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Design of Analog Integrated Circuits
Textbook Chapter 9
9.1 General Considerations
9.2 One-Stage Op Amps
9.3 Two-Stage Op Amps
9.4 Gain Boosting
9.5 Comparison
9.6 Output Swing
9.7 Common Feedback
9.8 Input Range Limitations
9.9 Slew Rate
9.10 High-Slew-Rate Op Amps
9.11 Power Supply Rejection
9.12 Noise in Op Amps
Chapter 6: Operational Amplifiers
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Op Amp Design Challenge
Three decades ago
•General-purpose blocks as an “ideal” op amp
•Design effort is to satisfy an ideal op amp
- infinite gain
- infinite input impedance
- zero output impedance
Today
•Design effort is to make trade-offs for a specific
application, often sacrificing the unimportant
aspects to improve the critical ones.
•E.g., gain error vs speed, open loop gain vs VDD
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Performance Parameters
• Gain(Precision)
• Small-signal Bandwidth(Speed): 3-dB/fu
• Large-Signal behavior (e.g. slew rate)
• Output Swing (especially for Low supply voltage)
• Linearity
• Noise and offset
• Supply Rejection
• Input CM Range, Input/Output Impedance
• Power dissipation
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One-Stage Op Amps
• Low-frequency gain:
• Bandwidth: usually proportional to 1/(CL*Rout)
• Output Swing (single-side): VDD-3VOV
• Mirror pole in single-ended circuit
• Noise: two input devices and two “load’ devices
( || )m ON OPg r r
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Telescopic Cascode Op Amps
• Low-frequency gain:
• Output Swing (single-side): VDD-5VOV
• Mirror pole at node X (at node Y) in single-ended
• Difficult to short telescopic op amp output to input
• Noise: input noise mainly has four devices contribution
2 2( || )mN mN ON mP OPg g r g r
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Example 9.5
Shorting their input and output to form an unity-gain buffer
To keep M2 and M4 in saturation
When , M4 is in triode, others are saturated;
M2, M4 are saturated;
M2, M1 in triode,M4 is in saturation.
2 4
4
4 4 2
and
( )
out X TH out b TH
X b GS
b TH out b GS TH
V V V V V V
V V V
V V V V V V
4 in b THV V V
4 4 2( )b TH in b GS THV V V V V V
4 2( )in b GS THV V V V
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Specifications: VDD = 3V, differential output swing = 3V, power dissipation
= 10mW, voltage gain = 2000. Assume nCox = 60 A/V2, pCox = 30
A/V2, n = 0.1V1, p = 0.2V1 (for an effective channel length of 0.5
m), = 0, VTHN = VTHP = 0.7V.
1.5mA1.5mA
Telescopic Cascode Op Amps Design
Power budget: IM9 = 3mA, IMb1 + IMb2 =
330A.
Output swing: Node X(Y) positive swing =
1.5V and M3-M6 are in saturation. Then, for
left half circuit, we have VOD7 + VOD5 +
VOD3 + VOD1 + VOD9 = 1.5V. Since M9 is
carrying largest current, VOD9 0.5V is
chosen. Four cascode transistors are shared
with 1V. Because of lower mobility, we
allocate overdrive of M5~M8 are 300mV, i.e.
|VOD5 = VOD6 =|VOD7 = VOD8 0.3V,
obtaining VOD1 + VOD3 0.4V.
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CM level & bias: Minimum allowable input CM level = VGS1 + VOD9 = 1.4V.
Vb1, min = VGS3 + VOD1 + VOD9 = 1.6V. Vb2, max = VDD (VGS5 + VOD7) = 1.7V.
- Finally, DC bias voltage circuits and a CMFB circuit are necessary
W/L: By ID =(1/2)Cox(W/L)(VOD)2, (W/L)14 = 1250, (W/L)58 = 1111,
(W/L)9 = 400.
Gain: Av gm1[(gm3ro3ro1) (gm5ro5ro7)]=1416. In order to increase the
gain, we recognize )/()/(2 DDoxom IILWCrg DIWL / , where
1/L. We can therefore increase the width or length, or reducing the drain
current.
