Two response characteristics of oscilloscopes

The measured waveform is sampled and processed from the input connector and displayed on the screen, while the data is saved. Once an inappropriate oscilloscope is selected, the waveform may be distorted. Especially when measuring waveforms of high-speed serial interfaces such as PCI Express, it is necessary not only to measure the sampling frequency and bandwidth, but also to have some understanding of the response characteristics of the oscilloscope. For example, when measuring very steep signal changes, there will be differences due to differences in the response characteristics of the oscilloscope.

Reaction systems are divided into two categories

The response characteristics of an oscilloscope generally refer to the "transfer characteristics" of the entire measurement system from the input connector to the screen display. It can usually be divided into two categories: Gaussian response system and brick-wall response system. The brick-wall response system is also called flat response.

The easiest way to distinguish or compare the differences between these two types of systems is to look at the two basic parameters: "-3dB frequency characteristics" and "step waveform response".

Commonly used analog oscilloscopes are Gaussian response systems, and their frequency characteristics will slowly decline at the right shoulder end. Even if the step waveform input is steep, it is not easy to produce waveform distortion, that is, there will be no instantaneous preshoot of the step waveform, overshoot after the waveform, or ringing of the waveform shaking up and down. This is an ideal characteristic when measuring digital circuit signals with short transition times.

Analog oscilloscopes must convert the tiny voltage signal of a few mV at the input end into a voltage of hundreds of mV through several stages of amplifier circuits to ensure that it is sufficient to drive the CRT display. The frequency response characteristics of these amplifier circuits are Gaussian.

When measuring the waveform of a high-speed serial interface, a broadband digital oscilloscope with real-time sampling is generally used. This type of oscilloscope often uses a brick-wall response type response system.

The brick wall response is also called the "highest flat response". The frequency response is extremely flat within the frequency band, and the signal is quite steep when it rolls off outside the frequency band. With such an ideal frequency characteristic, the signal amplitude within the frequency band will not be attenuated. Beyond the frequency band, the signal amplitude becomes zero.

Compared with Gaussian response oscilloscopes, brick wall response oscilloscopes still have several disadvantages:

• In response to the input step waveform, pre-shoot or over-shoot waveforms are likely to occur
• The oscilloscope has a longer rise time, in other words, it reacts more slowly

The oscilloscope rise time mentioned here refers to the rise time from the step input to the output waveform. The shorter this time is, the more faithfully the oscilloscope can show the waveform measured from the input connector. Therefore, the oscilloscope rise time is synonymous with its high-frequency characteristics. At the same time, the rise time of a digital signal generally refers to the time it takes to migrate from a low level to a high level. It usually refers to the rise migration time of 10% to 90% of the signal level, and for high-speed digital communications, it mostly refers to the time migration of 20% to 80%.

The following two mathematical formulas can be used to estimate the rise time of brick-wall and Gaussian oscilloscopes:

Brick wall response oscilloscope rise time (ns) = 0.45/bandwidth (GHz)

The rise time (ns) of a Gaussian response oscilloscope is 0.35/bandwidth (GHz), ideally it should be 0.338/bandwidth (GHz)

For example, for an oscilloscope with a bandwidth of 6 GHz, the rise time of a Gaussian response oscilloscope is about 58 ps, while the rise time of a mainstream brick-wall response oscilloscope with the same bandwidth is about 70 ps.

Although the rise time of the brick-wall response oscilloscope is slightly inferior, the real-time sampling broadband digital oscilloscope models mainly adopt the brick-wall response characteristics. A closer look reveals two main reasons. First, it is to avoid the error of the input signal and output signal voltage amplitude, because the amplitude error of the Gaussian response oscilloscope within the frequency band is too large. The frequency response diagrams of the two oscilloscopes shown in Figure 2 show their advantages and disadvantages in this regard. Assuming that the input signal bandwidth is 1GHz and the sampling frequency is 4GHz, it can be seen from Figure 2 that the frequency characteristics of the Gaussian response oscilloscope slowly decline at the right shoulder, especially in the frequency band area exceeding 1/3 of the bandwidth, the waveform is obviously attenuated, that is, the signal error is large.

