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?