Circuit Theory for the Amateur Extra Exam

A dynamical-systems and control perspective, for engineers who would rather understand the circuits than memorize the answers.

Alexander Dowling (KE9FZD) · Department of Chemical and Biomolecular Engineering, University of Notre Dame

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What this is

A free, source-available mini-textbook (231 pages) covering the circuit theory behind the United States Amateur Extra amateur-radio license exam.

The US Extra exam is mostly answerable by memorizing a published question pool. This book takes the opposite approach: it derives the circuit behavior the exam asks about, starting from the tools a control engineer already owns.

The organizing argument runs in one line:

Control theory gives you tools for modeling linear time-invariant systems. Those tools describe simple circuits built from ideal components. And understanding those simple circuits — plus their extensions — is what makes filters, antennas, transmission lines, receivers, and the rest of the exam's circuit content intelligible rather than arbitrary.

So a resonant circuit is a second-order system, its quality factor is a damping ratio in disguise, an oscillator is a pole placed deliberately on the imaginary axis, a transmission line is a delay, sampling is multiplication, and a vector network analyzer sweeping S₂₁ is drawing a Bode plot.

Who it is for

• Engineers and scientists studying for the Extra exam who know differential equations and want the physics rather than the answer key. A rusty acquaintance with poles, Bode plots, and the root locus is assumed but re-taught.
• Anyone curious how classical control theory and radio connect. Part II is a self-contained, circuit-free refresher on LTI modeling, frequency response, feedback, and higher-order systems; the rest of the book is that machinery cashed in on real hardware.
• Instructors looking for worked examples that tie state-space and frequency-domain views to the same physical object.

It is not a from-scratch introduction to electricity, and it is not a complete exam-prep course — see Scope and limitations below.

What is inside

Five parts, 26 chapters, 3 appendices.

Part	Contents
I — Exam-Ready Reference	A compact formula-and-symbol study guide
II — Mathematical and Control-Theory Foundations	Complex numbers and phasors · modeling LTI systems · frequency response, Bode, the s-plane · feedback · higher-order systems
III — Circuit Models	Circuit modeling · series and parallel networks · AC steady state · one circuit seen four ways · RC · RL · series RLC · parallel RLC
IV — Applying the Circuit Models	Filters and matching · transmission lines · active circuits and oscillators · sampling and DSP · noise and dynamic range · measurement · antenna patterns and design · signals, modulation, and receivers · device bias and regulation
V — Practice and Study	Worked examples and an exam map · reasoning through real pool questions · cross-chapter problems

Appendices: a formula index with a "Derived in" column pointing at the section that establishes each result, a units and prefix reference, and a glossary.

There is also a standalone two-page printable formula card (cheat_sheet.tex).

Getting the PDF

Download it from the Releases page — each tagged version publishes the book and the printable formula card as attachments. The PDF is not committed to the repository, so release assets are the way to get a prebuilt copy.

Or build it from source, which is the only way to get the current main.

Prerequisites

• A LaTeX distribution with pdflatex and latexmk (TeX Live or MacTeX)
• LaTeX packages: amsmath, siunitx, booktabs, tabularx, longtable, tcolorbox, tikz, circuitikz, pgfplots, hyperref, cleveref
• Python 3 with numpy, scipy, matplotlib — only needed to regenerate figures
• Poppler (pdfinfo, pdftoppm, pdftotext) — only needed for the checks

git clone <this repo> && cd radio-extra-book
make all            # book + printable card; PDFs land in output/
./scripts/check.sh  # should print ALL CHECKS PASSED

Other targets: make book, make cheat-sheet, make figures, make clean.

How it is built

A few standards are enforced mechanically rather than by good intentions, which is probably the most reusable thing here:

• Derive, don't assert. If the book states a formula, it derives it or cites the earlier section that did. The formula index's "Derived in" column is the audit trail.
• Every figure is reproducible. Data plots are generated by a same-named Python script in figures/src/ — nothing is traced, sketched, or copied. Schematics are inline circuitikz. make -C figures audit checks provenance and grayscale legibility.
• Cross-references are never hard-coded. Chapters get renumbered constantly; everything goes through \cref and stable labels.
• One command verifies the whole book. ./scripts/check.sh fails on undefined references, overfull boxes, multiply-defined or orphan labels, dangling references, hard-coded cross-references, glossary mis-ordering, and figure/include mismatches.
• Claims were audited against the literature. In September 2026 the technical claims and generated figures were checked against a separate corpus of RF, microwave, measurement, receiver, and control-theory texts; citations use printed page numbers. Method and privacy boundary: notes/literature-audit-2026-09-09.md.

Scope and limitations

This book alone will not get you through the Extra exam, and it does not try to.

It develops the circuit-theory portion of the syllabus and deliberately leaves the rest alone: rules and regulations, operating practice, propagation, safety and RF exposure, digital protocols and modes, digital logic, and detailed semiconductor device physics. Pair it with a conventional study guide for those.

Practice material is anchored to the 2024–2028 Element 4 pool, and the question identifiers cited in the practice chapter were verified against the official NCVEC release tracked in references/. Pool wording changes each cycle and questions are sometimes withdrawn mid-cycle, so check the current official pool and FCC rules before your exam.

This is an independent educational project. It is not affiliated with, endorsed by, or sponsored by the ARRL, NCVEC, or the FCC.

Provenance and AI use

This project is also an experiment in using generative AI to learn a new field, and it is worth being explicit about that. The book began as the author's own draft and was developed, corrected, and typeset iteratively with LLM assistance, with the author steering the pedagogy, setting the standards above, and critiquing the text throughout. The verification tooling exists precisely because generated technical prose needs checking: every numeric result is re-derived independently, every figure is regenerated from source, and the claims were audited against printed references.

Source prose, figures, and question text from the reference works were not copied into this repository.

No license file has been chosen yet, so default copyright applies; if you want to reuse something here, please ask.

Repository layout

Path	Contents
main.tex, preamble.tex, macros.tex	Entry point, style, notation macros
frontmatter/, chapters/, appendices/	The manuscript
figures/	Figure sources, committed PDFs, provenance, and the figure standard
references/	Official question pools and markdown extracts (details); commercial manuals are gitignored
scripts/	check.sh verification suite and build helpers
notes/	Working notes, audits, and per-round revision records (index)
PROJECT-STATUS.md	Running status, conventions, and the current work plan

Contributing or picking up the work? Start with PROJECT-STATUS.md — it carries the current state, the conventions in force, and what is planned next.