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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)

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Recap Filters

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  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

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