084-Filters and Equalizers

By: Raymond L. Barrett, Jr., PhD, PE

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Course Objective

This continuing education course is written specifically for professional engineers with the objective of relating to and enhancing the practice of engineering.

Course Description

This course reviews the notation for roots of polynomial expressions describing Linear-Time Invariant (LTI) systems in the frequency domain, and relates the operator notation to the time-domain response using complex exponential notation. A single pole circuit is introduced and responses analyzed in the frequency domain and time domain. An ideal delay is introduced for comparison and sets a reference for step response behaviors.

Polynomial root locations are described in the complex s-plane and complex conjugate pairs plotted and described using (w0, z) notation as well as (t0, Q) notation. Phasor notation is introduced for evaluation of steady-state sinusoidal excitation of transfer functions. Second-order, complex conjugate pole pairs are introduced and the asymptotic behaviors developed and contrasted to the single-pole behaviors in magnitude, phase, and group delay attributes. Straight-line approximations are produced and the errors of approximation discussed.

Classical Butterworth, Chebyshev, and Bessel filters are introduced and the construction formulae developed. The Cauer filter is also illustrated, but mathematical development using elliptic functions is not included. Frequency domain and time domain responses are developed using a 4th design form as representative of even-order forms and a 5th order design as representative of odd-order forms. Only the 5th order Bessel filter example is synthesized from the equations. A 5th order equalizer is examined for the 5th order Chebyshev and Cauer filter and shown to provide equivalent results for both Chebyshev and Cauer filters. An additional pole pair is added to the 5th order equalizer and the justification and improvements noted. Transformations are discussed to convert low-pass prototype designs to high-pass and band-pass filters.

The course is designed for a practicing engineer seeking a capability for designing and specifying filters and equalizers for frequency domain and time domain applications.

Questions about this course? Email the Author: raybarrett@comcast.net

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(4.3) 3 Reviews

084-Filters and Equalizers

Mark Brock

03/23/2020

Verified Buyer

Good technical course. Did a good job deriving the filters. Typo on page 12 referencing equation 3.19 which doesn't exist; and a typo on page 14 last sentence, the second reference to equation 4.14 should be 4.15.

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084-Filters and Equalizers

Brian Pohl

10/02/2019

Verified Buyer

excellent summary of filters

1 of 1 customers found this helpful.

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084-Filters and Equalizers

Wes Brown

02/02/2019

Verified Buyer

This is a very technical course, but it has easy to follow derivations and examples. I'd recommend this to an engineer with some background in filter design.

1 of 1 customers found this helpful.

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Course Code: 100206-10

Course PDH Hours: 4

Engineering Course Approvals

This course is accepted for engineering continuing education credit in all US states, territories, the District of Columbia, and Canadian provinces.
Ohio rules allow only 6-hours of unsupervised online courses such as this course per license renewal period
Kansas rules allow only 5-hours of self-study courses such as this course per license renewal period

About Course Approvals