Briefly describe the functions of waveform diagram, eye diagram and constellation diagram, that is, describe the characteristics of the signal from what angle.

In the field of digital communication, digital signals are often represented on the complex plane to intuitively represent the relationship between signals. This picture is a constellation. Digital signals can be represented by points on the complex plane, because digital signals themselves have complex expressions. Although the signal usually needs to be modulated to a higher frequency carrier for transmission, the final detection is still carried out on the baseband. Therefore, the modulated band-pass digital signal s(t) can be expressed by its equivalent low-pass form. Generally speaking, the equivalent low-pass signal is a complex number, that is

The bandpass signal s(t) can be obtained by multiplying it by the carrier and then taking the real part:

Therefore, the real part x(t) can be regarded as the amplitude modulation of cosine signal, and the imaginary part y(t) can be regarded as the amplitude modulation of sine signal. Is orthogonal to, so x(t) and y(t) are mutually orthogonal components on s(t). The former is usually called in-phase component and the latter is called quadrature component.

PS:

Carrier wave refers to the waveform, usually sine wave, that is modulated to transmit signals. Generally, the frequency of sinusoidal carrier is required to be much higher than the bandwidth of modulation signal, otherwise, aliasing will occur and the transmission signal will be distorted.

Quoting "constellation diagram" should start with I and Q modulation, and I and Q modulation should start with QAM modulation. QAM is quadrature amplitude modulation, that is to say, the signal from the signal source is divided into two paths and multiplied by two orthogonal signals, which can be achieved by multiplying one path of signal by a function and the other path of signal by the orthogonality of sub-functions (phase shift of 90 degrees). Then add up and output. The channels after 90-degree phase shift of sum function or function are called I modulation and Q modulation respectively.

Constellation map, that is to say, a coordinate, such as the unit circle in high school, takes I as the abscissa and Q as the ordinate, which corresponds to the in-phase component projected on the I axis and the orthogonal component projected on the Q axis. Due to the difference of signal amplitude, it may fall within the unit circle. Specifically, in 64QAM, there are 64 symbols, which are equal to the 6th power of 2, so each symbol needs 6 binaries to represent it. These 64 symbols fall in the unit circle, and they fall in different places according to their amplitude and phase. Jumping from one point to another means that phase modulation and amplitude modulation are completed at the same time. "

Eye diagram: Digital communication symbols displayed on the oscilloscope screen are formed by superposition of many waveforms, and their shapes are similar to "eyes". A large "eye" indicates that the transmission characteristics of the system are good; A small "eye" indicates that there is intersymbol interference in the system. "In the actual digital interconnection system, it is very difficult to completely eliminate the inter-symbol crosstalk, and the influence of inter-symbol crosstalk on the bit error rate can not be easily handled mathematically, nor can it be accurately calculated. In order to measure the performance of baseband transmission system, in the laboratory, the influence of intersymbol crosstalk and noise on the system performance is usually analyzed by observing the received signal waveform with an oscilloscope, which is eye diagram analysis.

In the ideal situation without intersymbol crosstalk and noise, the waveform will not be distorted and each symbol will overlap. Finally, what you see on the oscilloscope is the thin and clear "eye", which is the most open. When there is intersymbol crosstalk, the waveform is distorted, the symbols are not completely coincident, and the traces of the eye diagram will be unclear, resulting in the closure of the "eye" part. If noise is added, the lines of the eye diagram will become blurred and the "eyes" will become smaller. Therefore, the size of the "eye" opening indicates the degree of distortion and reflects the intensity of inter-symbol crosstalk. Therefore, the eye diagram can directly show the influence of intersymbol crosstalk and noise, and can evaluate the performance of a baseband transmission system. In addition, the diagram can also be used to adjust the characteristics of the receiving filter to reduce inter-symbol interference and improve the transmission performance of the system. Usually the eye diagram can be described by the following figure, from which it can be seen that:

The width of (1) eye diagram determines the time interval, during which the received waveform can be sampled and regenerated without crosstalk. Obviously, the best sampling time should be chosen at the moment when the eyes are most open.

(2) The slope of the hypotenuse of the eye diagram indicates the sensitivity of the system to timing jitter (or error). The greater the slope, the more sensitive the system is to timing jitter.

(3) The horizontal width of the shadow part at the left (right) corner of the eye diagram indicates the range of signal zero, which is called zero distortion. In many receiving devices, timing information is extracted from the position of signal zero, which is very important for zero distortion of such devices.

(4) At the sampling time, the vertical width of the shaded area indicates the maximum signal distortion.

(5) When sampling, half of the interval between the upper and lower shadow areas is the minimum noise tolerance. If the instantaneous value of noise exceeds it, misjudgment may occur.

(6) The horizontal axis corresponds to the decision threshold level. "

Second, some basic concepts of eye diagram

-"What is an eye diagram?"

"An eye diagram is a figure shaped like an eye.

Figure 5 eye diagram definition "

Eye diagram is the result of accumulating and displaying the bits of the collected serial signal by afterglow method. The shape of the superimposed figure looks like an eye, so it is named eye diagram. The eye diagram usually shows the time window of1.25ui. The eyes have various shapes, and so does the shape of the eye diagram. The signal quality can be quickly judged by the shape characteristics of the eye diagram.

The eye diagram in Figure 6 has "double eyelids", so it can be judged that the signal may have crosstalk or pre-(de-) emphasis.