Modulation: Since M1~M4 appear in signal path for keeping
minimum capacitance, we double the width and length of M5~M8 to
increase ro (gm remains constant). Choosing (W/L)58 = 1111m/1m and
p=0.1V-1, then Av 4000. VDS1=VGS1-VTHNVGS1=0.2+0.7
Telescopic Cascode Op Amps Design
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Gate Bias Voltage Generation
• Ensure bias voltage to track the input CM level
• Choose Mb1 to be a narrow, long, “weak” device
9
1 , 1,2 , 1
, 1 1,2 1,2 3,4( )
b in CM GS GS b
GS b GS TH GS
V V V V
V V V V
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• NMOS input higher gain
• NMOS input Lowering the pole at folding point
• PMOS input is less sensitive to flicker noise
• Slighter Higher Output Swing than telescopic
• Higher Power dissipation, lower voltage gain, lower pole
frequency and higher noise
• Input and output can be shorted: A better input CM range
1 3 3 3 1 5 7 7 7 9| | {[ ( || )] || [ ]}V m m mb o o o m mb o oA g g g r r r g g r r
Folded Cascode OP Amp
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Specifications: VDD = 3V, differential output swing = 3V, power dissipation =
10mW, voltage gain = 2000. Assume nCox = 60 A/V2, pCox = 30 A/V2, n
= 0.1V1, p = 0.2V1 (for an effective channel length of 0.5 m), = 0, VTHN
= VTHP = 0.7V.
Power budget: IM11 = 1.5mA, IM9 + IM10 = 1.5mA, IMb1 + IMb2 + IMb3 = 330A.
Output swing: one side o/p swing = 1.5V, M3-M10 in saturation.
Choose VOD5,6 0.5V, VOD3,4 0.4V, VOD7,8 = VOD9,10 0.3V.
W/L: (W/L)5,6 = 400, (W/L)3,4 = 313, (W/L)710 = 278.
O/p CM level: CMmin = VOD7 + VOD9 0.3V+0.3V0.6V,
CMmax = VDD - VOD5 - VOD3 3.0V-0.5V-0.4V 2.1V,
thus CMoptimum = 1.35V.
Folded Cascode OP Amp Design
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Determine (W/L)1,2: minimum input CM level = VGS1 + VOD11.
Minimum dimensions of M1,2: If input and output are shorted, then VGS2 + VOD11 =
1.35V. With VOD11 = 0.4V as initial guess, we have VGS1 = 0.95V VOD1,2 = 0.95-0.7 =
0.25V, and (W/L)1,2 = 400.
Maximum dimensions of M1,2: The maximum dimensions of M1,2 are determined by the
tolerable input capacitance at nodes X and Y.
CM level & bias: Minimum allowable input CM level = VGS1 + VOD11 = 0.95V+0.4V
=1.35V. Vb1, min = VGS7 + VOD9 = 0.7V+0.3V+0.3V=1.3V. Vb2, max = VDD (VGS3 + VOD5)
= 3.0V- (0.7V+0.4V+0.5V)=1.4V.
Gain: gm = 2ID / (VGS VTH) = 2ID / VOD, we have gm1,2 = 0.006 A/V, gm3,4 = 0.0038 A/V,
gm7,8 = 0.05 A/V.
For L = 0.5 m, rO1,2 = rO7-10=13.3k, and rO3,4 = 2rO5,6=6.67k.
The overall gain 400.
How to increase the gain?
1.Increase ro by decreasing bias current or increase channel length
2.Increase gm by increasing W/L or bias current
Folded Cascode OP Amp Design
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Low Voltage Single-ended Output
• Left implementation wastes one threshold voltage
• Still, single-ended output is unfavorable due to half
output swing and a mirror pole
• Note that almost all the differential output circuits need
a CMFB
Fig. (a) VX=VDD-|VGS5|-|VGS7|Vout,max=VDD-|VGS5|-|VGS7|+|VTH6|
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Two-Stage Op Amps
• Voltage headroom in today’s design is constrained with
low supply voltage and large output swing
• Gain:
• Output Swing: Vdd-2VOV
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Two-Stage Op Amps with cascode devices
• Voltage headroom in today’s design is constrained with
low supply voltage and large output swing
• Gain:
• Can we have more stages? Feedback stability limits
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Gain Boosting
• Increase the output impedance without adding more
cascode devices.
