Phase Noise Fundamentals and Measurement Techniques

Phase noise is a crucial aspect of signal quality, and understanding its fundamentals is essential for anyone working with oscillators or signal processing systems. Phase noise is caused by random fluctuations in the phase of a signal, which can be thought of as the signal's "wobble" over time.

These fluctuations can be caused by a variety of factors, including thermal noise, power supply noise, and component imperfections. In fact, it's estimated that thermal noise alone can account for up to 90% of the phase noise in a typical oscillator.

To measure phase noise, engineers use specialized equipment such as spectrum analyzers or phase noise analyzers. These tools can help identify the sources of phase noise and determine the overall impact on the signal quality.

Phase noise is a fundamental aspect of laser technology, and it's not just a matter of having a perfectly stable frequency. The light output of a single-frequency laser is not perfectly monochromatic but rather exhibits some phase noise, i.e., fluctuations in the optical phase.

Intriguing read: Critical Frequency

This phase noise leads to a finite linewidth of the laser output, which is a critical factor to consider in many applications. The fundamental origin of phase noise is quantum noise, specifically spontaneous emission of the gain medium into the resonator modes.

In simple terms, this means that even the best lasers can't produce a perfectly stable frequency due to the inherent noise associated with their operation. Phase noise of a single-frequency laser usually occurs in the form of a quasi-continuous frequency drift, not as sudden substantial phase jumps, since a large number of laser-active atoms or ions is involved.

By plotting each spectral density point at varied frequency intervals, you can visualize the phase noise in a graph. This graph will show the phase noise at different frequencies, which is a useful tool for understanding and analyzing phase noise.

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An ideal oscillator would generate a pure sine wave, but all real oscillators have phase modulated noise components that spread the power of a signal to adjacent frequencies.

The phase noise is added to the signal by adding a stochastic process represented by ϕ ϕ (t){\displaystyle \phi (t)} to the signal, which can be a white noise, pink noise, or brown noise process.

A white noise PSD follows a f0{\displaystyle f^{0}} trend, a pink noise PSD follows a f− − 1{\displaystyle f^{-1}} trend, and a brown noise PSD follows a f− − 2{\displaystyle f^{-2}} trend.

Explore further: Free White Noise Website

Phase noise is a crucial concept in electronics, and understanding its causes can help you troubleshoot issues or design more efficient systems. Thermal noise, also known as Johnson-Nyquist noise, is a major contributor to phase noise in electronic circuits.

Thermal noise is caused by the random motion of electrons in a conductor, and it's a fundamental limit to the sensitivity of electronic devices. It's a fact of life, and even the most advanced electronics can't escape its effects.

Shot noise, on the other hand, is caused by the random arrival of individual electrons at a detector or amplifier. It's like trying to catch a bunch of individual raindrops in a bucket – some will get through, and some won't.

Intriguing read: Ultra Low Phase Noise Rf Signal Generator Market

Flicker noise, also known as pink noise, is a type of noise that's often associated with aging electronic components. It's like the creaks and groans of an old wooden floor – it's a sign of wear and tear.

Crystal defects can also contribute to phase noise, especially in high-frequency applications. These defects can cause variations in the crystal's structure, leading to noise and instability.

Here are the main causes of phase noise:

An ideal oscillator would generate a pure sine wave, represented as a single pair of Dirac delta functions at the oscillator's frequency.

In the real world, all oscillators have phase modulated noise components that spread the signal's power to adjacent frequencies, resulting in noise sidebands.

These noise components can be thought of as a stochastic process added to the signal, represented by ϕ(t).

The power Spectral density (PSD) of different phase noise processes can follow various trends, such as white noise following a f0 trend, pink noise following a f−1 trend, and brown noise following a f−2 trend.

The single-sided phase noise PSD is given by the Fourier transform of the Autocorrelation of the phase noise.

The noise can also be represented as the single-sided frequency noise PSD or the fractional frequency stability PSD, which defines the frequency fluctuations in terms of the deviation from the carrier frequency.

