Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit:...
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Transcript of Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit:...
![Page 1: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/1.jpg)
Han Q Le©
ECE 3336 Introduction to Circuits & Electronics
Lecture Set #8Method for Linear Circuit: Phasor
Part 1: Background
Dr. Han LeECE Dept.
![Page 2: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/2.jpg)
Han Q Le©
Phasors: AC Circuits – Background Concepts
Note: The main lecture is in the Mathematica file – this is only for basic discussion
![Page 3: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/3.jpg)
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
![Page 4: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/4.jpg)
Han Q Le©
It is more natural to have time-varying signals & circuits than time-constant circuits
![Page 5: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/5.jpg)
Han Q Le©
An example of signal
6.04 s 22050 Hz 2 channels
![Page 6: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/6.jpg)
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
![Page 7: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/7.jpg)
Han Q Le©
So, phasor is worth learning because it makes things so easy
![Page 8: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/8.jpg)
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
![Page 9: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/9.jpg)
Han Q Le©
Fourier transform
Harmonic function
Complex numbers &analysis
Phasors
![Page 10: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/10.jpg)
Han Q Le©
Link to Mathematica file
![Page 11: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/11.jpg)
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
![Page 12: Han Q Le© ECE 3336 Introduction to Circuits & Electronics Lecture Set #8 Method for Linear Circuit: Phasor Part 1: Background Dr. Han Le ECE Dept.](https://reader030.fdocuments.us/reader030/viewer/2022032803/56649e2a5503460f94b18b1c/html5/thumbnails/12.jpg)
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