telescopic versus Folded Cascode
12SMEECE488 Set 7 - Opamp Design
Example Folded-Cascode Op Amp
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13SMEECE488 Set 7 - Opamp Design
Single-Ended Output Cascode Op Amps
14SMEECE488 Set 7 - Opamp Design
Triple Cascode
Av app. (gmro)3/2
Limited Output Swing
Complex biasing
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15SMEECE488 Set 7 - Opamp Design
Output Impedance Enhancement
1221 oomout rrgAR =
16SMEECE488 Set 7 - Opamp Design
Gain Boosting in Cascode Stage
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17SMEECE488 Set 7 - Opamp Design
Differential Gain Boosting
18SMEECE488 Set 7 - Opamp Design
Differential Gain Boosting
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19SMEECE488 Set 7 - Opamp Design
Differential Gain Boosting
20SMEECE488 Set 7 - Opamp Design
Two-Stage Op Amps
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21SMEECE488 Set 7 - Opamp Design
Single-Ended Output Two-Stage Op Amp
22SMEECE488 Set 7 - Opamp Design
Two-Stage CMOS Opamp
• Popular opamp design approach
• A good example to review many important design concepts
• Output buffer is typically used to drive resistive loads
• For capacitive loads (typical case in CMOS) buffer is notrequired.
A1 –A2 1
Differentialinput stage
Secondgain stage
Outputbuffer
VoutVin
Cc
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23SMEECE488 Set 7 - Opamp Design
Two-Stage CMOS Opamp Example
24SMEECE488 Set 7 - Opamp Design
Gain of the Opamp
• First Stage
Differential to single-ended
• Second Stage
Common-source stage
• Output buffer is not required when driving capacitive loads
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25SMEECE488 Set 7 - Opamp Design
Gain of the Opamp
Third Stage
• Source follower
• Typical gain: between 0.7 to1
• Note: go=1/ro and GL=1/RL
• gmb is body-effect conductance (is zero if source can be tied tosubstrate)
26SMEECE488 Set 7 - Opamp Design
Frequency Response
Q5
Q3 Q4
Q2Q1
300
300300
150
150
vin–
vin+
Vbias
–A2 A3 vout
CCv1
i = gm1 vin
v2
Ceq CC 1 A2+( )=
A3 1≅
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27SMEECE488 Set 7 - Opamp Design
Frequency Response
Simplifying assumptions:
• CC dominates
• Ignore Q16 for the time being (it is used for lead compensation)
Miller effect results in
• At midband frequencies
28SMEECE488 Set 7 - Opamp Design
Frequency Response
• Overall gain (assuming A3 ≈1)
which results in a unity-gain frequency of
• Note: ωta is directly proportional to gm1 and inverselyproportional to CC.
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29SMEECE488 Set 7 - Opamp Design
Frequency Response
• First-order model
20 A1A2( )log
Gain
(dB)
0 Freq
ωta
ωta gm1 CC⁄≅
20– dB/decade
Phase
(degrees)
0 Freqωta
180–
90–
ωp1
ωp1
(log)
(log)
30SMEECE488 Set 7 - Opamp Design
Slew Rate
• Maximum rate of output change when input signal is large.
• All the bias current of Q5 goes either into Q1 or Q2.
Q5
Q3 Q4
Q2Q1
300
300300
150
150
vin–
vin+
Vbias
–A2 A3 vout
CCv1
i = gm1 vin
v2
A3 1≅
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31SMEECE488 Set 7 - Opamp Design
Slew Rate
32SMEECE488 Set 7 - Opamp Design
Slew Rate
• Normally, the designer has not much control over ωta
• Slew-rate can be increased by increasing Veff1
• This is one of the reasons for using p-channel input stage:higher slew-rate
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33SMEECE488 Set 7 - Opamp Design
Systematic Offset Voltage
• To ensure inherent (systematic) offset voltage does not exist,nominal current through Q7 should equal to that of Q6 when thedifferential input is zero.
Q5
Q3 Q4
Q2Q1
Q6
Q7
VDD300
300300
150 150
300
300
Vin– Vin+
Vout
VSS
Ibias
Vbias
34SMEECE488 Set 7 - Opamp Design
Systematic Offset Voltage
• Avoid systematic offset by choosing:
• Found by noting
and
then setting
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35SMEECE488 Set 7 - Opamp Design
N-Channel versus P-Channel Input Stage
• Complimentary opamp can be designed with an n-channel inputdifferential pair and p-channel second-stage
• Overall gain would be roughly the same in both designsP-channel Advantages• Higher slew-rate: for fixed bias current, Veff is larger (assuming
similar widths used for maximum gain)• Higher frequency of operation: higher transconductance of
second stage which results in higher unity-gain frequency• Lower 1/f noise: holes less likely to be trapped; p-channel
transistors have lower 1/f noise• N-channel source follower is preferable (less voltage drop and
higher gm)N-channel Advantage• Lower thermal noise — thermal noise is lowered by high
transconductance of first stage
36SMEECE488 Set 7 - Opamp Design
Feedback and Opamp Compensation
)(1
)()(
sH
sHs
X
Y
β+=
• Feedback systems may oscillate
• The following two are the oscillation conditions:
180)(
1|)(|
−=∠=
ωβωβ
jH
jH
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37SMEECE488 Set 7 - Opamp Design
Stable and Unstable Systems
38SMEECE488 Set 7 - Opamp Design
Time-domain response of a feedback system
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39SMEECE488 Set 7 - Opamp Design
One-pole system
Bode plot of the Loop gain
0
0
1)(
ωs
AsH
+=
( )00
0
0
11
1)(
A
sA
A
sX
Y
βω
β
++
+=
( )00 1 AS p βω +−=
40SMEECE488 Set 7 - Opamp Design
Multi-pole system
Bode plot of the Loop gain
12 101.0 pp ωω >
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41SMEECE488 Set 7 - Opamp Design
Phase Margin
20 LG jω( )( )log
Loop Gain
(dB)
0ωt
-20 dB/decade
Phase
(degrees)
0Freq
ωt
180–
90–
ωp1
ωp1
(log)Loop Gain
PM
Freq(log)
GM(gain margin)
(phase margin)
42SMEECE488 Set 7 - Opamp Design
Phase Margin
Closed loop frequency response
175
1 1 je)(H −×=ωβ
β5.11
)( =sX
Y
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43SMEECE488 Set 7 - Opamp Design
Phase Margin (Cont.)
