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

Figure Index

This site has two kinds of figures: (a) figures we generate with Python (all teaching toy/conceptual models, not transistor-level), and (b) figures inside the cited paper PDFs. This page files every one of them, so you can trace any figure back to "which script, which function, what parameters, which formula behind it, which paper it comes from".

How to read this table:

• Toy? = whether it is a simplified teaching model (not transistor-level).
• Redrawn? = whether it was redrawn directly from a paper figure (our generated figures are always re-simulated, never traced, so mostly No).
• Verify? = manual_verification_needed; entries flagged ⚠️ still need manual confirmation of constants/correspondence.
• Re-run everything in one shot: python scripts/run_all_sims.py (outputs to static/figures/). Data comes from extracted/extracted_figures.json.

(a) Generated figures (14)

Figure	Generated By (script / function)	Formula Behind It	Source	Teaching Message	Toy?	Redrawn?	Verify?
limit_cycle_phase_amplitude.png	simulations/lab_01_sinusoidal_oscillator.py / fig_limit_cycle (params: f0=1.0, fs=4000, mu=0.6, start=(1.7,0))	2-D state model $\dot z=\omega_0 R(z)+\mu(1-r^2)z$; tangential=phase, radial=amplitude	[P1] Fig. 4(c) (limit cycle, peak vs ZC injection)	phase=tangential (persists), amplitude=radial (pulled back)	Yes	No	No
waveform_with_impulse_markers.png	lab_01_sinusoidal_oscillator.py / fig_impulse_markers (f0=1.0, amp=1.0)	$V(t)=\cos(2\pi f_0 t)$; at peak $\Gamma\approx0$, at ZC $\vert \Gamma\vert$ maximal	[P1] Fig. 4(a),(b)	same impulse, different injection phase → different effect (LTV)	Yes	No	No
lc_waveform_and_isf.png	lab_02_lc_toy_model.py / main (f0=1.0, fs=8000, mu=0.3, dq/qmax∈[-0.05,0.05])	$\Gamma_{LC}(\theta)=-\sin\theta$; $\Delta\phi=\Gamma\,\Delta q/q_{max}$	[P1] Figs. 4,6,7(a); Eqs (10),(11)	the LC's ISF; $\Delta\phi\propto\Delta q$; ZC injection = pure phase jump	Yes	No	No
ring_oscillator_timing_noise_accumulation.png	lab_03_ring_toy_model.py / fig_accumulation (f0=5e9, sigma_edge=50 fs, max_lag_periods=500, n_trials=2000)	edge-time random walk → $\sigma_{\Delta t}=\sigma_{edge}\sqrt{\Delta N}$	[P2] Eq.(8), accumulated jitter	accumulated jitter is a random walk, $\propto\sqrt{\Delta t}$	Yes	No	No
lc_vs_ring_isf_comparison.png	lab_03_ring_toy_model.py / fig_lc_vs_ring_isf (lc=-sin, ring_N=[5,15])	$\Gamma_{LC}=-\sin$ vs ring triangular (peak $\sim1/\sqrt{N}$); $\Gamma_{rms}$ scaling	[P1] Fig. 7; [P2] Fig. 8 ($\Gamma_{rms}$ vs $N$)	ring sensitivity concentrates at transitions; $N\uparrow$ gives $\Gamma_{rms}\downarrow$	Yes	No	No
sinusoidal_impulse_phase_sweep.png	lab_04_impulse_sweep.py / fig_isf_sweep (f0=1.0, fs=8000, dq/qmax=1e-3, n_points=48, mu=0.3)	$\Delta\phi(\theta)=-\sin\theta\cdot\Delta q/q_{max}$	[P1] Eqs (10),(11); Fig. 4	phase sensitivity varies with the injection phase $\theta$	Yes	No	No
isf_impulse_sweep_sinusoidal.png	lab_04_impulse_sweep.py / fig_isf_sweep (same params as above)	numeric $\Gamma=\Delta\phi/(\Delta q/q_{max})$ vs analytic $-\sin\theta$ (max err ~0.001)	validation of the [P1] ISF definition	numerically extracted ISF, near-perfect match to the theoretical $-\sin$	Yes	No	No
lti_vs_ltv_impulse_response.png	lab_04_impulse_sweep.py / fig_lti_vs_ltv (f0=1.0)	LTI $h(t-\tau)$ vs LTV $h_\phi(t,\tau)=\frac{\Gamma(\omega_0\tau)}{q_{max}}u(t-\tau)$	[P1] Sec. III (LTV nature); Fig. 3	LTV: step height changes with injection phase $\tau$	Yes	No	No
isf_fourier_reconstruction.png	lab_05_fourier_isf.py / fig_reconstruction (ISF=-sin+0.35 sin2+0.18 cos3+0.25, N=[1,2,4])	$\Gamma(\theta)=\frac{a_0}{2}+\sum(a_n\cos+b_n\sin)$ (Eq.12)	[P1] Eq.(12)	more harmonics, closer reconstruction of the original ISF	Yes	No	No
isf_fourier_coefficients.png	lab_05_fourier_isf.py / fig_coefficients (n_harmonics=8)	$c_n=\sqrt{a_n^2+b_n^2}$; Parseval $\sum c_n^2=2\Gamma_{rms}^2$ (Eq.20)	[P1] Eqs (12),(20)	coefficient spectrum; verifies $\sum c_n^2=2\Gamma_{rms}^2$	Yes	No	No
symmetric_vs_asymmetric_isf_c0.png	lab_05_fourier_isf.py / fig_symmetric_vs_asymmetric (sym=cos(θ), c0=0; asym=cos(θ)+0.4, c0=0.8)	$c_0$ (the ISF's DC) controls $1/f$ upconversion (Eq.24)	[P1] Eq.(24); [P2] symmetry results	only $c_0\neq0$ upconverts $1/f$ into $1/f^3$	Yes	No	No
white_noise_phase_noise_psd.png	lab_06_white_noise_phase_noise.py / main (f0=1.0, fs=256, n=1048576, q_max=1.0, S_i=1e-4, ISF=-sin)	$S_\phi(f)=\Gamma_{rms}^2 S_i/(q_{max}^2(2\pi f)^2)$; $-20$ dB/dec	[P1] Eq.(21) (the lab includes a factor-of-2 SSB note)	white noise → $1/f^2$ phase noise; simulation matches theory	Yes	No	No
flicker_upconversion_symmetric_vs_asymmetric.png	lab_07_flicker_noise.py / main (f0=1.0, fs=256, n=1048576, sym=cos, asym=cos+0.5, k_flicker=1e-4)	close-in $S_\phi\sim(c_0/2)^2 S_{flicker}/(2\pi f)^2\to1/f^3$; symmetry suppresses it	[P1] Eqs (23),(24); [P2] symmetry	waveform symmetry sets the close-in $1/f^3$ magnitude	Yes	No	No
phase_noise_to_jitter_integration.png	lab_08_jitter_integration.py / main (f0=5e9, L(1MHz)=-100 dBc/Hz, integrate 1-100 MHz, slope 1/f^2)	$\sigma_t=\frac{1}{2\pi f_0}\sqrt{\int 2\mathcal{L}(f)\,df}$; $1/f^2$ analytic closed form	standard jitter integration; SerDes practice	$\mathcal{L}(f)\to$ rms jitter; 5 GHz, $-100$ dBc/Hz → ~448 fs	No	No	No

