MOSFET Small-Signal Model

MOSFET Small-Signal Model - MOSFET Small-Signal Model s...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 105 Spring 1997 Lecture 12 MOSFET Small-Signal Model Concept: &nd an equivalent circuit which interrelates the incremental changes in i D , v GS , v DS , etc. Since the changes are small, the small-signal equivalent circuit has linear elements only (e.g., capacitors, resistors, controlled sources) Derivation: consider for example the relationship of the increment in drain current due to an increment in gate-source voltage when the MOSFET is saturated-- with all other voltages held constant . v GS = V GS + v gs , i D = I D + i d -- we want to find i d = (?) v gs We have the functional dependence of the total drain current in saturation: i D = μ n C ox ( W/2L ) ( v GS - V Tn ) 2 (1 + λ n v DS ) = i D ( v GS, v DS , v BS ) Do a Taylor expansion around the DC operating point (also called the quiescent point or Q point) defined by the DC voltages Q(V GS , V DS , V BS ): If the small-signal voltage is really ±small,² then we can neglect all everything past the linear term -- where the partial derivative is de&ned as the transconductance , g m . i D I D v GS i D Q v gs (29 1 2 -- v 2 2 i D Q v 2 ++ + = i D I D v i D Q v + I D g m v + ==
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EE 105 Spring 1997 Lecture 12 Transconductance The small-signal drain current due to v gs is therefore given by i d = g m v gs . D S G + _ B V DS = 4 V + _ 1 2 3 45 100 200 300 400 500 600 i D ( μ A) V DS (V) 6 v GS = V GS = 3 V V GS = 3 V + _ v gs i D = I D + i d v GS = V GS + v gs Q i d g m = i d / v gs
Background image of page 2
EE 105 Spring 1997 Lecture 12 Another View of g m * Plot the drain current as a function of the gate-source voltage, so that the slope can be identi&ed with the transconductance: D S G + _ B V DS = 4 V + _ 1 2 3 45 100 200 300 400 500 600 i D ( μ A) v GS (V) 6 v GS = V GS = 3 V V GS = 3 V + _ v gs i D = I D + i d v GS = V GS + v gs Q i d g m = i d / v gs i D ( v GS, V DS = 4 V)
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EE 105 Spring 1997 Lecture 12 Transconductance (cont.) Evaluating the partial derivative: Note that the transconductance is a function of the operating point, through its dependence on V GS and V DS
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 12

MOSFET Small-Signal Model - MOSFET Small-Signal Model s...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online