Elettronica I Materiale Didattico

7/31/2019 Elettronica I Materiale Didattico

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prof.ssa S. Rocchi

ing. M. Poli

Teaching guide: basic electronics2008-09


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ContentsIntroduzione . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Ringraziamenti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Link a equazioni, figure, lavagne, parti e riferimenti bibliografici . . . . . . . . . . . . . . . . . . . . . . . . 2NOTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Summary 4Part T1: Notes on Electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Part T2: Semiconductor physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Part T3: Diode as non-linear device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Part A1: Diode applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Part T4: MOSFET device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Part T5: Bipolar Junction Transistor (BJT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Part T6: MOSFET and BJT as non-linear devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Part N1: Basics of Electrical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Part A2: Single stage MOSFET and BJT configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Part E1: Esempio di progettazione di un amplificatore CS . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Part A3: Basic MOSFET-based configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Part T7: Amplifiers frequency response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Part A4: Time-constant method application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Part T8: Ideal voltage amplifier and feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Part A5: Ideal voltage amplifier and feedback applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Part T9: Stability analysis of feedback amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Part E2: Compensation examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Part T10: Techniques used to analyze feedback amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Part E3: Examples of the Rosenstark and Blackman formulas . . . . . . . . . . . . . . . . . . . . . . . . . 7Part E4: Esercizi su amplificatori, retroazione e compensazione . . . . . . . . . . . . . . . . . . . . . . . . 7

T1 Notes on Electricity 8Electric field E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Flux of E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Gauss law in vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Meaning of 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9permittivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Electric displacement field (or electric flux density) D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Electrostatic potential V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Electrostatic potential property (I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Electrostatic potential property (II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9E V on x dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Potential energy U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Energy conservation law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Example: potential energy barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Metal conductivity schematic picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 (mobility) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11J (current density) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11


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CONTENTS II

T2 Semiconductor physics 12Band Theory of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Insulators, semiconductors and conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Fermi-Dirac statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Electrical conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Semiconductors current pictures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Doped semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Conductivity for semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Intrinsic semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Doped semiconductors n-type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Doped semiconductors p-type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15p-n junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Reverse bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Forward bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17p-n diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Diode equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Diode dynamic effects: transaction capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Diode dynamic effects: diffusion capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Actual diode maximum limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Breakdown effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Zener diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

T3 Diode as non-linear device 20Diode as non-linear device: circuit analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Linear piecewise (OFF region) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Equivalent resistance and equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Graphic picture of the diode linear piecewise in OFF region . . . . . . . . . . . . . . . . . . . . . . . . . . 21Linear piecewise (ON region) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Differential conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Differential resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21iD in forward region and small signal conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Norton equivalent circuit (ON region) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22vD in forward region and small signal conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Thevenin equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Graphic picture of the diode linear piecewise in ON region . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Graphic picture of the diode linear piecewise in breakdown region . . . . . . . . . . . . . . . . . . . . . . . 24Zener voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Zener resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Zener diode equivalent circuit in breakdown region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Linear piecewise approximation (LPA) for diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25LPA for Zener diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Zener diode equivalent circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25How to choose the right region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

A1 Diode applications 27Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Bridge rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Rectifier with filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Amplitude-modulation detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Zener regulated power supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Zener limiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

prof. S. Rocchi, ing. M. Poli - Dipartimento di Ingegneria dellInformazione - Universit a degli Studi di Siena


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CONTENTS III

T4 MOSFET device 30MOSFET as capacitor with capacitance depending on gate voltage . . . . . . . . . . . . . . . . . . . . . . 30MOSFET device structure when inversion layer is present . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Charge in the inversion layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Medium charge density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Current iD when inversion layer is present . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Validity field of (T4.5): triode region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Graphics of iD vs. vDS in triode region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34MOSFET as Voltage Controlled Resistor (VCR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34MOSFET in saturation region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Pinch-off point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Saturation region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36MOSFET is a voltage-controlled current generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Channel modulation effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Body effect (substrate bias effect) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Extension to p-channel MOSFETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37MOSFET-p triode current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37MOSFET-p saturation current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37MOSFET: limits of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

T5 Bipolar Junction Transistor (BJT) 38Bipolar Junction Transistor (BJT): physical structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Conduction when B-E is forward biased and B-C is reverse biased (graphic picture) . . . . . . . . . . . . 38BJT current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39iB current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39iC current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39iE current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39BJT current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39iB current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39iE current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39iC current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40BJT current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40iC current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40iE current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40iB current when vBE = 0 and vBC = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40BJT non-linear circuit model: transport model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Forward Active Region (FAR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Reverse Active Region (RAR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41BJT: Saturation Region (SR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41BJT: Interdiction Region (IR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Graphics pictures of iC vs. iB and vCE in FAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Early effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43BJT physical limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

T6 MOSFET and BJT as non-linear devices 44

MOSFET: LPA with vBS = 0 in triode region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44MOSFET: LPA with vBS = 0 in saturation region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Geometric interpretation of g0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Geometric interpretation of gm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45MOSFET: LPA conditions in saturation region (small signal) . . . . . . . . . . . . . . . . . . . . . . . . . 46MOSFET equivalent circuit for id . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46MOSFET equivalent circuit when vBS = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Evaluation of iD by means of circuit theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46MOSFET parasitic capacitances: triode region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46MOSFET parasitic capacitances: saturation region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47MOSFET linear equivalent circuit in high frequency condition . . . . . . . . . . . . . . . . . . . . . . . . . 48When can parasitic capacitors be neglected? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

