Phase Noise Measurement Application using Modular Instruments

Phase Noise Measurement Application using Modular Instruments
Authors:
Jorge Martins, National Instruments
Ed Loewenstein, National Instruments
Abstract
The measurement of phase noise is a common requirement to evaluate the quality of many
modern products that use clocks or oscillators. Efficient and cost-effective measurement
techniques help product development, manufacturing, and field service. As a designer of highend RF instruments, National Instruments is challenged with validating the phase noise
capabilities of its own instruments in development, V&V, and production.
The best phase noise measurement performance is achieved by using cross-correlation
techniques. Many T&M manufacturers implement these techniques, in one form or another, to
produce some of the best phase noise test instruments available in the market today.
If adequate instruments are available, why bother to develop our own phase noise measurement
solution to test and manufacture our products? As with most manufacturing solutions, the cost of
purchasing and maintaining existing solutions were considered. We found that outfitting
complete development and manufacturing facilities would be very costly using available, off-theshelf systems. In addition to lowering the cost by developing our own systems, we took the
opportunity to improve measurement uncertainty and the control software interface.
While the hardware is the body of this application, the software is the heart and brain that allows
us to achieve what we believe is a state-of-the-art phase noise measurement system. As with
most dedicated modular instrument applications, software expertise and mastering the
measurement mathematics are required, but we believe that the results are worth the effort. An
evolving system, the instrument is currently in use at National Instruments.
In this paper we will share an overview of our implementation of a dedicated, cross-correlation
phase noise test set, built with discrete modular instruments. Preliminary measurement results,
and an explanation of how the instrument compares in cost and performance to other instruments
is discussed.
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Learning objectives
 Review the basic concept of what is single sideband phase noise (SSB phase noise) and
why it is important to characterize it on an instrument.
 Overview of the most common methods of measuring this parameter and discuss their
respective advantages and weaknesses.
 Present our approach to the development of a budget cross-correlation test system with
measurement performance that is comparable to the best units available on the market
today. Examine the tradeoffs we had to make and the results we have obtained with this
system.
1. Phase noise basic concepts
The term “phase noise” refers to the effects of random or deterministic phase fluctuations on an
otherwise stable periodic signal. Phase noise should not be confused with frequency stability,
which is a measure of how well a signal source maintains its frequency over a period of time,
although frequency fluctuations can be described in terms of phase noise. Conceptually, a perfect
sine-wave signal source does not have any phase noise and can be described in the following
form:
Where:
V0 = nominal amplitude of the signal
V (t )  V0 sin(t )
ωt = 2πf0t = instantaneous signal phase
f0 = nominal frequency of the signal
Real signals, however, are subject to variations in both phase and amplitude:
Where:
V (t )  V0   (t )sint   (t )
ε(t) = amplitude variation of the signal
Δφ(t) = phase variation of the signal
The term Δφ(t) includes two different types of phase variation: discrete (deterministic), and
random. The first may be caused by AC hum, vibration, signal leakage, or any of a number of
other periodic sources and shows up as discrete lines on a spectrum analyzer or phase noise
analyzer. The random component, characterized as phase noise spectral density, is mainly caused
by thermal and flicker noise generated in a source’s electronic components and is displayed on a
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spectrum analyzer or phase noise analyzer as a continuous curve. An illustration of these
components is shown in Figure 1.
Power
Random Noise
Spurious Signals
Frequency
f0
Figure 1. Spectrum analyzer representation of both phase variation components
The usual way of characterizing phase noise is by single-sideband (SSB) noise density, which
provides a measure of the noise’s power spectral density within a given bandwidth (BW) located
at a frequency offset f from the signal carrier frequency:
2
rms
S( f ) 
[rad 2 /Hz] ,
BW
2
where Δφrms
represents the phase noise power within the band at f.
The usual bandwidth is chose to be BW = 1 Hz.
In their specifications, equipment and component manufacturers describe the phase noise
characteristics of their products by referring the measured noise density to the signal carrier level
itself, since the absolute noise power normally goes up and down with the signal power. Thus,
SSB phase noise is specified in dBc/Hz at given frequency offsets from the carrier. It is the ratio
of the noise power measured on a sideband over a bandwidth of 1 Hz at a specific frequency
offset from the carrier (foffset) to the total signal power and is represented in dBc/Hz. Figure 2
shows a graphic representation of these concepts.
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Power
PS
SC
1 Hz BW
PSSB
foffset
f0
Frequency
Figure 2. SSB phase-noise–to-carrier ratio
In most cases, manufacturers specify the SSB phase noise of their products at different offsets
from the carrier at discrete frequencies or in plot form, as illustrated in Fig. 3.
