Oscilloscope Basics Series 1 - About Oscilloscope Bandwidth

Bandwidth is known as the first indicator of an oscilloscope and is also the most valuable indicator of an oscilloscope. The oscilloscope market is often divided 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 many stories about bandwidth.

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

We often say that digital oscilloscopes have five major functions, namely capture, view, measurement, analysis and documentation. The principle block diagram of these five major functions is shown in Figure 1.

Figure 1. Schematic diagram of a digital oscilloscope

The capture part is mainly composed of three chips and a circuit, namely, the amplifier chip, A/D chip, memory chip and trigger circuit. The principle block diagram is shown in Figure 2. The measured signal first passes through the probe and amplifier and is normalized into a voltage range that the ADC can receive. 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 for display and measurement analysis.

Figure 2, oscilloscope capture circuit block diagram

The typical circuit of an oscilloscope amplifier is shown in Figure 3. This circuit can be seen everywhere in textbooks on analog circuits. 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 Bode plot of the ideal amplitude-frequency characteristic is shown in Figure 5.

Figure 3. Typical circuit of an amplifier

Figure 4, Equivalent circuit model of the amplifier [page]

At this point, we know that the bandwidth f2 is the frequency point when the output voltage drops to 70.7% of the input voltage. Based on the equivalent model of the amplifier, we can further derive the relationship between the rise time and bandwidth of the oscilloscope, which is the 0.35 relationship we often mention: rise time = 0.35/bandwidth. 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 0.35-0.45. The "rise time" indicator is marked 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

The Bode plot of the amplitude-frequency characteristics of the oscilloscope front-end amplifier is the "birth certificate" of 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 10MHz and gradually increases the frequency 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 them to the oscilloscope and power meter through equal-length cables. The power divider and the cable are passive devices 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 needs to be used as the calibration value of the input amplitude of the oscilloscope. Sometimes customers are very interested in the Bode plot of the oscilloscope and directly use the signal source to connect 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, and the final Bode plot is the result of superimposing all gears. The measurement of the Bode plot takes half a day to complete, which 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. Many times, our competitors will show their Bode plots to customers as -10dB/div, with only one gear, and compare them with the results provided by LeCroy, which are -1dB/div and various gears are superimposed together. Then they tell customers that their Bode plots are flatter and cleaner, and even say that the dense points on the LeCroy Bode plot are "noisy". This is a bit ridiculous. The fact that competitors dare to adopt this approach again and again is an assumption that Chinese engineers have no discernment and the ability to think independently, and is a blatant deception that seriously disrespects engineers. I hope this can draw everyone's attention.

Figure 7, Measurement method of oscilloscope Bode diagram [page]

Figure 8: The actual Bode diagram of the oscilloscope

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. This is explained in great detail in a technical white paper from Lecroy. 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)

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, how much bandwidth of the 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: "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 oscilloscope bandwidth is usually 3-5 times the frequency of the measured signal. 100MHz margin is very large." 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 when the bandwidth is 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 rising edge slows down; 1GHz bandwidth and 6GHz bandwidth are almost the same for testing the rise time of 800ps.

Figure 13. Comparison of test waveforms of a 5MHz clock signal at different bandwidths such as 6GHz, 1GHz, and 200MHz

Figure 14. 5MHz clock rise time measured when bandwidth is limited to 200MHz [page]

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

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 of all, 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 N harmonics by Fourier transform.

The sum of the energy of the waves. When N equals to what, 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:

The bandwidth of the oscilloscope is > 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 bandwidth.

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

I like to tell the following story about bandwidth:

As we all 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. After all, buying an oscilloscope above 4GHz just to test USB.20 is a very 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 trace 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 1GHz and 6GHz bandwidth measurement results are almost completely consistent. 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 this, and it is difficult for us to explain that engineers accept bandwidth that does not meet the specifications. When we tested a certain brand of desktop USB port, the rise time when the bandwidth was set to 4GHz and 1GHz was only about 30ps different. The connecting cable I used between the computer and the fixture is very short, only a dozen centimeters. If a long USB cable is used, the rise time will be longer.