# lec13 - 6.012 Electronic Devices and Circuits Lecture 13...

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6.012 - Electronic Devices and Circuits Lecture 13 - Large-Signal Models - Outline Announcements Handout - Lecture Outline and Summary Review MOSFET model: gradual channel approximation (Example: n-MOS) 0 for (v GS – V T )/ a 0 v DS (cutoff) i D K (v GS – V T ) 2 /2 a for 0 (v GS – V T )/ a v DS (saturation) K (v GS – V T a v DS /2)v DS for 0 v DS (v GS – V T )/ a (linear) with K (W/L)μ e C ox * , V T = V FB – 2 f p-Si + [2 e Si qN A (|2 f p-Si | – v BS )] 1/2 /C ox * and a = 1 + [( e Si qN A /2(|2 f p-Si | – v BS )] 1/2 /C ox (frequently a 1) Comparison of MOSFET and BJT models and characteristics Refined device models Charge stores: 1. Junction diodes 2. BJTs 3. MOSFETs The Early Effect: 1. Base-width modulation in BJTs: w B (v CE ) 2. Channel-length modulation in MOSFETs: L(v DS ) Extrinsic parasitics: Lead resistances, capacitances, and inductances { Clif Fonstad, 10/03 Lecture 13 - Slide 1

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The gradual channel approximation - review Electrostatics problem in x-direction to find q n * (y) as a function of vGS, v BS , and v CS (y) Drift problem in y-direction to relate i D to v GS , v DS , and v BS Clif Fonstad, 10/03 Lecture 12 - Slide 2 i D ( v GS , v DS , v BS ) = W L m e C ox * v GS - V T ( v BS ) - a v DS 2 v DS When v DS reaches (v GS - V T )/ a , the channel vanishes at y = L and the current holds steady at its saturation value. i D v DS inc. v GS p-Si B G + v GS n+ D n+ S v DS v BS + i G i B i D L 0 y x 0 i D ( v GS , v DS , v BS ) = 1 2 a W L m e C ox * v GS - V T ( v BS ) { } 2
Clif Fonstad, 10/03 Lecture 13 - Slide 3 Valid for v BS £ 0, and v DS 0 : i G ( v GS , v DS , v BS ) = 0 and i B ( v GS , v DS , v BS ) = 0 i D ( v GS , v DS , v BS ) = 0 for 1 a v GS - V T ( v BS ) [ ] < 0 < v DS 1 2 a W L m e C ox * v GS - V T ( v BS ) [ ] 2 for 0 < 1 a v GS - V T ( v BS ) [ ] < v DS W L m e C ox * v GS - V T ( v BS ) - a v DS 2 v DS for 0 < v DS < 1 a v GS - V T ( v BS ) [ ]

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