How to perform jitter testing and analysis using a real-time oscilloscope

1. How much bandwidth do you need?
　　We are already in the era of digital oscilloscopes. Compared with only considering the bandwidth of analog amplifiers, you should consider the bandwidth of the oscilloscope more. In order to ensure that the oscilloscope provides enough bandwidth for the application, you must consider the bandwidth of the signal that the oscilloscope will examine.

　　Bandwidth is the most important characteristic of an oscilloscope because it determines the range of signals that can be displayed, and it also largely determines the price you pay. When making bandwidth decisions, you must balance your current limited budget with the anticipated needs during the life of the oscilloscope in your lab.

　　In current digital technology, the system clock is usually the highest frequency signal that an oscilloscope can display. The bandwidth of the oscilloscope should be at least three times higher than this frequency to properly display the shape of this signal.

　　Another signal characteristic in your system that determines the oscilloscope bandwidth requirement is the signal's rise time. Since you may be looking at more than a pure sine wave, the signal will contain harmonics at frequencies above the fundamental frequency of the signal. For example, if you are looking at a square wave, the signal will contain frequencies at least 10 times higher than the fundamental frequency of the signal. If you don't ensure the appropriate oscilloscope bandwidth when looking at a signal such as a square wave, you will see rounded edges on the oscilloscope display instead of the sharp, fast edges you expected. This in turn affects the accuracy of your measurements.

　　Fortunately, we have some very simple formulas that can help you determine the appropriate oscilloscope bandwidth based on your signal characteristics.

1. Signal bandwidth = 0.5/signal rise time
2. Oscilloscope bandwidth = 2 x signal bandwidth
3. Oscilloscope real-time sampling rate = 4 x oscilloscope bandwidth

　　After you have determined the appropriate oscilloscope bandwidth, you need to consider the sampling rate of each channel that the oscilloscope intends to use simultaneously. As listed in Equation 3 above, for each channel you intend to use, you must ensure that the sampling rate is four times the oscilloscope bandwidth so that these channels can fully support the rated bandwidth of the oscilloscope. We will discuss this in more detail later.

2. How many channels do you need?
At first glance, the number of channels seems to be a simple question. After all, don’t all oscilloscopes come with two channels or four channels? Nothing else! Digital content is everywhere in today’s designs, and no matter how high or low the proportion of digital content in the design, traditional 2-channel or 4-channel oscilloscopes cannot always provide the number of channels required to trigger and view all signals of interest. If you have encountered this situation, you will understand the problems involved in building external hardware or writing dedicated software to isolate the activities of interest.

　　For today's increasingly digital world, a new type of oscilloscope has enhanced the use of oscilloscopes in digital applications and embedded debugging applications. Mixed signal oscilloscopes (commonly referred to as MSOs) closely insert 16 additional logic timing channels in addition to the 2 or 4 oscilloscope channels of a typical oscilloscope. As a result, a full-featured oscilloscope is implemented that provides up to 20 time-correlated trigger, acquisition, and viewing channels.

　　We will take a common SDRAM application as an example to show how to use a mixed signal oscilloscope for daily debugging. To isolate the SDRAM write cycle, you must trigger the system on five different signal combinations - RAS, CAS, WE, CS and clock. A 4-channel oscilloscope alone is not enough to meet this basic measurement requirement.

　　As shown in Figure 2, 16 logic timing channels are used to set up the system to trigger on RAS high, CAS low, WE high, and CS. Oscilloscope channel 1 is used to view and extract the rising edge of the logic clock. In a logic analyzer and oscilloscope combination solution, the logic analyzer can only cross-trigger the oscilloscope or vice versa. Unlike this, a mixed signal oscilloscope can trigger full width on both the oscilloscope and the logic timing channels.

3. What is the sampling rate you require?
As mentioned earlier, sampling rate is a very important consideration when evaluating an oscilloscope. Why? Most oscilloscopes use an interpolation form, which only provides the maximum sampling rate on one or two channels in a four-channel oscilloscope when two or more channels are coupled to an analog-to-digital converter, thereby increasing the sampling rate. Many manufacturers only emphasize this maximum sampling speed in the main technical specifications of the oscilloscope, but do not tell the user that the sampling rate only applies to one channel! If you want to buy a 4-channel oscilloscope, then in fact you want to use and get full bandwidth on more than one channel.