BJT: LPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49BJT equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49BJT: Evaluation of ic and ib by circuit theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49BJT: LPA conditions in FAR region (small signal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50



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CONTENTS IV

N1 Basics of Electrical Theory 51Quadripoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Differential input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Single input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Differential output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Single output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Single-input, single-output linear quadripoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Input and output impedances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Voltage, current and power gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Differential-input single-output linear quadripoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Common mode and differential mode voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Common mode and differential mode gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Common-mode rejection ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Differential mode and common mode input impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Unidirectional Linear Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Voltage amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Trans-impedance amplifier (current-to-voltage converter) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Trans-conductance amplifier (voltage-to-current converter) . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Current amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Maximum voltage transfer to the input impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Maximum current transfer to the input impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Maximum voltage transfer to the load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Maximum current transfer to the load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Maximum voltage transfer from the input to the load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Maximum current transfer from the input to the load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59The Miller theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Miller theorem demonstration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Miller effect for capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A2 Single stage MOSFET and BJT configurations 62Common source (CS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62CS: biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Sensitivity (definition) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63CS: The design problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64CS: Small-signal (LPA) equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64CS: Norton equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65CS: equivalent conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66CS: voltage amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66CS: simplifying hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66CS: estimation of the maximum voltage amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Common drain (CD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67CD: biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67CD: small-signal equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68CD: short-circuit id = ieq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68CD: output equivalent conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68CD: voltage amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Common gate (CG) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69CG: biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69CG: small-signal equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70CG: short-circuit id = ieq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70CG: output equivalent conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71CG: current amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71CG: input conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72CG: voltage amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72MOSFET configurations summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Common emitter (CE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73CE: Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

CE: The design problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74CE: Small-signal circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75



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E1 Esempio di progettazione di un amplificatore CS 76Specifiche di progetto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Dati . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Analisi preliminare del circuito . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Circuito equivalente per lo studio della polarizzazione . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Corrente erogata dai generatori di polarizzazione . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Circuito equivalente di piccolo segnale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Guadagno di tensione . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Conversione delle specifiche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Verifica di centro banda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Sommario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

A3 Basic MOSFET-based configurations 82Diode-connected MOSFET connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Current mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Current mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Differential amplifier (DA): large differential signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83DA: iD1 = f1(vd)iD2 = f2(vd) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84DA: plots of iD1 and iD2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85DA: plots of vO1 and vO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

DA: verification of the saturation region for M1 and M2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86DA: evaluation of vO1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86DA: biasing equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86DA: biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86DA: small signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87DA: common-mode small signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87DA: differential-mode small signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88DA: complete vo1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88DA: CMRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89DA: common source configuration with RS = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

T7 Amplifiers frequency response 90

Frequency response (definition) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Bode plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Band-pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Reduction of a third order system to first order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Reduction of a n-th order system to first order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Time-constant method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Note on time-constant method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A4 Time-constant method application 94Time-constant method example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Output short-circuit current of circuit in Fig. A4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Output equivalent impedance of circuit in Fig. A4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Norton equivalent of circuit in Fig. A4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Transfer function of circuit in Fig. A4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Time-constant method applied to circuit in Fig. A4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Evaluation of R01 by means of the time-constant method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Evaluation of R02 by means of the time-constant method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Evaluation of R12 by means of the time-constant method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Evaluation of coefficient a1 by means of the time-constant method . . . . . . . . . . . . . . . . . . . . . . 98Evaluation of coefficient a2 by means of the time-constant method . . . . . . . . . . . . . . . . . . . . . . 98

T8 Ideal voltage amplifier and feedback 99Basic configuration of actual operation amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Ideal operation amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Ideal operation amplifier: parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Ideal operation amplifier: virtual short circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Negative feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Closed-loop gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100



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Negative feedback circuits based on the ideal operation amplifier . . . . . . . . . . . . . . . . . . . . . . . 101Feedback analysis of circuits based on the ideal operation amplifier . . . . . . . . . . . . . . . . . . . . . . 101Closed-loop ideal gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Sensitivity of AV0 with respect to A0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Sensitivity of AV0 with respect to B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Noise suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Feedback with non-linear amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Bandwidth extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Gain-bandwidth product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Transition angular frequency and gain-bandwidth product . . . . . . . . . . . . . . . . . . . . . . . . . . . 103The bifilar model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104Voltage (shunt) sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104Current (series) sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Voltage (series) mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Current (shunt) mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

A5 Ideal voltage amplifier and feedback applications 106Voltage follower based on OA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Non-inverting amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Inverting amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Inverting adder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Subtractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

