Lecture 1: The principle and practical skills of bandwidth of oscilloscope basics

Central topic: The principle of oscilloscope bandwidth The application of oscilloscope bandwidth in testing When engineers choose an oscilloscope, how do they determine the bandwidth? Bandwidth is called the first indicator of an oscilloscope and is also the most valuable indicator of an oscilloscope. The division of the oscilloscope market is often based on bandwidth as the primary basis. When engineers choose an oscilloscope, the first thing they need to determine is bandwidth. In the sales process, there are also many stories about bandwidth.

The bandwidth usually mentioned without special instructions refers to the bandwidth of the oscilloscope analog front-end amplifier, which is often called the -3dB cutoff frequency point. In addition, there are concepts such as digital bandwidth and trigger bandwidth. 

We often say that digital oscilloscopes have five major functions, namely capture (Capture), observation (View), measurement (Measurement), analysis (Analyse) and filing (Document). The principle block diagram of these five major functions is shown in Figure 1.


Figure 1, principle block diagram of digital oscilloscope

The capture part is mainly composed of three chips and a circuit, namely amplifier chip, A/D chip, memory chip and trigger circuit. The principle block diagram is shown in Figure 2 below. The measured signal is first converted into a voltage range that the ADC can receive after being normalized by the probe and amplifier. The sampling and holding circuit divides the signal into independent sampling levels at a fixed sampling rate. The ADC converts these levels into digital sampling points, which are stored in the acquisition memory and sent to display and measurement analysis. 


Figure 2, Schematic diagram of the oscilloscope capture circuit principle

. The typical circuit of the oscilloscope amplifier is shown in Figure 3. This circuit can be seen everywhere in analog circuit textbooks. This amplifier can be equivalent to an RC low-pass filter as shown in Figure 4. The relationship between the output voltage and the input voltage is derived from this equivalent circuit, and the ideal Bode diagram of the amplitude-frequency characteristic is obtained as shown in Figure 5.



Figure 3, Typical 



circuit  4, Equivalent circuit model of the amplifier



Figure 5, Ideal Bode diagram of the amplifier



So far, we know that the bandwidth f2 is the frequency point when the output voltage drops to 70.7% of the input voltage. According to the equivalent model of the amplifier, we can further derive the relationship between the rise time and bandwidth of the oscilloscope, that is, the 0.35 relationship we often mention: rise time = 0.35/bandwidth, and the derivation process is shown in Figure 6 below. It should be noted that 0.35 is a theoretical value based on Gaussian response. In actual measurement systems, this value is often between 0.35 and 0.45. The "rise time" indicator is indicated on the datasheet of the oscilloscope. There is the following relationship between the rise time measured by the oscilloscope and the actual rise time. In the test of fast-edge signals, this relationship is needed to correct the rise time of the actual measured signal.

Measured risetime(tr)2 = (tr signal)2+(tr scope)2+(tr probe)2 



Figure 6, the relationship between the rise time and bandwidth of the oscilloscope  .

Go to the welding process and testing community to see




the Bode plot of the amplitude-frequency characteristics of the oscilloscope front-end amplifier. It is the "birth certificate" issued by the new oscilloscope. The oscilloscope needs to be calibrated every year, and the Bode plot is the first data that needs to be calibrated. The measurement method of the oscilloscope Bode plot is shown in Figure 7. The signal source starts from a frequency of 10MHz and gradually increases to send a sine wave of a certain amplitude to the power divider. The power divider divides the input signal energy into two equal parts and sends it to the oscilloscope and power meter through equal-length cables. Power dividers and cables are passive components and can be strictly calibrated. The amplitude-frequency characteristics of the signal source itself cannot be used as a calibration instrument. The energy measured by the power meter is needed as the calibration value of the input amplitude of the oscilloscope. Sometimes customers are very interested in the Bode plot of the oscilloscope. They directly connect the signal source to the oscilloscope to evaluate the Bode plot of the oscilloscope. This method is very imprecise when the bandwidth exceeds 1GHz. A power meter is needed as a calibration tool! There is an article in EDN magazine in February 2006. http://www.edn.com/article/CA6305348.html#Calibrating

In addition, when measuring the Bode plot, it is necessary to measure each gear of the oscilloscope. The final Bode plot is the result of all gears superimposed together. It takes half a day to measure the Bode plot. It is not as easy as imagined. As shown in Figure 8, it is the Bode plot of LeCroy SDA9000. I specially show you a large amount of data in Excel so that you can have a deep understanding of the rigor of calibration. Its vertical axis is -1dB/div, and the test results of 10mv/div, 20mv/div, 50mv/div, 200mv/div, 500mv/div, 1v/div and other gears are superimposed. Often, our competitors will show their Bode plots to customers as -10dB/div, with only one gear, and compare them with the -1dB/div provided by LeCroy, with various gears superimposed and displayed together. Then they tell customers that their Bode plots are flatter and cleaner, and even describe the densely packed points on the LeCroy Bode plot as "noise". This is a bit ridiculous. Competitors dare to use this approach again and again, assuming that Chinese engineers have no discernment and independent thinking ability, and it is a blatant deception that seriously disrespects engineers. I hope it will attract everyone's attention. 



