NOC:Basic Electrical Circuits

Preliminaries

Current

Voltage

Electrical elements and circuits

Kirchhoff\'s current law(KCL)

Kirchhoff\'s Voltage law(KVL)

Voltage Source

Current Source

Resistor

Capacitor

Inductor

Mutual Inductor

Linearity of Elements

Series connection-Voltage sources in series

Series connection of R, L, C, current source

Elements in parallel

Current source in series with an element; Voltage source in parallel with an element

Extreme cases: Open and short circuits

Summary

Voltage controlled voltage source(VCVS)

Voltage controlled current source(VCCS)

Current controlled voltage source(CCVS)

Current controlled current source(CCCS)

Realizing a resistance using a VCCS or CCCS

Scaling an element\'s value using controlled sources

Example calculation

Power and energy absorbed by electrical elements

Power and energy in a resistor

Power and energy in a capacitor

Power and energy in an inductor

Power and energy in a voltage source

Power and energy in a current source

Goals of circuit analysis

Number of independent KCL equations

Number of independent KVL equations and branch relationships

Analysis of circuits with a single independent source

Analysis of circuits with multiple independent sources using superposition

Superposition: Example

What is nodal analysis

Setting up nodal analysis equations

Structure of the conductance matrix

How elements appear in the nodal analysis formulation

Completely solving the circuit starting from nodal analysis

Nodal analysis example

Matrix inversion basics

Nodal analysis with independent voltage sources

Supernode for nodal analysis with independent voltage sources

Nodal analysis with VCCS

Nodal analysis with VCVS

Nodal analysis with CCVS

Nodal analysis with CCCS

Nodal analysis summary

Planar circuits

Mesh currents and their relationship to branch currents

Mesh analysis

Mesh analysis with independent current sources-Supermesh

Mesh analysis with current controlled voltage sources

Mesh analysis with current controlled current sources

Mesh analysis using voltage controlled sources

Nodal analysis versus Mesh analysis

Superposition theorem

Pushing a voltage source through a node

Splitting a current source

Substitution theorem: Current source

Substitution theorem: Voltage source

Substituting a voltage or current source with a resistor

Extensions to Superposition and Substitution theorem

Thevenin\'s theorem

Worked out example: Thevenin\'s theorem

Norton\'s theorem

Worked out example: Norton\'s theorem

Maximum power transfer theorem

Preliminaries.

Two port parameters

y parameters

y parameters: Examples

Calculations with a two-port element.

z parameters

z parameters: Examples

h parameters

h parameters: Examples

g parameters

g parameters: Examples

Calculations with a two-port element

Degenerate cases

Relationships between different two-port parameters

Equivalent circuit representation for two ports

Reciprocity

Proof of reciprocity of resistive two-ports

Proof for 4-terminal two-ports

Reciprocity in terms of different two-port parameters

Reciprocity in circuits containing controlled sources

Examples

Solutions..

Feedback amplifier using an opamp

Ideal opamp

Negative feedback around the opamp

Finding opamp signs for negative feedback

Example: Determining opamp sign for negative feedback

Analysis of circuits with opamps

Inverting amplifier

Summing amplifier

Instrumentation amplifier

Negative resistance and Miller effect

Finding opamp signs for negative feedback-circuits with multiple opamps

Opamp supply voltages and saturation

KCL with an opamp and supply currents

First order RC response to a sinusoidal input-via the complex exponential

Circuits with storage elements(capacitors and inductors)

First order circuit with zero input-natural response

First order RC circuit with zero input-Example

First order circuit with a constant input

General form of the first order circuit response

First order RC circuit with a constant input-Example

First order circuit with piecewise constant input

First order circuit with piecewise constant input-Example

First order circuit-Response of arbitrary circuit variables

Summary: Computing first order circuit response

Does a capacitor block DC?

Finding the order of a circuit

First order RC circuits with discontinuous capacitor voltages

Summary: Computing first order circuit response with discontinuities

First order RL circuits

First order RL circuit with discontinuous inductor current-Example

First order RC circuit with an exponential input

First order RC response to its own natural response

First order RC response to a sinusoidal input

Summary: Linear circuit response to sinusoidal input via the complex exponential

Three methods of calculating the sinusoidal steady state response

Calculating the total response including initial conditions

Why are sinusoids used in measurement?

Second order system natural response

Second order system as a cascade of two first order systems

Second order system natural response-critically damped and underdamped

Generalized form of a second order system

Numerical example

Series and parallel RLC circuits

Forced response of a second order system

Steady state response calculation and Phasors

Phasors cont\'d

Magnitude and Phase plots

Magnitude and phase plotes of a second order system

Maximum power transfer and Conjugate matching