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exercise 7

publicité
July 28, 2015
Signals & Systems
Martin Loeser
ZHAW, SiSy HS2013, dqtm
List 4:
Exercise
Sheet
7 and–Bode
Bode
Plots
Frequency
Response
Diagram
Exercise 1 Stationary System-Response
1
The bode diagram of an LTI system is given below. Fill out the table by determining the
corresponding input signals and stationary output signals. Do also indicate in the graphics of the
Bode diagram, the amplitude and phase values that you assumed for your calculation.
Stationary LTI System
System-1
Both amplitude and phase response of LTI
a LTI system are depicted in Figure 1.
Input signal
Output signal
Figure
1: Bode plot of a LTI
system.
10 cos 100 t
………………………………………
4
Complete the following table:
Input Signal
………………………………………
Output Signal
π
4
10 cos 100t +
..................
. . . . . . . . . . . . . . . . ………………………………………
4 sin (2kt)
................
Zurich University of
Applied Sciences
4 sin 2k t
3 cos 100kt −
5π
8
Page 1/5
3 cos 100k t
5
8
SiSy_exer4_freqresp.docx
Exercise Sheet 7 – Bode Plots, Signals & Systems
2
2
Bode Plot and Transfer Function
A LTI system features the following transfer function:
G(ω) =
jωτ
.
1 + jωτ
(a) Derive an analytical expression for the modulus of the transfer function.
(b) Find an analytical expression for the argument (i.e., the phase) of the transfer
function.
(c) For the three cases
• ω
• ω=
• ω
1
τ
1
τ
1
τ
compute modulus and phase of the transfer function.
(d) Sketch a Bode plot of the transfer function for τ = 5 ms.
(e) Which kind of behaviour does the system show?
(f) How does the plot change when τ is increased or decreased?
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