About the oscilloscope's memory depth

When I was working as an engineer in a high-end company, I didn’t know this relationship until I started selling oscilloscopes. I learned that there was such a relationship and it was very important. When I was studying, I certainly didn’t know this relationship at all.

When I was an engineer, my boss told me that in order to ensure that the oscilloscope can accurately capture the peak voltage of the power MOS tube, you must not look at many waveforms on the screen at the same time, and try to display only one pulse on the oscilloscope. What he did was to constantly adjust the trigger level and stare at the oscilloscope with his naked eyes until he adjusted the trigger level to a high enough level (how high is high enough?), thinking that the peak voltage "captured" at a certain time should be the largest. Why didn't he capture more waveforms at the same time, just make sure that the sampling rate is the maximum or sufficient, and then turn on the statistical value of the parameter measurement, wouldn't it be better? But he only believed in the waveform that he stared at with his eyes, and concluded that a certain waveform must be the largest. Fortunately, he knew how to use the trigger level. Of course, we believed that he was an authority, because he was indeed a company-level expert at the time. …

This true story gave me a strong reason to hold 1,000 oscilloscope technology seminars. Engineers are reluctant to spend an hour listening to the basic course of oscilloscopes. They always think that oscilloscopes are very simple, but in fact, they still have too little knowledge of the ABCs of oscilloscopes. Some people regard this as one of the differences between Chinese engineers and foreign engineers. This judgment is somewhat infuriating, but it is indeed true to some extent. From another perspective, the professionalism of a company in using oscilloscopes can basically reflect the company's R&D level.

So today let's take a little time to quickly read this "shallow" article about oscilloscope memory depth. To meet everyone's needs for quick reading, the title of the article is excerpted as follows:
      1. The basic concept of memory depth
      2. The physical medium of oscilloscope memory
      3. The relationship between memory depth and sampling rate
      4. Maximum memory depth, the current maximum memory depth, the superposition of memory depth, the displayable memory depth, the analyzable memory depth,
      5. The application value of memory depth

Memory depth is called the
third most important indicator of an oscilloscope. Memory depth = sampling rate * sampling time. This relationship is called the first relationship of an oscilloscope by the author.

1. Basic concept of storage depth

"Memory Depth" is a translated word, and it is called "Record Length" in English. Some people translate it into "storage length", "record length", etc. It indicates the number of sampling points that the oscilloscope can save. The memory depth is "10 million sampling points", and oscilloscope manufacturers write it as 10Mpts, 10MS or 10M. Here, pts can be understood as the abbreviation of points, and S can be understood as the meaning of Samples.

The storage depth is actually the capacity of a certain memory in the physical medium. The English word for memory is "Memory". The size of the memory capacity is also called "storage depth". What happens when the memory is full and reaches the limit of the storage depth? We can think of the memory of the oscilloscope as a circular memory. The oscilloscope continuously samples and gets new sampling points, which will be filled in. The old sampling points will automatically overflow. This process will repeat until the oscilloscope is "stopped" by a "trigger signal" or is forced to "stop" after a certain period of time. After "stopping" once, the oscilloscope "moves" the sampling points stored in the memory to the screen of the oscilloscope for display. The waiting time between these two "moves" is extremely long compared to the sampling time, which is called "dead time".

The above process is often compared by the author as follows: the memory is like a "water tank", and the capacity of the "water tank" is the "storage depth". If a "faucet" is used to fill the water tank with water at a constant speed, the water flow rate of the faucet is the "sampling rate". When the water tank is already full of water, the faucet is still filling the water tank, and some of the water in the water tank will overflow, but the overall capacity of the water tank remains unchanged. Under certain conditions, all the water in the water tank will be poured out, and the cycle will repeat. Figure 1 vividly represents the concept of this circular memory.

Figure 1 Oscilloscope ring memory

2. Physical media of oscilloscope memory

What is the physical medium of the memory? Is it the DDR memory we are familiar with? Why is the capacity so small? Why can't we use a large-capacity medium such as a hard disk or SD card as the physical medium? If the hard disk is used as the storage medium, can't the oscilloscope be used as a data recorder?

It’s not easy to answer the above questions!

According to the author's understanding, the memory used in early oscilloscopes, including the current high-bandwidth oscilloscopes, is a dedicated chip designed by the oscilloscope manufacturer itself. At one time, the coordination between the memory chip and the ADC chip was even a technical bottleneck for Company A (later called Company K). Several years ago, after the storage depth of all oscilloscopes of Company K reached 2Mpts sampling points per channel, the sampling rate would automatically drop to 4GS/s. It was not until 2006 (it seems to be this year, or maybe later) that Company A acquired a chip company to solve this technical bottleneck. Now, in all series of low-bandwidth oscilloscopes of Company K, the storage depth index has not been able to exceed 2Mpts per channel. I guess it may still use old chips.