The only non-toy generated figure is phase_noise_to_jitter_integration.png: it performs the standard jitter integration (from $\mathcal{L}(f)$ to $\sigma_t$), which is a mathematically exact closed-form comparison that does not depend on any simplified oscillator model, hence toy_model=false. The other 13 are all teaching toy/conceptual models.

(b) Cited PDF figures

The figures below are not generated by this site; they are figures inside the cited paper PDFs (taken from source_pdf_figures_referenced in extracted/extracted_figures.json). On the corresponding teaching pages we describe their content and give page numbers — we do not redraw or repost them.

Figure	Source	Page	Teaching Message	Verify?
Fig. 4	[P1] general.pdf	182	different state-space effect of peak vs ZC injection (phase/amplitude split); conceptually reproduced in lab_01/02	No
Fig. 6	[P1]	182	"$\Delta\phi$ linear in small charge $\Delta q$" for a Colpitts LC and a 5-stage ring; supports the impulse→phase linearity assumption, reproduced in lab_02(b)	No
Fig. 7	[P1]	183	waveforms and ISF shapes for (a) LC, (b) ring; basis of lc_vs_ring_isf_comparison.png	No
Fig. 8	[P1]	183	noise near $n\omega_0$ downconverted to the carrier as sidebands (Fourier downconversion picture)	No
Fig. 12	[P1]	185	PSD of $\overline{i^2}/f$ and SSB $\mathcal{L}(\Delta f)$, showing the $1/f^3$, $1/f^2$, noise-floor regions and defining the $1/f^3$ corner	No
Fig. 8	[P2] jitter_ring.pdf	794	single-ended ring's $\Gamma_{rms}$ vs stage count $N$; the solid line is $4/N^{1.5}$ from [P2] Eq.(16) at $\eta=0.75$, i.e. evidence for $\Gamma_{rms}\propto N^{-3/2}$	No
Fig. 17	[P2]	802	ring phase noise vs symmetry (control) voltage, minimum at the symmetric point; supports the "symmetry → suppress $1/f$ upconversion" design rule	No
Fig. 18	[P2]	803	Appendix B's asymmetric triangular ring ISF model (different positive/negative lobe widths); the basis asymmetry_corner.png (lab_33) numerically checks Eqs.(52)-(57) against	No
Fig. 5	[P4] BHongGenTheor-II…	2126	ideal LC's ISF and APF, the amplitude decay function, and their orthogonality; used by phase_vs_amplitude_noise to explain "why amplitude noise decays"	No
Fig. 19	[P3]	2120	for a 17-stage single-ended ring, the lock-range gain (~2x) of a "matched injection waveform" over a same-power sinusoidal injection; optimal_injection_lock_range.png (lab_39) reproduces this numerically	No

