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 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?. - PowerPoint PPT Presentation

Text of Instructor : Po-Yu Kuo 教師 : 郭柏佑

  • InstructorPo-Yu KuoLecture3: Design Technique for Three-Stage AmplifiersEL 6033 ()Analog Filter (I)

  • *OutlineIntroductionStructure and Hybrid- ModelStability CriteriaCircuit 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 ConditionCascode 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]~20-40dBGain of two-stage amplifier [(gmro)2]~40-80dBGain of three-stage amplifier [(gmro)3]~80-120dB, which is sufficient for most applications

  • *Challenge and SoultionThree-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 NMCDC 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- ModelStructure

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

  • *Transfer FunctionAssuming gm3 >> gm2 and CL, Cm1, Cm2 >> C1, C2

    NMC has 3 poles and 2 zerosUGF = 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 CriteriaStability 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 negligible1 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 amplifierButterworth unity-feedback response ensures the Q value of p2,3 is

    PM of the amplifier

    where |p2,3| =

  • *Butterworth Unity-Feedback Response(2)

  • *Circuit ImplementationSchematic of a three-stage NMC amplifier

  • *Structure of NMC with Null Resistor (NMCNR)Structure

    Hybrid- Model

  • *Transfer functionAssume gmL >> gm2, CL, Cm1, Cm2 >> C1, C2

  • *Structure of Nested Gm-C Compensation (NGCC)Structure

    Hybrid- Model

  • *Transfer functionAssume CL, Cm1, Cm2 >> C1, C2