MOSFET Small-Signal Model

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

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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 + ==

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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
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)

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

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