T9 Stability analysis of feedback amplifiers 109Stability analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Single-pole amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Two-pole amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Amplifiers with at least three poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110The loop gain modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110The loop gain phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Loop gain phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Loop gain modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Gain and phase margins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112System with phase margin equal to 90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112System with phase margin equal to 60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113System with phase margin equal to 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113What is the best phase margin? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Compensation by reduction of the loop gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Narrow-banding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Pole dominant compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Miller compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Comparing the effectiveness of the pole dominant compensantion and the Miller compensantion . . . . . . 1 1 9

E2 Compensation examples 121Compensation example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Bode plots for the original and compensated systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Compensation example on a simple 3-stage amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Miller compensation example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

T10 Techniques used to analyze feedback amplifiers 125Rosenstarks formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Return ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Asymptotic gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Direct gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Blackmans formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126



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CONTENTS VII

E3 Examples of the Rosenstark and Blackman formulas 127Return ratio example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Asymptotic gain example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Direct gain example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Rosenstarks formula example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Blackmans formula example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Blackmans formula example: evaluation of Tsc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Blackmans formula example: evaluation of Toc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Blackmans formula example: evaluation of R0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Blackmans formula example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

E4 Esercizi su amplificatori, retroazione e compensazione 130Esercizio A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Esercizio B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Esercizio C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Esercizio D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Esercizio E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Esercizio F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Esercizio G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132



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Teaching guide: basic electronicsAnno 2007-08

Introduzione

Il materiale di studio e sostanzialmente un ipertesto organizzato in lavagne dovela parte descrittiva e essenziale, sono stati introdotti alcuni commenti raggiungibiliattraverso link.Fa parte del materiale una versione stampabile dellipertesto (in formato PDF) incui i commenti sono evidenti.Nel quadro 1 e riportata una sintesi del percorso didattico organizzato secondo unfilo logico in cui le singole parti sono numerate e richiamate con il corrispondentenumero scritto sopra e sotto la freccia quando da queste occorre prelevare concetti enozioni utili alla comprensione della parte considerata. Per esempio per comprenderela parte 4 sulla struttura e funzionamento del MOSFET occorre conoscere la fisicadei semiconduttori trattata nella parte 2.Si differenziano le parti applicative (app*,*) in cui sono riportate tipologie di circuitiper riflettere svolgendo esercizi.Lipertesto e organizzato secondo lo stesso filo logico, sopra le frecce che sisusseguono lungo il percorso sono riportate le formule e/o le figure utili per compren-

dere i diversi passaggi. Le definizioni, le dimostrazioni iniziano con un quadratinonero e terminano con le definizioni, le tesi, i commenti finali evidenziati con unrettangolo di contorno.

Lo studente, a lezione, dovrebbe avere una stampa delle lavagne, in cui volu-tamente sono lasciati spazi bianchi per commenti. Comunque si suggerisce diassociare ad ogni lavagna una o piu pagine di commenti desunti dalla lezione deldocente o da integrazioni e riflessioni in fase di studio. In questo modo lo studentepotra costruire un proprio libro per Elettronica I.

Ringraziamenti

La prima versione dellipertesto di Elettronica I (elettronicaI 2007.*), sviluppato sec-ondo il filo logico descritto, e frutto di incontri e letture di documenti sugli strumentidella Ricerca Metodologica Disciplinare sviluppati dal Prof. Filippo Ciampolini (Uni-versita di Bologna) al quale sono rivolti i nostri piu sentiti ringraziamenti.


10/144

Istruzioni per lutilizzo dellipertesto

Link aequazioni,

figure,lavagne, partie riferimentibibliografici

Il materiale di studio e consultabile come un qualsiasi ipertesto. Le equazioni, lefigure, i riferimenti a lavagne, i riferimenti a parti e i riferimenti bibliografici sono linkper consentire una navigazione dinamica e interattiva. Il seguente simbolo rappresentaun link a lavagna.

Dopo aver fatto click su un link e sufficiente premere il tasto BACKSPACE(versione HTML) o il pulsante INDIETRO del browser (versione HTML) o iltasto VISTA PRECEDENTE (versione PDF) per tornare alla pagina che si stavaconsultando prima della pressione sul link.


11/144

Istruzioni per lutilizzo dellipertesto 3

Inoltre per alcune lavagne sono presenti dei commenti in piu lingue identificati dabandiere in fondo alle lavagne stesse (si guardi la figura sottostante). Basta fare clicksulla bandiera della lingua voluta per far apparire o scomparire il commento.

Nella versione PDF i commenti iniziano con il simbolo

e sono scritti in corsivo.

NOTA

A causa delle nuove politiche di protezione di Internet Explorer, gli studentiche usano tale browser devono autorizzare la visualizzazione del contenuto bloccato

facendo click sulla barra gialla che compare in alto alla pagina e selezionandoConsenti contenuto bloccato... (si guardi limmagine sottostante).



12/144

Summary

Part T1:Notes on

Electricity

E (Electric Field),V (Electrostatic Potential),J (Current Density), (Conductivity), (Resistivity).

Part T2: Se-miconductor

physics

T1 Band Theory, Conductivity of Doped Semiconductors, p-n Junction, Diode,Zener Diode.

Part T3:Diode as

non-lineardevice

T2

Diode Equation Approximation, Linear Circuit Models of two terminals device.

Analysis methodology of circuits with diodes.

Part A1:Diode

applications

T3 Diode applications.

