Given the fully solved Example 14.2 from the text “Fundamentals of Electrical Circuit: Charles Alexander and Matthew Sadikuwith a) Calculate the inverse Fourier Transform of the ljw) H(jw) I(ju) (t), given as input sinusoid current i(t) defined in time domain as i(t) sinwt so that find the output current io Steps: i calculate the inverse Fourier Tranform of: (jw)=H(ju) (jw) ii) To do this, F{i(t)}= ,{jw) must be calculated (please, look at the appendix). Although, the Fourier transform of a sinusoid is provided on any table, please provide detailed steps. ili H(s) the transfer function of 14.2 and given as, the circuit was calculated in the appended Example s(s2 2+2s+ H(s)= where s-jw Detailed steps are offered under the appendix. b) Provide a thought discussion of Fourier Trasform and their usefulness in circuit analysis. c) Why we addressed the problem using Fourier Tranform rather a Laplace transform? The Decibel Scale 14.3 617 Example 14.2 For the circuit in Fig. 14.6, calculate the gain I(a)/I,() and its poles and zeros. 4Q Solution: 0.5 F By current division 2 H 4 j2 L(a) -1(0) 4 j21/0.5 Figure 14.6 For Example 14.2. + or L(a) j0.5(4 2) s(s 2) s =jo S j) 1 +j2 2 2s I L(w) The zeros are at 0,2-2 s(s +2)=0 The poles are at 22s (s 1) = 0 Thus, there is a repeated pole (or double pole) at p ww m APPENDIX FOURIER TRANSFORM IN ELECTRIC CIRCUITS x(t) У(1) circuit analysis H(jwX(jw) X(jiw) Y(jw) H(jw) e nust cafculafe it Calculate X(jw) Calculatew Directly from circuit analysis From differential equation, if given )through Fourir Transfry }ca/culeted Calculate (look up) the inverse Fourier transform of H(jw)X(jw) to get y(t) inped sind oar Fourier transform mm- Inverse Fourier transform