# Phase Noise: Keep it Down!

### Key Takeaways

• Phase noise is the short-term distortion of a signal from its ideal that occurs in a Gaussian distribution pattern around the carrier frequency.

• Mixing can amplify the effects of phase noise; circuit designers will want to be careful to minimize its effects pre-mixing with filters.

• Spectrum analyzers or more specific phase noise analyzers can quantify the level of distortion.

Measuring phase noise requires sophisticated instrumentation, but analysis methods can follow best practices.

Noise is an unavoidable aspect of signal propagation. Like a sonic equivalent to friction, designers can’t devise a circuit where signals are entirely noise-free; instead, best signal integrity practices that limit the total noise present and its potential impact provide the best design bang for the buck. Phase noise is one aspect of noise to consider: random fluctuations away from the ideal phase of a waveform result in small disturbances in the signal integrity visible with a spectrum analyzer and other measurement systems. In addition to distorting the signal, phase noise disrupts power delivery by spreading the spectral density over a greater frequency. For these reasons, designers will want to minimize phase noise in the design as much as possible for optimal performance.

## Understanding the Physics of Phase Noise

An oscillating signal does not follow a perfect path; instead, signals show some regular deviation of the phase angle within some distance of the “ideal” angular displacement. While phase noise can also apply to the long-term drift in the output of an oscillator or other signal-producing component, the short-term perturbations are of greater interest. If the ideal formula for a sinusoidal signal is

A - amplitude

f - frequency

t - time

then the observed signal would appear as

E(t) - time-varying amplitude

𝜙(t) - time-varying phase angle

In other words, because a signal has two degrees of freedom – amplitude and phase angle – there are equally as many noise sources. This noise follows a normal distribution around the “base” signal: there is no preference in direction for one side or the other from the median value. Phase modulation results in a spread of frequencies adjacent to either side of the carrier frequency, known as sidebands.

Phase noise is a modulation noise source that varies the carrier signal's phase or frequency proportionally to the message. When the amplitude and one of the phase or frequency are held constant, the remaining value changes due to the instantaneous amplitude of the modulating wave–phase modulation and frequency modulation represent the class of angle modulation. Phase modulation exhibits amplitude and frequency modulation characteristics: at low amplitudes, the baseband bandwidth doubles (an undesired outcome); large sinusoidal signals have a bandwidth similar to frequency modulation of

Δθ - peak angular displacement

m - highest angular velocity in modulating signal

## Sources of Phase Noise and Detection Methods

Understanding mixing is a good jumping-off point to determine a circuit's phase noise source. Mixing moves signals to a new frequency by combining an input with an oscillator frequency in additive and subtractive fashions. Mixers commonly perform operations on signals before conditioning for transmission; generally, signals are easier to work with at low frequencies. Performing the necessary processing before mixing up to integrate with fixed-frequency elements of a system (amplifiers, filters, etc.) significantly reduces the number of possible system states during operation.

Consider these three sources of phase noise in a system:

• Spectral regrowth - As described in mixing, combining the input and oscillator signal results in an output signal that can be either the sum or difference. However, modulation processes result in intermodulation products formed by the nonlinearity of the signal processing system. The intermodulation products distort while their frequencies drift from the targeted sum or difference of the mixer signals, resulting in phase noise in adjacent channels. When the overall phase noise is low, the total effect of the phase noise is localized and minimal. As the total phase noise grows, so does the interference and the bandwidth over which it disrupts signal integrity – this makes spectral regrowth especially nefarious for wideband technologies like LTE and 5G networks.

• Sensitivity/selectivity - The proximity of noise to a desired signal can also significantly affect the signal integrity. In this case, a mixer can apply filters to select the signal range that excludes the nearby noise source in a process known as intermediate frequency (IF) mixing. The greater the spectral density of a source (i.e., the more closely a signal or noise represents a Dirac delta function), the more effective the IF mixing technique, even for sources with little separation. However, phase noise distributes normally to either side of the carrier frequency, resulting in significant distortion, especially if the noise source is more powerful than the targeted signal in absolute terms.

• Bit error - Some communication systems use phase and amplitude modulation in their protocol. These protocols rely on constellation maps that use points to indicate a unique ordered pair of amplitude and phase. Disturbances to the phase via phase noise cause these points to rotate from their expected position, indicated by a “blurring” of the point as its phase becomes a probability distribution. As the phase spreads, the points become harder to pinpoint, and interpretation of the phase may result in bit errors during transmission or reconstruction.

### Quantifying Phase Noise in the Lab

Detecting and measuring phase noise can be crucial to discern between design and manufacturing errors. A spectrum analyzer is a good general tool to detect phase noise: its wide range of suitable applications in electronics labs makes it ubiquitous, and multiple detection methods are available. A more specific tool known as a phase analyzer allows for greater precision:

• Spectrum analyzer - Most technicians/engineers are familiar with spectrum analyzers. The most basic operation measures the power at the carrier frequency and the power of the noise at regular intervals away from the carrier frequency to construct a map of the relative strength of signal and noise.

• Phase noise analyzer - The phase noise analyzer improves on the base spectrum analyzer by using a cross-correlation method to minimize the impact of noise generated by the measuring device. Removing the measuring noise increases the sensitivity of the measurement, which supports low-power phase noise analysis.

## Cadence Solutions Support Signal Integrity

It’s impossible to eliminate all noise – phase noise included – but good signal integrity practices and filtering applications will help minimize the effects on circuit performance. More often than not, it's better to eliminate noise at its source (as much as possible) than attempt to mitigate it downstream in a design. Still, every board is a series of reasonable performance compromises, and this may not always be possible. As always, measuring and modeling are key to determining the impact of noise in design, and Cadence’s PCB Design and Analysis Software suite gives design teams all the tools necessary to ensure signal integrity propagation. With the constraint-driven OrCAD PCB Designer, product development doesn’t have to sacrifice performance for speed or ease of use.

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