Figure 7, oscilloscope Bode plot measurement method

For a deeper discussion on bandwidth, we need to talk about the flatness and roll-off characteristics of the amplitude-frequency characteristics of the oscilloscope front-end amplifier. LeCroy
's technical white paper has a very detailed explanation of this. http://www.lecroy.com/tm/Library/WhitePapers/PDF/Eye_Patterns_in_Scopes-designcon_2005.pdf (The first author of this white paper, Peter, is the inventor of the original technologies such as DSP bandwidth enhancement, Eye Dcotor and DBI)

There are three amplitude-frequency characteristic curves in the industry, representing three brands: Gaussian (Tektronix), 4th oder Bessel (LeCroy) and Maximally Flat (Agilent). 

The Gaussian response still decays very slowly after -3dB. Its advantage is that it allows the harmonic energy of the higher frequency components of the measured signal to pass through the amplifier (this is assumed that its sampling rate is much higher than Nyquist), which is helpful for particularly fast fast edge measurements. Its disadvantage is that it severely attenuates the measured signal in the low frequency band, especially the 3rd harmonic, resulting in "peanut eyes" in eye diagram measurement.
　 
Maximally Flat response or rectangular response seems to be the closest to the definition of amplitude-frequency characteristics in our textbooks. However, the fact that the amplitude-frequency characteristics are close to the ideal state does not mean that it is the most suitable amplifier front end for oscilloscopes. It has advantages for measuring sine waves within the bandwidth, but since the actual measurement signals are mostly square wave signals, the rectangular response completely eliminates the high-order harmonics beyond the bandwidth, which will cause serious phase distortion. Suppose the 1GHz oscilloscope you bought is used for 200MHz signal measurement, the rectangular response will completely eliminate the energy above the 5th harmonic. This is problematic for measuring pulse signals with fast rising edges.　
　
LeCroy's 4th oder Bessel response curve is a compromise between the first two. It has little attenuation of the 3rd harmonic content with the richest frequency content, and there is no distortion of phase information in the frequency band close to the bandwidth. This is a very perfect amplitude-frequency characteristic curve for serial signal measurement.

Figure 9 below is a 5Gbps eye diagram measured by LeCroy sampling oscilloscope WE100H. Because the sampling oscilloscope has high bandwidth, low noise, and high A/D bit number, it can be used as a standard for measuring the eye diagram of periodic repetitive signals. Figure 10 is a 5Gbps eye diagram measured by LeCroy SDA1100. Figure 11 is a 5Gbps eye diagram measured by a 12GHz oscilloscope of another brand. An interesting phenomenon is that the eye diagram measured with 12GHz bandwidth has "peanut eyes". Figure 12 can clearly reveal the cause of the "peanut eyes". The third harmonic of the 5Gbps serial signal is 7.5GHz, and the Gaussian response curve has a large attenuation at the third harmonic.



Figure 8, the actual Bode diagram of the oscilloscope. 





Figure 12, comparison of different amplitude-frequency characteristic curves.

We know that bandwidth limitation will have the following effects on signal capture: 1. Slow down the rising edge of the measured signal. 2. Reduce the frequency component of the signal. 3. Distort the phase of the signal. So, "For a 5MHz clock signal, what bandwidth of oscilloscope is needed to measure it?" This is a question I often ask during training. I rarely get a satisfactory answer. Few engineers ask me in return: "Is this 5MHz clock signal a square wave or a sine wave? If it is a square wave, what is its rise time?" The answer I often get is, "100MHz bandwidth is enough. The bandwidth of the oscilloscope is usually 3-5 times the frequency of the signal being measured. 100MHz has a large margin." Figure 13 shows the waveforms of a 5MHz square wave signal tested at different bandwidths. Among them, M1 and M2 are waveforms at 6GHz and 1GHz respectively, and C3 is the test result with the bandwidth limited to 200MHz. Figure 14 shows that the average rise time of 5MHz measured when the bandwidth is limited to 200MHz is 1.70357ns, while Figure 15 shows that the rise time at 6GHz bandwidth is 873.87ps. This shows that for a 5MHz clock, because its rise time is relatively fast, it is best to use an oscilloscope with a bandwidth of more than 1GHz to measure its rise time. At 200MHz, its rise edge slows down; 1GHz bandwidth and 6GHz bandwidth have almost the same results for testing a rise time of 800ps.




