A Brief Discussion on the Storage Depth of Oscilloscope

Thanks to the development of electronic technology, in the field of oscilloscopes monopolized by the three foreign giants, domestic oscilloscopes have also sprung up like mushrooms after rain. Representatives of excellent domestic oscilloscopes: Dingyang (Siglent) Technology and Beijing Puyuan Jingdian have now made great progress. However, due to the link bottleneck of signal transmission and IC blockade, the domestic oscilloscopes growing in the cracks are destined to take the low-end route for the time being, which has led to serious homogeneity of domestic oscilloscopes and uneven performance and quality of oscilloscopes produced by various manufacturers. Looking around, the appearance and even the interface of various manufacturers all adopt the so-called "mainstream" operation method. As a measure of the technical indicators of oscilloscopes, engineers consider more those listed in the titles of product manuals and magazine advertisements. Among these main technical indicators, bandwidth, sampling rate and storage depth are well known. Of course, the bandwidth indicator is very important. Bandwidth determines the basic measurement capability of the oscilloscope for signals. As the signal frequency increases, the oscilloscope's ability to accurately display the signal will decrease. Without sufficient bandwidth, the oscilloscope will not be able to distinguish high-frequency changes. The amplitude will be distorted, the edges will disappear, and the detailed data will be lost. Without sufficient bandwidth, all the characteristics of the signal, ringing and humming, etc. are meaningless. This specification indicates the frequency range that the oscilloscope can accurately measure. Every engineer pays enough attention to the impact of bandwidth on measurement, so everyone follows the five-fold rule of measurement: the bandwidth required by the oscilloscope = the highest signal frequency of the measured signal * 5. The measurement error of the oscilloscope selected using the five-fold rule will not exceed +/-2%, which is sufficient for most operations. Regarding the sampling rate, it refers to the frequency at which the digital oscilloscope samples the signal, similar to the concept of frames in a movie camera. The faster the sampling rate of the oscilloscope, the higher the resolution and clarity of the displayed waveform, the lower the probability of losing important information and events, and the more realistic the signal reconstruction. The sampling rate is divided into real-time sampling rate and equivalent sampling rate. The sampling rate we usually refer to is the real-time sampling rate, because the real-time sampling rate can be used to capture non-periodic abnormal signals in real time, while the equivalent sampling rate can only be used to collect periodic stable signals. Although memory depth is one of the important indicators, its importance is often ignored when measuring oscilloscopes. It has always been regarded as a "secondary" indicator. It is not very clear what effect a large memory depth has on measurement. In addition, some oscilloscope manufacturers mislead about "memory depth". At the same time, the hidden relationship between memory depth and sampling rate has led to memory depth being a meaningless indicator. In order to correct these misunderstandings, let's discuss what memory depth is? What effect does a large memory depth have on measurement? What is memory depth?

Memory depth is a measure of how many sampling points an oscilloscope can store. If you need to capture a pulse train continuously, the oscilloscope must have enough memory to capture the entire event. The required memory depth, also known as record length, can be calculated by dividing the length of time to be captured by the sampling speed required to accurately reproduce the signal. It is not as some second-rate domestic manufacturers claim that "memory depth refers to the longest record of the waveform that can be recorded when recording the waveform." This substitution of concepts completely guides people's understanding in the opposite direction. No wonder their technical indicators are as high as "1042K" record length. This is why they don't say that the memory depth is the number of waveform points that can be stored in a real-time acquisition of the waveform under high-speed sampling.

The storage of the oscilloscope is to store the eight-bit binary waveform information after A/D digitization in the high-speed CMOS memory of the oscilloscope. This process is called the "write process". The capacity (storage depth) of the memory is very important. For DSO, its maximum storage depth is fixed, but the storage length used in actual testing is variable.

When the storage depth is constant, the faster the storage speed, the shorter the storage time, and there is an inverse relationship between them. At the same time, the sampling rate and the time base are linked, that is, the smaller the time base is adjusted, the higher the sampling rate. The storage speed is equivalent to the sampling rate, and the storage time is equivalent to the sampling time. The sampling time is determined by the time represented by the display window of the oscilloscope, so:

Memory depth = sampling rate × sampling time (distance = speed × time)

Since the horizontal scale of the DSO is divided into 12 grids, the time length represented by each grid is the timebase (timebase), and the unit is s/div, so the sampling time = timebase × 12. From the storage relationship, we know that: increasing the storage depth of the oscilloscope can indirectly increase the sampling rate of the oscilloscope. When measuring waveforms for a longer time, since the storage depth is fixed, the sampling rate can only be reduced to achieve it, but this will inevitably cause a decrease in waveform quality; if the storage depth is increased, it can be measured at a higher sampling rate to obtain an undistorted waveform.