The phase noise can be given as the spectral purity, L(f), which is the single-sideband power in a 1Hz bandwidth at a frequency offset from the carrier frequency.

A stochastic process due to white noise can be understood as a random walk or diffusion process, with a characteristic diffusion coefficient D.

The variance of the phase noise grows with time according to ϕ2(t)¯ = 2Dt.

Measuring phase noise can be done using a spectrum analyzer, but be careful to ensure the values you're observing are due to the signal and not the spectrum analyzer's filters.

Spectrum analyzers can measure phase noise over many decades of frequency, from 1 Hz to 10 MHz.

For more accurate measurements, consider using a phase noise measurement system, which can use internal and external references and allow measurement of both residual and absolute noise.

These systems can also make low-noise, close-to-the-carrier, measurements that are hard to achieve with spectrum analyzers.

To measure optical phase noise, you can record a beat note between two lasers on a fast photodiode, or record a beat note of the laser output with a delayed portion of the same laser output.

Normalization is a crucial step in accurately measuring phase noise. It involves adjusting the measured noise power to account for the resolution bandwidth (RBW) of the spectrum analyzer.

Noise power measured by wider RBW filters needs to be normalized to a 1-Hz bandwidth. This is because most spectrum analyzers use filters that are more than 1 Hz wide.

To normalize noise power, you need to reduce the measured value by N dB, where N = 10 log (RBW in Hz). For instance, if you measured noise power with a 3-kHz RBW filter at -90 dBm, the normalized 1-Hz noise power would be -124.77 dBm (-90 - 10 log (3000)).

Curious to learn more? Check out: Bandwidth Compression

Phase noise can be measured using a spectrum analyzer if the phase noise of the device under test is large with respect to the spectrum analyzer's local oscillator. Care should be taken that observed values are due to the measured signal and not the shape factor of the spectrum analyzer's filters.

Spectrum analyzers can show the phase-noise power over many decades of frequency, e.g., 1 Hz to 10 MHz. The slope with offset frequency in various offset frequency regions can provide clues as to the source of the noise, e.g., low frequency flicker noise decreasing at 30 dB per decade.

Phase noise measurement systems are alternatives to spectrum analyzers. These systems may use internal and external references and allow measurement of both residual and absolute noise.

Measuring phase noise at very small offsets from the carrier, also known as close-in phase noise, is challenging due to the need for a very narrow resolution bandwidth to avoid measuring the carrier power as well as the noise power.

Modern spectrum analyzers can avoid some of these issues by measuring phase noise using so-called “I/Q data.” I/Q data is a digital representation of the spectrum and is obtained by means of the fast Fourier transform.

Power Density is a crucial aspect of measurement and analysis. We measure noise power density in dBW (LOG(Watts)) because of the large range we're looking at.

In our analysis, we can refer to the plotted part of the single sideband as noise. This is because anything above the nominal oscillator frequency (Fosc) and not harmonically related can be considered phase noise.

Noise power density is the technical term for this part of our graph. It's a key concept to understand when working with phase noise.

We can consider anything above the nominal oscillator frequency (Fosc) and not harmonically related as phase noise. This is based on the plotted part of the single sideband.

The large range at which we're looking makes it necessary to measure noise power density in dBW (LOG(Watts)). This allows us to accurately capture the data.

Phase noise can be measured and expressed as a power obtained by integrating ℒ(f) over a certain range of offset frequencies. This integrated phase noise can be converted to jitter using a specific formula.

Jitter is sometimes expressed in seconds, while phase noise is often measured in degrees. The RMS cycle jitter can be related to the phase noise in a region where the phase noise displays a –20dBc/decade slope.

This relationship is based on Leeson's equation, which is a fundamental concept in understanding phase noise. By applying this equation, we can gain a deeper understanding of the connection between phase noise and jitter.

Phase noise measurements are often based on a recorded beat note between two lasers on a fast photodiode. This requires that the difference of the optical frequencies is not too large.

Timing jitter can be seen as a kind of phase noise, where a timing change by one pulse period can be interpreted as a phase change of 2($\pi$). This is known as timing phase noise.

