Definition: Frequency Response

From Open Energy Information

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Frequency Response

(Equipment) The ability of a system or elements of the system to react or respond to a change in system frequency. (System) The sum of the change in demand, plus the change in generation, divided by the change in frequency, expressed in megawatts per 0.1 Hertz (MW/0.1 Hz).[1]

Wikipedia Definition

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. In simplest terms, if a sine wave is injected into a system at a given frequency, a linear system will respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Also for a linear system, doubling the amplitude of the input will double the amplitude of the output. In addition, if the system is time-invariant (so LTI), then the frequency response also will not vary with time. Thus for LTI systems, the frequency response can be seen as applying the system's transfer function to a purely imaginary number argument representing the frequency of the sinusoidal excitation. Two applications of frequency response analysis are related but have different objectives. For an audio system, the objective may be to reproduce the input signal with no distortion. That would require a uniform (flat) magnitude of response up to the bandwidth limitation of the system, with the signal delayed by precisely the same amount of time at all frequencies. That amount of time could be seconds, or weeks or months in the case of recorded media. In contrast, for a feedback apparatus used to control a dynamic system, the objective is to give the closed-loop system improved response as compared to the uncompensated system. The feedback generally needs to respond to system dynamics within a very small number of cycles of oscillation (usually less than one full cycle), and with a definite phase angle relative to the commanded control input. For feedback of sufficient amplification, getting the phase angle wrong can lead to instability for an open-loop stable system, or failure to stabilize a system that is open-loop unstable. Digital filters may be used for both audio systems and feedback control systems, but since the objectives are different, generally the phase characteristics of the filters will be significantly different for the two applications., Sagedusreaktsioon on süsteemi või seadme väljundspektri kvantitatiivne mõõtmine vastusena stiimulile ning seda kasutatakse süsteemi dünaamika iseloomustamiseks. See on väljundi suuruse ja faasi mõõtmine sageduse funktsioonina võrreldes sisendiga. Lihtsustatult öeldes, kui süsteemi sisestatakse teatud sagedusel siinuslaine, reageerib lineaarne süsteem samal sagedusel teatud suuruse ja faasinurgaga võrreldes sisendiga. Ka lineaarse süsteemi puhul kahekordistab sisendi amplituudi kahekordistumine väljundi amplituudi. Lisaks sellele, kui süsteem on ajas muutumatu, siis ei muutu ka sagedusreaktsioon ajas. Seega võib ajas muutumatute süsteemide puhul vaadelda sagedusvastet kui süsteemi rakendamist puhtalt kujuteldava arvu argumendi suhtes, mis kujutab endast sinusoidse ergutuse sagedust. Kaks sagedusreaktsiooni analüüsi rakendust on seotud, kuid nende eesmärgid on erinevad. Helisüsteemi puhul võib eesmärk olla sisendsignaali moonutusteta reprodutseerimine. See eeldab ühtlast (lamedat) vastuse suurust kuni süsteemi ribalaiuse piirini, kusjuures signaal on kõikidel sagedustel täpselt sama aja võrra hilinenud. See aeg võib olla sekundid või salvestatud meedia puhul nädalad või kuud. Seevastu dünaamilise süsteemi juhtimiseks kasutatava tagasisideseadme puhul on eesmärk anda suletud süsteemile kompenseerimata süsteemiga võrreldes parem reageering. Tagasiside peab tavaliselt reageerima süsteemi dünaamikale väga väikese arvu võnkesageduste jooksul (tavaliselt vähem kui üks täielik tsükkel) ja kindla faasinurgaga võrreldes käskitud juhtimissisendiga. Piisava võimendusega tagasiside puhul võib faasinurga valesti määramine põhjustada avatud ahelaga stabiilse süsteemi ebastabiilsust või mitte stabiliseerida süsteemi, mis on avatud ahelaga ebastabiilne. Digitaalseid filtreid võib kasutada nii audiosüsteemide kui ka tagasiside juhtimissüsteemide puhul, kuid kuna eesmärgid on erinevad, on filtrite faasiomadused nende kahe rakenduse puhul üldiselt oluliselt erinevad., Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. For a linear system, doubling the amplitude of the input will double the amplitude of the output, and summing two inputs produces an output that is the sum of the two corresponding outputs to the individual inputs. In addition, if the system is time-invariant (so LTI), then the frequency response also will not vary with time, and injecting a sine wave into the system at a given frequency will make the system respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Thus for LTI systems, the frequency response can be seen as applying the system's transfer function to a purely imaginary number argument representing the frequency of the sinusoidal excitation. Two applications of frequency response analysis are related but have different objectives. For an audio system, the objective may be to reproduce the input signal with no distortion. That would require a uniform (flat) magnitude of response up to the bandwidth limitation of the system, with the signal delayed by precisely the same amount of time at all frequencies. That amount of time could be seconds, or weeks or months in the case of recorded media. In contrast, for a feedback apparatus used to control a dynamic system, the objective is to give the closed-loop system improved response as compared to the uncompensated system. The feedback generally needs to respond to system dynamics within a very small number of cycles of oscillation (usually less than one full cycle), and with a definite phase angle relative to the commanded control input. For feedback of sufficient amplification, getting the phase angle wrong can lead to instability for an open-loop stable system, or failure to stabilize a system that is open-loop unstable. Digital filters may be used for both audio systems and feedback control systems, but since the objectives are different, generally the phase characteristics of the filters will be significantly different for the two applications.



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References
  1. Glossary of Terms Used in Reliability Standards


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