A. V. Oppenheim, A. S. Willsky & S. Hamid Nawab, Signals and Systems, 2nd ed., Prentice Hall, 1997.
LTI eigenfunction reasoning, frequency response, magnitude/phase interpretation and the connection between complex exponentials and system behaviour.
AC-02
Course overview
Frequency response, transfer functions & Bode foundations
AC-01 solved one sinusoidal frequency at a time. AC-02 asks what happens when the same declared input/output experiment is repeated while angular frequency changes. The result is not a bag of unrelated gains: for a linear time-invariant system it is a complex function of frequency. This course builds that function first, then magnitude/phase, poles and zeros, Bode representations, bandwidth and first filter interpretations.
5 chapters5 available · 0 plannedintermediate
Prerequisites
- AC-01 — phasors, impedance & sinusoidal steady state
- Elementary complex algebra
By the end of the course
- Build frequency response directly from a one-frequency AC solution.
- Distinguish phasors, H(jω), transforms and the later H(s) notation.
- Interpret magnitude and phase versus frequency.
- Understand poles, zeros and characteristic frequencies before using them graphically.
- Construct and check Bode representations.
- Relate bandwidth and first filter behaviours to measurable circuits.
Syllabus
Five readings from one-frequency complex ratios to bandwidth interpretation.
AC-01 solved one sinusoidal frequency at a time. AC-02 asks what happens when the same declared input/output experiment is repeated while angular frequency changes. The result is not a bag of unrelated gains: for a linear time-invariant system it is a complex function of frequency. This course builds that function first, then magnitude/phase, poles and zeros, Bode representations, bandwidth and first filter interpretations.
- 01→
From one-frequency AC solutions to frequency response
Start from AC-01's sinusoidal steady-state solution and repeat the same declared input/output experiment versus angular frequency. Define H(jω) as the complex output/input phasor ratio of an LTI network, derive it from a linear differential equation, distinguish phasors from functions, make port references and units part of the definition, and verify the idea on an ideal RC low-pass without using Bode asymptotes.
145–185 min · Intermediate · available - 02→
Magnitude, phase & normalized frequency
Decompose the complex response H(jω) into magnitude and phase without losing units or reference conventions. Derive exact first-order low-pass and high-pass magnitude/phase relations, introduce the dimensionless normalized frequency Ω=ω/ω₀, distinguish phase shift from true time delay, and use limiting values and complementary outputs as independent checks before logarithmic Bode scales appear.
135–175 min · Intermediate · available - 03→
Poles, zeros & characteristic frequencies
Introduce the generalized complex frequency s=σ+jω from exponential trial functions rather than memorizing pole/zero vocabulary. Derive H(s)=B(s)/A(s) for constant-coefficient LTI differential equations, connect denominator roots to natural modes and numerator roots to transfer zeros, recover H(jω) on the imaginary axis, and interpret first-order pole/zero locations, characteristic frequencies, stability caveats and imperfect pole-zero cancellation before any Bode slope rules.
145–190 min · Intermediate · available - 04→
Bode magnitude & phase plots
Derive Bode representations from logarithms and the pole/zero factors of chapter 03 rather than memorizing slope tables. Define amplitude-ratio decibels carefully, keep dimensional transfer functions referenced, derive exact and asymptotic first-order pole/zero contributions, explain decades and octaves, add factor contributions in magnitude and phase, quantify corner error, and work a multi-break example before using Bode as a design shortcut.
150–195 min · Intermediate · available - 05→
Bandwidth & first filter interpretations
Turn frequency-response curves into defensible filter specifications. Define passband, stopband, transition region and bandwidth from an explicit threshold and reference level; show why the familiar −3.010 dB point is exact for a first-order pole but not a universal bandwidth definition; interpret low-pass, high-pass and band-pass regions, derive a cascaded-pole counterexample, include source/load/instrument effects in measured bandwidth, and close with a reproducible sweep-to-bandwidth workflow.
145–190 min · Intermediate · available
Reference backbone
References used
AoN keeps three objects separate: real time-domain signals, underlined lowercase single-frequency phasors, and non-underlined frequency-response/transfer functions such as H(jω). The distinction is normative under ADR-0018 and is repeated whenever a new frequency-domain object appears.
A. Agarwal & J. H. Lang, Foundations of Analog and Digital Electronic Circuits, Morgan Kaufmann, 2005.
Frequency-dependent circuit response derived from circuit laws, impedance and small-signal network equations.
C. K. Alexander & M. N. O. Sadiku, Fundamentals of Electric Circuits, McGraw-Hill.
Transfer functions, frequency response, first-order circuit examples and Bode foundations.
J. W. Nilsson & S. A. Riedel, Electric Circuits, Pearson.
Frequency-selective circuit behaviour, transfer functions, poles/zeros and engineering checks.
MIT OpenCourseWare 6.002 / 6.200 frequency-response material.
Pedagogical bridge from sinusoidal steady-state circuit solution to gain/phase versus frequency.
AoN ADR-0018 — Electrical notation and sign conventions.
Normative distinction among instantaneous functions, harmonic phasors and frequency-domain/system functions.