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Theory Map

β: This English translation is in beta — the Traditional-Chinese original is the authoritative version.

Prerequisites: learning_path (the page order of the twelve-step spine; this page highlights the corresponding nodes in gold), notation (the symbol table — this page introduces no new symbols, but every page name in the graph can be looked up there) | Next: cheat_sheet, paper_summary_table

This page does exactly one thing: it draws the "who must be read before whom" relationship among the site's 92 pages (Chinese originals; every page also has an English mirror under i18n/en/) as a single graph. The graph was not hand-drawn — its edges were extracted programmatically by scanning the "> Prerequisites: … | Next: …" breadcrumb line (or the older format, "> Prerequisite Reading: …") at the top of every page and pulling out the markdown links, so it reflects the site's actual link structure, not an idealized sketch drawn from memory.

How to read this map​

  • Arrow direction = prerequisite relation: A --> B reads "A is a prerequisite of B / what A teaches is used directly by B." Following the arrows gives a valid reading order; conversely, a node's incoming edges are the prerequisite pages it lists, and its outgoing edges are the downstream pages that list it as a prerequisite.
  • Rectangular nodes = a single page (chapters 02 Foundations and 03 Core Theory are the main spine, so every page there gets its own node, per the map's editorial rule; the three small chapters 00/01/05 are also drawn page-by-page). Rounded (stadium) nodes = several pages clustered into one node (all of chapter 04 Simulation Labs is clustered; chapter 06 Design Insights and chapter 99 Appendix cluster their lower-degree pages), because drawing all 92 pages as separate nodes would be unreadable — after clustering, the whole graph has only 56 nodes (see the "How 92 pages compress to 56 nodes" table below). Exactly which pages sit inside each clustered node is listed in the "Grouped-Node Legend" section below.
  • Gold highlight = nodes touched by the 12 steps of the learning path. This is the site's recommended main spine; every other node is an extension, a deeper dive, or reference material beyond the spine. A clustered node is marked gold as soon as any one of its member pages falls inside the 12 steps (e.g. "Systems & Advanced Labs" is entirely gold because it contains lab_36 — that does not mean every page in the cluster is on the spine).
  • Click a node to open its page: every node carries a mermaid click directive that opens the page in a new tab (clustered nodes have no single destination, so they carry no click — use the legend table below instead). If your browser or viewer blocks the navigation, every link in the legend table and the rest of this page still works normally.
  • This is not a strict DAG: a handful of pages list each other as prerequisites in both directions (page A explains half a concept and links to B for the rest; B in turn lists A under further reading) — the graph shows this as a back-and-forth pair of arrows. That is a faithful reflection of the site's actual cross-referencing, not an extraction error.
  • Two pages with a different edge source: tank_Q_and_energy_restoration and capstone_lc_end_to_end do not carry the standard "Prerequisites / Next" breadcrumb (they are either an earlier-style page or the site's capstone/wrap-up page), so their edges were instead taken from the "Further Reading" links explicitly listed in the page body (copied verbatim from the page text — no relationship was added beyond what is actually written there). Apart from those two pages, all 236 edges (including a handful of "hands-on verification" pointers to the matching lab) come directly from markdown links inside the breadcrumb line.

Full Dependency Map​

How 92 pages compress to 56 nodes​

ChapterOriginal pagesNodes in graphTreatment
00 - Overview66One node per page (small chapter, mostly reference hubs)
01 - Paper Map44One node per page
02 - Foundations1010One node per page (main spine, kept individual per the map's rule)
03 - ISF Core Theory1515One node per page (main spine, kept individual per the map's rule)
04 - Simulation Labs243Clustered by the sidebar's three sub-categories (Foundations Labs / Noise & Jitter Labs / Systems & Advanced Labs)
05 - Paper Deep Dives66One node per page (each page maps 1:1 to one paper — small in count but high in meaning, not clustered)
06 - Design Insights2010The 6 highest-degree pages (symmetry, tank_swing, lc_vs_ring, pll_noise_budget, serdes_clocking_connection, exercises) keep their own node; the remaining 14 pages are clustered into 4 themed groups
99 - Appendix72Clustered into "Rigorous Math Foundations" and "Reference Tools"
Total9256

Top-8 Hub Pages​

"Degree" = a page's in-degree + out-degree in the page-level directed graph (before clustering) extracted from the breadcrumbs. A high in-degree means "this page itself lists many prerequisites"; a high out-degree means "many downstream pages list this page as their prerequisite" — pages with a high out-degree are usually the site's real conceptual hubs. Ties are broken by: higher degree first, then higher in-degree, then alphabetically by page id (see the note below).

RankPageChapterDegree (in+out)Listed as prereq (in)Listed as prereq for (out)
1How White Noise Becomes 1/f² Phase Noise03_isf_core_theory24420
2Capstone — One Ideal LC from State Equations to BER (Fully Rigorous, End to End)03_isf_core_theory18171
3Fourier Series of the ISF03_isf_core_theory16313
4From ISF to SerDes Clocking06_design_insights14104
5Design Chapter Exercises (with Full Solutions)06_design_insights13103
6Phase Noise → Jitter02_foundations13310
7What Is Oscillator Phase?02_foundations13211
8Tank Q and Energy Restoration02_foundations1275

