Cross Correlation in Phase noise analysis

Phase noise is a property of an oscillator that can extend in magnitude from the carrier of several volts down to a mere nano-volt far from the carrier. In many cases the lowest noise OCXOs, SAWs and other specialty oscillators have carrier to noise ratios in excess of -180 dBc/√Hz. The noise level of these oscillators often extends below that of even the mixers and low noise amplifiers at baseband. Cross correlation is a method used in phase noise analysis to extend the range of any single channel measurement by introducing a second channel and utilizing signal processing to locate the noise that is common to the DUT, yet uncommon to each individual channel. With this method, a typical noise floor improvement of 20 dB is very realistic, allowing for high accuracy measurements of extremely low noise oscillators. This article presents the mathematics with an example of how cross correlation can accurately identify signals or noise that is below the level of the measurement instrument. Most phase noise measurement systems use what is called carrier cancellation. Phase noise is not measured directly, but down-converted to baseband. In an absolute phase noise measurement, where the absolute noise level of an oscillator is being measured, two oscillators are phase locked to one another. Once the two signals are locked with a mixer, the phase noise of both channels is down-converted directly to baseband without the carrier which is at DC and cancelled. In a residual or additive phase noise measurement, whereby the additive noise of a component such as an amplifier is to be measured, the oscillator is split into two parts. One path drives the LO port of the mixer while the other path goes through the DUT prior to going into the RF port of the mixer. Within the noise level and isolation of the mixer, the carrier and its noise are canceled, being common between the two paths, while the noise of the DUT is measured directly at an offset and its carrier frequency centered at DC. In both cases, low noise, low frequency techniques are then applied to amplify and sample this signal. However, in both cases, noise levels of system components may limit the measurement dynamic range or noise floor. In absolute measurements, the reference oscillator typically is the limitation. In additive measurements, even a very good mixer can often contribute as much noise as a low noise DUT. Cross correlation has been used by NIST for metrology level phase noise measurements for quite some time (see the references for more information or go to www.nist.gov). Through-