The curve below reveals the relationship between sampling rate, memory depth, and sampling time, as well as the impact of memory depth on the actual sampling rate of the oscilloscope. For example, when the time base is set to 10us/div, the sampling time of the entire oscilloscope window is 10us/div * 12 grids = 120us. At a memory depth of 1Mpts, the current actual sampling rate is: 1M÷120us︽8.3GS/s. If the memory depth is only 250K, then the current actual sampling rate is only 2.0GS/s!

In a word, the memory depth determines the ability of DSO to analyze high-frequency and low-frequency phenomena at the same time, including high-frequency noise of low-speed signals and low-frequency modulation of high-speed signals.

The impact of long memory on measurement
After understanding the close relationship between memory depth and sampling speed, let's talk about the impact of long memory on our usual measurements? Usually, a very stable sine signal only needs a record length of 500 points; but if you want to analyze a complex digital data stream, you need a memory depth of tens of thousands of points or more, which is impossible for ordinary storage. At this time, we need to choose long memory mode. Fortunately, domestic oscilloscopes now have such options. For example, the ADS1000CA series oscilloscopes launched by Dingyang (Siglent) have a memory depth of up to 2M, which is the largest memory depth oscilloscope among domestic oscilloscopes at present, breaking the function that only high-end oscilloscopes can have a large memory depth. By selecting the long memory mode, some details in some operations can be optimized, and at the same time, it is equipped with a 1G real-time sampling rate and a high refresh rate to perfectly reproduce the captured waveform.
The most obvious impact of long storage on ordinary measurements is in the data link and power measurement with fast changes in the header. This is because the frequency of power electronics is relatively low (mostly less than 1MHz), which is sufficient for us to choose the bandwidth of the oscilloscope. The bandwidth of 300MHz oscilloscope is relatively high compared to the power switching frequency of several hundred KHz, but many times we ignore the selection of sampling rate and storage depth. For example, in the test of common switching power supplies, the frequency of voltage switching is generally 200KHz or faster. Since there is often power frequency modulation in the switching signal, engineers need to capture a quarter cycle or half cycle of the power frequency signal, or even multiple cycles. The rise time of the switching signal is about 100ns. We recommend that in order to ensure accurate reconstruction of the waveform, there should be more than 5 sampling points on the rising edge of the signal, that is, the sampling rate should be at least 5/100ns=50MS/s, that is, the time interval between two sampling points should be less than 100/5=20ns. For the requirement of capturing at least one power frequency cycle, it means that we need to capture a 20ms long waveform, so we can calculate the required storage depth of each channel of the oscilloscope = 20ms/20ns=1Mpts! This is why we need a large storage depth! What if the storage depth does not reach 1 Mpts, but only a few K of an ordinary oscilloscope? Then either we cannot observe such a long-period signal, or we can only sample at a low sampling rate when observing such a long-period signal. As a result, the waveform of the switching frequency cannot be displayed in detail when the waveform is reconstructed.
In the long storage mode, it is guaranteed that the sampling is performed at a high rate and the signal is recorded for a long time. If only a single capture or stop acquisition is performed at this time, then when the waveform is expanded under different time bases, due to sufficient data points, abnormal signals such as small glitches superimposed on the signal can be well observed, which is very convenient for engineers to find problems and debug equipment. If it is ordinary storage, in order to maintain a high sampling rate, during the long recording time, due to the continuous sampling of the oscilloscope, several frames of data have been recorded in the memory. The data in the memory is not the data obtained by one acquisition. At this time, if the acquisition is stopped and the waveform rotation time base is enlarged and displayed, only a limited number of gears can be reached, and the observation of the full scan range cannot be achieved.
In DSO, the spectrum of a signal can be obtained by fast Fourier transform (FFT), and then a signal can be analyzed in the frequency domain. For example, the measurement of power supply harmonics requires FFT to observe the spectrum. In the measurement of high-speed serial data, FFT is often used to analyze the noise and interference that cause system failure. For FFT operation, the total amount of acquisition memory available in the oscilloscope will determine the maximum range (Nyquist frequency) of the signal components that can be observed, and the memory depth also determines the frequency resolution △f. If the Nyquist frequency is 500 MHz and the resolution is 10 kHz, consider determining the length of the observation window and the size of the acquisition buffer. To obtain a resolution of 10kHz, the acquisition time is at least: T = 1/△f = 1/10 kHz = 100 ms. For a digital oscilloscope with 100kB memory, the highest frequency that can be analyzed is:
△f × N/2 = 10 kHz × 100kB/2 = 500MHz. For DSO, long memory can produce better
FFT results, increasing both frequency resolution and signal-to-noise ratio.

In short, long memory plays an important role in providing an overview of the whole picture and presenting details. The memory depth determines the ability of DSO to analyze high-frequency and low-frequency phenomena at the same time, including high-frequency noise of low-speed signals and low-frequency modulation of high-speed signals.