EE$-20500$

Exam $9$:$30-10$:$45$ AM

April $17,2024$

NOTE:

i$.$ Make sure your name and last $4$ digits of your ID are on the test booklet

ii$.$ No electronic devices allowed except for a stand$-$alone calculator

iii. Once you begin the test you cannot leave the exam room until you hand in your test

iv$.$ Start each answer on a new page.

You must show all your work for credit!!!

The system below has zero energy when the input signal is $v_i(t)=(t)V$ and the output is $v_o(t)=4e^{-2t}+2e^{-4t}V.$ Find the output when the input is $v_i(t)=4e^{-t}u(t)V$ and the network has zero initial energy.

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For the system above the input is $v_i(t)=2+4sin(0\mathrm{.}25t+20)+5cos(t-25)$

a$)$ Determine the output signal $v_o(t).$

b$)$ Determine the input normalized power pertaining to $v_i(t)$

c$)$ Determine the percent of input normalized power that is transferred to the output $v_o(t)$

The signal $i(t)$ below is periodic. Determine:

a$)$ The trigonometric Fourier series for $i(t)$

b$)$ An expression for the normalized power of $i(t)$

c$)$ Plot the magnitude and phase spectrum up to and including the $6^{th}$ harmonic. Be sure to label the axis and graph values.