**What is Phase Noise?**

Wikipedia defines phase noise as, “the frequency domain representation of rapid, short-term, random fluctuations in the phase of a waveform, caused by time domain instabilities (jitter)”. The inclusion of the word noise in the name tells us that this does not refer to any spurious or deterministic terms. The mention of “short-term” in the definition is meant to distinguish from other ways to determine the cleanliness of a clock source such as stability in points per million, ppm. This is usually measured over a much longer timescale such as seconds or minutes.

Phase Noise information is usually presented in a log frequency plot such as the one shown below (Fig 1) where the amplitude units are dBc/Hz (decibels relative to the carrier power normalized to a 1Hz bandwidth). The x-axis is the frequency offset from the nominal signal or “carrier” frequency.

*Fig. 1*

For a more complete explanation of what phase noise is I recommend the application note, “Using Clock Jitter Analysis to Reduce BER in Serial Data Applications.”

**Why use an Oscilloscope?**

Before describing how to measure phase noise using an oscilloscope it would probably be a good idea to ask “why use a real time scope for this kind of measurement?” There are instruments dedicated to the measurement of phase noise such as the Keysight E5052B Signal Source Analyzer which have a much lower phase noise measurement floor than any oscilloscope. An SSA is also able to accurately measure much closer-in phase noise offsets and much quicker than any oscilloscope. However there are typically some measurement restrictions such as limits on the maximum frequency offset range available. 100 MHz is a typical maximum offset for a phase noise analyzer. For clock frequencies greater than 100 MHz it may be desirable to measure out to higher frequency offsets than can be measured with these tools. Also an oscilloscope can measure the phase noise transferred onto a data signal, not just on a clock.

An oscilloscope may also simply be good enough for the measurement requirements if your budget doesn’t allow for a dedicated instrument for measuring phase noise.

**Extracting the Phase**

An oscilloscope captures and digitizes the complete signal waveform and there is more than one way to extract the phase noise information from the digitized waveform. In this article we will briefly describe two methods:

- Clock Recovery
- Phase Demodulation using Vector Signal Analysis

**Phase Demodulation via Serial Data Clock Recovery**

Oscilloscopes measure timing variations (jitter) of a serial data or clock signal by analyzing where a signal crosses a voltage threshold and comparing that to the edges of some reference clock. In the case of phase noise we want the reference clock to be an ideal, constant frequency clock. Most modern oscilloscopes have clock recovery algorithms to extract a clock from the signal. In many cases it is desirable that the algorithm emulates a Phase Locked Loop (PLL) but in our case we simply want to extract a constant period ideal clock so that we do not “track out” any of the phase variations like a PLL would. An example of the setup of clock recovery is shown below. (Fig 2) The algorithm can be set to adjust to the nominal signal frequency and phase based on each captured acquisition.

*Fig 2*

A time interval error (TIE) measurement on an oscilloscope will produce a time series of the absolute time error of each edge relative to the ideal clock. To convert to phase (radians) error we simply multiply by *2*pi*f _{c}* where

*f*is the clock carrier frequency.

_{c}φ[rad]=2*π*TIE(t)*fc

A Time Interval Error trend can be transformed to frequency space with an FFT to give something called a Jitter Spectrum. Most modern oscilloscopes have this capability built in or as an option (Fig 3).

*Fig 3*

Averaging of the jitter power spectrum over multiple acquisitions is necessary to get a clean view of the measured phase spectral density.

The Jitter Spectrum approach yields a maximum frequency offset (*fφ*_{_}_{max}*)* equal to the carrier frequency itself (when both rising and falling edges are included in the TIE).

The minimum frequency offset (*fφ*_{_}_{min}*) *is principally bounded by the length of time of the TIE capture. I.e.: no frequency content is captured lower than the inverse of the time between the first edge in the TIE trend and the last.

Herein lies the difficulty with measuring phase noise on a real-time sampling oscilloscope. A high enough sampling rate must be maintained to accurately capture the edges in time, but in order to also get the low frequency content very large acquisition memory depths must be used to capture more time.

Example:

*SaRate* = 80 GSa/s

*fφ _{_}*

*= 100 Hz*

_{min}Required Memory Depth = 800 Mpts

Each acquisition must then be processed to find the edges using clock recovery, Fourier transformed to create the jitter spectrum and then multiple acquisitions must be averaged. The oscilloscope must have deep memory available and be able to process it quickly.

We now have the fundamental information contained in a phase noise measurement but ideally we’d like to have units of dBc/Hz as is common practice for these measurements. Also most phase noise plots have a log frequency scale to enhance the viewing of close-in phase noise offsets.

As an example if we set up the TIE measurement in units of seconds rather than radians then to convert to units of dBc we do the following:

However note that the phase noise above contains the energy from both sides of the carrier. Most often people think of the Single-Sideband (SSB) phase noise which is defined as the noise on a single side of the carrier spectrum & denoted by the use of the symbol L. Thus we must divide the above phase noise by 2 since L(*f** _{j}*) =

*0.5*S*

_{φ}(f*and also divide by the square root of the resolution bandwidth of the jitter spectrum to normalize to a 1Hz bandwidth.*

_{j})

Thus:

An example of such a measurement and conversion is shown below. (Fig. 4) This is a measurement of a very clean 100 MHz sine wave using a Keysight Infiniium DSAV334A oscilloscope in conjunction with an application called Infiniium Phase Noise. In addition to the averaging of the jitter spectrum, smoothing and spur removal techniques are employed in this application to get a better measure of the random phase noise floor.

* Fig. 4*

**Phase Demodulation via Vector Signal Analysis**

Vector Signal Analysis software such as the Keysight 89600B can use a variety of hardware to acquire data including real-time oscilloscopes. Analog Phase Demodulation algorithms work differently than serial data clock recovery but with a very similar outcome.

Shown in Fig 5 is a high-level block diagram of how the phase demodulation is performed in the 89600B VSA software. An ideal local oscillator (LO) is mixed mathematically with 2 copies of the digitized signal – one of which is 90 degrees out of phase with the other. The resultant signals are then low-pass filtered to remove the high-frequency mixing products and leave just the phase (and frequency) error. This can then be displayed in many formats including the phase spectrum.

*Fig 5*

The VSA PM demodulation algorithm has optional automatic carrier frequency and phase tracking algorithms as shown below (Fig. 6):

*Fig. 6*

The auto-carrier frequency algorithm adjusts the clock frequency to the measured nominal signal clock frequency rather than the value input by the user (just like the serial data clock recovery). This frequency is re-calculated for each new waveform acquisition.

The auto-carrier phase algorithm also adjusts to the nominal phase of the incoming signal on each acquisition.

Below (Fig. 7) is a measurement of the same clean 100 MHz sine wave with the same DSAV334A oscilloscope but using the VSA software to control the scope acquisition, demodulate the phase and average the phase noise spectrum. There is excellent agreement between the two phase demodulation techniques.

*Fig. 7*

**Summary**

Different algorithms can be applied to digitized waveforms acquired by real-time oscilloscopes in order to recover the phase noise information and thus present phase noise plots. There are tradeoffs between the techniques which are outside the scope of this article but we can conclude that it is both possible and useful to be able to make phase noise measurements with an oscilloscope if the need arises. In part 2 of this article, we will explore tradeoffs and accuracy of using a real-time oscilloscope for these kinds of measurements.

Questions? Visit the Infiniium phase noise forum.