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Instructor : Po-Yu Kuo 教師 : 郭柏佑 PowerPoint PPT Presentation

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EL 6033 類比濾波器 ( 一 ). Analog Filter (I). Instructor : Po-Yu Kuo 教師 : 郭柏佑. Lecture3: Design Technique for Three-Stage Amplifiers. Outline. Introduction Structure and Hybrid- π Model Stability Criteria Circuit Structure. Why We Need Three-Stage Amplifier?.

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Instructor : Po-Yu Kuo 教師 : 郭柏佑

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EL 6033類比濾波器 (一)

Analog Filter (I)

Instructor:Po-Yu Kuo


Lecture3: Design Technique for

Three-Stage Amplifiers


  • Introduction

  • Structure and Hybrid-πModel

  • Stability Criteria

  • Circuit Structure

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.

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

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

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

Hybrid-π Model



Hybrid- model is used to derive small-signal transfer function (Vo/Vin)

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

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

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

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

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| =

Butterworth Unity-Feedback Response(2)

Circuit Implementation

Schematic of a three-stage NMC amplifier

Structure of NMC with Null Resistor (NMCNR)



Transfer function

  • Assume gmL >> gm2, CL, Cm1, Cm2 >> C1, C2

Structure of Nested Gm-C Compensation (NGCC)



Transfer function

  • Assume CL, Cm1, Cm2 >> C1, C2

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