Part T4:MOSFET

device

T2 MOSFET as capacitor, Ohmic and Saturation Regions, Modulation channeleffect, Body effect.

Part T5:Bipolar

JunctionTransistor

(BJT)

T2T4

Bipolar Junction Transistor (BJT), Forward and Reverse Active Regions, Satu-ration Region... Base width modulation effect parasitic capacitors. Comparisonwith MOSFET.


13/144

Summary 5

Part T6:MOSFET

and BJT asnon-linear

devices

T2,T4T5

MOSFET equations approximations, Linear Circuit Models, Analysis method-ology of circuits with MOSFET (CS configuration as example of biasing circuitand small signal equivalent circuits). Parasitic capacitors. BJT equationsapproximations, Linear Circuit Models, Analysis methodology of circuits withBJT (CE configuration as example of biasing circuit and small signal equivalentcircuits).

Part N1:Basics ofElectrical

Theory

Notes on two-port networks (Quadripoles). The Miller theorem.

Part A2:Single stage

MOSFETand BJT

configura-tions

T6N1

MOSFET: CS, CD and CG configurations: voltage gain, current gain, inputand output conductances. BJT: CE configuration: voltage gain, current gain,input and output conductances.

Part E1:Esempio di

proget-

tazione di unamplificatoreCS

T6A2

Esempio di progettazione con MOSFET.

Part A3:Basic

MOSFET-based

configura-

tions

T6,A2N1

MOSFET: diode configuration, current mirror, differential amplifier.

Part T7:Amplifiersfrequencyresponse

T4T5

Bandwidth, pole-dominant approximation, time-constant method.



14/144


15/144

Summary 7

Part E3:Examples of

theRosenstark

andBlackman

formulas

T10 Examples of the Rosenstark and Blackman formulas.

Part E4:Esercizi su

amplificatori,retroazione e

compen-sazione

T7,T8T9,T10

Esercizi su amplificatori, retroazione e compensazione.



16/144

Part T1

Notes on ElectricitySee [?]

Electric fieldE

E = limQ0

F

Q

F

Q

P

(Static conditions)

The electric field vector E in a point is the electric force per unit charge exerted ona probe placed in the same point and whose charge tend to 0.

Flux ofE(T1.1) Sclosed =

Sclosed

E n dS

Gauss law invacuum

Sclosed

E

=

Q

0

experimentallyassumed

S

E

n

Q2

Q1

Q3

Q5

Q4 Q6

Q7

Figure T1.1

where the electrical permittivity in vacuum (0) is equal to 0 = 8.85412 1012

Fm

Example (Fig. T1.1)Sclosed

E n S = Sclosed

En S =Q

1+ Q

2+ Q

3+ Q

50


17/144

Notes on Electricity 9

Meaning of 0

Joint constant between dimensions of Sclosed

E

and Q

(T1.1) [Force] [Surface][Charge]

=[Charge]

[0] [0] =

C2

[N m2]

permittivity

for homogeneous and infinite (i.e., unbounded) media

(T1.2) Sclosed

E

= Q Sclosed

E

=Q

where = r 0 r > 1

Electricdisplacement

field (orelectric fluxdensity) D

In most ordinary materials D = E

Electrostaticpotential V

(T1.3) VP = WPO

E

where WPO

E

is the work (the amount of energy) transferred by E along an arbitrary

path connecting points P and O.

Electrostatic

potentialproperty (I)

WPO

+ WOP

= 0

WPO

= WOP

VPO = VOPO

P

Figure T1.2

Electrostatic

potentialproperty (II)

(T1.4) WPP

= VP O + VOP

(T1.4) WPP

= VP O VPO (T1.5)

O

P

P

b

c

a

Figure T1.3



18/144

Notes on Electricity 10

E V on xdimension

(T1.5) WPP = V (V + V)(T1.3) WPP = Ex x

WPP = Exx

Ex = V

x

(T1.6) Ex = limx0

Vx

= d Vd x

V

P xP

V+V

E

Ex

Figure T1.4

Potential

energy U

U = qV

if q = qel = 1.6 1019 C

q 1 V = 1 eV = 1.6 1019 J(1 eV is a very small amount of energy)

Energyconservation

law

W = U + EC where EC =1

2mv2

Example:potential

energy barrier

(T1.6) V (x) = E x + CONSTU(x) = q V (x)U(0) = 0

U(0) +1

2mv20 = W

x0 : vx0 = 0

U(x0) + 0 = W

Ec must be positive so U(x) is a potentialenergy barrier for electrons; in the figure elec-trons cannot be at a distance greater than x0from electrode P.

x0

d

P P

.

E

V

x

V (x)

x

U(x)

W

x0

P

EC

Figure T1.5

Metalconductivity

schematicpicture

+ + + + +

+ + + + +

Bound iones

Free electrons

+ + + + +

+ + + + +

..

.

Figure T1.6



19/144


20/144

Part T2

Semiconductor physicsSee [?]

Band Theory

of Solids

Plot of the available energies for electrons in the materials. The available energylevels form bands instead of discrete energies.

Conduction

For the conduction process is crucial whether or not electrons are in the con-duction band and the energy gap amplitude (Eg) between the valence band and theconduction band.

