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

Chinese–English Glossary

See also: notation (rigorous symbols and units), math_identities (math toolbox), references (source codes [P1]–[P5], external [E1]–[E4])

The biggest friction when reading English papers alongside Chinese teaching pages is "one concept, two languages." This page pairs the site's terminology Chinese–English, each with one line of Chinese intuition (not a rigorous definition, just "get the feel first") plus the page it comes from. Click through for depth.

How to use this page: when you hit an unfamiliar term on some page, come back here, scan a one-liner, then decide whether to click through to the source page for detail. For rigorous symbols and units, cross-reference notation. Terms marked (external) mean they are not among the five downloaded PDFs, supplemented from standard literature.

Core ISF terminology

English	Chinese	One-line intuition	Source page
ISF (Impulse Sensitivity Function)	脈衝敏感度函數	The oscillator's "phase-sensitivity weighting" to noise — tells you "kick it at this phase of the waveform, and this much phase results." Dimensionless, $2\pi$ -periodic.	isf_definition
excess phase	多餘相位 $\phi(t)$	The deviation beyond the ideal phase $\omega_0 t$ ; both phase noise and jitter live here.	impulse_to_phase_shift
phase noise	相位雜訊	Random jitter of the oscillator signal's phase, appearing in the frequency domain as skirts on either side of the carrier.	white_noise_to_phase_noise
timing jitter	時間抖動	The time-domain statement of the same thing: the random error of when an edge actually occurs relative to ideal.	psd_phase_noise_jitter
phase perturbation	相位擾動	The component of noise that pushes the state point "tangent to the limit cycle"; no restoring force, it persists forever.	phase_vs_amplitude_noise
amplitude perturbation	振幅擾動	The component of noise that pushes the state point "radially"; a restoring mechanism pulls it back, does not persist.	phase_vs_amplitude_noise
limit cycle	極限環	The closed trajectory the oscillator circles in steady state in state-space; phase = how far along the cycle, amplitude = how far off the cycle.	oscillator_phase

System and noise properties

English	Chinese	One-line intuition	Source page
LTI (Linear Time-Invariant)	線性非時變	Impulse response depends only on "how long ago" $t-\tau$ ; the oscillator's response to noise is not LTI.	math_identities
LTV (Linear Time-Variant)	線性時變	Impulse response also depends on "when you kick it" $\tau$ — the same impulse has different effect at different phases, which is exactly the spirit of the ISF.	convolution_derivation
cyclostationary noise	週期穩態雜訊	The noise strength itself varies periodically with the oscillation period (the device does not leak noise at every instant equally).	effective_isf
noise-modulating function (NMF) $\alpha(\omega_0 t)$	雜訊調變函數	A periodic function with $0\le\alpha\le1$ describing "when the device is leaking noise"; multiplied by the ISF gives the effective ISF.	effective_isf
white noise	白噪	Noise whose PSD is frequency-independent (autocorrelation is a delta); converted by the ISF integrator into $1/f^2$ phase noise.	white_noise_to_phase_noise
flicker noise (1/f noise)	閃爍雜訊／ $1/f$ 雜訊	Device noise with large low-frequency energy; only upconverted through the ISF's $c_0$ into close-in $1/f^3$ phase noise.	flicker_noise_upconversion
upconversion	上轉（頻率搬移）	The ISF acts like a mixer, moving device noise at low frequency (or near $n\omega_0$ ) up to near the carrier as phase noise.	fourier_series_of_isf

Fourier and statistical quantities

English	Chinese	One-line intuition	Source page
rms / effective ISF	rms ISF $\Gamma_{rms}$ / 有效 ISF $\Gamma_{eff}$	$\Gamma_{rms}$ is the rms of the ISF, directly setting the size of $1/f^2$ phase noise; $\Gamma_{eff}=\Gamma\cdot\alpha$ folds in cyclostationarity.	rms_isf
$q_{max}$	最大電荷擺幅	The nodal charge swing $=C\cdot V_{max}$ , used to normalize the ISF; larger means lower phase noise.	impulse_to_phase_shift
$c_0$ (DC ISF coefficient)	ISF 的 DC 係數	The key controlling $1/f$ upconversion; the ISF's DC value $=c_0/2$ . For a symmetric waveform $c_0\approx0$ .	symmetry
Fourier series / coefficients $c_n,\theta_n$	傅立葉級數／係數	Decomposes the $2\pi$ -periodic ISF into DC plus harmonics; the $n$ -th harmonic moves noise near $n\omega_0$ .	fourier_series_of_isf
PSD (Power Spectral Density)	功率譜密度	Noise power per unit bandwidth; $S_i$ (A²/Hz), $S_\phi$ (rad²/Hz). Integrating over frequency gives variance.	psd_phase_noise_jitter
SSB phase noise $\mathcal{L}(\Delta f)$	單邊帶相位雜訊	Phase-noise power relative to the carrier, in a single sideband, per Hz; $\approx\frac12 S_\phi$ .	psd_phase_noise_jitter
dBc/Hz	分貝（相對載波）每赫茲	The unit of $\mathcal{L}$ : "c" = relative to carrier, "/Hz" = per unit bandwidth, taking $10\log_{10}$ .	math_identities

