Lect2UP110_(100324)

# Lect2UP110(100324) - Lecture 110 Linear Circuit Models Page 110-1 LECTURE 110 LINEAR CIRCUIT MODELS LECTURE ORGANIZATION Outline Frequency

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Lecture 110 – Linear Circuit Models (3/24/10) Page 110-1 CMOS Analog Circuit Design © P.E. Allen - 2010 LECTURE 110 – LINEAR CIRCUIT MODELS LECTURE ORGANIZATION Outline • Frequency independent small signal transistor models • Frequency dependent small signal transistor model • Noise models • Passive component models • Interconnects • Substrate interference • Summary CMOS Analog Circuit Design, 2 nd Edition Reference Pages 86-91 and new material Lecture 110 – Linear Circuit Models (3/24/10) Page 110-2 CMOS Analog Circuit Design © P.E. Allen - 2010 FREQUENCY INDEPENDENT SMALL SIGNAL TRANSISTOR MODELS What is a Small Signal Model? The small signal model is a linear approximation of a nonlinear model. Mathematically: i D = ± 2 ( v GS - V T ) 2 i d = g m v gs Graphically: The large signal curve at point Q has been approximated with a small signal model going through the point Q and having a slope of g m . 060311-03 i D = β ( v GS -V T ) 2 i d = g m v gs v GS V GS i D I D Q V T i d v gs Large Signal to Small Signal

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Lecture 110 – Linear Circuit Models (3/24/10) Page 110-3 CMOS Analog Circuit Design © P.E. Allen - 2010 Why Small Signal Models? The small signal model is a linear approximation to the large signal behavior. 1.) The transistor is biased at given DC operating point (Point Q above) 2.) Voltage changes are made about the operating point. 3.) Current changes result from the voltage changes. If the designer is interested in only the current changes and not the DC value, then the small signal model is a fast and simple way to find the current changes given the voltage changes. 060311-04 i d = g m v gs Δ i D ʼ Δ V GS Q i d v gs Large Signal Model Δ i D Lecture 110 – Linear Circuit Models (3/24/10) Page 110-4 CMOS Analog Circuit Design © P.E. Allen - 2010 How Good is the Small Signal Model? It depends on how large are the changes and how nonlinear is the large signal model. • The parameters of the small signal model will depend on the values of the large signal model. • The model is a tradeoff in complexity versus accuracy (we will choose simplicity and give up accuracy). • What does a simulator do? Exactly the same thing when it makes an ac analysis (i.e. frequency response) • Regardless of the approximate nature of the small signal model, it is the primary model used to predict the signal performance of an analog circuit.
Lecture 110 – Linear Circuit Models (3/24/10) Page 110-5 CMOS Analog Circuit Design © P.E. Allen - 2010 Small-Signal Model for the Saturation Region The small-signal model is a linearization of the large signal model about a quiescent or operating point. Consider the large-signal MOSFET in the saturation region ( v DS ± v GS V T ) : i D = W μ o C ox 2 L ( v GS - V T ) 2 ( 1 + ² v DS ) The small-signal model is the linear dependence of i d on v gs , v bs , and v ds . Written as, i d ³ g m v gs + g mbs v bs + g ds v ds where g m ´ di D dv GS | Q = µ ( V GS - V T ) = 2 I D g ds ´ D dv DS | Q = I D 1 + V DS ³ I D and g mbs ´ d D dv BS | Q = · ¸ ¸ ¹ º » » ¼ D dv GS · ¸ ¸ ¹ º » » ¼ dv GS dv BS | Q = · ¸ ¸ ¹ º » » ¼ - D dV T · ¸ ¸ ¹ º » » ¼

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Lect2UP110(100324) - Lecture 110 Linear Circuit Models Page 110-1 LECTURE 110 LINEAR CIRCUIT MODELS LECTURE ORGANIZATION Outline Frequency

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