Insulators, se-miconductors

andconductors

Valence band

Conduction band

Eg 5 eV

Insulators

Valence band

Conduction band

Eg 1 eV

Semiconductors

Valence band

Conduction band

Conductors.

.

Eg = 4 eV is the energy threshold between insulators and semiconductors.


21/144

Semiconductor physics 13

Fermi-Diracstatistics

Conduction band and Valence band

Although the number of states in the bands is actually infinite, in an unchargedmaterial the number of electrons is equal to the number of protons in the atoms, i.e.not all the possible states are occupied by electrons at any time.The probability of a given energy level to be occupied by an electron is given by:

(T2.1) f(E) =1

1 + eEEF

kT

f(E) =1

1 + e

E

EF1

EFkT

0 1 2 3 4 5 6

0

1

2

3

4

5

6

0 1 2 3 4 5 6

0.2

0.4

0.6

0.8

1.0

1.2 EF/kT = 100

EF/kT = 0.1

EF/kT = 1

E/EF

f(E)

where k is the Boltzmann constant (k = 1.380 1023 J/K), T is the temper-ature in Kelvin, EF is the Fermi energy.

Electricalconductivity

Electrons must move between states to conduct an electrical current, so due tothe Pauli exclusion principle full bands do not contribute to the electrical conductivity.

Semiconduc-tors

(T2.1)

E

EF

Valenceband

Conductionband

T = 0 K

f(E)

E

EF

Valenceband

Conductionband

Medium temp.

f(E)

E

EF

Valenceband

Conductionband

High temp.

f(E)

The electrons population in a given energy state depends on the Fermi function andon the electrons density in that state. In the gap there are no electrons because thedensity state is zero. At T = 0 K and for energies higher than the Fermi level, theFermi function is zero (see figure) and so there are no electrons in the conductionband even though many free states are available.



22/144


Semiconduc-tors current

pictures

If a voltage is applied to the semiconductor, for T > 0 K we have:

Si Si Si SiSi

Si Si

Electrons current

Holes current

Si SiSi

Si Si Si SiSi

e hole+

.

.

+

V.B.+ + + + + +

holes

C.B.

electrons

.

.

Doped semi-conductors

.

.

n-type

P

Si

SiSi

Si

donor impuritycontributes to free

electrons

p-type

B

Si

SiSi

Si

acceptor impuritycreates holes

F L

Valenceband

Conductionband

F LValence

band

Conductionband



23/144


24/144


25/144


26/144


Diodedynamiceffects:

diffusioncapacitance

Forward biasing: the number of electrons crossing the junction depends on theforward voltage and the time before an electron recombines with a hole is finite,conseguently a capacitive effect arises.

CD =Q

vQ = iDT

where T is the time before an electron recombines with a hole.

CD =

TiDv = T

TSevDVT

VT

(T2.6) CD TiDVT

Actual diodemaximum

limits

Maximum reverse voltage: vbreakdown (reverse biasing)

Maximum power dissipation: PD = vD iD (forward biasing)

Breakdowneffect

Breakdown effect is due to two different phenomena:

Zener breakdown occurs predominantly with heavily doped junction regions and a

low reverse voltage (< 6 V). The high E removes electrons that can pass throughthe junction [?].

Avalanche breakdown occurs at high reverse voltage ( 6 V): free electronsnear the junction acquire high kinetic energy (being in a uniform acceleration field)and so a high speed. As these high-speed electrons move through the material theyinevitably strike atoms knocking an electron free from it. Both electrons are thenaccelerated by the electric field and strike other atoms knocking additional electronsfree and so on. In this way the reverse current rapidly increases [ ?].

Reverse bias

.

.

- +

p n+

+

-

-

+-+

E



27/144


Zener diode

From a technological point of view, the Zener diodes are built so that thebreakdown effect is possible at a sufficiently low reverse voltage thus preventing theovercoming of the maximum PD.

.

.

iD [A]

vD [V]

forward biasreverse bias

breakdownregion

-+

iD

vD



28/144

Part T3

Diode as non-linear device

Diode asnon-linear

device: circuitanalysis

The diode equation (T2.4) can be expanded in Taylor series, linear circuit lawsare usable when the series can be limited to the first order:

(T2.4) iD = iD0 +d iDd vD

vD=VD0

(vD VD0 ) +1

2

d2 iDd v2D

vD=VD0

(vD VD0 )2 +

Linearpiecewise

(OFF region)

VD0 = V

D0= 0V vD VD0 = vD = vd = vD

iD = 0 +

a

ISVT vD +b

12 ISV2T v2Dif a b (i.e., a 10 b IS

VTvD 10

2

ISV2T

v2D vD VT5

= 5mV) then

(T3.1) iD ISVT

vD

Equivalentresistance and

equivalentcircuit

(T3.1) rOF F = vDiD

=VTIS

rOF FiD

vD


29/144


30/144

Diode as non-linear device 22

iD in forwardregion and

small signalconditions

(T3.2) vd = vD VD0(T3.3) iD = ID0 +

ID0VT

vD VD0

iD = ID0

1 V

D0

VT + g vD

Nortonequivalent

circuit (ONregion)

Ieq = ID0

1 V

D0

VT

.

.

