RF Theory › Phase Noise

Phase Noise

Phase noise is the random, short-term fluctuation of an oscillator's output frequency — measured as single-sideband (SSB) noise power relative to the carrier, in dBc/Hz at a given offset. It limits receiver selectivity, transmitter spectral purity, and EVM in every radio system.

01 — Definition

What is Phase Noise?

An ideal oscillator produces a pure sinusoid at exactly f₀. A real oscillator produces a signal whose instantaneous phase θ(t) = 2πf₀t + φ(t), where φ(t) is a small, random noise process. This random phase modulation spreads energy from the carrier into the sidebands — visible on a spectrum analyser as a "skirt" around the carrier peak.

L(f) — The Phase Noise Specification

Phase Noise Definition
L(f) = Pnoise(f₀+f, 1 Hz BW) / Pcarrier   [dBc/Hz]

Example: L(10 kHz) = −120 dBc/Hz means the noise power in a 1 Hz band at 10 kHz offset is 120 dB below the carrier.

Integrated phase noise (rad²) = ∫f1f2 2·L(f)·df
RMS phase error (°) = √(integrated noise) × 180/π

Phase Noise Spectrum Regions

Figure 1 — Typical VCO phase noise spectrum. Four regions: 1/f³ (−30 dB/dec) close-in flicker, 1/f² (−20 dB/dec) white FM noise, 1/f (−10 dB/dec) white phase noise, and flat noise floor. The flicker corner fc separates 1/f³ from 1/f².
RegionSlopeNoise SourceTypical Offset
1/f³−30 dB/decadeFlicker noise upconverted to FM<1 kHz from carrier
1/f²−20 dB/decadeWhite noise upconverted to FM — resonator thermal noise1 kHz – 1 MHz
1/f−10 dB/decadeWhite phase noise — direct thermal additionAbove resonator BW/2
FloorFlatThermal noise floor: −174 + NF dBm/Hz normalised to carrierFar offsets
02 — Leeson's Equation

Leeson's Equation

Leeson's Phase Noise Model
L(f) = 10·log₁₀ { (FkT/2Ps) · [1 + (f₀/2QLf)²] · (1 + fc/f) }

F = oscillator noise figure (linear) · k = 1.381×10⁻²³ J/K · T = 290 K
Ps = signal power (W) · f₀ = carrier freq · QL = loaded Q · fc = flicker corner

Each Term Explained

FkT/2Ps — white noise floor. Lower NF and higher signal power both improve it.
[1 + (f₀/2Q_L·f)²] — resonator transfer. Inside resonator half-BW, noise rises as 1/f². Higher Q = narrower BW = lower phase noise.
(1 + fc/f) — flicker term. Si BJT fc ≈ 1–10 kHz. GaAs pHEMT fc ≈ 1–10 MHz.

Worked Example — 10 GHz VCO

VCO: f₀=10 GHz, Q_L=30, F=10 dB, Ps=1 mW, fc=100 kHz

White noise floor: FkT/2Ps = 10×4×10⁻²¹/(2×10⁻³) = 2×10⁻¹⁷ = −167 dBc/Hz

Resonator half-BW: f₀/2Q_L = 10G/(2×30) = 166.7 MHz

Offset fL(f)
10 kHz−71 dBc/Hz (1/f³ region)
100 kHz−100 dBc/Hz (flicker corner)
1 MHz−123 dBc/Hz (1/f² region)
10 MHz−143 dBc/Hz
The single biggest lever: Q_L² appears in the denominator. Doubling Q_L improves phase noise by 6 dB at all offsets inside the resonator bandwidth.
03 — Figure of Merit

Oscillator FOM

Oscillator FOM
FOM = L(f) − 20·log₁₀(f₀/f) + 10·log₁₀(Pdc/1mW)   [dBc/Hz]
Better FOM = more negative. State of the art: −185 to −195 dBc/Hz
Oscillator TypeTypical L(1 MHz)Use Case
Crystal OCXO−170 dBc/Hz @100 HzGPS, atomic clock reference
MEMS oscillator−155 dBc/Hz @1 kHzCrystal replacement
LC VCO (silicon)−130 dBc/HzPLL in WiFi, cellular
LC VCO (GaAs)−120 dBc/HzMicrowave synthesisers
DRO−140 dBc/HzSatellite LNB, microwave links
YIG oscillator−130 dBc/HzWideband sweep, test equipment
04 — PLL Phase Noise

PLL Phase Noise

In-Band vs Out-of-Band

PLL Phase Noise Regions
Inside loop BW (f < floop): Lout(f) ≈ Lref(f) + 20·log₁₀(N)
Outside loop BW (f > floop): Lout(f) ≈ LVCO(f)
The fundamental PLL trade-off: Wider loop BW suppresses VCO noise but lets more reference noise through. Optimum BW is where L_ref(f)+20·log(N) = L_VCO(f).

