9.1.2 Inductors

• Idealized toroidal inductor ( u = magnetic permeability)

• Magnetic flux density, B

• Magnetic flux density across the core

• Total magnetic flux linkage (Weber/Wb)

• Inductance (Webers/Ampere, Henry)

• For linear time-invariant inductor:

• Inductor memory property:

• Inductor energy property:

9.1.1 Capacitors

• Idealized parallel-plate linear capacitor:

• Capacitance (Coulombs/Volt or Farads)

• For linear (permittivity) time-invariant (capacitance) capacitor

• Capacitor memory property:

• Capacitor energy storage property:

9.1 Constitutive Laws

• Analysis of circuit containing capacitors and inductors involve differential equations in time

Chapter 9: Energy Storage Elements

• Ideal response of an inverter to an square wave input:

• Observed response:

• The circuit delay on observed response is due the capacitance internal to the MOSFET
• Behavior of a real interconnect between two inverters:

• To satisfy lumped matter discipline, one must model these circuit effects ( parasitic resistance, capacitance, inductance etc) on physical wiring of the circuit:

8.2 Small Signal Model

• Small-signal discipline - restricting signals to small perturbations about an operating points so the circuit response to the perturbations is linear
• Small segment of Vo vs. Vi curve:

• 
  

8.1 Overview of the Non-Linear MOSFET Amplifier

Chapter 8 The Small-Signal Model

• The non-linear relationship between input and output voltage make it difficult to analyze and build circuit using MOSFET amplifier

7.8 Switch Unified (SU) MOSFET Model

• This section presents a more elaborate model of the MOSFET and can be skipped without loss of continuity.
• For a fixed VGS, we approximated the behavior as a linear resistor using the SR model.
• Clearly, the SR model does not capture MOSFET behavior if we vary VGS.
• Worse yet, even for a given value of VGS, the SR model becomes inaccurate as the value of VDS approaches VGS − VT.
• For more accuracy, we can develop a more elaborate model for the triode region operation of the MOSFET.
• Abandoning the piecewise-linear method, this more elaborate model characterizes the behavior of the MOSFET in the triode region as a nonlinear resistor, whose characteristics depend on VGS.
• When combined with the SCS model for the saturation region, the nonlinear resistor model in the triode region results in a continuous set of MOSFET curves.
• The resulting combined model for the triode and saturation regions is called the switch unified model or the SU model of the MOSFET.