ABE425 Engineering Measurement Systems Filters Dr. Tony E. Grift

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Presentation transcript:

ABE425 Engineering Measurement Systems Filters Dr. Tony E. Grift Dept. of Agricultural & Biological Engineering University of Illinois

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

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

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

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

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

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

Concept of impedance (Capacitor) Laplace transform

Concept of impedance (Inductor (coil)) Laplace transform

Low-Pass filter using RC network

Derivation transfer function with impedance

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)

The transfer function of a RC circuit is a complex number

First order system analysis in standard notation (laborious)

First order system analysis in standard notation (laborious)

First order system analysis in Euler’s notation

First order system analysis in Euler’s notation

RC circuit as a Low-Pass filter Transfer function has an Absolute value (Magnitude of complex number) Phase (argument of complex number) Analyze three points: Very low frequencies ‘Corner’ frequency Very high frequencies

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

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

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

Summary 1st order low pass filter characteristics

Bode plot of a Low-Pass filter for t = 1s MatLab: bode([0 1],[1 1])

High-pass filter using RC network

High-Pass filter characteristics

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

1st order High Pass filter characteristics

Bode plot of a High-Pass filter for t = 1s MatLab: bode([1 0],[1 1])

Band-Pass filter through cascading

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

ABE425 Engineering Measurement Systems Filters The End Dept. of Agricultural & Biological Engineering University of Illinois