Note: [P1]'s Fig. 11 (the noise→phase panorama) is also conceptually referenced on teaching pages, but is not in the exact source_pdf_figures_referenced list; for a page-by-page comparison see the paper_001 deep dive. [P3] Fig. 19 (p.2120) and [P2] Fig. 18 (p.803) are only cited once the Wave-G labs (lab_33, lab_39) were added, and are backfilled here as part of this audit; [P5]'s figures are still not cited by this site (unrelated to ISF).

Where each generated figure is used

For reverse lookup (from each figure's used_in):

Figure	Used on
limit_cycle_phase_amplitude.png	oscillator_phase
waveform_with_impulse_markers.png	oscillator_phase, lti_vs_ltv
lc_waveform_and_isf.png	lab_02, isf_definition
ring_oscillator_timing_noise_accumulation.png	lab_03, lc_vs_ring
lc_vs_ring_isf_comparison.png	lc_vs_ring, rms_isf
sinusoidal_impulse_phase_sweep.png	lti_vs_ltv, lab_04
isf_impulse_sweep_sinusoidal.png	isf_definition, lab_04
lti_vs_ltv_impulse_response.png	lti_vs_ltv
isf_fourier_reconstruction.png	fourier_series_of_isf, lab_05
isf_fourier_coefficients.png	fourier_series_of_isf, rms_isf
symmetric_vs_asymmetric_isf_c0.png	flicker_noise_upconversion, symmetry
white_noise_phase_noise_psd.png	white_noise_to_phase_noise, lab_06
flicker_upconversion_symmetric_vs_asymmetric.png	flicker_noise_upconversion, lab_07
phase_noise_to_jitter_integration.png	psd_phase_noise_jitter, lab_08, numerical_feeling, worked_examples, serdes_clocking_connection
rf_spectrum_phase_noise_sidebands.png	lab_10
monte_carlo_jitter_histogram.png	lab_11
serdes_eye_ber_bathtub.png	capstone_lc_end_to_end, lab_12, worked_examples
pll_cdr_jitter_transfer.png	lab_13
cyclostationary_effective_isf.png	lab_14
nonlinear_oscillator_isf.png	lab_15
leeson_vs_isf_overlay.png	lab_16, measurement_and_spurs, derivation_leeson
design_tradeoff_sweeps.png	lab_17
lorentzian_carrier_lineshape.png	lorentzian_linewidth
allan_deviation.png	allan_variance
pll_noise_budget.png	pll_noise_budget
cross_coupled_vco_isf.png	real_oscillator_topologies
allan_flicker_floor.png	allan_variance
am_noise_spectrum.png	phase_vs_amplitude_noise
aperture_jitter_snr.png	adc_aperture_jitter
asymmetry_corner.png	asymmetric_isf_closed_form
clock_chain_budget.png	clock_chain_budget
correlated_supply_selection.png	lab_34
device_noise_isf_bands.png	device_noise_mapping
diffusion_dictionary.png	diffusion_dictionary
dual_dirac_bathtub.png	dj_dual_dirac
flicker_lineshape.png	beyond_lorentzian
floquet_ppv_numeric.png	derivation_floquet_ppv
fom_limit.png	fom_limit
htm_band_folding.png	ltv_htm
ilfd_lock_ranges.png	paper_004_injection_locking_part2
impulse_phase_decomposition.png	impulse_to_phase_shift
injlock_noise_shaping.png	injection_locking_noise
isf_three_methods.png	isf_from_waveform
jitter_kernels_mc.png	jitter_kernels
jitter_two_regime.png	jitter_kernels
lock_acquisition.png	lab_36
lock_characteristic_omega.png	paper_003_injection_locking_part1
mos_level1_ring_isf.png	lab_32
optimal_injection_lock_range.png	injection_locking_noise
pulling_spectrum.png	injection_locking_noise
supply_pushing_ring.png	varactor_tuning_supply_pushing
xcorr_floor.png	measurement_and_spurs
subharmonic_injection.png	lab_40_subharmonic_injection
large_injection_transient.png	paper_004_large_injection_transient

v5 additions (subharmonic injection / large-injection transient)

