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Name

Rocket Number(RN) (Last Six Digits) _ _ _ _ _ _

ZD ZC ZB ZA A1 A2

It is strongly recommended that you finish the Project before taking the final exam.

ZA = resistor (ohm value ZA from your RN)

ZB = capacitor (farad = 1/ZB from your RN)

ZC = inductor (henry = ZC from your RN)

ZD = resistor (ohm value = ZD from your RN)

Above is the circuit for your project. The elements of the circuit are resistors, capacitors and inductors, and the values are found from your rocket number. Read the last four numbers of your rocket number backwards (start from the last number) and enter those numbers in the circuit as the values described above.

If there is a zero in these last four digits, enter it as 10 (ten). No elements in the circuit should have zero value! Notice that ZD is the ‘load’.

1) If the voltage of a source is given as an integral of a function:

v(t) = ∫{1 ()−1(−6)+2(−1)−2(−3)} 0

Graph (below) the function inside the integral and then find the integral.

2) Draw the transformed circuit above in the s-domain. (Implement actual resistors, inductors and capacitors in the appropriate locations in the circuit along with their corresponding s-domain values.)

LOAD

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3) Find the Thevenin impedance for the circuit in the s-domain (this will not include your load).

4) Find the Thevenin voltage for the circuit in the s-domain (this will not include your load). Do NOT try to use the value for v(t) given in Question 1. Simply leave the input as V(s) for now. (VTH(s) will be some ratio or multiple of V(s))

5) Draw the Thevenin circuit in the s-domain (this will not include your load).

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6) If the voltage source is () = 100 () (a voltage of 100 turned on at time zero), determine the initial current (t-domain) through the load and the steady state current through the load (t-domain) – do not use s-domain equations for this, start back at the original circuit with elements having their time-domain values.

(Hint: Using a dc source, what does a capacitor/inductor look like at t=0? And t = ∞?)

7) Determine the load current, (), and identify the transient and steady state portion of the current. (Let ()=100 ()).

8) Determine the transient and steady state current in the t-domain by taking the inverse LaPlace (L-1)of Question 7.

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9) Show that your transient and steady state solution gives the same result for = 0 and = ∞ as you found in Question 6.

10) Determine the impedance transfer function ()= ()()

11) Plot the poles on a graph (below) of real and img axis and state whether the system is stable or unstable.

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12) Find () if () becomes a unitary impulse function (t). (Repeat Question 7 for new ())

13) Find () if () becomes a unitary impulse function (t). (Repeat Question 8 for new ())

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14) Find () if ()=()=100 (). This time use the convolution integral. (Hint: Be sure to show all your work, but your answer should be identical to the solution of Question 8 if both have been done correctly.)

15) Simulate this circuit on http://www.falstad.com/circuit/ and show that the current, (()),you calculated above for Zload is correct. (screenshot here)