Increase sampling frequency to suppress aliasing

Another important reason for choosing a brick-wall response type for a high-speed digital oscilloscope is to avoid or minimize the phenomenon of aliasing. When using a digital oscilloscope to measure high-speed signals, aliasing occurs, mainly because when reproducing the sampled high-speed signal, some signals are mixed with unnecessary waveforms. These mixed signal frequency components will distort the original signal waveform, and in severe cases, will cause measurement errors.

The phenomenon of image aliasing mostly occurs in the continuous signal of the analog-to-digital converter, which contains a component that exceeds the Nyquist frequency, that is, half of the sampling frequency. This component folds back in the Nyquist frequency domain and appears within the oscilloscope measurement bandwidth. It can be clearly seen from the frequency characteristic diagram that the image aliasing effect of the brick-wall response oscilloscope is minimal.

Under the same conditions, it can be clearly seen that there is almost no signal in the area beyond the Nyquist frequency of 2 GHz, which can suppress the occurrence of aliasing.

In addition, if you measure a waveform with a period of 2.2ns and a rise time of about 90ps at three different sampling frequencies, 20GHz, 10GHz, and 5GHz, you will get different results. The lower the sampling frequency, the longer the actual measured value of the rise time, and the less faithfully the waveform can be presented.

Currently, the real-time sampling broadband digital oscilloscopes used for high-speed serial interface measurements have high sampling frequencies of up to 20 GHz for analog-to-digital converters on high-performance models. Generally, in order to reduce the occurrence of image aliasing, the sampling frequency of a Gaussian response oscilloscope needs to be 4 to 6 times that of the input signal, while a brick-wall response oscilloscope only needs 2.5 times.

Usually the frequency band is below 1 GHz, so most of them use Gaussian response system, while instruments above 1 GHz mostly use brick wall response system. Table 2 shows the advantages and disadvantages of the two response oscilloscopes.

Select an oscilloscope based on performance requirements

So how do you choose the best oscilloscope for your application? Here are 4 simple steps:

• _{Calculate the highest frequency component f max} of the measured signal . That is, the upper limit of the signal frequency component can be calculated by measuring the rise time of the signal. Assuming that the rise time migrates from 20% to 80%, the approximate value can be estimated using the mathematical formula (0.4/signal rise time) instead of directly estimating from the data transmission rate. For the popular third-generation bus PCI Express, its rise time is about 100ps in most cases.
• Select the response characteristics of the oscilloscope, that is, choose a suitable one between the Gaussian response system and the brick wall response system. Generally, the latter is chosen for applications that measure high-speed serial interfaces or buses.
• The necessary input bandwidth must be determined. It is related to the measurement error of the rise time. An instrument company has conducted a simulation experiment: if the brick wall reaction system allows a 3% error, the bandwidth can be calculated using (1.4×fmax); if the error is suppressed to 10%, it can be calculated using (1.2×fmax); when the allowable error is 20%, it can be calculated using (1.0×fmax).
• Estimate the minimum sampling frequency value that will utilize the bandwidth value above, and for a brick-wall oscilloscope, a minimum of (2.5 x bandwidth) is required.

The above four points can be used to illustrate a case: a digital signal with a rise time of 100ps and an f _max of 4GHz, choose a brick-wall response oscilloscope, and assume that the error of the rise time is limited to 3%. Then the bandwidth of the input signal is 5.6GHz, so the minimum sampling frequency needs to be 14GHz.

If the sampling frequency of 14GHz is applied to a Gaussian response system, the input bandwidth becomes 3.5GHz, and the measurable signal rise time is 220ps, which is half of that of a brick-wall response system. Some broadband real-time oscilloscopes rely on the use of digital signal processing to achieve the characteristics of a brick-wall response system. After all, it is difficult to achieve ideal characteristics by circuit technology alone.

In short, the appropriateness of bandwidth and sampling frequency is an important indicator when choosing an expensive oscilloscope. In addition, understanding the characteristics of the test instrument is also a key factor in mastering correct measurements.