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

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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

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

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

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

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

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

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Concept of impedance (Capacitor)

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Concept of impedance (Inductor (coil))

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Low-Pass filter using RC network

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Derivation transfer function with impedance

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Decibel notation Addition is much simpler than multiplication Notation in Bel (after Alexander Graham Bell) For Power For Voltages (Power ~ Voltage 2 ) In deciBel (0.1 Bel)

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Transfer function of RC circuit is complex number i

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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

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

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

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

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Summary 1 st order low pass filter characteristics

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

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High-pass filter using RC network

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High-Pass filter characteristics

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

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Summary 1 st order High Pass filter characteristics

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

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Band-Pass filter through cascading

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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

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The End

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R. T. HoweEECS 105 Fall 2001 Lecture 5 Dept. of EECS University of California at Berkeley Lecture 5 Last time: –Bode plots for first-order transfer functions.

R. T. HoweEECS 105 Fall 2001 Lecture 5 Dept. of EECS University of California at Berkeley Lecture 5 Last time: –Bode plots for first-order transfer functions.

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