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Periodic Waveform Analyzer

A New Class of Instruments

The Periodic Waveform Analyzer (PWA) is a type of synchronous detector used for the analysis of periodic signals. Synchronous detection comes in different flavors, but is generally defined as a method to optimize the signal-to-noise ratio (SNR) when extracting signals from a noisy background. Distinct synchronous detection schemes all make use of the fact that the signal of interest is periodic and the associated frequency is a known reference. Lock-in detection and boxcar averaging are two examples of synchronous detection. Each of these schemes is tailored to a specific signal type: a sinusoidal signal for lock-in detection, a low duty-cycle signal for boxcar averaging.

The PWA enters this scenario by taking a continuous stream of samples and linking them synchronously to the phase of the reference oscillator. Additionally, the samples are averaged with previous samples displaying the same phase. Performing this operation over many periods of the reference frequency leads to a dense set of phase and sample pairs (where the phase is a value between 0 and 2π). This can be viewed as a digital signal averager for periodic signals. Plotting the averaged values with the phase on the X axis provides the phase-domain representation of the considered signal.

The PWA also overcomes the limit imposed by the physical sampling rate of the ADC by several orders of magnitude, similarly to what is achieved by a sampling oscilloscope.

Zoom into Periodic Waveforms

scope vs. periodic waveform analyzer

The UHF-BOX Boxcar Averager categorizes the phase values into 1024 bins, leading to a waveform with sub-degree (i.e., 2π/1024 or 0.4°) resolution and providing a phase-domain representation. If this resolution is not sufficient, it is possible to reference the input signal to a higher harmonic of the reference frequency: this is equivalent to zooming into the region of interest, thus increasing the temporal resolution down to millidegrees.

Boxcar or Lock-in? Ask the Harmonic Analyzer

The PWA makes it easy to select the most efficient signal recovery method. The duty cycle and the signal energy available in the first harmonic scale almost linearly. For instance, in a rectangular signal pulse with 50% duty cycle only 1/3 of the signal is in the first harmonic; if the duty cycle is divided by a factor of two, the signal energy in the first harmonic is halved too.

The FFT performed on the PWA dataset yields the spectral distribution of the signal amplitude over the higher harmonics of the reference frequency: specifically, this corresponds to the energy distribution at DC together with the first 511 harmonics of the reference frequency. In this way, users can easily identify the most appropriate measurement method – lock-in amplification or boxcar averaging. For example, if the signal spreads out over many harmonic components without any prominent peak, boxcar detection may be the wiser choice to achieve the best possible SNR.

Pulsed signal in LabOne

Averaging of Periodic Signals

The reference frequency for the PWA is provided by the instrument itself or, when externally generated, carefully tracked with a phase-locked loop of adjustable bandwidth. Compared to the analysis performed with a standard oscilloscope, this comes with the significant advantage of averaging without trigger jitter. Even more important is the possibility to perform dead-time free detection; many real-time oscilloscopes suffer from a considerable re-arm delay after each triggering event. The PWA can capture and average a data stream of 10 seconds or more, corresponding to 800 million periods for an 80 MHz laser, without missing a single sample.

Low Duty-Cycle Signal Analysis

The scope-like functionality of the PWA is helpful when selecting a window of interest for boxcar measurements. In the phase-domain representation, it is straightforward to choose the region that contains the valuable signal; if the resolution of 512 bins is insufficient, it is possible to reference the input signal to a higher harmonic of the reference frequency to zoom into the region of interest and increase the temporal resolution as needed.

The PWA is a versatile and powerful measurement instrument that provides value when combined with instruments such as a lock-in amplifier, a signal averager or a boxcar averager. The PWA replaces a sampling oscilloscope in many setups and can be part of any type of standard measurement instrumentation.

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