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Figure 3. SSB Phase noise plot of a PXIe Vector Signal Analyzer
2. Phase noise typical measurement methods
Many papers have been written describing different techniques of making phase noise
measurements of signals. One classic method uses a single mixer as a phase detector. It, in turn,
is driven by the DUT signal source and an LO source which is phase-locked to the DUT using
the phase detector’s output signal. The output of the phase detector is then filtered by a low pass
filter, amplified with a low noise amplifier, and measured with an FFT or spectrum analyzer.
DUT
Low Noise
amplifier
Mixer
LP filter
FFT or
Spectrum
Analyzer
LO
PLL
Figure 4. Single channel SSB phase noise test method
The achievable noise floor of this method is dominated by the phase noise of the tunable LO and
is also limited by the characteristics of the mixer, filter, and amplifier. If the noise contributed by
these components is not significantly lower than the noise of the DUT, then the system will for
all practical purposes be measuring its own noise rather than the DUT.
To overcome these limitations, the cross-correlation method was developed. It uses two identical
single-channel systems to drive a cross-correlation analyzer. The DUT signal is split into two
identical copies, which are mixed with independent LOs. The signal in each channel is then
filtered and amplified before being fed to the cross-correlation analyzer. The noise introduced by
each channel’s components is uncorrelated with the noise introduced by the other channel and
with the DUT signal, and thus averaging a sufficient number of cross-spectra can eliminate both
channels’ noise. Theoretically, the resulting residual correlated noise is only the actual noise of
the DUT, although in practice system imperfections may allow small amounts of other noise to
leak in.
The cross-correlation method has been around for a long time, but originally it was timeconsuming and very expensive to implement. This method requires a large number of averages
of the two channels to be able to cancel the incoherent noise of each channel, which requires
processing enormous amounts of data.
Recent developments in digital signal processing (DSP) techniques and data processing speed
have allowed the development of cross-correlation phase noise analyzers that have reasonably
fast measurement speed and extremely low noise floors, but still with a price tag of more than
$100k.
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3. Cross-correlation phase noise implementation overview
Due to the increased demand for test speed, low noise, and test capacity in our manufacturing
test systems, we decided to replace our current manufacturing test stations. A project team was
formed to evaluate the available measurement instruments, our test requirements, and the
investment needed to overhaul our test stations. The conclusion of this working group was that
the commercially available phase noise test systems’ up-front investment and yearly
maintenance costs were not acceptable. The team recommendation was simple: develop an inhouse, high-performance SSB phase noise test system with the following characteristics:







Very low noise floor
High measurement speed
Automatic measurements
Relative low cost
Customizable for different frequency ranges
Low measurement uncertainty
Low maintenance costs
To meet these apparently conflicting requirements the development team made these critical
decisions:





Employ a cross-correlation technique
Use a high-speed analyzer
Develop dedicated software
Use mostly off-the-shelf components
System dedicated to phase noise measurement exclusively
Unfortunately, very low phase noise generators can be very expensive. To resolve this problem
the designer had to devise a way to make the system work with relatively inexpensive LOs with
modest phase noise specifications. The solution is as simple as elegant: to use two independent
relatively low cost generators that are not frequency-locked together, whose output frequencies
are strategically changed in real-time by the software to optimize the measurement. Figure 5. Inhouse cross-correlation SSB phase noise test system illustrates the schematics of the test system.
Depending on input frequencies of interest, different combinations of splitters and mixers are
used, since these components have specific ranges of operation. We may not be able to find a
splitter and mixer than can cover input frequencies from 1 MHz to 10 GHz, but one can find
combinations of splitters and mixers that cover subsets of that range. For example, if the phase
noise carrier that we want to measure is in a lower frequency range, say 10 MHz to 1.5 GHz, or
if it is in a higher range, such as 1 GHz to 10 GHz, it is fairly easy to find sets of splitters and
mixers that operate well within each of those ranges. The main concern with those components,
besides the operating frequency range, is to maintain sufficient channel-to-channel isolation.
Leakage is directly related to the magnitude of cross-channel frequency offset spurs, and we
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believe that at least 25 dB isolation, across the splitter and attenuators, is required to achieve
adequate spur suppression.
LO2
+13 dBm
-10 dBm
to
+13 dBm
DUT
10 dB attenuators
LP 50 MHz
+14 dB Amp
LP 30 MHz
FFT
Analyzer
0 MHz
IF’s range
from 0.48
MHz to
10.66 MHz
LO1
+13 dBm
Figure 5. In-house cross-correlation SSB phase noise test system
While the hardware is an important contributor to the overall performance of the system, it
doesn’t perform any of the actual measurements – the hardware just has the job of delivering the
signals to the digitizers with as much fidelity as possible. The software, on the other hand, does
the heavily lifting by:






Controlling the instruments
Capturing the data
Processing the data
Analyzing the data
Correcting for imperfections of the hardware
Presenting the data
All these functions need to be performed at a very high speed, since the cross-correlation
technique is extremely data intensive, involving tens of thousands of averages per point and
millions per sweep.
