What sampling rate is required for an oscilloscope to measure various types of signals?

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What sampling rate is required for an oscilloscope to measure various types of signals? [Copy link]

We know that the operation process of the oscilloscope is roughly as shown in the following figure:

We input a signal to the oscilloscope through the probe. After the measured signal passes through the amplification, attenuation and other signal conditioning circuits at the front end of the oscilloscope, the high-speed ADC analog-to-digital converter performs signal sampling and digital quantization. The sampling rate of the oscilloscope is the frequency of the sampling clock when the input signal is converted to digital, which is commonly known as the sampling interval. One sampling point is collected at each sampling interval. For example, a sampling rate of 1GSa/s means that the oscilloscope has the ability to collect 1 billion sampling points per second, and its sampling interval is 1 nanosecond.

For real-time oscilloscopes, real-time sampling is currently widely used. Real-time sampling means that the waveform signal being measured is sampled continuously at high speed at equal intervals, and then the waveform is reconstructed or restored based on these continuously sampled points. In the real-time sampling process, a key point is to ensure that the sampling rate of the oscilloscope is much faster than the change of the measured signal.

So how much faster? The Nyquist theorem in digital signal processing states that if the bandwidth of the measured signal is finite, then when sampling and quantizing the signal, if the sampling rate is more than twice the bandwidth of the measured signal, the information carried in the signal can be completely reconstructed or recovered without aliasing.

The following figure shows signal aliasing caused by insufficient sampling rate. It can be seen that the frequency of the collected signal is much smaller than the original signal.

If you are not familiar with the concept of oscilloscope sampling rate, you can search and read our previous article "Detailed Explanation of Oscilloscope Sampling Rate Concept" to learn. Today, we will put aside the theory and use the oscilloscope to actually measure 1MHz sine wave, 1MHz square wave, 100KHz sawtooth wave, and 100KHz triangle wave to see the results.

We first use a signal generator to generate a sine wave with an amplitude of 10V and a frequency of 1MHz and input it into the oscilloscope. By adjusting the memory depth and time base, we can reduce the sampling rate to the desired value. As shown in the figure below, the time base of the oscilloscope is 2ms, the memory depth is 28K, and the sampling rate = memory depth/(time base*14), which is exactly 1MSa/s.

It can be seen that when the sampling rate is equal to the signal frequency, the oscilloscope cannot display a normal sine wave graph, and the waveform is distorted. We continue to increase the time base, and the storage depth remains unchanged. At this time, the sampling rate drops to 20KSa/s. It can be seen on the oscilloscope screen that the signal is a sine wave, but the signal frequency drops from the actual 1MHz to 1.668Hz, which means that the signal aliasing caused by the above-mentioned insufficient sampling rate has occurred.

Next, we adjust the time base to a smaller value, so that the sampling rate becomes larger, and we adjust the sampling rate to 2 and 10 times the signal frequency to observe the signal changes, that is, 2MSa/s and 10MSa/s. The signal on the left in the figure below is at a sampling rate of 2MSa/s. You can see that the frequency of the signal has returned to 1MHz, which is the correct frequency value of the signal. However, the original sine wave has become a triangle wave, and the waveform has been distorted. When the sampling rate is changed to 10MSa/s, that is, the signal on the right in the figure below, you can see that the signal is getting closer and closer to the appearance of a sine wave, but it is still not very beautiful.

We continue to reduce the time base so that the sampling rate is 20 times the signal frequency, that is, 20MSa/s. At this time, we can see a beautiful sine wave. Therefore, we can conclude that when observing a 1MHz sine wave, the sampling rate should be at least 20 times that of the signal to restore its true appearance.

We use the same method to measure the 1MHz square wave, 100KHz triangle wave, and 100KHz sawtooth wave. The results are shown in the following figure:

It can be seen that the sampling rate requirement for measuring a 1MHz square wave is much higher than that for measuring a 1MHz sine wave. When measuring a 1MHz sine wave at a sampling rate of 20 times, it is close to the real signal, while when measuring a 1MHz square wave, even at a sampling rate of 40 times, the rising edge is still not straight.

Let's look at the 100KHz triangle wave:

Finally, let's look at the 100KHz sawtooth wave: