The frequency response refers to the phenomenon that when the sound signal outputted by a constant voltage is connected to the system, the sound pressure generated by the speaker increases or decreases with the change of the frequency, and the phase changes with the frequency. The sound pressure and phase The change relationship associated with the frequency is called the frequency response. It also refers to the range of frequencies that the sound system can reproduce within the range allowed by the amplitude, and the amount of change in the signal within this range is called the frequency response, also called the frequency characteristic. The ratio of the maximum value to the minimum value of the output voltage amplitude over the rated frequency range, expressed in decibels (dB). Frequency response is often referred to in the power quality concept as the impedance of a system or metering sensor as a function of frequency.
Frequency response determination method analysisThe theoretical calculation method based on the physical mechanism is only applicable to the case where the structural composition of the system is easy to determine. After the structural composition of the system is given, the corresponding physical laws can be used to determine the frequency response of the system through derivation and calculation. The degree of accuracy of the analysis depends on how accurate the system structure is. For complex systems, the analytical calculations are computationally intensive.
The frequency response atlas uses a direct meter measurement method that can be used in situations where the system structure is difficult to determine. A common experimental method is to use a sinusoidal signal as a test signal, and select several frequency values ​​in the frequency range under consideration to measure the amplitude and phase angle values ​​of the input and steady-state output sinusoidal signals at each frequency. The ratio of the amplitude ratio of the output to the input as a function of frequency is the amplitude-frequency characteristic, and the phase-off difference between the output and the input varies with frequency as the phase-frequency characteristic.
Frequency response performanceThe transition process of the system has a definite relationship with the frequency response and can be obtained mathematically. But in addition to the first- and second-order systems, this often takes a lot of time, and in many cases it doesn't really make much sense. A common method is to directly estimate the performance of the system transition process based on the feature quantity of the frequency response. The main characteristic quantities of the frequency response are: gain margin and phase margin, resonance peak and resonance frequency, bandwidth and cutoff frequency.
Gain margin and phase marginIt provides information on whether the control system is stable and has a large margin of stability.
Resonance peak Mr and resonance frequency ωrMr and ωr are specified as the maximum value of the amplitude-frequency characteristic |G(jω)| and the corresponding frequency value. For high-order linear stationary systems with a pair of conjugate complex dominant poles (see root locus method), when the Mr value is in the range of (1.0-1.4) M0, a satisfactory transient process performance can be obtained. Where M0 is the magnitude of the frequency response when ω=0. The size of ωr characterizes the rapidity of the transition process: the larger the ωr value, the better the output response of the system under unit step.
The cutoff frequency ωc is defined as the critical frequency at which the amplitude-frequency characteristic |G(jω)| reaches 0.7M0 and continues to fall. The corresponding frequency range 0 ≤ ω ≤ ωc is called the bandwidth. The meaning of the cutoff frequency is that the system has a filtering function for signal components with a frequency higher than ωc, while a signal component with a frequency lower than ωc can pass directly or slightly attenuate. From the perspective of reproducing the input signal, the bandwidth is often required to be larger, which corresponds to a smaller rise time and a faster response speed. However, from the perspective of suppressing high frequency noise, the bandwidth should not be too large. Therefore, determining the bandwidth needs to be fully considered.
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