1

gvDIeq

iD

vD in forwardregion and

small signalconditions

T hevenintheorem

Veq = Ieqg

= ID0

1 V

D0

VT

1

g

Veq = ID0

VT VD0VT

VTID0

= VD0 VT

(T3.6) vD = Veq +iDg

Theveninequivalent

circuit

(T3.6)

.

.

+

Veq

1/g

iD

vD



31/144


Graphicpicture of the

diode linearpiecewise inON region

.

.

A V

d0; I

d0B (V ; 0)

2103

0.5103

1103

A

B

0.62 0.65

iD [A]

vD [V]

iD (A) vD [V]

5 104 0.621

103 0.63

2 103 0.655 103 0.67

Figure T3.2

(T3.7) tg iDvD

iDvD

VD0

= g

(T3.6),Fig. T3.2 V = Veq = VD0 VT (T3.8)

ID0 =2 103Ag=0.08S V = 0.62Vr=1/g = 12.5



32/144


Graphicpicture of the

diode linearpiecewise inbreakdown

region

See Breakdown effect ( pag. 18)

.

.

ID0

iD [A]

vD [V]

VZtg

Figure T3.3

(T3.7) without considering the analytic expression of iD in breakdown zone, theangular coefficient of the geometric tangent in ID0 can be outlined; tg = gZ =

1

rZ(T3.6)

Veq = vD when iD

0

Zener voltage graphically Veq = VZ

Zenerresistance

(T3.5),(T3.7) rZ = 1tg

Zener diodeequivalent

circuit inbreakdown

region

(T3.5),(T3.6) vD = VZ + iDrZ (T3.9)

actually iD is negative

.

.

+

VZ

rZ

iD

vD



33/144


Linearpiecewise ap-proximation

(LPA) fordiodes

Generally the three linear piecewise are extended for larger values of vD (largesignal conditions)

region condition

(T3.1).

.

I OFF vD = rOF FiD; iD 0A for Vbr. < vD < V (T3.10)

(T3.5),(T3.7)

(T3.6) .

.

II ON vD = V + rONiD for vD > V (T3.11)

LPA for Zenerdiodes

region condition

(T3.10).

.

I OFF vD = rOF FiD; iD 0A for VZ < vD < V

(T3.11).

.

II ON vD = V + rONiD for vD > V

(T3.8)

.

.

III Zener vD =

VZ + rZ iD for vD

VZ (T3.12)

Zener diodeequivalent

circuits

iD

vD

region condition

.

.

I OFF

rOF FiD

vD

VZ vD < V

.

.

II ON

ViD rON

vD

vD V

.

.

III Zener

iD

vD

vD VZ

VZiD rZ

iZ

vD



34/144


How tochoose the

right region

.

.

BEGIN

Choose a

region

simpler, but it

could be time

consuming

randomly

Slitly more

complex because

a preliminary

circuit analysis is

required, but less

time consuming

by means of circuit

considerations

Insert in the circuit

the equivalent

circuit associated

with the choosenregion

Solve the linear

circuit obtained after

substitution

Are constraints of

the choosen region

verified?

NO

The right operating

region was choosen

YES

END



35/144

Part A1

Diode applications

Rectifier vI vO

vI

t

vO

t

Bridge

rectifier

vI

vO

vI

t

vOt


36/144

Diode applications 28

Rectifier withfilter

vI vO

vI

t

vOt

Amplitude-modulation

detector

The circuit schematic is the same of the rectifier with filter but with a differentRC time constant: the RC time constant must be higher compared with the periodof the carrier, and it must be lower compared to the period of the modulated signal.

Zenerregulated

power supply



37/144

Diode applications 29

Zener limiter

vI vO

vI

t

vOtV

VZ

vI vO

vI

t

vOt

(VZ+V)

VZ+V



38/144

Part T4

MOSFET device

MOSFET ascapacitor with

capacitancedepending on

gate voltage

vG

GATE

OXIDE SiO2

P-SUBSTRATE (BODY)

SUBSTRATEMETAL CONTACT

tox

L

W

L

WGATE

MAP VIEW

1 vG < 0

holes move towards the surface that becomes a zone where electrons can move.

Ceq1 =oxA

tox

tox is the SiO2 thicknessox is the SiO2 electrical constantA = L W is the gate area

vG

GATE

OXIDE SiO2

P-SUBSTRATE (BODY)


tox

L

W

2 0 < vG < Vth (Vth 1V)

Near the surface a depletion charge zone is created (negative ions). In this regionelectrons cant move.

Ceq2 =oxA

tox + tdp vG

GATE

OXIDE SiO2

P-SUBSTRATE (BODY)


tox

L

W

+ + + + +

tdp


39/144

MOSFET device 31

3 vG Vth

INVERSION LAYERFree electrons in the p-substrate move towards the surface under the oxide.

Ceq3 =oxA

tox= Ceq1 = Cox

vG

GATE

OXIDE SiO2

P-SUBSTRATE (BODY)


tox

L

W

++++++++++

til (inversion zone)

Figure T4.1

(T4.1) QIN V = Cox (vG Vth) = Cox (vOX Vth) (vG = vOX )

Ceq

vG

Cox

Ceq2

VT



40/144

MOSFET device 32

MOSFETdevice

structurewhen

inversion layeris present

x

i(x)

SOURCEn+ DRAINn+

SiS

DiD

GATE

B

DEPLETION ZONE

BODY

P-SUBSTRATE

vGS+

vDS+

vBS

+

Figure T4.2

A position on the inversion layer is characterizedby v(x) and i(x) where v(0) = v(S) 0, further-more iD = iS .