PLL Noise Budget — 2.4 GHz Synthesiser

f_ref=10 MHz TCXO, f_out=2400 MHz, N=240, f_loop=100 kHz

Reference multiplication: 20·log₁₀(240) = 47.6 dB

TCXO L(100 kHz) = −155 dBc/Hz → output: −155+47.6 = −107 dBc/Hz

VCO at 100 kHz: −120 dBc/Hz → optimum crossover ≈ 100 kHz ✓

Integrated jitter (1 kHz–10 MHz): ≈ ~1.2 ps RMS @ 2.4 GHz

05 — System Impact

Impact on System Performance

Phase Noise → EVM

Phase Noise → EVM
EVM²PN ≈ 2 · ∫−BW/2+BW/2 L(f) df   (linear)
For flat L₀ over BW: EVMPN ≈ √(2·L₀·BW) × 100%
ModulationMax EVML(f) budget (20 MHz BW)
64-QAM8.0%−123 dBc/Hz
256-QAM3.5%−130 dBc/Hz
1024-QAM (WiFi 6)1.5%−138 dBc/Hz

Reciprocal Mixing

Reciprocal Mixing Noise
NRM = Pblocker + L(Δf) + 10·log₁₀(BWIF)   [dBm]

Example: Blocker −30 dBm, Δf=10 MHz, L=−150 dBc/Hz, BW=200 kHz:
NRM = −30+(−150)+53 = −127 dBm — OK vs sensitivity −110 dBm ✓
Reciprocal mixing is why LO phase noise specs matter for adjacent channel selectivity. A noisy synthesiser can desensitise a receiver even when all amplifier and filter specs are met.
06 — Measurement

Phase Noise Measurement

MethodFloorNotes
Direct spectrum (SA)~−120 dBc/HzSimple; analyser LO limits floor
Phase detector / PLL<−175 dBc/HzNeeds clean reference at same freq
Cross-correlation~−185 dBc/HzTwo analysers; slow; expensive
Delay line discriminatorModerateSelf-referenced; poor at close offsets
07 — Design Rules

Phase Noise Thumb Rules

Rule 01
Double Q_L → −6 dB phase noise
Q_L² in Leeson's denominator. Biggest lever for oscillator designers.
Rule 02
+3 dB power → −3 dB phase noise
Noise floor FkT/2Ps improves linearly with signal power.
Rule 03
×10 frequency → +20 dB phase noise
Leeson scales as f₀². Frequency multiplication: ×N → +20·log(N) dB.
Rule 04
PLL in-band = ref + 20·log(N)
Reference noise multiplied by divide ratio N at PLL output.
Rule 05
−20 dB/decade = thermal FM noise
Improving Q or power helps. Changing transistor type does not.
Rule 06
GaAs fc >> Si BJT fc
Si BJT fc ≈ 1–10 kHz. GaAs pHEMT fc ≈ 1–10 MHz. Prefer Si BJT for close-in phase noise.
ApplicationCritical OffsetRequired L(f)
5G NR FR1 256-QAM1 MHz≤ −130 dBc/Hz
WiFi 6 1024-QAM1 MHz≤ −128 dBc/Hz
LTE UE TX1 MHz≤ −136 dBc/Hz
FMCW Radar LO100 kHz≤ −110 dBc/Hz
GSM base station400 kHz≤ −143 dBc/Hz
PLL Theory → Oscillator Design → RF Noise Theory → EVM & Modulation →

Phase Noise in RF and Microwave Systems

Phase noise is the random frequency fluctuation of an oscillator output, measured as single-sideband noise power relative to the carrier at a given offset frequency. It limits the sensitivity of radar receivers, the spectral purity of transmitters, the EVM of digital radios, and the minimum detectable velocity in Doppler systems.

Why Phase Noise Matters for 5G and WiFi

Modern wireless standards use high-order QAM — 256-QAM for 5G NR and 1024-QAM for WiFi 6 (802.11ax). Phase noise from the local oscillator rotates constellation points randomly, degrading EVM. A synthesiser with L(f) = −128 dBc/Hz integrated over 20 MHz contributes about 0.5% EVM — the single largest contributor in most radio architectures.

Leeson's Equation and the Role of Resonator Q

Leeson's equation shows that phase noise scales inversely with Q² — doubling the resonator Q reduces phase noise by 6 dB. This is why crystal oscillators (Q = 10⁵–10⁶) have vastly better phase noise than LC oscillators (Q = 10–100) at the same power level.