July 28, 2015
Signals & Systems
Martin Loeser
Exercise Sheet 7 – Bode Plots
1 Stationary LTI System
Both amplitude and phase response of a LTI system are depicted in Figure 1.
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List 4:
Frequency Response and Bode Diagram
Exercise 1 Stationary System-Response
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.
Input signal Output signal
4
100cos10
t
………………………………………
………………………………………
tk2sin4
………………………………………
8
5
100cos3
tk
System-1
LTI
Figure 1: Bode plot of a LTI system.
Complete the following table:
Input Signal Output Signal
10 cos 100t+π
4..................
................ 4 sin (2kt)
................ 3 cos 100kt −5π
8
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
•ω1
τ
•ω=1
τ
•ω1
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 τis increased or decreased?
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