Learning Objective

Reading

Laplace transform

Step functions

Example (pdf)

3.1.    Use step functions to express functions of limited duration.

Chap 12

Sec   12.1-

         12.2

Laplace transform

Transform pairs:

Example (pdf)

3.2.    Find the Laplace transform of the functions of time commonly used in circuit theory.

Chap 12

Sec   12.4

Laplace transform

Identities:

Example 1 (pdf)

Example 2 (pdf)

Example 3 (pdf)

3.3.    Apply the operational transform identities commonly used in circuit theory, including differentiation, integration, translation in the time domain, translation in the frequency domain, and scale changing.

Chap 12

Sec   12.5-

         12.6

Laplace transform

Inverse transform

Partial fractions

Example 1 (pdf)

Example 2 (pdf)

3.4.    Find inverse Laplace transforms of rational functions of s, including those with complex and repeated roots.

Chap 12

Sec   12.7

Laplace transform

Poles and zeros

Example 1 | (pdf)

Example 2 (pdf)

3.5.    Plot the poles and zeros of a rational function of s in the s plane.

Chap 12

Sec   12.8

Laplace transform

Initial/final value thms

Example (pdf)

3.6.    Apply the initial- and final-value theorems.

Chap 12

Sec   12.9

Laplace transform

Circuits

s-domain circuit elements

Example (pdf)

3.7.    Transform circuits (including initial conditions) to the s domain.

Chap 13

Sec   13.1

Laplace transform

Circuits

s-domain solutions

Example (pdf)

3.8.    Apply Kirchhoff's laws and techniques used for resistive circuits to circuits in the s domain, including impedance relationships, super-position, and source transformations.

Chap 13

Sec   13.2

Laplace transform

Circuits

t-domain waveforms

Example (pdf)

3.9.    Obtain expressions for specified voltages and currents in circuits in the s domain, and transform them to the time domain.

Chap 13

Sec   13.3

Impulse Function d(t)

Definition

Impulse Identity Convolve

Laplace transform

Circuits

Impulse function

Example (pdf)

3.10.  Analyze and design circuits that include impulse functions.

Chap 12

Sec   12.3

Chap 13

Sec   13.8

3.11.  Make consistency checks in s domain.

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