Oscillator types and advanced concepts

English	Chinese	One-line intuition	Source page
ring oscillator	環形振盪器	$N$ inverter stages in a ring; ISF is concentrated at the transition, $\Gamma_{rms}\propto N^{-3/2}$ .	lab_03
LC oscillator	LC 振盪器	Tank resonance, near-sinusoidal waveform; ideal ISF $=-\sin\theta$ .	lab_02
accumulated jitter	累積（長期）jitter	An open-loop oscillator has no absolute time reference, so its error grows like a random walk $\sigma_{\Delta t}=\kappa\sqrt{\Delta t}$ .	lab_03
injection locking / pulling	注入鎖定／拉扯	An injected external signal "pulls" the oscillator's frequency toward it; the same ISF also governs this phenomenon (generalized Adler).	paper_003_injection_locking_part1
APF (Amplitude Perturbation Function) $\Lambda(\phi)$	振幅擾動函數	What the ISF is to phase, the APF is to amplitude; unit 1/A. Orthogonal (in quadrature) to the ISF in an ideal LC.	paper_004_injection_locking_part2
Adler's equation	Adler 方程	The first-order differential equation describing the injection-locked phase difference (1946); the ISF generalizes it to arbitrary waveforms.	paper_003_injection_locking_part1

Rigorous mathematical foundations (external literature)

English	Chinese	One-line intuition	Source page
PPV (Perturbation Projection Vector)	擾動投影向量 (external)	The rigorous generalization of the ISF: the vector projecting a perturbation onto the phase direction; corresponds to the theory of Demir et al. 2000. Not among the five source PDFs.	effective_isf
adjoint method	伴隨法 (external)	A numerical method for computing the PPV/ISF from the periodic steady-state solution (solving the adjoint system). Not among the five source PDFs.	effective_isf
Floquet theory	Floquet 理論 (external)	Stability theory for linear systems with periodic coefficients; gives the mathematical foundation of the PPV. Not among the five source PDFs.	effective_isf
Wiener–Khinchin theorem	維納–辛欽定理 (external)	The PSD is the Fourier transform of the autocorrelation function; connects time-domain and frequency-domain noise. A standard stochastic-process theorem.	math_identities
Leeson model	Leeson 模型 (external)	The 1966 empirical phase-noise model; the ISF theory subsumes it as a special case. Not among the five source PDFs.	references

One-line reminders (the pairs most often confused)

phase noise vs timing jitter: the same thing, the former in the frequency domain (dBc/Hz), the latter in the time domain (fs); interconvert via $\sigma_t=\sigma_\phi/(2\pi f_0)$ .
phase perturbation vs amplitude perturbation: phase stays, amplitude gets pulled back — which is why phase noise is the star of the show.
LTI vs LTV: the difference is whether the impulse response depends on the absolute time $\tau$ ; the oscillator is LTV.
$c_0$ vs the $1/f^3$ corner: $c_0$ determines whether flicker upconverts at all; the $1/f^3$ corner $=\omega_{1/f}(c_0/c_1)^2$ , is not equal to the device's $\omega_{1/f}$ .
device $1/f$ corner $\omega_{1/f}$ vs phase-noise $1/f^3$ corner $\Delta\omega_{1/f^3}$ : two different things, do not confuse them (see flicker_noise_upconversion).

Core ISF terminology​

System and noise properties​

Fourier and statistical quantities​

Oscillator types and advanced concepts​

Rigorous mathematical foundations (external literature)​

One-line reminders (the pairs most often confused)​

Further reading​