How do I measure the phase noise of an oscillator using a cross-correlation technique?
Cross-Correlation Phase Noise Measurement
Cross-correlation is the gold standard for measuring ultra-low phase noise sources because it overcomes the fundamental limitation that the measurement system noise floor must be below the DUT phase noise.
| Parameter | SOLT Cal | TRL Cal | eCal |
|---|---|---|---|
| Accuracy | Good | Excellent | Good-very good |
| Standards Needed | 4 (S,O,L,T) | 3 (T,R,L) | 1 (module) |
| Bandwidth | Broadband | Band-limited | Broadband |
| Setup Time | 5-10 min | 10-20 min | 1-2 min |
| Best For | Coaxial, general | On-wafer, waveguide | Production, speed |
Calibration Procedure
A direct phase noise measurement (single-channel) is limited by the phase noise of the reference oscillator: if the reference has -150 dBc/Hz at 10 kHz offset, the measurement floor at 10 kHz is -150 dBc/Hz (cannot distinguish DUT noise from reference noise). Cross-correlation overcomes this: (1) Two independent reference channels: each has its own LO, mixer, and ADC. The LO noise in channel 1 is independent of the LO noise in channel 2. (2) The DUT noise is common to both channels (it comes from the same source, split by a power divider). (3) Cross-correlation: multiply the two channel outputs and average. The DUT noise (correlated) adds coherently: amplitude grows as N. The reference noise (uncorrelated) adds randomly: amplitude grows as sqrt(N). (4) After N correlations: the effective measurement floor is: L_floor = L_reference - 5×log10(N) dBc/Hz. For L_reference = -150 dBc/Hz and N = 100,000: L_floor = -150 - 25 = -175 dBc/Hz. The measurement time: T = N × (1/f_offset) for the lowest offset frequency. For f_offset = 10 Hz and N = 100,000: T = 100,000 / 10 = 10,000 seconds ≈ 2.8 hours. For f_offset = 10 kHz: T = 10 seconds. The cross-correlation time increases dramatically at lower offset frequencies because the FFT segment length = 1/f_offset.
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
- Interface compatibility: verify impedance, connector type, and mechanical form factor match the system architecture
Error Sources
(1) Reference oscillator selection: the two reference oscillators should have phase noise at least 10-20 dB below the channel noise floor to avoid systematic errors. In practice: use two identical high-quality oscillators (OCXO, sapphire, or hydrogen maser). Even if each reference has the same phase noise as the DUT: the cross-correlation will eventually converge to the DUT phase noise (just takes more correlations). (2) Power divider: the splitter at the DUT output must provide equal power to both channels with good isolation (> 20 dB) to prevent crosstalk between channels. A degraded isolation creates a correlated leakage path that does not average out, setting a hard measurement floor. (3) ADC requirements: the ADC must have sufficient dynamic range to capture both the carrier (strong) and the phase noise (very weak). For phase noise at -170 dBc/Hz in a 1 Hz bandwidth: the noise is 170 dB below the carrier. A 16-bit ADC has 96 dB dynamic range: the noise is below the ADC quantization floor by 74 dB. The cross-correlation must bring this up. Alternatively: use an analog mixer to downconvert to baseband (removing the carrier) before the ADC, which provides much better dynamic range for the noise sideband. This is the standard approach in dedicated phase noise analyzers.
Frequently Asked Questions
How many correlations do I need?
The number of correlations depends on how far below the single-channel noise floor you need to measure: 10 dB below: N = 100. 20 dB below: N = 10,000. 30 dB below: N = 1,000,000. 40 dB below: N = 100,000,000 (impractically long for most measurements). For a practical example: measuring -170 dBc/Hz at 10 kHz offset from a 100 MHz OCXO. Single-channel floor: -155 dBc/Hz at 10 kHz (using a good quality reference OCXO). Required improvement: 15 dB → N = 10^(15/5) = 1000 correlations. At 10 kHz offset: T = 1000 / 10000 = 0.1 seconds per correlation × 1000 = 100 seconds ≈ 2 minutes. This is very practical.
What is the advantage over PLL-based phase noise measurement?
PLL-based (phase-locked loop) method: locks a clean reference to the DUT using a PLL, and measures the PLL error voltage (which represents the phase difference). Advantages: simple, one reference needed. Limitations: the reference must have better phase noise than the DUT (by at least 10-20 dB). The PLL bandwidth limits the measurement range (cannot measure at offsets within the PLL bandwidth). Only one PLL time constant can be set, creating a gap in the measurement near the PLL bandwidth. Cross-correlation advantages: no need for a reference better than the DUT (the cross-correlation process separates DUT noise from reference noise). No PLL bandwidth limitation (measures all offset frequencies simultaneously using FFT). Achieves measurement floors of -175 to -185 dBc/Hz (unachievable with PLL methods). The cross-correlation method is universally preferred for precision phase noise measurement.
Can I measure phase noise with a spectrum analyzer?
Yes, using the direct spectrum method: (1) Set the SA center frequency to the DUT carrier frequency. (2) Use a narrow RBW (10 Hz to 1 kHz). (3) Measure the power spectral density at the desired offset: L(f_offset) = P_sideband(dBm/Hz) - P_carrier(dBm). Limitations: (1) The SA LO phase noise must be better than the DUT. The SA LO phase noise is typically -100 to -120 dBc/Hz at 10 kHz offset, which limits the measurement to DUTs with phase noise worse than this. (2) The SA cannot distinguish AM noise from PM noise (measures both). (3) The SA calibration accuracy for noise power density is ±1-2 dB at best. For quick, approximate phase noise measurement: the SA method is acceptable. For precision measurement: use a dedicated phase noise analyzer or cross-correlation system.