Figure	Generated By (script / function)	Formula Behind It	Source	Teaching Message	Toy?
subharmonic_injection.png	simulations/lab_40_subharmonic_injection.py / main (2×3 panels)	Subharmonic (×N) pulse injection: impulse-train map (lock range $\omega_L=q_{inj}\vert\tilde\Gamma\vert_{max}/(NT_0)$) vs the unaveraged time-synchronous ODE; realignment factor $\beta=-q_{inj}\tilde\Gamma'(\theta_{ss})$; first-order discrete noise shaping $H_{osc}(z)$, corner $\approx\beta f_{ref}/2\pi$	[P3] Sec. IV footnote 7, p.2112; [P4] Eq.(28)–(30), p.2129 (taking $(M,N)_{[P4]}=(N,1)$)	lock range $\propto1/N$ (log-log slope $-1.000$); $\beta$'s ODE step response vs the first-order prediction; output jitter $\propto\sqrt N$, reference spur independent of $\beta$	toy (phase-only, weak-injection pedagogical toy)
large_injection_transient.png	simulations/lab_41_large_injection_transient.py / main (4 panels)	Exact pull-in solution $\tan(\tilde\theta/2)=\tan(\tilde\theta_0/2)\tanh((\omega_pt+\phi_0)/2)$ ([P4] Eq.(31)); APF-driven amplitude transient $A=a\cos\theta$; large-injection lock characteristic $\sin\theta/(1+a\cos\theta)$; pulled spectrum with AM-lifted $k=0,2$ comb lines	[P4] Eq.(27),(31)–(34), p.2128–2130 (verified)	ISF-only vs. ISF+APF pull-in rates differ by a factor $(1+a)$; the lock characteristic becomes unbounded as $a\to1$ (a nonphysical zero-amplitude solution); AM makes the pulling spectrum grow mirror lines	toy (ideal LC, phase+APF quasi-static/first-order-lag model)

Key takeaways

• All 54 generated figures are fully traceable to script/function/parameters/formula/source, and none are orphaned (every one is embedded on at least 1 page). Except for phase_noise_to_jitter_integration.png, most are teaching toy/conceptual models; mos_level1_ring_isf.png and supply_pushing_ring.png are device-equation-level (MOS Level-1, not SPICE — closer to a real circuit than a toy).
• The 10 PDF figures are only cited and described, never redrawn; among them [P2] Fig. 17 (p.802) and [P4] Fig. 5 (p.2126) have been verified against the original PDFs.
• Embed syntax: ![description](/figures/<name>.png). Re-run: python scripts/run_all_sims.py.

Further reading

• Equation → derivation page → source: equation_index
• Paper roles: paper_summary_table
• Teaching-claims cross-reference: claims_cross_reference

v2 added simulation figures (Wave C)

Figure	Generated By	Formula Behind It	Source	Teaching Message	Toy?
rf_spectrum_phase_noise_sidebands.png	lab_10_rf_spectrum.py main	$v=\cos(\omega_0 t+\phi)$, FFT	[P1] Fig.8 concept	phase noise→carrier skirts	toy
monte_carlo_jitter_histogram.png	lab_11_monte_carlo_jitter.py main	$\sigma=\sigma_{edge}\sqrt{\Delta N}$	[P2] Eq.(8)	RJ Gaussian, grows as $\sqrt{\Delta N}$	toy
serdes_eye_ber_bathtub.png	lab_12_serdes_eye_ber.py main	BER bathtub (RJ)	standard SerDes	jitter→eye→BER	model
pll_cdr_jitter_transfer.png	lab_13_pll_cdr_transfer.py main	$\lvert H_{lp}\rvert^2,\lvert H_{hp}\rvert^2$	standard PLL	VCO high-passed / ref low-passed	model
cyclostationary_effective_isf.png	lab_14_cyclostationary_isf.py main	$\Gamma_{eff}=\Gamma\alpha$	[P1] cyclostationary	injection phase sets the rms	toy
nonlinear_oscillator_isf.png	lab_15_nonlinear_isf.py main	van der Pol	external (toy)	ISF is not always $-\sin$	toy
leeson_vs_isf_overlay.png	lab_16_leeson_vs_isf.py main	Leeson vs ISF	Leeson 1966 (external)	three-region comparison	model
design_tradeoff_sweeps.png	lab_17_design_sweep.py main	$\mathcal{L}\propto\Gamma_{rms}^2/q_{max}^2$	[P1] Eq.(21)	swing/Γrms/N curves	toy

v3 added figures (deepening)

