Instructor : Po-Yu Kuo 教師 : 郭柏佑

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EL 6033 ( ). Analog Filter (I). Instructor Po-Yu Kuo . Lecture3: Design Technique for Three-Stage Amplifiers. Outline. Introduction Structure and Hybrid- Model Stability Criteria Circuit Structure. Why We Need Three-Stage Amplifier?. - PowerPoint PPT Presentation

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<ul><li><p>InstructorPo-Yu KuoLecture3: Design Technique for Three-Stage AmplifiersEL 6033 ()Analog Filter (I) </p></li><li><p>*OutlineIntroductionStructure and Hybrid- ModelStability CriteriaCircuit Structure</p></li><li><p>*Why We Need Three-Stage Amplifier?Continuous device scaling in CMOS technologies lead to decrease in supply voltage</p><p>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.</p></li><li><p>*High DC Gain in Low-Voltage ConditionCascode approach: enhance dc gain by stacking up transistors vertically by increasing effective output resistance (X)</p><p>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</p></li><li><p>*Challenge and SoultionThree-stage amplifier has at least 3 low-frequency poles (each gain stage contributes 1 low-frequency pole)Inherent stability problem</p><p>General approach: Sacrifice UGF for achieving stability</p><p>Nested-Miller compensation (NMC) is a classical approach for stabilizing the three-stage amplifier</p></li><li><p>*Structure of NMCDC gain=(-A1)x(A2)x(-A3)=(-gm1r1) x(gm2r2) x(-gmLrL)</p><p>Pole splitting is realized by both</p><p>Both Cm1 and Cm2 realize negative local feedback loops for stability</p></li><li><p>*Hybrid- ModelStructure</p><p>Hybrid- ModelHybrid- model is used to derive small-signal transfer function (Vo/Vin)</p></li><li><p>*Transfer FunctionAssuming gm3 &gt;&gt; gm2 and CL, Cm1, Cm2 &gt;&gt; C1, C2</p><p>NMC has 3 poles and 2 zerosUGF = DC gain p-3dB = gm1/Cm1</p></li><li><p>*Review on Quadratic Polynomial (1)When the denominator of the transfer function has a quadratic polynomial as</p><p>The amplifier has either 2 separate poles (real roots of D(s)) or 1 complex pole pair (complex roots)Complex pole pair exists if</p></li><li><p>*Review on Quadratic Polynomial (2)The complex pole can be expressed using the s-plane:</p><p>The position of poles:</p><p>2 poles are located at </p><p>If , then</p></li><li><p>*Stability CriteriaStability criteria are for designing Cm1, Cm2, gm1, gm2, gmL to optimize unity-gain frequency (UGF) and phase margin (PM)</p><p>Stability criteria:Butterworth unity-feedback response for placing the second and third non-dominant pole</p><p>Butterworth unity-feedback response is a systematic approach that greatly reduces the design time of the NMC amplifier</p></li><li><p>*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</p><p>PM of the amplifier </p><p>where |p2,3| = </p></li><li><p>*Butterworth Unity-Feedback Response(2)</p></li><li><p>*Circuit ImplementationSchematic of a three-stage NMC amplifier </p></li><li><p>*Structure of NMC with Null Resistor (NMCNR)Structure</p><p>Hybrid- Model</p></li><li><p>*Transfer functionAssume gmL &gt;&gt; gm2, CL, Cm1, Cm2 &gt;&gt; C1, C2</p></li><li><p>*Structure of Nested Gm-C Compensation (NGCC)Structure</p><p>Hybrid- Model</p></li><li><p>*Transfer functionAssume CL, Cm1, Cm2 &gt;&gt; C1, C2</p></li></ul>

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