How to confirm the effective bandwidth of a power analyzer?

1. What is the effective bandwidth of a power analyzer?

　　The effective bandwidth of a power analyzer refers to the highest frequency of the signal that the power analyzer can measure and analyze.

　　The spectrum of a periodic signal consists of an amplitude spectrum and a phase spectrum. The envelope of the spectrum passes through a zero point at every other angular frequency. After a certain zero point, the amplitude of the harmonic will gradually decrease. The frequency range containing the main harmonic components is usually called the effective bandwidth of the measured signal.

　　The effective bandwidth of the measured signal must be smaller than the effective bandwidth of the power analyzer. In other words, the effective bandwidth of the power analyzer must be larger than the effective bandwidth of the measured signal to avoid causing significant attenuation or distortion to the measured signal.

　　The effective bandwidth of a power analyzer measuring a signal is inversely proportional to the rise time of the step response.

　　The effective bandwidth of a power analyzer is an important indicator of the instrument's frequency characteristics and has practical application significance. Within the effective bandwidth of a power analyzer, most of the harmonic components of the measured signal must be concentrated. In other words, if the signal loses harmonic components outside the effective bandwidth, it will not have a significant impact on the signal, and such a measurement will be meaningful. Similarly, any system has its effective bandwidth. When a signal passes through a system, the effective bandwidth of the signal and the system must be "matched". If the effective bandwidth of the signal is greater than the effective bandwidth of the system, when the signal passes through this system, many important components will be lost and greater distortion will be generated; if the effective bandwidth of the signal is much smaller than the effective bandwidth of the system, the signal can pass smoothly, but it is a huge waste of system resources.

2. Under what circumstances will aliasing occur in the effective bandwidth of a power analyzer?

　　When the power analyzer samples a continuous signal at equal intervals, if the sampling theorem is not satisfied, that is, the sampling frequency is lower than twice the effective bandwidth of the power analyzer, when the sampled signal is subjected to spectrum analysis, the frequency will overlap, that is, the frequency components higher than half the sampling frequency will be reconstructed into signals lower than half the sampling frequency. The distortion caused by this spectrum overlap is called aliasing. In this case, the effective bandwidth of the power analyzer is too wide or the sampling frequency is too low. Only by increasing the sampling frequency to more than twice the highest signal frequency, or reducing the effective bandwidth of the power analyzer to less than half the sampling frequency, can the signal be correctly restored using the sampled samples;

　　Anti-aliasing filter: It is a low-pass filter used to reduce the aliasing frequency component to a negligible level in the output level. This filter removes the high-frequency signal of the signal and is a pre-processing of the original signal to make the signal meet the requirement of "matching" with the effective bandwidth of the power analyzer.

3. Under what circumstances can the effective bandwidth of a power analyzer be undersampled?

　　Some power analyzers use undersampling technology. Undersampling means that the sampling frequency is less than twice the effective bandwidth of the power analyzer, which violates the sampling theorem. However, when the signal is a strictly periodic signal, multiple consecutive cycles are undersampled, and the sampling sequence of each cycle has a fixed delay. For example, the sampling frequency is 100kHz, the sampling period is 10nS, the first cycle starts sampling at time 0, and the second cycle starts sampling at 5nS (from half of the sampling period). Then, the sampling data of the two cycles are combined to obtain a sampling sample sequence of a cycle with a sampling frequency of 200kHz. When the signal is not a strictly periodic signal, the undersampling technology will have a large error.