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# Impact of phase noise in signal generators

Leonard Dickstein, Giga-tronics- August 21, 2012

Phase noise is the result of small random fluctuations or uncertainty in the phase of an electronic signal. We specify and measure phase noise because it is a fundamental limitation in the performance of systems, limiting dynamic range.  In radar and communications, phase noise manifests itself as a loss of sensitivity, in imaging it results in a lack of definition, and in digital systems it contributes to a higher bit error rate. While this discussion will focus primarily on phase noise in the frequency domain, phase noise can also be quantified as jitter in the time domain.

Background and Basics

Most electronic signals derive from oscillators.

V(t) is the oscillator output in volts versus time at the oscillator frequency.
We can describe an ideal signal as V(t) = Ao sin 2πfot where Ao is the nominal amplitude and fo is the nominal frequency.

In the frequency domain, an ideal sine wave signal is shown as a single frequency in the spectrum.

We can describe a “Real-world” signal as V(t) = [Ao + E(t)] sin [2πfot + Ø(t)] where E(t) is the random amplitude fluctuations and Ø(t) is the random phase fluctuations.

In the frequency domain, this signal now appears as the familiar spectrum of carrier with sidebands.

It is important to point out that the amplitude noise and phase noise are small perturbations. The goal in signal generator design is to have these as small as possible, from at least 40 dB less than the carrier to as much as 170 dB less than the carrier, limited only by the kTB thermal noise floor.

Phase Noise in Signal Generators
Phase noise is quantified in the unit of measure called “script L of F”, where

Measured directly on a microwave spectrum analyzer, L(f) is the ratio of the noise power in a 1 Hz bandwidth, at a specified offset from the carrier, to the carrier signal power.

In the literature, the term Sφ(f) is often used to describe the two-sided “spectral density” phase noise. There are other terms, but these two are the most common. In product performance specifications, the L(f) single sideband phase noise is the industry standard. The two are related by the equation:

L(f), the single sideband (SSB) phase noise, is graphed as amplitude versus the frequency offset.

The above example is a typical log-log plot of signal generator phase noise, as measured on a phase-noise test set.  The vertical axis is amplitude relative to the carrier, which is not shown. The horizontal axis is frequency offset from the carrier. The scale will vary depending on both phase-noise test set limitations and on what the signal generator manufacturer wants to highlight.

This example is for one frequency of the carrier, but it is common to see multiple traces for different carrier frequencies shown on one graph. You read the value of phase noise from the curve as the value at the offset (at that carrier frequency). From this example, the phase noise is -110 dBc/Hz at 100 kHz offset (at that carrier frequency).

In the literature, it is common practice to refer to the values of phase noise as “close-in” for the frequency offset range of 1 Hz to 100 Hz. That is, “close in phase noise” refers to the phase noise close to the carrier, less than 1 kHz away. Similarly, “far out” phase noise commonly refers to values 1 MHz or more from the carrier.  That is, “far out phase noise” refers to the phase noise far from the carrier, more than 100 kHz away. The mid-range region, 1 kHz to 100 kHz offset, especially for signal generator phase noise, is sometimes referred to as the pedestal region.

The example above also is shown with spurious signals (in red). These spurious signals are not phase noise. They are not random, but systematic of any given signal generator. While many phase noise test sets will measure both phase noise and spurious signals together, most often the phase noise measurements are shown without the spurious signals. While spurious signals are always present in every signal generator, they have separate specifications, behave differently and removing them from the phase noise plot is a means of separating deterministic from non-deterministic artifacts.
A side note: while consistently shown as the upper sideband, it is generally agreed that the noise of the upper and lower sidebands are equal [1].

The above example is measured phase noise performance of the Giga-tronics 2500B Microwave Signal Generator, with curves for six different carrier frequencies, plotted without the spurious signals. Note that the phase noise increases as the carrier frequency increases, while holding the same general shape of the curve.

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