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Phase Noise at PLL Output

This example shows how to measure and analyze the phase noise at the output of a phase-locked loop (PLL) using the PLL testbench.

The five sections of this example demonstrate three phase noise effects, individually and collectively:

  1. Numerical noise baseline

  2. The effect of reference phase noise only

  3. The effect of VCO phase noise only

  4. The effect of VCO phase noise subsampling by the feedback prescaler

  5. The combined effect of all three phase noise sources.

The PLL Testbench generates a reference signal and measures the phase noise at the PLL output.

The reference phase modulation in this model is used to contrast the response to reference phase variation with the response to VCO phase noise. The PLL Testbench does not currently include a specfication of reference phase noise; however the user can insert reference phase noise between the PLL Testbench output and the PLL reference input, as is done in this example.

The Resample blocks at the inputs of two of the spectrum analyzers convert the variable step discrete sampled signals to the fixed step discrete sampled signals the spectrum analyzer requires. The Resample block is a block inside the Slew Rate block found in the Mixed Signal Blockset Utilities library. It is a low pass filter whose impulse response is described by a closed form equation. It is therefore able to calculate an output sample value for any sample time step, independent of the input sample time step.

The model uses a reference frequency fref of 30 MHz and a feedback divider ratio N of 70 for all but one section. The output frequency fout is N*x*fref, or 2.1 GHz for those sections.

% Make sure genPrbs7 has been run.
if ~exist( 'prbs7', 'var' ) || ~exist( 'prbs7time', 'var' )
    [prbs7, prbs7time] = genPrbs7(30e6,500e3,-110);
end
% Make sure PllPhaseNoiseExample.slx has been loaded.
open_system('PllPhaseNoiseExample.slx');

Baseline

This section measures the limitations of the example model due to numerical noise or other inaccuracies. All of the sources of phase noise are disabled and the phase noise is measured to establish the baseline phase noise level. When sources of phase noise are enabled in subsequent sections, the effect of the phase noise source is the difference between the measured phase noise and the baseline phase noise level measured in this section.

  • VCO free-run frequency: N*x*fref

  • Feedback prescaler ratio: N

  • VCO phase noise: Disabled

  • Reference modulation: Through path selected

The target phase noise shown in the PLL Testbench phase noise plot is a PLL Testbench parameter. In this example, it is not actually a performance target, but rather was set equal to the VCO phase noise for comparison to the phase noise at the output of the PLL.

% Configure the model
configurePhaseNoiseExample( 'PllPhaseNoiseExample', 2.1e9, 70, 'off', '1');
% Run the simulation
sim('PllPhaseNoiseExample.slx');
% Plot the PLL Testbench phase noise analysis
plotPhaseNoiseAnalysis();

Reference Source Phase Modulation

In this section, measure the amplification of phase modulation at the reference input of the PLL.

Unlike the very low level, random reference phase noise that is typical of most practical applications, this example uses PRBS7 reference phase modulation. This phase modulation produces discrete spectral components that contrast with the smooth spectral density of the VCO phase noise and in-band phase noise generated internal to the PLL. Such a reference phase modulatioon might be used in a spread spectrum application, though usually at a much higher modulation amplitude.

  • VCO free-run frequency: N*x*fref

  • Feedback prescaler ratio: N

  • VCO phase noise: Disabled

  • Reference modulation: Phase modulated reference selected

The reference input spectrum has many closely spaced spectral components of nearly the same amplitude across the entire spectrum.

The PLL output spectrum with reference phase modulation includes spectral components at the same frequency offsets as for the modulated reference input, but at very different levels. The spectral components within the PLL loop bandwidth are amplified by the feedback prescaler divider ratio. Beyond the loop bandwidth, the spectral components fall off much more rapidly than the spectral components at the input, due to the filtering of the PLL control loop.

The spectrum at the output of the loop filter includes spectral components at the same frequency offsets as for the modulated reference input, but at levels that are very different from either the reference input or the PLL output. The loop filter output is integrated by the VCO; and in order to produce spectral components that are nearly coonstant within the PLL control loop bandwidth, the level of the spectral components at the loop filter output must be proportional to the frequency offset.

