Chapter 10 First-Order Transients in Linear Electrical Networks

• Systems with one storage element (capacitor/inductor) are described by first-order differential equations

9.5 Energy, Charge and Flux Conservation

• Circuit analysis with initial charge/flux linkage (switch closed at t = 0s):

• Energy is lost when v1 is not equal to v2:

Inductors Series and Parallel Connection

• Series Connection:

• Parallel Connection:

9.2.1 Capacitors Series and Parallel Connections

• Series connection:

• Parallel connection:

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:

•