Fig. 6 Eye diagram of "double eyelids"

The eye diagram in Figure 7 is "bloodshot eyes", indicating that the signal quality is too poor, which may be due to an error in the test method or an obvious error in PCB wiring.

Fig. 7 Eye diagram of "bloodshot eyes"

The eye diagram in Figure 8 is very beautiful, which may be measured by a sampling oscilloscope.

Figure 8 The most beautiful "eyes"

Eye diagram is the most important tool to measure the signal quality because it completely represents the bit information of serial signal. Eye diagram measurement is sometimes called "signal quality test, SQ test". In addition, it is usually based on "mask" to judge whether the eye diagram measurement results are qualified or not. The template specifies the tolerance of "1" level, "0" level, rise time and fall time of serial signal. Therefore, eye measurement is sometimes called "mask test". The shapes of templates are also varied, and the common templates of NRZ signals are shown in the blue part of Figures 5 and 8.

At different nodes of serial data transmission, the template of eye diagram is different, so we should pay attention to the specific sub-template type when choosing the template. If you use the sender's template as the receiver's eye pattern template, you may always encounter the template. But signals such as Ethernet signals and E 1/T 1 are not NRZ codes, and their templates are quite special. When a bit touches the template, we think that the signal quality is not good and we need to debug the circuit. Some products require 100% not to touch the template, and some products are allowed to touch the template within a certain probability. (Interestingly, products with 85% eyes passing the template often have no problems in functional testing. For example, the computer network port I use now always fails the test, but I have no problem surfing the Internet. This makes many companies feel that they can make good products without buying oscilloscopes for signal integrity testing. As for the fake version, they won't buy an oscilloscope eye diagram. ) There are measurement parameters in the oscilloscope, which can automatically count the number of contact with the template. In addition, according to the position of the "infringement" template, we can know what is wrong with the signal and guide debugging. The main problem of the signal shown in Figure 9 is that the falling edge is too slow. The figure 10 shows that the 1 level and the 0 level have "collapsed", which may be caused by the ISI problem.

Fig. 9 Eye diagram of falling edge contacting template

The figure 10 template is "folded" with "1" and "0" levels.

There are many eye diagram parameters related to eye diagram, such as eye height, eye width, eye width, eye intersection ratio, "1" level, "0" level, extinction ratio, Q factor, average power and so on. Figure 12 shows the definition of amplitude-dependent measurement parameters.

Figure 1 1 eye diagram parameter definition

"1" and "0" indicate that the middle 20%UI part of the eye diagram is projected as a histogram onto the vertical axis, and the central values of the histogram are "1" and "0" respectively. Eye amplitude means "1" level minus "0" level. The 3sigm difference between the upper and lower histograms indicates the eye height. Figures 12, 13, 14 and 15 give the definitions of other eye diagram parameters, which are clear at a glance and will not be repeated here.

Figure 12 eye diagram parameter definition

Definition of parameters of diagram 13 eye diagram

Figure 14 eye diagram parameter definition

Definition of eye diagram parameters of figure 15

Three, eye diagram measurement method (traditional eye diagram measurement method)

As mentioned above, there are two kinds of eye diagram measurement methods: the traditional eye diagram measurement method is understood as eight words in Chinese: "synchronous trigger+superimposed display", and the modern eye diagram measurement method is also understood as eight words in Chinese: "synchronous cutting+superimposed display". The difference between the two methods is four words: the traditional method is triggering, and the modern method is cutting. "Synchronization" is the key to accurately measure the eye diagram, and the traditional method is different from the modern one. "Overlay display" is a continuous cumulative display of simulated afterglow.

The traditional eye diagram method is to trigger once synchronously and then superimpose once. Every time it is triggered, a UI is added to the eye diagram, and the data of each UI is arranged relative to the trigger point, so every time it is triggered, only one bit is added to the eye diagram. Figure 1 shows the process of forming an eye diagram by this method.

Figure 1 Principle of traditional eye diagram measurement method

The first disadvantage of traditional methods is that they are too inefficient. For the current high-speed signals such as PCI-Express Gen2, PCI-SIG needs to measure 1 10,000 UI eye diagram, which may take several hours to complete by traditional methods. The second disadvantage is that only one UI can be superimposed at a time, and it takes 1 10,000 times to form the eye diagram of 1 10,000 UIS, so the trigger jitter of the oscilloscope itself will inevitably be introduced into the eye diagram in the process of continuous triggering. For high-speed signals above 2.5GBbps, this trigger jitter cannot be ignored.

How to synchronize triggers, that is, how to arrange the data of each UI relative to the trigger point? There are also two ways. One method is to find the clock synchronized with serial data on the tested circuit board, and lead the clock to the oscilloscope as the trigger source, and the edge of the clock as the trigger condition. Another method is to input the serial signal into the input channel of the oscilloscope and the hardware clock recovery circuit (CDR) channel at the same time, and the hardware CDR recovers the clock embedded in the serial data as the trigger source. This synchronization method introduces CDR jitter, which is the third disadvantage of traditional methods. In addition, hardware CDR can only detect continuous serial signals to work normally. If the detected signal is discontinuous, for example, there is a low level between two consecutive bits, the hardware CDR cannot recover the correct clock. In addition, the working principle of the traditional method determines that it cannot make intermittent serial signals, save waveforms and calculate the eye diagram of waveforms, which limits the application scope. This is the fourth shortcoming of the traditional method.