Instructor ： Po-Yu Kuo
教師：郭柏佑
Lecture3: Design Technique for Three-Stage Amplifiers
EL 6033類比濾波器 ( 一 )
Analog Filter (I)
2
Outline
Introduction Structure and Hybrid-π Model Stability Criteria Circuit Structure
3
Why We Need Three-Stage Amplifier? Continuous device scaling in CMOS technologies lead to decrease in
supply voltage
High dc gain of the amplifier is required for controlling different power management integrated circuits such as low-dropout regulators and switched-capacitor dc/dc regulators to maintain the constant of the output voltage irrespective to the change of the supply voltage and load current.
4
High DC Gain in Low-Voltage Condition Cascode approach: enhance dc gain by stacking up transistors vertically by
increasing effective output resistance (X)
Cascade approach: enhance dc gain by increasing the number of gain stages horizontally (Multistage Amplifier)
Gain of single-stage amplifier [gmro]~20-40dB
Gain of two-stage amplifier [(gmro)2]~40-80dB
Gain of three-stage amplifier [(gmro)3]~80-120dB, which is sufficient for most applications
5
Challenge and Soultion Three-stage amplifier has at least 3 low-frequency poles (each gain stage
contributes 1 low-frequency pole) Inherent stability problem
General approach: Sacrifice UGF for achieving stability
Nested-Miller compensation (NMC) is a classical approach for stabilizing the three-stage amplifier
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Structure of NMC
DC gain=(-A1)x(A2)x(-A3)=(-gm1r1) x(gm2r2) x(-gmLrL)
Pole splitting is realized by both
Both Cm1 and Cm2 realize negative local feedback loops for stability
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Hybrid-π Model
Structure
Hybrid-π Model
Hybrid- model is used to derive small-signal transfer function (Vo/Vin)
8
Transfer Function
Assuming gm3 >> gm2 and CL, Cm1, Cm2 >> C1, C2
NMC has 3 poles and 2 zeros UGF = DC gain p-3dB = gm1/Cm1
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9
Review on Quadratic Polynomial (1)
When the denominator of the transfer function has a quadratic polynomial as
The amplifier has either 2 separate poles (real roots of D(s)) or 1 complex pole pair (complex roots)
Complex pole pair exists if
20
2
0
1)(w
s
Qw
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2
1
041
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Review on Quadratic Polynomial (2)
The complex pole can be expressed using the s-plane:
The position of poles:
2 poles are located at
If , then
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14
22200
3,2 QQ
wj
Q
wp
2/1Q
2200
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wp
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Stability Criteria
Stability criteria are for designing Cm1, Cm2, gm1, gm2, gmL to optimize unity-gain frequency (UGF) and phase margin (PM)
Stability criteria: Butterworth unity-feedback response for placing
the second and third non-dominant pole
Butterworth unity-feedback response is a systematic approach that greatly reduces the design time of the NMC amplifier
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Butterworth Unity-Feedback Response(1)
Assume zeros are negligible 1 dominant pole (p-3dB) located within the passband, and 2
nondominant poles (p2,3) are complex and |p2,3| is beyond the UGF of the amplifier
Butterworth unity-feedback response ensures the Q value of p2,3 is
PM of the amplifier
where |p2,3| =
2/1
60
/1
/tantan180
23,2
3,21
3
1
pUGFQ
pUGF
p
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dB
)/( 232 mLmm CCgg
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Butterworth Unity-Feedback Response(2)
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Circuit Implementation
Schematic of a three-stage NMC amplifier
15
Structure of NMC with Null Resistor (NMCNR)
Structure
Hybrid-π Model
16
Transfer function
Assume gmL >> gm2, CL, Cm1, Cm2 >> C1, C2
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Structure of Nested Gm-C Compensation (NGCC)
Structure
Hybrid-π Model
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Transfer function
Assume CL, Cm1, Cm2 >> C1, C2
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