Do you really understand oscilloscopes? Oscilloscope knowledge that will be used in job interviews

I remember when I went to EMC to interview for a hardware engineer position in 2013, I performed well throughout the interview. At the end, they asked me some questions about oscilloscopes. They mentioned a question: What would happen if I used an oscilloscope with a bandwidth of 50M to sample a 100M signal? I had no idea at the time and didn't know how to do it. Fortunately, the engineer who interviewed me was my undergraduate alumnus and gave me some hints, so I was able to answer the question. In the following period of time, I deliberately did this experiment, and then did some research and study on oscilloscopes. I'll post some basic and important things. If you are interested in this question, you can also do the experiment yourself to see the specific results.

The sampling rate is digital, which refers to the number of samples per second. The bandwidth is analog, which refers to the range of signal frequencies that can be tested.

If the sampling frequency of an ADC is 5G, but a 100M low-pass filter is placed in front of it, then the sampling rate is 5G and the bandwidth is 100M. The bandwidth reflects the frequency range that the oscilloscope can test. If it exceeds this frequency range, it will be inaccurate. However, there is a basic principle: the sampling frequency must not be less than twice the signal bandwidth.

1. Oscilloscope application market demand for bandwidth and sampling rate

Oscilloscopes have placed increasingly higher demands on bandwidth and sampling rate.

Generally speaking, the sampling rate of an oscilloscope should be at least twice its bandwidth.

The write bandwidth of an oscilloscope is 40Mhz. 40MHZ refers to the ability of the oscilloscope to measure standard sine waves. However, because the waves tested with the oscilloscope are basically not sine waves, when we consider the bandwidth of the oscilloscope, we usually consider it as three times the frequency of the signal being measured. Of course, a higher multiple is best. So be sure to note that not a 40 MHZ oscilloscope can measure all 40MHZ signals. If it is a digital oscilloscope, it is very important to pay attention to the storage depth and sampling rate.

2. Principle block diagram of oscilloscope

To be proficient in an oscilloscope, you must know its internal structure. The oscilloscope includes an amplifier, which limits the bandwidth of the oscilloscope; an analog-to-digital converter, acquisition memory, which determines the storage depth of the oscilloscope; data processing and final display.

3. The bandwidth of a signal is not directly related to the frequency of the signal, but is related to the rise time of the signal

 

An oscilloscope is a test device, and its bandwidth should be larger than the bandwidth of the signal being tested, so that there will be no distortion and you will not miss what you want to observe.
    For example, the frequency of a square wave is 1 MHz, but its effective harmonics are over 5 MHz. If you use an oscilloscope with a bandwidth of only 1 MHz to display it, you will get a display that is almost a sine wave. If you use a 30 MHz oscilloscope to see it, the square wave is just a square wave.

 The first concept is that the bandwidth of a signal is not directly related to the frequency of the signal, but is related to the rise time of the signal.

     For example, a square wave is a signal with many spectral components, including the fundamental wave and higher harmonics. It can be composed of many sine waves superimposed. However, the bandwidth of an oscilloscope is limited. Therefore, when using an oscilloscope to observe a square wave, if the bandwidth is not enough, the higher harmonics will be filtered out, and the square wave will look like a sine wave.

  
 

So how do you calculate the bandwidth of a signal and how do you choose the bandwidth of an oscilloscope? The bandwidth of a signal can be calculated based on 0.35/Tr, where Tr is the rise time. Of course, the larger the bandwidth of the oscilloscope, the closer the measured signal is to the actual value, but generally, a bandwidth of three times the bandwidth of the oscilloscope is sufficient.

Oscilloscope bandwidth/signal bandwidth	Measurement error
1	<41.4%
3	<5.4%
5	<2.0%
10	<0.5%

       So how is this 0.35/Tr obtained? The bandwidth of the oscilloscope usually mentioned without special explanation refers to the bandwidth of the oscilloscope analog front-end amplifier, which is often called the -3dB cutoff frequency point. The front-end amplifier circuit of the oscilloscope can be equivalent to an RC low-pass filter, as shown in the figure:

      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. 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 always indicated on the oscilloscope's datasheet.

4. Spectrum range and resolution bandwidth of the oscilloscope

 

These are some commonly used conclusions. Being familiar with these conclusions can make us use the oscilloscope more handy.