When using electronic measurement tools, observing waveforms is one of the most frequently utilized functions. How do we typically acquire and reconstruct waveforms? Two common devices that employ different acquisition methods are the oscilloscope and the power analyzer. Today, I’ll briefly explain the general waveform acquisition techniques used by both transient and steady-state measurement instruments.
According to the Nyquist Sampling Theorem, the sampling frequency needed to reconstruct a waveform should be at least double the highest frequency of the signal being measured. When the oscilloscope's maximum sampling rate exceeds the frequency of the signal being measured by more than two times, it acquires data in what’s known as “real-time sampling.†This is the standard method used in digital oscilloscopes and is essential for capturing fast, single-shot, or transient signals.
For instance, if you're working with a digital oscilloscope, real-time sampling ensures that enough samples are collected during a single sweep to create an accurate representation of the signal. This method allows us to visualize even the fastest changes in the waveform.
However, when the sampling frequency doesn’t meet the requirements set by the Nyquist theorem, we turn to an alternative approach: equivalent sampling. The core idea behind equivalent sampling is to transform high-frequency, fast-changing signals into lower-frequency, slower, repetitive signals for easier acquisition. To achieve this, the measured signal must exhibit periodic behavior. Instead of taking samples from the same part of the waveform in each cycle, equivalent sampling collects points from different periods. Through mathematical processing, these points are then combined to reconstruct the original signal. This method allows us to restore the original signal without distortion, even when the sampling frequency is less than twice the original signal’s frequency. It works particularly well for analyzing high-frequency periodic signals.
Equivalent sampling can further be divided into two types: sequential equivalent sampling and random equivalent sampling. In sequential equivalent sampling, we take a sample at regular intervals—every k cycles—and slightly delay the sampling by Δt after each interval. For example, if k equals 1, we collect N points per cycle, and these points are eventually pieced together to form one complete cycle. The effective sampling frequency becomes the inverse of the small delay Δt. By adjusting Δt, we control the equivalent sampling frequency, while changing K affects the actual sampling frequency—the larger K is, the lower the actual sampling frequency becomes. Conversely, the smaller Δt is, the higher the equivalent sampling frequency gets.
On the other hand, random equivalent sampling uses an internal clock that is asynchronous with the input signal and relies on triggering based on the signal itself. Samples are acquired continuously and independently of the trigger position. The waveform is reconstructed by tracking the time difference between the sampled data and the trigger point to establish the correct position of each sample within the signal. However, this introduces challenges in accurately determining the sample’s position relative to the trigger point. While the samples occur sequentially in time, they appear random concerning the signal’s periodicity, resulting in what’s termed “random†equivalent time sampling.
Unlike an oscilloscope, which is designed for transient signal analysis, a power analyzer—a tool used for steady-state signals—can also apply equivalent sampling concepts. However, this requires the measured signal to be stable and periodic; otherwise, the measurement results could be significantly off. Thus, a power analyzer is better suited for steady-state measurements with limited transient analysis capabilities.
In some cases, when an instrument uses a fixed sampling rate, the sampling points might always align at the same position within the measured signal. To address this issue, random sampling was introduced. This technique dynamically modifies the sampling rate so that there’s no integer multiple relationship between the measured signal and the sampling rate. This helps prevent the sampling points from consistently landing in the same position, ensuring more accurate measurements.
When the sampling rate is lower than the input signal’s frequency, certain high-frequency components may be lost, leading to aliasing—a situation where high-frequency components are incorrectly interpreted as lower-frequency data. Random sampling addresses this issue by increasing the sampling rate and then randomly selecting samples, effectively shifting the sampling points over time. This approach helps to ensure that all relevant information is captured without distortion.
For example, when the input signal frequency exceeds 100 kHz, a sampling rate of 200 kHz (a 5 microsecond interval) wouldn’t be sufficient to describe an entire signal period. However, by collecting multiple periodic samples, the envelope formed matches the input signal’s amplitude and lowers its apparent frequency. This allows the measured effective value to align closely with the true effective value, enabling the analysis of signals beyond half the sampling rate (fs/2). This process can be thought of as a kind of “frequency conversion.â€
But it’s important to note that aliasing must be avoided when the signal frequency is an integer multiple of fs/2, such as 100 kHz, 200 kHz, etc. In these cases, random sampling becomes crucial.
Additionally, a power analyzer often struggles to fully represent signal details due to the limited number of display pixels compared to the number of sampling points per cycle. When displaying a waveform, the power analyzer offers two extraction methods: equal interval extraction and peak extraction.
Equal interval extraction involves selecting one point every 1,000 points from the total 2M sampling points, displaying only 1k points. Meanwhile, peak extraction selects two points per 2,000 sampling points, identifying the maximum and minimum values within each segment before reconstructing the waveform.
In conclusion, oscilloscopes excel at capturing transient signals, providing dense waveform reconstructions that emphasize transient capabilities. In contrast, power analyzers focus on steady-state measurements, especially RMS calculations, with an emphasis on signal amplitude and characteristics. This makes them ideal for applications requiring stable signal analysis. With technological advancements, modern devices like the ZLG Zhiyuan Electronic PA8000 power analyzer, boasting a basic power accuracy of 0.01% and a bandwidth of 5 MHz, showcase significant improvements in waveform acquisition and reconstruction. I’m confident that future developments will bring power analyzers ever closer to the capabilities of oscilloscopes, offering even greater functionality and precision.
H2R Bone Conduction Helmet Speaker
H2R Bone Conduction Helmet Speaker,Waterproof Bluetooth Speaker,Waterproof Helmet Headphone,Bone Conduction Speaker
Shenzhen Lonfine Innovation Technology Co., Ltd , https://www.lonfinesmart.com