For high-end oscilloscopes, memory chips have always been the core technology, and I know very little about the technical details. The ADC speed in the oscilloscope is too fast, and ordinary storage media simply cannot "throughput" such a large amount of data in such a short time.

Let's use specific numbers to understand the requirements of high-speed ADC's ultra-large data volume on memory "throughput". For example, the sampling rate of ADC is 20GS/s, which means that 20G points are sampled per second, and each point is composed of 8 0s and 1s. If the output of ADC is transmitted to the memory completely in serial data, then the transmission rate is 160Gbps. What is this concept? The current PCI-Express 3.0 rate is 8Gbps. The highest-speed high-speed chip can reach a transmission rate of 25Gbps on a single board, but it is not mature yet and has not been used on oscilloscopes. How to transmit the sampling points of high-speed ADC to memory is a difficult problem! In fact, such a high-speed ADC cannot be designed as a single chip. It is realized by "interweaving and splicing" many "small" ADCs of 2.5GS/s, 1.25GS/s, and 250MS/s. Since it is not completely implemented in a serial way, after adopting parallel transmission, how to calibrate and align the data transmitted to the memory, and then display it regularly on the oscilloscope screen through the trigger mechanism? This is a little secret of oscilloscope manufacturers. The threshold for oscilloscope development in this area is not very high today, but it is still a little bit.

You may ask another question, how is the data in the memory transmitted to the CPU for analysis and display? This is also a question, which involves the data processing architecture of the oscilloscope. With the development of oscilloscope technology, there are currently two architectures, one is based on the PC platform, and the other is embedded, mainly based on FPGA. With the increase in DDR memory rate and the enhancement of FPGA computing power, the memory chips based on the FPGA computing platform are no longer mysterious. Most of them use industrial DDR memory particles. Therefore, the memory depth indicator can be made very large without considering whether the stored sampling points are really displayed and analyzed. But often the real situation is that although the memory depth is very high, the number of displayed sampling points and the number of analyzed sampling points may be only a few thousandths, which mainly depends on the "computing resources" of the FPGA or the cost. In other words, it depends on the definition of the oscilloscope product. Of course, without considering the cost, you can brag to outsiders about the advantages of the algorithm. In this type of product, the storage depth corresponding to the waveform seen on the screen is not equal to the sampling rate multiplied by the sampling time, which is sometimes really entangled.

3. Relationship between storage depth and sampling rate
Storage depth = sampling rate * sampling time. The author has always persistently called it the first relationship in the oscilloscope, because many engineers make mistakes when using the oscilloscope because they forget this relationship. Figure 2 shows the display interface of China's first intelligent oscilloscope SDS3000. In the red box at the bottom right, the two values ​​on the right, 50MS/s and 20ms/div, multiplied by 10, equal the number on the left, 10MS. The current sampling rate is 50MS/s, and the current time base is 20ms/div. Because the horizontal axis is 10 grids (some oscilloscopes are 12 or 14 grids), the sampling time is 200ms, 50MS/s * 200ms = 10MS. That is to say, to capture a 200ms waveform at a sampling rate of 50MS/s, the storage amplitude of the oscilloscope needs to be 10MS. This is the same concept as filling a water tank with water. If the flow rate of the "faucet" is 50 million (50M) drops of water per second, then if you continue to fill the "water tank" with water for 200ms, there will be 10 million (10M) drops of water in the tank. It is such a simple product relationship. [page]

Figure 2 Display interface of SDS3000 from Dingyang Technology

This first relationship is reinforced by many wonderful metaphors used by oscilloscope manufacturers. One of the most classic metaphors is related to "Mona Lisa's charming smile": when the memory depth is too low, it is equivalent to the digital camera's pixel being too low. The photo taken of this famous painting cannot vividly reproduce Mona Lisa's charming smile, but it can realistically capture Mona Lisa's pretty nose, because capturing a charming smile requires capturing the entire face, which requires higher pixels, while the nose is only a part, and the pixel requirements are not high.

The diagram in Figure 3 also clearly demonstrates the importance of this relationship. The first diagram shows that under the premise of sufficient sampling rate, observing multiple cycles of samples requires a long storage depth, which requires 36 sampling points in the diagram. The sampling rate in the second diagram remains unchanged, but the storage depth is reduced to only 9 sampling points, so only waveforms with multiple points in one cycle can be sampled. The third waveform still has a very small storage depth of only 9 sampling points, but it still needs to sample waveforms with multiple cycles like the first diagram. As a result, the sampling rate is reduced and the measured waveform will be distorted.

Figure 3 Deduction of the relationship between sampling rate and memory depth

　　
4. Maximum memory depth, currently set maximum memory depth, memory depth superposition, displayable memory depth, analyzable memory depth. The maximum memory depth of each oscilloscope with standard configuration and the maximum memory depth after adding options may be different. The maximum memory depth of each oscilloscope is limited by the physical medium. The maximum memory depth of the purchased oscilloscope needs to be set in the menu. In order to pursue the operating experience, the oscilloscope manufacturer often does not set the factory default memory depth to the maximum memory depth that the oscilloscope can achieve.

