han q le© ece 3336 introduction to circuits & electronics lecture set #8 method for linear...

Han Q Le©

ECE 3336 Introduction to Circuits & Electronics

Lecture Set #8Method for Linear Circuit: Phasor

Part 1: Background

Dr. Han LeECE Dept.

Han Q Le©

Phasors: AC Circuits – Background Concepts

Note: The main lecture is in the Mathematica file – this is only for basic discussion

Han Q Le©

Outline

• Time-varying circuits and signals• Introduction to mathematical techniques:

– Harmonic functions– Complex analysis– Fourier analysis and transform– Phasors

• Applications of mathematical techniques to physical problems and circuits

Han Q Le©

It is more natural to have time-varying signals & circuits than time-constant circuits

Han Q Le©

An example of signal

6.04 s 22050 Hz 2 channels

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• Certain mathematical tools and techniques are highly useful for certain types of problems

• For NVM and MCM, linear algebra (the math principle) and matrix (the tool) is highly useful

• For time-varying signals and AC circuits, it will be Fourier transform (the math principle) and phasor (the tool)

• Again, it is important to use the tool rather than get lost or tangled with the tool

Mathematical tools and techniques

Han Q Le©

So, phasor is worth learning because it makes things so easy

Han Q Le©

Outline

• Time-varying circuits and signals• Introduction to mathematical techniques:

– Harmonic functions– Complex analysis– Fourier analysis and transform– Phasors

• Applications of mathematical techniques to physical problems and circuits

Han Q Le©

Fourier transform

Harmonic function

Complex numbers &analysis

Phasors

Han Q Le©

Link to Mathematica file

Han Q Le©

Outline

• Time-varying circuits and signals• Introduction to mathematical techniques:

– Harmonic functions– Complex analysis– Phasors– Fourier analysis and transform

• Applications of mathematical techniques to physical problems and circuits

Han Q Le©

Applications of mathematical techniques

Fourier transform

Harmonic function

Complex number

&analysisPhasors

Signal and AC circuit problems• RLC or any time-varying linear

circuits. Applicable to linear portion of circuits that include nonlinear elements

• Signal processing• signal analysis (spectral

decomposition)• filtering, conditioning (inc

amplification)• synthesizing