Figure	Generated By	Formula Behind It	Teaching Message	Toy?
lorentzian_carrier_lineshape.png	lab_18_lorentzian.py	$S\propto D/(D^2+\Delta\omega^2)$	the carrier is Lorentzian, flattening near the carrier	model
allan_deviation.png	lab_19_allan.py / main	$\sigma_y(\tau)$ slopes: white FM $\propto\tau^{-1/2}$, flicker FM flat floor, RW FM $\propto\tau^{+1/2}$	time-domain fingerprint of FM noise	model
pll_noise_budget.png	lab_20_pll_budget.py	$S_{out}=\sum$ sources×transfer	PLL budget + optimal BW	model
cross_coupled_vco_isf.png	lab_21_topology_isf.py	tank vs tail effective ISF	tail $c_0,c_2$ upconversion (illustrative)	toy

v4 added figures (Wave-G backfill, 26 figures)

The 26 figures below were generated progressively after v3 but had not yet been logged in this page's table. Each was cross-checked against its generating script in simulations/ and its embedding page(s) in docs/. The classification continues section (a)'s columns (Generated By / Formula / Source / Teaching Message / Toy?), with the corresponding paper equation noted where applicable.

Figure	Generated By (script / function)	Formula Behind It	Source	Teaching Message	Toy?
allan_flicker_floor.png	lab_19_allan.py / verify_flicker_floor (with verify_sin4_integrals)	flicker-FM Allan floor $\sigma_y^2=2\ln2\cdot h_{-1}$; using the site's canonical example C $h_{-1}=8.11\times10^{-19}$, measures the ADEV floor against $\sqrt{2\ln2\,h_{-1}}=1.06\times10^{-9}$; a mixed white+flicker run verifies the knee $\tau_{knee}=1/(4\ln2\,f_c)=113\,\mu s$	standard stochastic-process math (external literature, not among the 5 PDFs)	the Allan variance floor is not just a slope — flicker floor has an exact closed-form constant	model
am_noise_spectrum.png	lab_28_am_noise.py / main	OU (Ornstein-Uhlenbeck) amplitude process $S_{a,2s}(\omega)=c\tau_0^2/(1+\omega^2\tau_0^2)$ vs Wiener phase $S_{\phi,2s}(\omega)=c/\omega^2$; $\tau_0=2Q/\omega_0$	[P4] Sec. III-F, p.2128 (verified on this site) + OU process (external: Uhlenbeck & Ornstein 1930)	amplitude noise converges (flat floor) due to the restoring force; phase noise diverges ($1/f^2$); the AM floor and PM asymptote meet at the corner $f_c=f_0/(2Q)$	model
aperture_jitter_snr.png	lab_30_aperture_jitter.py / main	ADC aperture jitter: $\text{SNR}_{jitter}=-20\log_{10}(2\pi f_{in}\sigma_t)$, $\text{ENOB}=(\text{SNR}-1.76)/6.02$; Monte-Carlo FFT verification using the site's canonical example C $\sigma_t=447.9$ fs	standard ADC theory (external: Kester MT-007; Walden JSAC 1999), not among the 5 PDFs	clock jitter directly eats into ADC SNR/ENOB; higher $f_{in}$ is more sensitive to jitter	model
asymmetry_corner.png	lab_33_asymmetry_corner.py / main	[P2] Appendix B (p.803) closed-form solutions Eqs.(52)-(57) for the asymmetric triangular ring ISF: $\Gamma_{rms}^2$, $\Gamma_{dc}$, $1/f^3$ corner $f_{1/f^3}$ vs asymmetry ratio $A=f'_{rise}/f'_{fall}$	[P2] Eqs.(52)-(57), p.803; a factor-of-2 convention gap vs [P1] Eq.(24) (flagged)	numerically verifies the [P2] Appendix B closed forms; the corner forms a symmetric V vs $A$ (symmetric in $\log A$)	toy ([P2] triangular approximation, not transistor-level; see lab_32 for how far real devices deviate)
clock_chain_budget.png	fig_clock_chain.py / main	clock-chain bookkeeping: reference flat floor, PLL ×N (in-band $+20\log_{10}N$), ÷N ($-20\log_{10}N$), buffer additive floor; integrated jitter for the whole chain	site canonical parameters (representative, not a specific silicon design), [P1] Eq.(21) "/4" SSB convention	one figure that shows the ×N/÷N/PLL/buffer noise/jitter addition rules at a glance	model (illustrative chain, not a specific design)