G B

D

S

G

D

S

Symbols

(T2.4)vBS : n+ source - p substrate and n+ drain - p substrate diodes are reversebiased.

Charge in theinversion layer

(T4.1)Fig. T4.2

Q(x) = W L oxtox

(vOX (x) VTn) = W L Cox (vOX (x) VTn) (T4.2)

where Cox =oxtox

F

m2

Mediumcharge density

Fig. T4.1 (T4.3) v = QW L til

where til is the thickness of the inversion zone (Fig. T4.1).

Current iDwhen

inversion layeris present

i(x) = J(x) W til

where J(x) is the current density.

(T1.9)(T4.3)

i(x) =Q

W L tilvd W til =

Q(x)vdL

(T4.2) i(x) = W L oxtox

(vOX (x) VTn)vdL



41/144

MOSFET device 33

(T1.7) i(x) = W oxtox

(vOX (x) VTn) (n E(x))

where n is the electrons (n carriers) mobility.

(T1.6) i(x) = W oxtox

Cox(vOX (x) VTn) n

d v(x)

d x

with

(T4.4) vOX (x) = vGS v(x) v(x) = vGS vOX (x)

(T4.4) i(x) = W Cox (vGS v(x) VTn) nd v(x)

d x

i(x)d x = n W Cox (vGS v(x) VTn) d v(x)

by integrating x from 0 to the channel length L and v(x) from 0 to vDS

L

0

i(x)d x =

n W C

ox vDS

0

[(vGS

VTn)

v(x)] d v(x)

iD L = n W Cox

(vGS VTn) vDS

v2DS2

being i(x) = iD = constant

(T4.5) iD = kn

vGS VTn

vDS2

vDS

with kn = n Cox and kn = k

n

W

L. [kn] =

A

V2kn depends on the technology characteristic.

Validity fieldof (T4.5):

triode region

(T4.4) vOX (x) VTnvOX (x) = vGS v(x) VTn

v(x) as its maximum for x = L where v(x) = vDS

vGS vDS VTn

(T4.6) vDS vGS VTn



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MOSFET device 34

Graphics ofiD vs. vDS intriode region

(T4.5) iD = 0 for

vDS = 0vDS = 2 (vGS VTn)

d iDd vDS

= kn [(vGS VTn) vDS ] = 0 vDS = vGS VTn maximum

0 1 2 3 4 5 6

0

1

2

3

4

5

6

vGS

vDS

iD/kn

(T4.6) vGS VTn = vDSiD =

kn2

(vGS VTn)2 =kn2

v2DS

MOSFET asVoltage

ControlledResistor(VCR)

for vDS vGS VTn vDS vGS VTn

10

(T4.5) iD kn (vGS VTn) vDSvDSiD

=1

kn (vGS VTn)= ReqV CR =

1

iD

vDS vDS=0

MOSFET insaturation

region

Fig. T4.3

for vDS vGS VTn when vDS = vGS VTn(T4.4)

vOX (0) = vGSvOX (L) = vGS vDS = VTn

and

(T4.2) Q(x)|x=L = 0

therefore for x = L the inversion layer thickness is 0 and the current reachesits maximum value.



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MOSFET device 35

POFF

SOURCE

n+DRAIN

n+

SiS

DiD

GATE

B

DEPLETION ZONE

BODY

P-SUBSTRATE

vGS+

vDS+

vBS

+

Figure T4.3

for vDS > vGS VTn Find x : vOX (x) = VTn(T4.4) vOX (x) = vGS v(x) = VTn v(x) = vGS VTn < vDS

and

(T4.2) Q(x)|x=L = 0

therefore for x = L the inversion layer thickness is 0 and the current reachesits maximum value.

POFF

SOURCE

n+DRAIN

n+

SiS

DiD

GATE

B

DEPLETION ZONE

BODY

P-SUBSTRATE

vGS +

vDS+

vBS

+

Figure T4.4

Pinch-offpoint

for x = POF F the inversion layer is depleted, but electrons in POF F can stillreach the drain due the electrical field created by the voltagevDS VPOFF = vDS (vGS VTn).

id does not decrease and therefore the current reaches a saturation value.



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MOSFET device 36

Saturationregion

(T4.6) iD = kn2

(vGS VTn)2 (T4.7)

vGSVTn

iD

Figure T4.5

MOSFET is avoltage-

controlled

currentgenerator

0 1 2 3 4 5 6

0

1

2

3

4

5

6

vGS

vDS

iD/kn

Figure T4.6

Channelmodulation

effect

Actually for vDS vGS VTn (saturation region) the inversion layer length isLil L(T4.7)

iD =kn

2

W

Lil (vGS VTn)2

with Lil 1vDS

L = Lil + L(vDS )(T4.7) iD = k

n

2

W

L L(vDS ) (vGS VTn)2

(T4.8) iD kn

2

W

L kn

(vGS VTn)2 (1 + vDS ) = kn (vGS VTn)2 (1 + vDS )

103 < < 101 V1

Body effect(substratebias effect)

The substrate tension should be kept as lower as possible to avoid the conduction ofdiodes B-S and B-D. When vBS = 0, the width of the depletion layer and thereforealso the voltage across the oxide are modified due to a change in the charge of thedepletion region. This results in a different threshold voltage

(T4.9) VTn = VT0 +

vSB + 2F

2F

being F a physical parameter such that 2F = 0.6 V

= 0.4 V1/2 a technology related parameter andVT0 = Vth when vBS = 0.



