Frequency Response Methods
• The system is described in terms of its response
to one form of basic signals – sinusoid.
• The reasons of using frequency domain
techniques for the analysis & design of system
are as follows:
– The use of the sinusoid as a basic signal is not as
restrictive as first appears. By use of Fourier method it
is possible to construct a range of signals by linear
combinations of sinusoids.
– The mathematical methods used in the frequency
domain are simpler to apply that the corresponding
time domain methods. In particular, differential
equations are replaced by algebraic equations (with
the variable as a complex quantity)
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Reasons for using frequency
domain techniques (continues)
– Response in the time domain can be obtained from
frequency domain results. If some degree of
approximation is allowable this can be done by use of
simple graphical methods.
– For many applications, design in the frequency
domain is conceptually easier and gives a greater
physical insight into the system.
– Sophisticated equipment exists for measuring
frequency responses and thus enabling a frequency
domain model to be obtained from practical
measurement
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Response of a continuous System
to a sinusoidal input
• Consider right block
diagram x(t) is applied
to a LTI system at
time t=0
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Response of a continuous System to a
sinusoidal input
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Response of a continuous System to a
sinusoidal input
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General plot for a first order system
• A first order system
has a frequency
response function like
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General plot for a first order system
• General features of the first order response:
– The magnitude plot starts at K ( The system gain
factor) at w=0 and fall to zero as w-> infinite
– The magnitude of the gain has fallen by a factor ½
form its low frequency gain when w = 1/T
– The phase plot start to 0 when w=0 and approach -90
degree (legging) as w-> infinite
– The phase shift is -45 degree when w=1/T
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General plot for a second order
system
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General plot for a second order
system
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Bode Plot
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Bode Plot
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