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lec14 - 6.012 Electronic Devices and Circuits Lecture 14...

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6.012 - Electronic Devices and Circuits Lecture 14 - Linear Equivalent Circuits - Outline Announcements Handout - Lecture Outline and Summary Review - Adding refinements to large signal models Charge stores: depletion regions, excess carriers, gate charge Active-length modulation: the Early effect Extrinsic parasitics: Lead resistances, capacitances, and inductances Small signal models What are they good for? Linear equivalent circuits pn diodes: linearizing the exponential diode incorporating the charge stores BJTs: linearizing the Ebers-Moll model incorporating the charge stores adding the Early effect and possible parasitics MOSFETs: linearizing the Gradual-Channel model incorporating the charge stores adding the Early effect and possible parasitics Clif Fonstad, 10/03 Lecture 14 - Slide 1
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BJT: MOSFET: Circuit symbols: B E C B E C B E C npn pnp pnp as frequently oriented in circuits S G D B n-channel p-channel (usual circuit orientation) S G D B S G D B S G D B Digital schematics Digital schematics Linear schematics Linear schematics Clif Fonstad, 10/03 Lecture 14 - Slide 2
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Output Characteristics Clif Fonstad, 10/03 Lecture 14 - Slide 3 v CE i C 0.2 V Forward Active Region Cutoff Saturation i C b F i B BJT: npn i C b F (1 + l v CE )i B v DS i D Saturation (FAR) Cutoff Linear or Triode i D K [v GS - V T (v BS )] 2 /2 a MOSFET: n-channel i D K[v GS - V T (v BS ) - v DS /2]v DS i D K[v GS - V T (v BS )] 2 [1 + l v DS ]/2
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Creating a linear equivalent circuit, LEC: Suppose we have a device with three terminals, X, Y, and Z, and that we have expressions for the cur- rents into terminals X and Y in terms of the voltages v XZ and v YZ : Suppose we also have expressions for the charge stores associated with terminals X and Y: We begin with the static model for the terminal characteristics, and linearize them about an bias point, Q, defined as a specific set of v XZ and v YZ that we write, using our notation, as V XZ and V YZ For example, for the current into terminal X we have: For sufficiently small (v XZ -V XZ ) and (v YZ -V YZ ), we have: continued on the next page Clif Fonstad, 10/03 Lecture 14 - Slide 4 Y X Z q X (v XZ , v XY ) q Y (v YZ , v YX ) i X (v XZ , v YZ ) i Y (v XZ , v YZ ) i X ( v XZ , v YZ ) and i Y ( v XZ , v YZ ) q X ( v XZ , v YZ ) and q Y ( v XZ , v YZ ) i X ( v XZ , v YZ ) = i X ( V XZ , V YZ ) + i X v XZ Q ( v XZ - V XZ ) + i X v YZ Q ( v YZ - V YZ ) + higher order terms i X ( v XZ , v YZ ) i X ( V XZ , V YZ ) + i X v XZ Q ( v XZ - V XZ ) + i X v YZ Q ( v YZ - V YZ )
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