MATLAB Examples

# View Phase Noise Effects on Signal Spectrum

This example shows the effects that spectral and phase noise have on a 100 kHz sine wave.

## Open Example Model and Explore Its Contents

Open the example model slex_phasenoise.

A Sine Wave block generates a 100 kHz tone. A Phase Noise block adds phase noise of:

• -85 dBc/Hz at a frequency offset of 1e3 Hz
• -118 dBc/Hz at a frequency offset of 9.5e3 Hz
• -125 dBc/Hz at a frequency offset of 19.5e3 Hz
• -145 dBc/Hz at a frequency offset of 195e3 Hz

To analyze the spectrum and phase noise, the model includes three Spectrum Analyzer blocks. The Spectrum Analyzer blocks use the default Hann windowing setting, the units are set to dBW/Hz, and the number of spectral averages is set to 10.

Additionally, the model includes blocks that calculate and display the RMS phase noise. The subsystem that calculates the RMS phase noise finds the phase error between the pure and noisy sine waves, then calculates the RMS phase noise in degrees. In general, to accurately determine the phase error, the pure signal must be time aligned with the noisy signal. However, the periodicity of the sine wave in this model makes this step unnecessary.

## Run the Model to Generate Results

In the Simulink Editor, click Run to simulate the model.

When the resolution bandwidth is 1 Hz, the dBW/Hz view for the spectrum analyzer shows the tone at 0 dBW/Hz. The Spectrum Analyzer block corrects for the power spreading effect of the Hann windowing.

The visual average of the phase noise achieves the spectrum defined by the Phase Noise block.

When the resolution bandwidth is 10 Hz, the dBW/Hz view for the spectrum analyzer shows the tone at -10 dBW/Hz. That same tone energy is now spread across 10 Hz instead of 1 Hz, so the sine wave PSD level reduces by 10 dB. With the resolution bandwidth at 10 Hz, the visual average of the phase noise still achieves the phase noise defined by the Phase Noise block.

The Spectrum Analyzer block still corrects for the power spreading effect of the Hann window, and it achieves better spectral averaging with the wider resolution bandwidth. For more information, see docid:signal_ug.brbq7fh.

## Further Exploration

In the Phase Noise block, change the Phase noise level (dBc/Hz) parameter, rerun the model, and notice how the spectrum shape changes. With more noise, the side lobes increase in amplitude. As more phase noise is added, the 100 Hz signal becomes less distinct and the measured RMS phase noise increases.