Optional: In the mask for the PLL, go to the loop filter tab and change the loop bandwidth (e.g., reduce the loop bandwidth by a factor of the), then re-run this section. Note the effect of the PLL control loop bandwidth on the spectrum at the PLL output.

% Configure the model.
configurePhaseNoiseExample( 'PllPhaseNoiseExample', 2.1e9, 70, 'off', '0');
% Run the simulation
sim('PllPhaseNoiseExample.slx');
% Plot the PLL Testbench phase noise analysis
plotPhaseNoiseAnalysis();

VCO Phase Noise

In this section, observe the direct output of VCO phase noise as filtered by the PLL loop response. This is done by selecting the unmodulated reference, setting the feedback prescaler divider ratio to one, setting the VCO free running frequency equal to the reference frequency, and enabling the VCO phase noise. The loop filter design is automatically updated so you can compare the results with other feedback prescaler ratios.

  • VCO free-run frequency: fref

  • Feedback prescaler ratio: 1

  • VCO phase noise: Enabled

  • Reference modulation: Through path selected

In both the PLL output spectrum and the PLL Testbench phase noise analysis, the phase noise sidebands nearest the main spectral component are significantly reduced. The sidebands beyond the loop bandwidth decay more slowly.

In the loop filter output spectrum, the spectral density at small frequency offsets is quite significant. The loop filter output cancels out a significant portion of the VCO phase noise close to the main output signal.

Optional: Run with different loop bandwidths, phase margins or filter orders and the the effect on the PLL output spectrum.

% Configure the model.
configurePhaseNoiseExample( 'PllPhaseNoiseExample', 30e6, 1, 'on', '1');
% Run the simulation
sim('PllPhaseNoiseExample.slx');
% Plot the PLL Testbench phase noise analysis
plotPhaseNoiseAnalysis();

In-band Phase Noise

In this section, generate an in-band noise floor through the feedback prescaler. The PLL control loop filters the newly introduced phase noise. In a PLL with feedback prescaler ratio greater than one, the phase noise at the output of the feedback prescaler is a subsampled version of the VCO phase noise. The phase noise that the PLL control loop is responding to is therefore not a perfect replica of the VCO phase noise, resulting in incomplete suppression of the VCO phase noise. The resulting tracking error is commonly referred to as an in-band noise floor.

For this section, the feedback divider ratio is set to 70, resulting in a PLL output frequency of 2.1 GHz. The unmodulated reference is chosen and the VCO phase noise is enabled.

  • VCO free-run frequency: N*x*fref

  • Feedback prescaler ratio: N

  • VCO phase noise: Enabled

  • Reference modulation: Through path selected

In contrast to the case with unity feedback prescaler ratio, the PLL output phase noise sidebands nearest the main spectral component are essentially constant. This is what is referred to as an "in-band noise floor".

In the loop filter output spectrum, the spectral density at small frequency offsets is significant; however in this case the cancellation of the close-in VCO phase noise by the loop filter output is not as effective as in the case of a divider ration equal to one.

Optional: Experiment with other divider ratios and note how the in-band noise floor changes.

Optional: Run width different loop bandwidths, phase margins or filter orders and note the effect on the in-band noise floor.

% Configure the model.
configurePhaseNoiseExample( 'PllPhaseNoiseExample', 2.1e9, 70, 'on', '1');
% Run the simulation
sim('PllPhaseNoiseExample.slx');
% Plot the PLL Testbench phase noise analysis
plotPhaseNoiseAnalysis();

Total Phase Noise

In this section, observe the total effect of all phase noise components at the PLL output.

  • VCO free-run frequency: N*x*fref

  • Feedback prescaler ratio: N

  • VCO phase noise: Enabled

  • Reference modulation: Phase modulated reference selected

% Configure the model.
configurePhaseNoiseExample( 'PllPhaseNoiseExample', 2.1e9, 70, 'on', '0');
% Run the simulation
sim('PllPhaseNoiseExample.slx');
% Plot the PLL Testbench phase noise analysis
plotPhaseNoiseAnalysis();