1 / 27

Recap Filters

Recap Filters. Tony Grift, PhD Dept. of Agricultural & Biological Engineering University of Illinois. ABE425 Engineering . Agenda. Recap complex numbers Relationship Laplace, frequency (Fourier) domain Relationship time, s and frequency domains decibel notation (dB)

ewan
Télécharger la présentation

Recap Filters

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Recap Filters Tony Grift, PhD Dept. of Agricultural & Biological Engineering University of Illinois ABE425 Engineering

  2. Agenda • Recap complex numbers • Relationship Laplace, frequency (Fourier) domain • Relationship time, s and frequency domains • decibel notation (dB) • RC circuit as a Low-Pass and High-Pass filter • Bode plots • Combination filters

  3. Complex number in complex plane Argument of s Absolute value of s (aka Modulus or Magnitude)

  4. Operations on complex numbers cont. Multiplication/division using Euler’s notation

  5. Operations on complex numbers cont. Complex conjugate Multiplying a complex number by its conjugate gives a real number

  6. Relation Laplace and Fourier Transform Time domain Time domain s-domain (Laplace Domain) -domain (Frequency Domain) Transient response (step, impulse) Frequency response (filters)

  7. Relation time, s and frequency domain Time domain i Laplace (s)-domain -domain

  8. Concept of impedance (Capacitor)

  9. Concept of impedance (Inductor (coil))

  10. Low-Pass filter using RC network

  11. Derivation transfer function with impedance

  12. Decibel notation • Addition is much simpler than multiplication • Notation in Bel (after Alexander Graham Bell) • For Power • For Voltages (Power ~ Voltage2) • In deciBel (0.1 Bel)

  13. Transfer function of RC circuit is complex number i

  14. RC circuit as a Low-Pass filter • Filter response has a • Absolute value (Magnitude of complex number) and • Phase (argument of complex number) • Analyze three points: • Very low frequencies • ‘Corner’ frequency • Very high frequencies

  15. RC Filter response at very low frequencies • Magnitude • Magnitude in dB • Phase (argument)

  16. RC Filter response at corner frequency • Magnitude • Magnitude in dB • Phase (argument)

  17. RC Filter response at very high frequencies • Magnitude • Magnitude in dB • Phase (argument)

  18. Summary 1st order low pass filter characteristics

  19. RC circuit as a Low-Pass filter: Bode plot bode([0 1],[1 1])

  20. High-pass filter using RC network

  21. High-Pass filter characteristics

  22. RC circuit as a High-Pass filter • Filter response has a • Absolute value (Magnitude of complex number) and • Phase (argument of complex number)

  23. Summary 1st order High Pass filter characteristics

  24. RC circuit as a High-Pass filter: Bode plot bode([1 0],[1 1])

  25. Band-Pass filter through cascading

  26. Cascade of High-Pass and Low-Pass filters to obtain a Band-Pass filter • Since the sections are separated by a buffer: Add absolute values in dB;s. Add phase angles Buffer

  27. The End

More Related