Routt A1gm2ro2ro1
•Avoid headroom limitation, PMOS common-source
stage is better, but M3 could go in triode
•Folded-cascode inserts one more stage
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Differential Folded Cascode Gain Boosting
The minimum level at the
drain of M3 is equal to VOD3 +
VGS5 + VISS2.
The minimum allowable level
of VD3 is given by VOD3+VOD1,2
+ VISS1.
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Gain Boosting in Signal Path and Load
• Gain boosting can be utilized in the load current source
• To allow maximum swings, A2 employs NMOS-input.
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• In fully-differential op amps, the output CM level is usually
not well defined.
- Case 1: , Vx,Vy decreases, Iss triode;
- Case 2: In reverse, Vx,Vy increases, M3,M4 triode.
Common-Mode Feedback
3,4 / 2D SSI I
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Conceptual topology
• Measure output CM level;
• Compare with a reference;
• Apply the error to correct the level.
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CM Sensing Techniques
R1 and R2 or I1 and I2 must
be large enough to ensure
that M7 or M8 is not
“starved” when a large
differential swing appears
at the output.
If Vout2 is quite higher than Vout1,
I1 must sink both IX (Vout2
Vout1)/(R1 + R2) and ID7.
Consequently, if (R1 + R2) or I1is not sufficiently large, ID7
drops to zero and Vout,CM no
longer represents the true
output CM level.
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CMFB using MOSFETs in triode region
• M7 and M8 operate in deep triode region,
THoutoutoxn
THoutoxnTHoutoxn
ononP
VVVL
WC
VVL
WCVV
L
WC
RRR
2
1
11
21
21
87
RP is a function of Vout1 + Vout2 but
independent of Vout2 Vout1.
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Differential-mode Voltage
Common-mode Voltage
outout VV ,
CMFBV constant
CMFBV outout VV ,
IB
IB/2+I IB/2-I
Q1
Q2 Q3
Q4
Q5
Q6
IB
IB
IB
IB/2+IIB/2-I
Vout+
VCMFB
Vout-
VREF
CMFB Using Differential Pairs
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CMFB Techniques
• Control cascade current source
• Control tail current source
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CMFB Techniques
• Deep triode sensing feedback
- Limited Output Swing Due to the drop of M7 and M8
- Large C Reduce the drop and increase M7 and M8
- Device variation Output CM is not constant
• Deep triode folded-cascade sensing feedback
- Improved output swing without the drop of M7 and M8
5
7,8 1 2
1
2( ) 2
b GS
Dn ox out out TH
V V
W IC V V VL
ID
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CMFB Techniques
• Modification of deep triode sensing feedback
• The output level is relatively independent of device
parameters and lowers sensitivity of Vb
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CM Feedback Techniques
• Modification of deep triode sensing feedback
• M17, M18 reproduces the drain of M15 a voltage equal to the
source voltage of M1 and M2
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CMFB Techniques
• Another type of CM feedback topology
• Diode-connected loads’ output CM level is well-defined
• Differential small signal gain
• Common-mode work as a diode-connected
• Low supply voltage design
3
3 3
Output CM= | |
| |
DD GS
SD GS
V V
V V
3 3 1
3 3
| | / 2
| | | |
SD GS F
GS TH
V V R I
V V
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CMFB in Two-Stage Op Amps
• CMFB around second stage, but not for first one
• CMFB from second stage to first stage
• 3 or 4 poles, which makes it difficult for the loop stable
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CMFB at both Stages
• All the drain currents are copied from Iss
• The differential voltage gain is equal to
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CMFB for Cascode First Stage
• First stage use deep triode feedback loop to avoid loading.
• Achieving high gain
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Slew Rate of Telescopic Op Amp
• Each side appears a ramp with slope equal to
• The total slew rate for Vout1- Vout2 equal to
maxSlew rate |outdV
dt
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Power Supply Rejection
• Power line contains noise
• PSRR(power supply rejection ration):
- Gain from input to output divided by the gain from
supply to the output
• At low frequency