What Is Phase Noise?
An ideal oscillator produces a pure sinusoid at frequency f₀. A real oscillator has random phase and amplitude fluctuations. Phase noise L(f) is the single-sideband (SSB) noise power in a 1 Hz bandwidth at offset frequency f from the carrier, normalized to the carrier power:
L(f) = P_noise(f₀ + f, 1 Hz BW) / P_carrier [dBc/Hz]
Typical specification: −100 dBc/Hz at 10 kHz offset for a 1 GHz VCO.
Leeson's Phase Noise Model
Leeson's empirical equation describes the phase noise spectrum:
L(f) = 10·log[ (2F·k·T/P_sig) · (f₀/2·Q·f)² · (1 + f_c/f) ]
Where:
| Symbol | Parameter | Typical Value |
|---|---|---|
| F | Amplifier noise figure (linear) | 2–10 |
| k | Boltzmann constant | 1.38×10⁻²³ J/K |
| T | Temperature | 290 K |
| P_sig | Oscillator output power | 1–10 mW |
| Q | Loaded Q of resonator | 10–1000 |
| f_c | Flicker corner frequency | 1–100 kHz |
Phase Noise Slope Regions
The phase noise spectrum has characteristic slope regions:
- 1/f³ region (−30 dB/decade): Close-in offsets dominated by flicker noise upconversion
- 1/f² region (−20 dB/decade): Main thermal noise region, dominates above flicker corner
- Noise floor: Far from carrier, amplifier thermal noise floor (−160 to −170 dBc/Hz)
Impact on RF System Performance
| System | Phase Noise Requirement | Critical Offset |
|---|---|---|
| GSM handset | <−121 dBc/Hz | 600 kHz |
| LTE BS LO | <−110 dBc/Hz | 1 MHz |
| Radar | <−130 dBc/Hz | 10 kHz |
| Satellite | <−100 dBc/Hz | 100 Hz |
Improving Phase Noise
- Maximize resonator Q (cavity > crystal > SAW > LC)
- Increase oscillator power level P_sig
- Reduce amplifier noise figure F
- Reduce flicker corner frequency with careful bias and device selection
- Use PLL with clean reference crystal to lock VCO
S-Parameter Relevance
Phase noise cannot be directly measured from S-parameter files, but RF View's group delay calculation (from S21 phase) relates to resonator bandwidth and hence Q. A narrow-band resonator (high Q, sharp S21 roll-off) predicts better phase noise performance in oscillator circuits.