Get a handle on phase noise

In today's crowded radio networks, the signal generators in wireless products must generate highly accurate and stable frequencies. To ensure that your wireless products use bandwidth efficiently, you can measure the phase noise in your signal generators with a spectrum analyzer and then evaluate the data with Matlab software. Furthermore, you can integrate the instrumentation and software into corporate networks, simplifying the documentation of test results.

The phase noise of a receiver's local oscillator determines the sensitivity of the receiver in the presence of strong signals in the adjacent channel. In signal generators, the phase noise of the synthesizer, in conjunction with the modulator characteristics, determines the power radiated into the adjacent channel.

The output signal of an ideal oscillator can be expressed as:

u(t) = U₀ sin(2πf₀t)

where:

U₀ = signal amplitude
f₀ = signal frequency
2πf₀t = signal phase

In a real signal, both the signal amplitude and the signal phase vary:

u(t) = (U₀ + e(t)) sin(2πf₀t + Δj(t))

where:

e(t)= amplitude variation of signal and
Δj(t)= phase variation, or phase noise, of signal.

Phase variation can be divided in two types:

• deterministic phase variation and
• random phase variation.

Random phase variation is what is known as phase noise. For example, you can express phase noise as the noise power density in a single sideband (SSB) within a 1-Hz bandwidth. In practice, the SSB signal-to-noise ratio (SNR), L, normally describes the phase-noise characteristics of an oscillator. The SSB SNR equals the ratio of the noise power in an SSB measured within a 1-Hz bandwidth to the total signal power at a frequency offset, f_m, from the carrier:

If the modulation sidebands produced by noise are very narrow—that is, phase deviation is considerably smaller than 1 rad—then you can calculate the SSB SNR from the noise power density. The SSB SNR is usually specified on a logarithmic scale and is, therefore, expressed in dBc/Hz.

You can easily measure oscillator phase noise with a spectrum analyzer that offers these features:

• The frequency drift of the analyzer's local oscillator should be small relative to the analyzer sweep time. Too large a frequency variation of the oscillator during the sweep would invalidate results.
• The internal oscillators should have sufficiently low phase noise to prevent the characteristics of the spectrum analyzer, rather than those of the DUT, from being measured.
• Thermal noise should be lower than the noise power to be determined.

Many spectrum analyzers have special marker functions for measuring phase noise, but these analyzers furnish phase noise for a single frequency only. Thus, they aren't suitable for determining phase noise over an entire frequency band.

Figure 1. When linked to a spectrum analyzer via a LAN, Matlab can generate a diagram showing the phase noise of a signal generator.

In contrast to measurements in which several sweeps are made with different filter and level settings, only the frequency points of interest are measured in the list mode. You can select filter and level settings to match the carrier-frequency offset for each frequency value. This yields minimum measurement time for the complete test sequence.

First, you use normal marker search functions to measure the carrier signal. Then, select the list mode. The frequency list takes up a maximum of 100 points, enabling the processing of one list per decade in the example described at the bottom of this page. Matlab analysis software (The MathWorks, Natick, MA; www.mathworks.com) converts the measurement values obtained to phase noise values referenced to the carrier signal level, taking into account the resolution filter used. Also, a correction factor for the filter characteristic is taken into account. Then, the phase-noise diagram can be generated with the aid of Matlab functions. Figure 1 shows the phase noise of a signal generator for a 1-GHz, 0-dBm carrier signal.