　　Recall from the formula given in Consideration 2 that the oscilloscope's sample rate should be at least 4 times the oscilloscope's bandwidth. It is best to use a 4x multiplier when the oscilloscope uses some form of digital reconstruction, such as sin(X)/X interpolation. When the oscilloscope does not use a form of digital reconstruction, the multiplier should actually be 10x. Since most oscilloscopes use some form of digital reconstruction, a 4x multiplier should be sufficient.

　　Let's look at an example using a 500MHz oscilloscope that uses sin(X)/X interpolation. For this oscilloscope, to support a full 500MHz bandwidth on each channel, the minimum sampling rate required for each channel is 4 x (500MHz), or 2GSa/s per channel. Some 500MHz oscilloscopes on the market today claim a maximum 5GSa/s sampling rate, but do not specify that the 5GSa/s sampling rate applies to only one channel. When using three or four channels, these oscilloscopes actually only have a sampling rate of 1.25GSa/s per channel, which is insufficient to support a 500MHz bandwidth on several channels.

　　Another way to think about sampling rate is to determine the desired resolution between application points. The sampling rate is the inverse of the resolution. For example, suppose you want to achieve a resolution of 1ns between sample points. The sampling rate that will improve this resolution is 1/(1ns) = 1GSa/s.

　　In general, make sure the oscilloscope you are considering can provide sufficient per-channel sampling rate for all the channels you want to use simultaneously so that each channel can support the rated bandwidth of the oscilloscope.

4. How much memory depth do you need?
　　As mentioned earlier, bandwidth and sampling rate are closely related. Memory depth is also closely related to sampling rate. The analog-to-digital converter digitizes the input waveform and stores the resulting data in the oscilloscope's high-speed memory. An important factor in selecting an oscilloscope is understanding how the oscilloscope uses this stored information. Memory technology allows users to capture acquisition data, zoom in to see more details, or perform math operations, measurements, and post-processing functions on the acquired data.

　　Many people assume that the maximum sample rate specification of an oscilloscope applies to all timebase settings. This is certainly a good thing, but it would require a very large memory, and few people can afford an oscilloscope with such memory. Because the memory depth is limited, all oscilloscopes must reduce the sample rate as people set the timebase to a wider and wider range. The deeper the memory of the oscilloscope, the more time can be captured at the full sample rate. There is a popular oscilloscope on the market today that has a sample rate of several gigasamples per second and a memory of 10,000 samples. When the timebase is set to 2ms/div and slower, this oscilloscope is forced to reduce the sample rate to a few thousand samples per second. You must look at the oscilloscope in question to understand the effect of the timebase setting on its sample rate. The oscilloscope in question will only provide a few thousand hertz of bandwidth when operating at the required scan rate to display the entire system operation cycle.

　　The depth of memory you need depends on the number of displays you want to view and the sample rate you want to maintain. If you want to view longer periods of time with higher resolution between samples, you need deeper memory. A simple formula can tell you how much memory you need, taking into account the time interval and the sample rate:

Memory depth = sampling rate x display time

　　If you need to zoom in and take a closer look at a waveform, maintaining a high sample rate at all time settings on the oscilloscope can prevent aliasing and provide more detailed information about the waveform.

　　Once the memory depth has been determined, it is also important to examine how the oscilloscope operates when using the deepest memory setting. Oscilloscopes with traditional deep memory architectures are slow to respond, which can negatively impact productivity. Because of the slow response, oscilloscope manufacturers often relegate deep memory to a dedicated mode, and engineers typically only use deep memory when it is absolutely necessary. Although oscilloscope manufacturers have made great strides in deep memory architectures over the years, some deep memory architectures are still slow and time-consuming to operate. Before purchasing an oscilloscope, be sure to evaluate the oscilloscope's responsiveness at the deepest memory setting.

5. What display features do you need?
All oscilloscope vendors know that they sell waveform images. Back in the days of analog oscilloscopes, the design features of the oscilloscope's CRT display determined the quality of the image. In today's digital world, the actual performance of an oscilloscope depends largely on digital processing algorithms rather than the physical characteristics of the display device. Some oscilloscope manufacturers have added dedicated display modes to their products to overcome some of the differences between traditional analog oscilloscope displays and digital displays. There is no good way to determine which oscilloscope is best suited for your lab environment by studying the oscilloscope's technical specifications. Only when you demonstrate it in real time on your workbench and use your own waveforms can you determine which oscilloscope is best suited to meet your needs.