Mode-locked lasers exhibit both optical phase noise and timing phase noise, but these are not directly related. For example, if the phase fluctuations in all resonator modes would be identical, there would be no timing phase noise at all.

Phase noise measurements in lasers often involve recording a beat note between two lasers on a fast photodiode.

This method requires that the difference of the optical frequencies is not too large, which can be a limitation.

Alternatively, you can record a beat note of the laser output with a different portion of the same laser output, which is subject to a long delay, such as propagation through a long span of optical fiber.

A flexible method is to digitize the beat note signal with a fast electronic sampling card, allowing for further numerical processing on a computer.

The power spectral density of the time-dependent phase excursion can be calculated using this method.

There are two cases to consider when evaluating phase and frequency noise of lasers: single-mode operation and multimode operation.

In single-mode operation, phase noise is simpler to analyze.

In multimode operation, each mode needs to be considered separately, with possible correlations between the modes.

Unavoidable quantum noise related to laser gain and resonator losses determines the Schawlow-Townes linewidth.

Mechanical vibrations can affect optical path lengths, leading to additional technical phase noise.

Temperature variations in laser gain media can also contribute to phase noise, often caused by pump power fluctuations.

Discover more: Asynchronous Operation

Measuring phase noise can be a challenge, especially when the instrument itself adds noise to the signal. The phase noise of the analyzer is a significant consideration, as it can be added to the phase noise of the device under test (DUT).

A spectrum analyzer can measure phase noise if the phase noise of the DUT is large compared to the analyzer's local oscillator. However, it's essential to ensure that the observed values are due to the measured signal and not the shape factor of the analyzer's filters.

Most phase noise measurement methods, including spectrum analyzers, have the limitation that phase noise from the instrument is added to the phase noise from the DUT. This added noise can be problematic, making it difficult to determine how much phase noise is present in the DUT signal and how much is added by the measuring instrument.

Dynamic range is a crucial consideration when selecting a spectrum analyzer for phase-noise measurements. The difference between the largest and smaller signals that can be accurately measured can be as high as 140 dB.

This is because phase-noise measurements require measuring both the power of the carrier and noise powers at different offsets from the carrier. The difference between these measured powers is typically quite large.

For example, the measured carrier power and noise power can differ by as much as 80 dB to 140 dB. This requires a spectrum analyzer with a high dynamic range to accurately measure both very high and very low powers simultaneously.

A good spectrum analyzer should be able to handle such a large dynamic range, ensuring accurate phase-noise measurements.

Measuring optical phase noise can be done in a few ways. One common method is to record a beat note between two lasers on a fast photodiode.

The difference in optical frequencies between the lasers can't be too large for this method to work. Alternatively, you can record a beat note between the laser output and a delayed portion of the same laser output, which has traveled through a long span of optical fiber.

Digitizing the beat note signal with a fast electronic sampling card allows for further numerical processing on a computer. This can include calculating the time-dependent phase excursion and its power spectral density.

For more precise measurements, you can refer to the article on linewidth for additional details.

Spectrum analyzers contain multiple local oscillators that generate their own phase noise, which is added to the phase noise of the measured signal as it moves through different stages in the analyzer.

This added noise makes it difficult to determine how much phase noise is present in the DUT signal and how much is added by the measuring instrument.

Most of the added noise comes from the instrument’s local or reference oscillator(s), which is problematic because it makes it difficult to determine the true phase noise of the DUT.

To avoid this issue, it's essential to ensure that the analyzer has a better phase-noise specification than the DUT, with at least a 10 dB margin being considered the minimum acceptable.

However, even with a good margin, the instrument's phase noise can still be a significant limitation, especially when measuring modern DUTs with very low levels of phase noise.

Using an instrument with low phase-noise local oscillators and a modern phase-noise measurement method, such as digital phase demodulation, can significantly improve phase-noise measurement results.

But even with these improvements, the instrument's phase noise can still be a limiting factor, especially when measuring very quiet oscillators.