The spectral noise density is measured by obtaining a large number of blocks of data from the
two channels in the time domain, calculating the cross-power spectrum of each block of data,
and averaging the resulting complex spectra. The averaging is fundamental for two main reasons:
a) It reduces the uncertainty of the density estimations. The measured noise data is random
in nature, which causes the resulting power spectral density measurement also to be
random.
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b) More importantly, it suppresses the contributions of interfering signals from the test
system by vector-averaging them. If the unwanted noise contributions are uncorrelated to
each other and to the DUT signal, the average vector cross power spectral density of
those combinations is zero.
To make an analogy with a person, the hardware is the body while the software is the brain.
Because we were developing our own specialized software application we could concentrate on
optimizing the code for the specific hardware solution to measure phase noise. We didn’t have to
develop generic software to support a number of functions or parameters that are not of interest
for this particular measurement. The challenges posed to the software performance and
capabilities are already formidable as they are, without adding complexity to support other
general purpose measurements.
As with any cross-correlation measurement system, the better the hardware the fewer averages
the system needs to perform to obtain the same results. The use of low phase noise local
oscillators (LOs) to drive the mixers, for example, has a direct impact on the time needed
(number of averages) to obtain a satisfactory measurement. The system will always converge to
the final result, but the choice of LOs can make the difference in measurement time between a
few seconds and a few minutes, or even a few hours. For example, an improvement in the test
system’s noise of 5 dB can improve the measurement time of a low-noise DUT by a factor of 10.
Likewise, a 10 dB system noise improvement can speed up the measurement time by a factor of
100.
The software for an application such as this is very complex and requires expert software
developers. In our case it took about one man/year of software development to achieve lownoise, stable, repeatable and reproducible measurements that were comparable and in some cases
better than other commercially available solutions.
The current system, already implemented on several of our test stations, is still a work in
progress but it can already achieve a very respectable performance with very low noise floor.
Figure 6 illustrates the achievable noise floor of our system in its simplest configuration.
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dBc/Hz
Frequency offset
Figure 6. Prototype Phase Noise system noise floor
4. Cross-correlation phase noise uncertainty estimate
We developed an error metric for this system, with the expectation that we would keep
perfecting it to obtain a more accurate metric in the future. The metric estimates the 95%
confidence bounds of the measured phase noise data based on the number of acquisitions
averaged and the relationship between the measured cross-spectral density and the individual
channels’ power spectral density. It allows us to run a phase noise measurement test as quickly
as possible by informing the software when the statistics give us enough confidence in the
results.
Figure 7 illustrates a simulation testing the accuracy of the metric. The simulation is based on
675,000 sets of random correlation data, with number of averages ranging randomly from 1 to
50,000 and the ratio of uncorrelated power to correlated power in each channel ranging randomly
from -20 dB to +30 dB. The ideal error metric would produce a straight diagonal line, as shown
by the dotted line. The error metric follows the ideal very well, until the true errors are high and
so the statistical confidence is low. When the true error is high, the metric estimates the error on
the high side, i. e. conservatively.
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95.45% Cumulative Error Distribution (dB)
10
1
0.1
0.1
1
10
20
EM103 Uncertainty Estimate (dB)
Figure 7. Simulation test of the phase noise uncertainty metric
5. Benchmarking with other cross-correlation test systems
We performed an experiment to compare the results obtained by a reference cross-correlation
test set available in the market to our internally-developed system. We captured a number of
phase noise measurements at offsets from the carrier ranging from 10 Hz to 10 MHz, using a set
of five high performance synthesizers, an example is shown in Figure 8.
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Ref
Figure 8. Phase noise plot of 8.3 GHz carrier at different offset
The comparison shows good agreement overall between the reference system and our IF-RIObased system across the all offsets. The IF-RIO-based system shows a better performance for
offsets in the range between 30 Hz and 300 Hz, up to 9 dB improvement from the reference
system. On the other hand the reference system shows better performance on the far end of the
offset range. We believe that the performance at the far end can be considerably improved by
increasing the IF signals amplification, but that’s future work.
We believe we were able to develop a cross-correlation phase noise test system using modular
instruments and off-the-shelf components that perform at the level of the best available
instruments at a fraction of the cost. We estimate that the hardware cost of our system is about
20% of an equivalent cross–correlation instrument. The software development cost and test can
be conservatively estimated at $250 k, and if one plans to deploy ten phase noise test systems, it
will increase the cost by $25 k/unit, with total cost of $45 k. This represents only about 45% of
the cost of the currently available units in the market.
References
Loewenstein, E. B., Spectral Noise Density Estimation, National Instruments, 2011
Bendat, J. S., and Piersol, A. G., Engineering Applications of Correlation and Spectral Analysis,
Wiley-Interscience, New York, 1980. (pp 71 – 77)
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