Once the current maximum storage depth is set, adjust the horizontal time base. As the sampling time increases, the storage depth of the oscilloscope will automatically increase, and the sampling rate will remain unchanged during this process. After the storage depth increases with the sampling time to the currently set maximum storage depth, if the sampling time continues to increase, the sampling rate will automatically decrease and the storage depth will remain unchanged. However, in some cases, because the steps of the sampling rate and sampling time jump at a fixed number of gears and are not continuously fine-tuned, the multiplication of the two may not be the same as the value of the maximum storage depth. At this time, the oscilloscope may automatically adjust the current sampling rate or storage depth so that the three of them meet the product relationship. As shown in Figure 4, the product relationship between the three is deduced using specific values.

Figure 4 Relationship between storage depth, sampling rate, and sampling time (horizontal time base)

When multiple channels of the oscilloscope work at the same time, the sampling rate and storage depth can work in superposition mode. Most oscilloscopes have 2 channels superimposed, and some have 4 channels superimposed. Figure 5 shows the working principle diagram of two channels superimposed. Channel 1 and channel 2 are sampled alternately, and one channel is delayed by 1/2 of the sampling period to double the sampling rate. The oscilloscope reads the sampling points in the memory alternately during the sampling process, and the overall storage depth is also doubled accordingly. Therefore, in order to obtain the maximum sampling rate and storage depth, when only two channels are used for measurement, for the two-by-two superposition mode, it is recommended to open only one of channels 1 and 2, and one of channels 3 and 4.

Figure 5 Schematic diagram of two channels of the oscilloscope working in superposition mode

Although modern oscilloscopes have a high storage depth and can easily capture tens of thousands of data samples, the image resolution of the oscilloscope's display screen in the horizontal direction is often only 1280 pixels or even less. How does an oscilloscope squeeze so many points on such a small screen? The display compression algorithm solves this problem. The compression algorithm divides the captured large number of data samples into many small segments, and only extracts the maximum value and the maximum value data point from each segment to display on the screen. As shown in Figure 6, only 770 samples of the captured 1K-1M data samples are displayed on the display screen, and the maximum and minimum points are displayed in pairs on the screen. This compression algorithm aggravates the visual effect of the peak-to-peak value of the signal on the display, which is manifested in that the waveform looks more noisy than the partially enlarged, uncompressed waveform after expansion, and the waveform trajectory appears thicker. [page]

Figure 6 Simple illustration of the compression algorithm

However, even if some oscilloscopes use display compression algorithms, the storage depth displayed on the screen is not equal to the current sampling rate multiplied by the sampling time. Only part of the waveform is displayed on the screen, corresponding to a part of the "sampling time". There is also a part of the "sampling time" "outside" the screen! You need to rotate the "position" key on the oscilloscope panel to "move" the waveform collected outside the screen to the window displayed on the screen. This is very confusing.

Some oscilloscopes are not only unable to fully display the captured data through compression algorithms, but also unable to fully measure and analyze the captured data. This is a major "common problem" of Tektronix oscilloscopes. Even if this type of oscilloscope has a large storage depth, it is not of great practical value to users. The waveforms are just compressed and "stacked" there for users to take a "rough look". Dingyang Technology's smart oscilloscope SDS3000 does not have such a problem. Please see Figures 7 and 8 below to see it clearly! In Figure 7, Dingyang Technology's SDS3000 measures a signal with varying pulse widths. The minimum pulse width is 13.9ns and the maximum is 399.8898us, which is consistent with the actual situation; in Figure 8, the Tektronix MDO3000 is used to measure a signal with varying pulse widths. The minimum pulse width is 37.32us and the maximum is 37.52us. The minimum pulse width on the screen is only about 13.9ns, in the middle of the screen, as seen by the naked eye, but the Tektronix oscilloscope cannot measure it.

Figure 7: Signal of pulse width variation measured by SDS3000 of Dingyang Technology. The minimum pulse width is 13.9ns and the maximum is 399.8898us, which is consistent with the actual value.

Figure 8: Tektronix MDO3000 measures the pulse width of the signal, the minimum pulse width is 37.32us, the maximum pulse width is 37.52us. The minimum pulse width on the screen is in the middle of the screen, but it cannot be measured.

5. Application value of storage depth
Some low-frequency signals contain high-frequency noise, some high-speed signals contain low-frequency modulation, some signals change very slowly, and some analyses are meaningful only when the number of samples is large enough. In these four cases, long storage is required. In the first two cases, the low-frequency components of interest need to be captured completely before meaningful analysis can be performed. Many practical applications fall into the application categories of the above four long storages, such as the measurement of power soft start process, power ripple and power noise, FFT analysis, spread spectrum clock analysis, finding random or rare errors, statistical analysis, jitter tracking analysis, eye diagrams, etc. There are many application documents on this aspect, and this article will not go into details.