Note: this column is computed from the full breadcrumb extraction — every wording variant used across the site (> Prerequisites:, > **Prerequisites**:, > **Prerequisite Reading**:, > **Prerequisite knowledge (read first)**:, and the lab pages' "breadcrumb ... upstream/downstream" style — not only the single canonical format; the two breadcrumb-less exception pages tank_Q_and_energy_restoration and capstone_lc_end_to_end still use their "Further Reading" links), which is more complete — and closer to the site's true link volume — than counting only the one canonical format. Ranks 5-7 are tied at degree 13; the tie-break rule above (higher in-degree first) orders them exercises (in=10) > psd_phase_noise_jitter (in=3) > oscillator_phase (in=2). Rank 8 (degree 12) is tied with 03_isf_core_theory/isf_definition (in=3, out=9); because tank_Q_and_energy_restoration has the higher in-degree (7 > 3) it takes rank 8, with isf_definition just behind at rank 9. Four more pages sit at degree 11: 06_design_insights/symmetry, 06_design_insights/tank_swing, 03_isf_core_theory/rms_isf, and 02_foundations/stochastic_noise_basics — genuine hubs in their own right and worth noting on the map. symmetry, lc_vs_ring, tank_swing, isf_definition, and tank_Q_and_energy_restoration all kept their own node (not clustered) precisely because of their high degree, so they are easy to spot in the 02/03/06 sections of the diagram.

Grouped-Node Legend​

Clustered nodes have no single destination, so they carry no click; the tables below list, by chapter, exactly which pages each clustered node contains.

04 - Simulation Labs​

Foundations Labs (numerical_feeling / worked_examples / interactive_calculator / lab01-05) (node g_lab_basic): Interactive Calculator, Lab 01 — Sinusoidal Oscillator and the Phase/Amplitude Geometry of the Limit Cycle, Lab 02 — Ideal LC oscillator toy model: Γ(θ) = −sin θ and charge linearity, Lab 03 — Ring-oscillator toy model: accumulated-jitter random walk and ISF comparison, Lab 04 — impulse injection sweep and LTI vs LTV, Lab 05 — ISF Fourier coefficients and Parseval, Numerical Feeling, Worked Examples

Noise & Jitter Labs (lab06-12) (node g_lab_noise): Lab 06 — White Noise → 1/f² Phase Noise, Lab 07 — 1/f Noise Upconversion and ISF Symmetry, Lab 08 — rms Jitter by Integrating L(f), Lab 09 — Design trade-off scaling synthesis, Lab 10 — how phase noise smears the carrier into an RF skirt, Lab 11 — Monte Carlo accumulated jitter — RJ is Gaussian, σ grows as √ΔN, Lab 12 — From jitter to eye to BER (SerDes bathtub)

Systems & Advanced Labs (lab13-17, 32, 34, 36, final_exam) (node g_lab_sys): Final Exam: A 5 GHz LC VCO into a 25 Gb/s SerDes, End to End, Lab 13 — PLL/CDR jitter transfer: VCO high-pass, reference low-pass, Lab 14 — Cyclostationary noise and the effective ISF, Lab 15 — ISF of a Nonlinear Oscillator (van der Pol), Lab 16 — Leeson Model vs ISF Model (Three-Region Comparison), Lab 17 — Design Sweeps: Three Design Curves for swing / Γrms / N, Lab 32 — MOS Level-1 Equation-Level Ring: Extracting the ISF from Transistor Equations, Lab 34 — The N·f0 Selection Rule for Correlated Supply/Substrate Noise (P2 Eq.37–38), Lab 36 — Lock-Acquisition Transient and Noise-Induced Cycle Slips

06 - Design Insights​

Waveform & Device Mapping (node g_dsg_map): Device noise → ISF harmonics mapping, Waveform slope and phase sensitivity

Measurement, Budget & Pitfalls (node g_dsg_meas): ADC aperture jitter: how clock jitter eats SNR and ENOB, Common Mistakes Showroom: 12 Real-World Landmines, DJ and the Dual-Dirac Model, The Theoretical Ceiling of FOM, Phase-noise measurement and spurs

System Clocking & References (node g_dsg_sys): Clock-chain noise accounting: ×N, ÷N, PLL, buffer — a one-page lookup table, Reference oscillators: crystal and MEMS phase noise, Sampling / sub-sampling PLL — kicking the divider out of the loop

Real Topologies & Injection (node g_dsg_topo): Noise shaping under injection locking and the injection-pulling spectrum, Quadrature generation and coupled-oscillator phase noise, ISF in real topologies: cross-coupled LC VCO, Colpitts, CMOS ring stage, Tuning-line and supply-pushing phase noise

99 - Appendix​

Reference Tools (node g_app_ref): Chinese–English Glossary, Python Environment, References

Rigorous Math Foundations (node g_app_theory): Floquet / adjoint / PPV: the rigorous foundation of the ISF, Leeson Model Derivation and ISF Comparison, Rigorous LTV framework: Zadeh's time-varying transfer function and the harmonic transfer matrix, Math Toolbox — Math Identities

Key takeaways​

  • Every edge on this map comes from a page's own declared "Prerequisites / Next" (two exception pages use "Further Reading" instead, see above) — it is a mirror of the site's actual dependency structure, not a redesigned "ideal" teaching order (the ideal order is still the learning path's twelve steps, highlighted in gold here).
  • 92 pages -> 56 nodes: the two core chapters (02/03) keep one node per page as the authoring spec requires; chapter 04 is fully clustered, and 06/99 are partially clustered by connectivity, so the map stays a size you can scan at a glance.
  • The highest-degree hubs are not in 00/01 (reference/dictionary pages are rarely listed as anyone's prerequisite, so their breadcrumb-degree is naturally low) — they are white-noise-to-1/f², SerDes clocking, the capstone, the ISF Fourier series, and the chapter-end exercise pages. These are where the site's teaching logic genuinely converges.
  • The graph is not a strict DAG: a few pages list each other as mutual prerequisites — that is a faithful reflection of the site, not an extraction bug.

Further Reading​