correlated_supply_selection.png	lab_34_correlated_supply.py / make_figure	[P2] Sec. VI, p.797, Eqs.(37)-(38): correlated supply noise summed across N phase-shifted per-stage ISFs leaves only the Fourier components $n=0\ (\mathrm{mod}\ N)$, forming an $N\cdot f_0$ selection comb	[P2] Eqs.(37)-(38), p.797; conceptually matches [P2] Fig. 11 (bench measurement)	correlated vs uncorrelated noise upconvert via different selection rules: correlated noise is folded to the carrier only near $k\cdot N f_0$	toy (per-stage ISF is a pedagogical triangle wave, not transistor-extracted)
device_noise_isf_bands.png	fig_device_noise_bands.py / main	ISF Fourier coefficients $c_n$ as the gains of a "frequency-converting receiver"; device-noise-PSD bands at DC / $f_0$ / $2f_0$ are each folded to the carrier by $c_0,c_1,c_2$	[P1] Eqs.(12),(13),(19),(23)	ISF harmonics = receive-channel gains; $c_0$ upconverts near-DC flicker, $c_1,c_2$ fold white noise near $f_0,2f_0$ down into the $1/f^2$ region	toy (illustrative asymmetric ISF, not transistor-extracted)
diffusion_dictionary.png	lab_23_diffusion_dictionary.py / main	diffusion-constant dictionary: $\kappa^2=\Gamma_{rms}^2 S_i/(2q_{max}^2)$ cross-checked four independent ways — phase-variance slope, Lorentzian FWHM, overlapping ADEV, $S_\phi(f)(2\pi f)^2/2$ plateau	[P2] Eq.(8)/(10)/(11)/(12), p.792-793	$\kappa$, $D$, linewidth, ADEV, and the $1/f^2$ coefficient are really the same number in different units	model (single ISF-weighted white-noise phase integral, not a specific circuit)
dual_dirac_bathtub.png	lab_31_dual_dirac.py / main	dual-Dirac jitter model: TJ=RJ(Gaussian)+DJ(bounded); Q-scale tail straight-line fit extracts $(DJ_{dd},\sigma)$; bathtub BER and $TJ_{@BER}=DJ_{dd}+2\,Q^{-1}(BER)\sigma$	industry standard (external: Fibre Channel MJSQ INCITS T11.2; PCIe/OIF-CEI), not among the 5 PDFs	dual-Dirac extrapolates TJ@BER from the deep tail's straight line; the model parameter $DJ_{dd}$ is smaller than the true peak-to-peak $DJ_{pp}$	model (standard DSP/statistical method, not an oscillator physics model)
flicker_lineshape.png	lab_29_flicker_lineshape.py / main (2x2 panels)	white-FM carrier lineshape is Lorentzian (FWHM=$D/\pi$); flicker-FM ($S_\phi\propto1/f^3$) has variance $\propto t^2\ln t$, giving a near-Gaussian line core; -10dB/-3dB half-width ratio: Lorentzian=3.00, Gaussian=1.8226	standard stochastic-process/linewidth theory (external literature)	white noise → Lorentzian, flicker → near-Gaussian core; the line shape itself can be used to infer the noise type	model
floquet_ppv_numeric.png	lab_25_floquet_numeric.py / main	van der Pol oscillator: monodromy matrix, Floquet multipliers, backward-integrated adjoint system extracting the periodic left eigenvector $v_1(t)$, whose component along the kicked axis is $\Gamma_{ppv}(\theta)/q_{max}=\omega_0 v_{1,y}(\theta)$	Floquet/adjoint/PPV theory (external literature: e.g. Demir 2000, not among the 5 PDFs), compared against the [P1] ISF definition	directly computes the adjoint/PPV ISF numerically; matches the impulse-extraction method and the harmonic-limit $-\sin\theta$ three ways	toy (van der Pol, not transistor-level; compare fig_isf_three_methods)
fom_limit.png	fig_fom_limit.py / main (2 panels)	FOM ceiling: $C_{ref}(T)=-10\log_{10}(kT\cdot1\text{Hz}/1\text{mW})$ (300K=173.83dB); general form $FOM=C_{ref}(T)-10\log_{10}(F_{eff})$; ring [P2] Eq.(23) $F_{eff}=(8/3\eta)(V_{DD}/V_{char})$; LC $F_{eff,LC}$ back-derived from [P1] Eq.(21)	[P1] Eq.(21), p.185; [P2] Eqs.(23),(25), p.796	FOM has a theoretical ceiling set by temperature and $F_{eff}$ (topology/process efficiency); the ring has a lower bound at $V_T=0$	model (LC/ring analytic formulas substituted in, not a specific circuit simulation)
htm_band_folding.png	fig_htm_bandfold.py / fig_htm_band_folding	harmonic transfer matrix of an LPTV system: ISF Fourier coefficients are the gain of each fold, $\tilde c_0=c_0/2$, $\tilde c_{\pm k}=(1/2)c_k e^{\pm j\theta_k}$; band-folding diagram + Toeplitz HTM heatmap	[P1] Eqs.(12),(13), p.183; the HTM framework is external literature (Zadeh 1950), not among the 5 PDFs	ISF harmonics are the complex gains an LTV system uses to fold any band to $f+kf_0$ — one figure shows every folding path	toy (illustrative teaching asymmetric ISF)