How much bandwidth is needed for testing USB2.0 signals? How much bandwidth is needed for testing PCI-E G2 signals? How much bandwidth is needed for power supply testing? How much bandwidth is needed for testing 1000Base-T signals? How much bandwidth is needed for testing 10Gbps backplanes? ... We often have to answer these questions. The following three rules are our answers.

1. First, it depends on the type of signal you need to test and the test accuracy you want. 

2. For square wave signals, the most important factor is the rise time. Any square wave signal can be decomposed into the sum of the Nth harmonic energy through Fourier transform. When N equals, the energy of the measured signal is close to zero? It depends on the rise time! This is also discussed in great detail in Peter's white paper. 

3. For serial data signals, data bit rate and rise time are the two most important factors. A very good evaluation criterion is: oscilloscope bandwidth > 1.8 x signal bit rate. Under this criterion, if the rise time of the measured signal is > 20% UI, then a bandwidth of 1.8 can capture 99% of the signal energy. The following chart shows the relationship between different rise times and bandwidths. 





Figure 13, 5MHz clock signal test waveform comparison at different bandwidths such as 6GHz, 1GHz and 200MHz



Figure 14, 5MHz clock rise time measured when bandwidth is limited to 200MHz



Figure 15, 5MHz clock rise time measured at 6GHz bandwidth


Based on the above principles, we can easily understand why some customers use a 6GHz oscilloscope to test a 100MHz clock, but use a 6GHz oscilloscope to test a 3.125Gbps XAUI signal. Please forget the so-called 3-5 times relationship, which is too imprecise!

Regarding bandwidth, I often like to tell the following story:

As you know, for USB2.0 compliance testing, the USB-IF specification initially required a 4GHz bandwidth oscilloscope, because at that time only one oscilloscope company released this test software package. So when USB2.0 was very popular, this company's 4GHz oscilloscope was very popular, but when the other two USB2.0s were released, USB-IF lowered the specification standard to 2.5GHz oscilloscopes, but when another non-mainstream fourth oscilloscope manufacturer also came up with a USB2.0 software package, USB-IF also recognized this 1.5GHz bandwidth oscilloscope. This actually just shows that the company's public relations ability is quite strong, and it also shows that foreign authoritative standard organizations are also political. For the test of USB2.0 signals, what bandwidth oscilloscope is suitable? If you have money to invest, it is of course better to buy 4GHz or 6GHz, because the flatness of the amplitude-frequency characteristics in the low frequency band will always be better. But we need to make responsible investments. Buying an oscilloscope with a bandwidth of more than 4GHz just to test USB.20 is an irresponsible investment for the company. We know that the signal rate of USB2.0 high speed is 480Mbps, 1UI is approximately equal to 2ns, 20%UI is approximately equal to 400ps, and the minimum USB rise time is 500ps. For the signal of the USB chip pin, its rise time may be 500ps. For system-level applications, the USB2.0 high speed signal tested by the oscilloscope usually passes through a section of PCB traces and a section of USB connection line from the USB chip output pin. The rise time tested by the oscilloscope often exceeds 1ns! The example in Figure 13 clearly shows that for the 800ps rise time, the measurement results of 1GHz and 6GHz bandwidth are almost exactly the same. Therefore, a 1GHz oscilloscope can meet the USB2.0 high speed test in system-level applications. But we are not willing to recommend a 1GHz oscilloscope for USB2.0 high speed testing, because the USB-IF specification does not recommend it, and it is difficult for us to explain that engineers accept bandwidth that does not meet the specification. Figure 16 and Figure 17 are the rise time comparisons when we tested a certain brand of desktop USB port with the bandwidth set to 4GHz and 1GHz. The difference is only about 30ps. The connection cable between the computer and the fixture I used is very short, only a dozen centimeters. If a long USB cable is used, the rise time will be longer.
If you have any questions about bandwidth, please contact me at frankie.wang@lecroy.com 



Figure 16, the rise time of USB2.0 high speed signal tested at



1GHz bandwidth Figure 17, the rise time of USB2.0 high speed signal tested at 3GHz bandwidth