Phase Margin = 45°
)(HPM GXωβ∠+=180
44SMEECE488 Set 7 - Opamp Design
Phase Margin (Cont.)
Phase Margin = 45°
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45SMEECE488 Set 7 - Opamp Design
Phase Margin (Cont.)
• At PM = 60o results in a small overshoot in the step response.• If we increase PM, the system will be more stable but the time
response slows down.
46SMEECE488 Set 7 - Opamp Design
Frequency Compensation
• Push phase crossing point out
• Push gain crossing point in
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47SMEECE488 Set 7 - Opamp Design
Telescopic Opamp (single-ended) -example
48SMEECE488 Set 7 - Opamp Design
Compensation (Cont.)
• Assume we need a phase margin of 45 o (usually inadequate) and other non-dominant poles are at hig h frequency.
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49SMEECE488 Set 7 - Opamp Design
Compensation of a two-stage opamp
Miller Effect Ceq = CE + (1+ Av2)CC
f pE = 1
2πRout [CE + (1+ Av 2)CC ]
50SMEECE488 Set 7 - Opamp Design
Compensating Two-Stage Opamps
Q5
Q3 Q4
Q2Q1
Q6
Q7
VDD300
300300
150 150
300
300
Vin-Vin+ Vout2
Vbias1
CcQ16
Vbias2
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51SMEECE488 Set 7 - Opamp Design
Compensating Two-Stage Opamps
• Q16 has VDS16 = 0 therefore it is hard in the triode region.
• Small signal analysis: without RC, a right-half plane zero occursand worsens the phase-margin.
gm1vin
gm7v1
v1
R1 C1
RC CC
R2 C2
52SMEECE488 Set 7 - Opamp Design
Compensating Two-Stage Opamps
• Using RC (through Q16) places zero at
• Zero moved to left-half plane to aid compensation
• Good practical choice is
• satisfied by letting
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53SMEECE488 Set 7 - Opamp Design
Design Procedure
Design example: Find CC with RC=0 for a 55o phase margin
– Arbitrarily choose C’C=1pF and set RC=0
– Using SPICE, find frequency ωt where a –125° phase shiftexists, define gain as A’
– Choose new CC so ωt becomes unity-gain frequency of theloop gain, resulting in a 55o phase margin.
Achieved by setting CC=CCA’
– Might need to iterate on CC a couple of times using SPICE
54SMEECE488 Set 7 - Opamp Design
Design Procedure
Next: Choose RC according to
– Increasing ωt by about 20 percent, leaves zero near final ωt
– Check that gain continues to decrease at frequencies above thenew ωt
Next: If phase margin is not adequate, increase CC while leavingRC constant.
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55SMEECE488 Set 7 - Opamp Design
Design Procedure
Next: Replace RC by a transistor
SPICE can be used for iteration to fine-tune the devicedimensions and optimize the phase margin.
56SMEECE488 Set 7 - Opamp Design
Process and Temperature Independence
• Can show non-dominant pole is roughly given by
• Recall zero given by
• If RC tracks inverse of gm7 then zero will track ωp2:
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57SMEECE488 Set 7 - Opamp Design
Process and Temperature Independence
• Need to ensure Veff16/Veff7 is independent of process andtemperature variations
• First set Veff13=Veff7 which makes Va=Vb
Q11
Q12
Q13
Q6
CC
25
25
25
300
300
Q16Va
Vb
Vbias
Q7
Vb
58SMEECE488 Set 7 - Opamp Design
Process and Temperature Independence
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59SMEECE488 Set 7 - Opamp Design
Stable Transconductance Biasing
60SMEECE488 Set 7 - Opamp Design
Stable Transconductance Biasing
• Transconductance of Q13 (to the first order) is determined bygeometric ratios only.
• Independent of power-supply voltages, process parameters,temperature, etc.
• For special case (W/L)15=4(W/L)13
gm13=1/RB
• Note that high-temperature will decrease mobility and henceincrease effective gate-source voltages.
• Roughly 25% increase for 100 degree increase
• Requires a start-up circuit (might have all 0 currents)
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