ilfd_lock_ranges.png	lab_37_ilfd_lock.py / main	[P4] Eq.(28)-(30), p.2129 M:N sub-/super-harmonic locking: $\omega_L=I_{inj}\vert G_N\vert/2$ (p.2130); beat frequency outside the lock range $\omega_b=N\sqrt{\Delta\omega^2-\omega_L^2}$ (Eq.34, p.2130)	[P4] Eqs.(28)-(30),(34), p.2129-2130	integrating the unaveraged time-synchronous phase ODE directly verifies that only the resonant N-th ISF harmonic can lock; a symmetric ISF ($c_2=0$) cannot divide by 2	toy (3-harmonic controllable ISF, illustrative)
impulse_phase_decomposition.png	fig_impulse_decomp.py / fig_impulse_decomp	ideal-LC state-plane geometry: a charge impulse causes a purely horizontal step $\Delta V=\Delta q/C$; its tangential component gives the permanent $\Delta\phi$, its radial component gives the decaying $\Delta A$; at a zero crossing the kick is almost purely tangential, at a peak almost purely radial	[P1] Eq.(9) charge→voltage step; Eqs.(10)-(11) phase impulse response	makes it geometrically obvious why the ideal LC's $\Gamma(\theta)=-\sin\theta$	toy (ideal lossless LC, small-signal limit)
injlock_noise_shaping.png	lab_26_injlock_noise.py / main	an injection-locked oscillator's phase noise is high-pass filtered (1st order): $\omega_c=\omega_L\cos\theta_{ss}=\sqrt{\omega_L^2-\Delta\omega^2}$; linearized to an OU process, $S_\theta(f)=S_n/(\omega_c^2+\omega^2)$ vs free-running $S_n/\omega^2$	[P3] Eqs.(30),(34)-(35),(38)-(40), p.2113-2115	a locked oscillator behaves like a first-order PLL: its own $1/f^2$ skirt is suppressed below $\omega_c$	model ([P3]'s verified deterministic pulling equation plus an added noise drive; the noise-shaping extension is this site's own)
isf_three_methods.png	fig_isf_three_methods.py / duel	[P1] Appendix (pp.192-193) three-method duel: Method A direct impulse measurement, Method B closed-form-from-waveform Eq.(37) $\Gamma=f'/(f'^2+f''^2)$, Method C first-order approximation Eq.(38) $\Gamma_i=f_i'/f'^2_{max}$, tested on a van der Pol oscillator	[P1] Eqs.(31)-(38), pp.192-193	all three methods agree near-harmonically ($\mu=0.2$); on a distorted waveform ($\mu=2.0$) Methods B/C degrade and only the impulse method (Method A) stays accurate	toy (van der Pol, same as lab_15/lab_25)
jitter_kernels_mc.png	lab_24_jitter_kernels.py / make_figure	three jitter kernels: TIE (kernel=1), N-period ($4\sin^2(\pi fNT)$), cycle-to-cycle ($16\sin^4(\pi fT)$), Monte-Carlo checked against closed forms under a single one-sided-$S_\phi$ convention	[P2] Eq.(8), p.792; Eq.(11)/(12), p.793 ($\kappa$ has no $\omega_0$)	the three jitter definitions correspond to three frequency-domain kernels; for white FM, $\sigma_{\Delta\phi}^2(N)=\kappa^2 NT$ holds exactly	model (standard DSP kernel integrals + Monte-Carlo, convention-focused)
jitter_two_regime.png	lab_24_jitter_kernels.py / make_figure_two_regime	two-regime jitter growth $\sigma(\Delta t)=\sqrt{\kappa^2\Delta t+\zeta^2\Delta t^2}$ ([P2] Fig.16, p.802; Eq.(8)/(9), p.792); mixed white+flicker FM simulation, slope transition 0.5→~1, corner $\Delta t_c=\kappa^2/\zeta^2$	[P2] Eq.(8)/(9), p.792; Fig.16, p.802	white noise dominates at short times ($\sqrt{\Delta t}$), flicker dominates at long times ($\propto\Delta t$); the corner maps to the frequency-domain $1/f^3$ corner	model
lock_acquisition.png	lab_36_lock_acquisition.py / main (2 panels + inset)	exact deterministic lock-acquisition solution of the Adler equation, $R(\theta(t))=R(\theta_0)e^{-\omega_c t}$ (matches the [P3] Eq.(39)-(40) pull-in frequency); noise-induced cycle slips via Kramers escape rate (external: Kramers 1940)	[P3] Eqs.(30),(33),(35),(39)-(40), p.2113-2115; Kramers/Risken/Ambegaokar-Halperin (external, not among the 5 PDFs)	lock acquisition critically slows near the edge ($T\sim1/\omega_c$); noise can occasionally make a locked oscillator "slip" a whole cycle	model (Adler equation + white-FM drive; the washboard potential is standard stochastic theory)
