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.

7.7 Operating Point Selection

• We are often interested in amplifying time-varying signals.
• Because the amplifier turns off for input voltages less than VT, it is important to add an appropriate DC offset voltage to the time-varying input signal so that the amplifier remains in the saturation region for the entire range of input voltage variation.
• This input DC offset voltage defines the operating point of the amplifier.
• The DC offset must be chosen carefully, for if it is too large, the amplifier will be pushed into the triode region, and if it is too low, the amplifier will slide into the cutoff region.
• The input offset voltage is also called the input bias voltage or the input operating voltage
• The corresponding output voltage and the output current define the output operating point of the amplifier.
• Valid range for operating point under the saturation discipline: