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PRITESH VASOYA (130420105057)VISHVARAJ CHAUHAN(130420105058)
VIVEK MISTRY (130420105059)MILAN HIRAPARA (140423105004)
FREQUENCY RESPONSE ANALYSIS
Active Learning Assignment, Instrumentation & Process Control
BE SEM VChemical Engineering
INTRODUCTION
Frequency responses are generally derived by using the standard Laplace transform of sinusodial forcing functions.
We shall look at a convenient graphical technique for obtaining frequency response of linear systems.
AMPLITUDE RATIO AND PHASE ANGLE
AMPLITUDE RATIO AND PHASE ANGLE
AMPLITUDE RATIO AND PHASE ANGLE
AMPLITUDE RATIO AND PHASE ANGLE
After sufficient time elapses, the response of a first order system to a sinusodial input of frequency ω also a sinusoid of frequency ω.
Amplitude Ratio is defined as output amplitude upon input amplitude, and is denoted by |G (jω)|.
To obtain AR and phase angle, one merely substitutes jω instead of s in the transfer function and then finds the magnitude and angle of the resulting complex number.
CHARECTERISTICS OF A STEADY STATE SINUSODIAL RESPONSE
CHARECTERISTICS OF A STEADY STATE SINUSODIAL RESPONSE
The output is also a sine wave.Input frequency=output frequency=ω.In general, AR < 1, which means output
amplitude is greater than input amplitude.The output is shifted in time, that is it lags
the input by a phase angle of φ.Amplitude ratio (AR) and phase angle are
both functions of frequency.
BODE DIAGRAMS
There is a convenient graphical representation of AR and phase lag’s dependence on frequency.
This is called Bode Diagram.It consists of two graphs: logarithm of AR VS
logarithm of frequency and phase angle versus logarithm of frequency.
It is plotted on semilog papers.
BODE DIAGRAMS
BODE DIAGRAMS (FOR FIRST ORDER SYSTEMS)
BODE DIAGRAMS (FOR FIRST ORDER SYSTEMS)
BODE DIAGRAMS (FOR FIRST ORDER SYSTEMS)
Some asymptotic considerations can simplify the construction of this plot. As ωτ 0, we can see that AR1. This is indicated by the low frequency asymptote.
As ωτ∞ the equation becomes asymptotic to,log AR = - log(ωτ), which is a line of slope -1, passing through the point ωτ=1. This is indicated as the high frequency asymptote.
The frequency ω=1/τ, where the two asymptotes intersect, is known as the corner frequency.
BODE DIAGRAMS (FOR FIRST ORDER SYSTEMS)
In the second part of the Bode Diagram, the phase curve is given by φ= tan-1 (ωτ)= -tan-1 (ωτ).
φ approaches 0 at low frequencies and -90 at high frequencies. At corner frequency, φ= tan-1 (ωτ)= -tan-1 (ωτ)=-tan-1 (1)= -45.
It should be noted that AR is often reported in decibels. It is defined by, dB= 20 log(AR).
THANK YOU.