The sampling rate is lower than the bandwidth, so why can it be measured accurately?

　　The high-bandwidth power analyzers on the market often have a low sampling rate, only half of the bandwidth or less. Is this really reasonable? Can the input signal be sampled reliably? Can such a sampling method support high-precision electrical parameter measurements? Compared with high sampling rate sampling, what are the benefits of such a sampling method? This article will analyze the principle behind this phenomenon.

　　Sampling high frequency signals with a lower and appropriate sampling rate has the following implications for the power analyzer:

　　1. Use the equivalent sampling principle to finely sample high-frequency signals, so that the sampled discrete signals have better phase resolution;

　　2. It is not necessary to use an ADC with a high sampling rate (a high ADC sampling rate means a reduction in the number of conversion bits).

　　Unlike instruments such as oscilloscopes that use a sampling rate higher than their bandwidth (oscilloscopes require a high sampling rate to ensure the restoration of waveform lines), power analyzers can use a sampling rate lower than their bandwidth to ensure the accuracy and stability of the measurement results.

　　For high-frequency signals, from the perspective of sampling, the key to the accuracy and stability of the measurement results lies in: 1. The phase uniformity and phase coverage density of the collected signal; 2. The balance of the number of samples in each phase; 3. A sufficient number of sampling points. When measuring high-frequency signals, points 1 and 2 are more important and must be guaranteed. Point 3 can also be met when the sampling rate is lower than the bandwidth.

figure 1

　　It can be seen that the equivalent sampling method samples only one point in one cycle of the input signal and the phase of each cycle sampling has an increasing relationship (△t in Figure 1). Adjusting this increasing phase can achieve the purpose of adjusting the phase resolution.

　　In addition, to ensure high-precision sampling, power analyzers usually use ADCs with higher conversion bits rather than higher sampling rates. Sampling accuracy is a very important basis for high-precision measurement. This is because high-speed ADCs are often not ideal in other characteristics, such as conversion bits, signal-to-noise ratio, etc. By using the equivalent sampling method, power analyzers do not have to sacrifice accuracy and use high-speed ADCs in order to measure high-frequency signals.

　　The power analyzer uses equivalent sampling method for high-frequency signals to ensure the above points. Therefore, even if the sampling rate is lower than the bandwidth, the high-frequency signal can be accurately measured.