lock_characteristic_omega.png	fig_lock_characteristic.py / main	[P3] Eq.(33), p.2114 generalized Adler equation's lock characteristic $\Omega(\theta)$: sinusoidal injection → symmetric lock range, harmonic-rich injection → asymmetric lock range (an effect the plain Adler equation cannot show)	[P3] Eqs.(26),(33)-(35), p.2113-2114	lock range = the value-range width of $\Omega(\theta)$; a harmonic-rich ISF can make the lock range asymmetric	toy (illustrative harmonic-rich ISF and injection waveform; the ideal-LC case is exactly $-\sin$)
mos_level1_ring_isf.png	lab_32_mos_level1_ring.py / main	a 3-stage CMOS inverter ring, integrated directly in numpy using MOS Level-1 (Shichman-Hodges, $\lambda=0$) device equations; ISF extracted by the impulse method ([P1] Eq.(9) $\Delta V=\Delta q/C_L$ plus comparing perturbed vs unperturbed threshold-crossing times)	[P1] Eq.(9); ISF shape compared against [P2] Fig.5/Fig.6, p.793 and Eq.(16), p.794	an ISF extracted at the device-equation level (not SPICE) shows the [P2]-predicted dual-lobe shape (sensitive near transitions, ~0 near the rails)	device-eq (MOS Level-1 equation integration; closer to a real circuit than a toy, but not SPICE/BSIM)
optimal_injection_lock_range.png	lab_39_optimal_injection.py / main	[P3] Sec. VI, p.2119-2120: for a fixed rms injection current, Cauchy-Schwarz gives the optimal injection waveform $i^*_{inj}\propto\Gamma_{tilde}$ and the maximal lock range $\omega_L^*=I_{rms}\Gamma_{tilde,rms}$ (Eqs.43-45)	[P3] Eqs.(33),(43)-(45), p.2119-2120	a matched injection waveform (proportional to the ISF itself) beats a same-power sinusoidal injection's lock range; ~2.06x gain for a 17-stage ring (echoing [P3] Fig.19)	toy + [P2] App.B triangular ring model (not transistor-extracted)
pulling_spectrum.png	lab_27_pulling_spectrum.py / main	outside the lock range ($\vert\Delta\omega\vert>\omega_L$), integrating the Adler equation gives beat frequency $\omega_b=\sqrt{\Delta\omega^2-\omega_L^2}$ ([P4] Eq.34, p.2130); the output spectrum is a one-sided geometrically-decaying comb with ratio $r=\omega_L/(\Delta\omega+\omega_b)$ (external: Armand 1969)	[P3] Eq.(30), p.2113; [P4] Eq.(34), Sec. V-B, p.2130	the injection-pulling spectrum is a one-sided comb, asymmetric about the injection frequency; one sideband lands exactly at the injection frequency	model (deterministic Adler equation, RK4-integrated, noise-free to isolate the pulling comb)
supply_pushing_ring.png	lab_38_supply_pushing_ring.py / main	supply pushing $K_{push}=df_0/dV_{DD}$ of the MOS Level-1 3-stage ring: static sweep + dynamic small-signal $V_{DD}$ ripple, verifying the narrowband-FM prediction $\beta=K_{push}V_r/f_m$ and the Bessel sidebands $20\log_{10}(J_1(\beta)/J_0(\beta))$	circuit core reused from lab_32 (MOS Level-1, not SPICE); FM/Bessel sideband math is standard communications theory	supply noise directly frequency-modulates the oscillator; small-signal sideband amplitude matches the narrowband-FM Bessel formula	device-eq (same level as lab_32, not SPICE)
xcorr_floor.png	lab_35_xcorr_measurement.py / make_figure	cross-correlation phase-noise measurement: single-channel auto-spectrum is masked by instrument noise above the DUT floor; the cross-spectrum $\langle Y_1 Y_2^*\rangle$, averaged over M segments, has its uncorrelated residual fall as $1/\sqrt{M}$ (i.e. $-5\log_{10}M$ dB) while the DUT-correlated term does not decay	external measurement technique (not among the 5 PDFs); the underlying PSD/cross-spectrum statistics are standard DSP	cross-correlation measurement pushes instrument noise far below the single-channel floor, revealing the true DUT floor	model (standard DSP statistics, not an oscillator physics model)