han q le© ece 3336 introduction to circuits & electronics lecture set #8 method for linear...
TRANSCRIPT
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
Han Q Le©
• 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