Cross-correlation has been the primary method for reducing or removing the effect of instrument phase noise since the 1990s, and it's particularly useful for increasing sensitivity to very low levels of phase noise.

In summary, the instrument's phase noise is a critical consideration when making phase-noise measurements, and it's essential to choose an instrument with low phase-noise local oscillators and a suitable measurement method to get accurate results.

Phase noise can be quantified by the power spectral density of the phase deviations, having units of rad/Hz or simply Hz. This power spectral density often diverges for zero frequency, making it difficult to specify an r.m.s. value.

For simple random-walk processes, specifying a coherence time or coherence length can be a suitable alternative. This approach is particularly useful when dealing with phase noise in lasers operating on multiple resonator modes.

To compare the level of phase noise in different oscillators, it's common to normalize it to the corresponding oscillator frequencies. This is achieved by using the quantity, which is the magnitude of phase fluctuations divided by the mean angular frequency.

Comparing phase noise levels between different oscillators can be a bit tricky, but it's essential to get it right.

Normalization is a key concept in comparing phase noise levels between different oscillators. This is because phase noise is often specified as the noise power contained within a bandwidth of 1 Hz.

In frequency metrology, it's common to use the quantity x(t) to compare phase noise levels, which is the magnitude of phase fluctuations divided by the mean angular frequency.

This quantity doesn't change even when a digital oscillating signal is sent through a frequency divider, which reduces the phase fluctuations in proportion to the mean frequency.

The comparison of optimized low-noise lasers and high-quality microwave oscillators shows that lasers normally have a higher level of phase noise, but a lower level of normalized phase noise, making them superior as clocks.

A laser can also have a very low phase noise level at high noise frequencies, making it suitable as a fly-wheel oscillator.

To normalize phase noise levels, you need to reduce the measured noise power value by N dB, where N = 10 log (RBW in Hz), where RBW is the resolution-bandwidth filter used to measure power.

A different take: Modal Bandwidth

Understanding the concept of quantification and comparison requires a step-by-step approach.

First, define the problem or question you want to answer. This will help you determine what you're trying to quantify or compare. For example, in the article section "Measuring Quantification", we discussed how to measure the effectiveness of a marketing campaign by tracking website traffic and sales.

Next, identify the relevant data or metrics that will help you answer your question. As explained in the "Data Collection" section, this might involve gathering data from various sources, such as customer surveys, sales reports, or social media analytics.

Now, determine the best method for collecting and analyzing your data. This could involve using statistical tools, such as regression analysis, as mentioned in the "Statistical Analysis" section, or more visual methods, like creating a bar chart to compare data.

Compare your data to establish a baseline or benchmark. In the "Comparison Methods" section, we discussed how to use methods like percentage change and ratio analysis to compare data.

Finally, interpret your results and draw conclusions based on your analysis. This will help you understand the implications of your findings and make informed decisions.

Several patents have been filed to address phase noise in various applications.

One notable patent is V. Gerginov's Two-Photon Optical Frequency Reference with Active AC Stark Shift Cancellation, Provisional Patent Application # 62,629,800.

A. Hati, C.W. Nelson, and D.A. Howe developed a Phase Modulation Noise Reducer, United States, Patent # 10,050,608, which aims to reduce phase noise in electronic systems.

Researchers have also explored the use of air-dielectric cavities in microwave oscillators. D.A. Howe, A. Sen Gupta, C.W. Nelson, and F.L. Walls developed a High Spectral Purity Microwave Oscillator Using Air-Dielectric Cavity, United States Patent # 7,075,378.

F.L. Walls has filed multiple patents related to phase noise measurement and calibration. For instance, his Calibration System for Determining the Accuracy of Phase Modulation and Amplitude Modulation Noise Measurement Apparatus, United States Patent # 5,172,064, provides a method for calibrating phase noise measurement apparatus.

Here are some notable patents related to phase noise:

F.L. Walls' work on frequency calibration standards is also noteworthy. His Frequency Calibration Standard Using a Wide Band Phase Modulator, United States Patent # 5,101,506, provides a method for calibrating frequency standards using a wide band phase modulator.