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MOSFET device 37

Extension top-channel

MOSFETs

(T4.5),(T4.8)(T4.9)

SOURCE

p+DRAIN

p+

SiS

DiD

GATE

B

DEPLETION ZONE

BODY

N-SUBSTRATE

vGS+

vDS+

vBS

+

Figure T4.7

G B

D

S

G

D

SB

Symbols

inversion layer is present when vGS < 0 V

holes (positive charges) produce a current iD < 0 and move from the source

when vGS < 0 V

Regions S-B and D-B are diodes

substrate (body) must not conduct then vBS > 0 V (the substrate tensionshould be kept as higher as possible to avoid the conduction of diodes S-B and S-D).

VTp < 0 V

MOSFET-ptriode current

(T4.10) iSD = kp

vSG

VTp vSD2

vSD

MOSFET-psaturation

current

(T4.11) iSD =kp2

vSG

VTp 2 (1 + vSD )

MOSFET:limits of

operation

Due to the MOSFET physical structure, it mainly has the following limits: Gate oxide breakdown (maximum VGS voltage): the gate oxide thickness (tox) isvery thin (in the order of 100 nm or even less for the technologies), so it can onlysustain a limited voltage. Exceeding this limit can result in destruction of the deviceor in the reduction of its lifetime.

Maximum VDS voltage: the MOSFET device has a maximum specified drain tosource voltage, beyond which breakdown may occur. Exceeding the breakdownvoltage causes the device to turn on, potentially damaging itself and other circuitelements due to excessive power dissipation.



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Part T5

Bipolar Junction Transistor (BJT)

BipolarJunction

Transistor(BJT):

physicalstructure

iC iE

iB

C E

B

n n+p

C E

B B-EB-C

C EB

n

n+

p

Si

tB

n - p - nE - B - C

tB=0.1100m

Figure T5.1

A BJT cannot be considered as two back-to-back diodes due to the thin thickness ofthe base region (tB ).

Conductionwhen B-E is

forward

biased andB-C is reverse

biased(graphicpicture)

C EB

Energy

x

B - C B - E

Figure T5.2

vBEvCB

C E

B

n n+p

C-B-E: energy bands when the BEjunction is forward biased and the BCjunction is reverse biased.

The forward bias on the BE junc-tion causes electrons to move towardthe base. Some of the electrons willcombine with holes. However, sincethe base region length (tB) is very thin

and usually smaller than the electronsdiffusion length (mean length withinwhich electrons combine with holes),the percentage of combined electrons isvery small. Thus, most of the electronsreach the boundary of the BC depletionregion. Because the collector is morepositive than the base (the BC junctionis reverse biased), these electrons aredragged into the collector across theBC depletion region.


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Bipolar Junction Transistor (BJT) 39

BJT currentwhen

vBE = 0

andvBC = 0vBE

C E

B

n n+p

iE

iB

iF

vCB

iC

n-p-n BJT

C

E

B

iC = iF

iB currentwhen vBE = 0and vBC = 0

(T5.1) iB =iFF

20 < F < 500

iC current

when vBE = 0and vBC = 0

iF = iC

(T2.4) iC IS evBE/VT 1 (T5.2) forward transport current

iE currentwhen vBE = 0and vBC = 0

iE = iC + iB

(T5.3) iE =F + 1

FIS

evBE/VT 1

BJT currentwhen

vBE = 0and

vBC = 0vBE

C E

B

n n+p

iE

iB

iR

vCB

iC

iE = iR


(T5.1) iB = iRR

(T5.4) 0 < R < 20


iR = iE(T5.2) iR IS

evBC/VT 1

(T5.5) inverse transport current



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iC currentwhen vBE = 0and vBC = 0

iC = iR iB

(T5.3) iC = R + 1R

IS

evBC/VT 1

(T5.6)

BJT currentwhen

vBE = 0and

vBC = 0

(T5.2)(T5.6)

iC = IS

evBE/VT 1

R + 1

RIS

evBC/VT 1

iC = IS

evBE/VT evBC/VT

IS

R

evBC/VT 1

iC current

when vBE = 0and vBC = 0

(T5.5)

iC = iT iR

R (T5.7)


(T5.3)(T5.5)

iE = ISF + 1

F

evBE/VT 1

IS

evBC/VT 1

iE = IS

evBE/VT evBC/VT

+

ISF

evBE/VT 1

(T5.2) iE = iT + iFF

(T5.8)


iB =iRR

+iFF

iB =ISR

evBC/VT 1

+

ISF

evBE/VT 1

(T5.9)

BJT

non-linearcircuit model:transport

model

(T5.1),(T5.7)(T5.4),(T5.9)

C E

B

iC iE

iB

iT

iFF

iRR



49/144


ForwardActive Region

(FAR)

Elettronica I Materiale Didattico

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