Sinusoidal signals

Basic Parameters of Sinusoidal Signals

Review of Sinusoidal Signals

Leading and Lagging Signals

Review of Sinusoidal Signals

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Review of Sinusoidal Signals

Signal Delay on Transmission Lines

Review of Sinusoidal Signals

Engineering Design

The purpose of this section is to show one application of sinusoidal signals to engineering design.

Complex numbers

Review of Complex Numbers

This section aims to introduce two different ways we represent complex numbers: Cartesian coordinates, and Polar coordinates. We often use complex numbers in Cartesian coordinates when we discuss impedance or admittance. We often use complex numbers in polar coordinates to discuss magnitude and phase of voltages, currents, transfer functions, and Bode Plots. We can also represent sinusoidal signals with complex numbers with phasors. It is critically important that we understand this chapter.

Operations with Complex Numbers

The purpose of this section is to review arithmetic operations with complex numbers. We use complex numbers to describe circuits. When we solve circuits to find voltages, currents, and power, we often encounter addition, subtraction, multiplication, division, and the complex conjugate of complex numbers.

Euler’s Formula

The purpose of this section is to relate sinusoidal signals and complex numbers using Euler’s formula.


Review of Phasors

Phasors are essential tool in circuit analysis, used in many applications. Phasors are a special case of superposition, that simplifies circuit analysis.

Kirchoff’s Laws

Phasors are essential tool in circuit analysis.

Example of circuit analysis with phasors

Phasors are essential tool in circuit analysis.

Waves on Transmission Lines

Types of Transmission Lines

Wave Equation

Visualization of waves on lossless transmission lines

Propagation constant and loss

Transmission Line Impedance

Reflection Coefficient

Input impedance of a transmission line

Forward voltage on a transmission line

Traveling and Standing Waves

Example Transmission Line Problem

Smith Chart

Smith Chart

Impedance and admittance circles on the Smith Chart

Impedance and Admittance on Smith Chart

Electrical Length

Input Reflection Coefficient and Impedance on Smith Chart

Impedance Matching


Power Transfer on a transmission line

Simple impedance matching case

Mixed Impedance Matching

Transmission-line impedance matching

Lumped element impedance matching


Electrostatic Force

Electrostatic Field

Electrostatic Potential

Electrostatic fields from distributed charges

Calculation of electric field using Gauss’s Law

Electrostatic Boundary Conditions


Method of images


Charged particles in static electric and magnetic fields

Force on Conductors

Force on Conductors

Biot-Savart’s Law

Ampere’s Law


Changing electromagnetic fields

Faraday’s Law

Lenz’s Law


Magnetic Coupling

Flying ring

Falling Magnet

Voltage droop

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