CANPRA4/102/0/2013

Tutorial letter 102/0/2013 Circuit Analysis IV (Practical)

CANPRA4 Year Module Electrical and Mining Engineering

IMPORTANT INFORMATION:

This tutorial letter contains important information about your module.

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PLEASE COMPLETE THE ATTACHED PRACTICAL EXPERIMENTS AND IGNORE THE EXPERIMENTS IN TUTLETTER 101.

ASSIGNMENT 2

Make use of the Multisim software to simulate the circuits and give graphic presentations, for example schematics, to show the results where necessary (you can do simulation in the laboratory of the department of Electrical and Mining Engineering, Florida Campus, UNISA).

QUESTION 1

For the circuit in Fig 1:

1) Using the information provided in Fig 1, determine the resistance R1. (2)

2) Determine the current through R1 and R2. (2)

3) Using Multisim, determine the solutions 2). (6)

Note: The schematics in Multisim should also be provided.

Fig 1 Circuit for question 1

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QUESTION 2

For the circuit in Fig 2:

Fig 2. Circuit for question 2

1) Find the mathematical expression for the transient behavior of the voltage vc

following the closing of the switch (position 1 at t=0 s and the circuit is stable

before the closing).

Hint: find the Thevenin equivalent circuit for

(8)

2) Draw the resultant waveform of voltage vc based on 1). (2)

3) Find the resultant waveform of voltage vc using Multisim software. (10)

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QUESTION 3

Find the driving-point impedance of the linear time-invariant circuits shown in Fig 3 and plot their poles and zeros on the complex plane.

Fig 3 Circuit for question 3

[9] QUESTION 4

For a given connected digraph and for a fixed tree, the fundamental loop matrix is given by

1) Write, by inspection, the fundamental cut-set matrix which corresponds to the same tree. (5)

2) Draw the digraph. (5)

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QUESTION 5

Assume the two-port shown in Fig 5 is the sinusoidal steady state at frequency ω; calculate the transmission matrix of this two-port.

Fig 5 Circuit for question 5

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CANPRA4/102

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QUESTION 6

For the circuit shown in Fig 6:

Fig 6 Circuit for question 6

1) Find all the natural frequencies of the circuit shown in Fig 6. (3)

2) Find the poles of Zin(s). (3)

3) Verify that the circuit is not exponentially stable and that Zin(s) has all its poles in the open LHP. (4)

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QUESTION 7

1) Given: 4 3 24 3 2 1 0

2( ) sH sb s b s b s b s b

+=+ + + +

find the values for , 0,1, 2,3,4ib i = to make H(s) realizable as a Butterworth filter. (8)

2) Given 1 1( )H ss a s b

= −+ +

choose a and b to realize H(s) by a Butterworth filter. (8)

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QUESTION 8

Consider the following transfer function:

2

1( )1

H ss−=−

1) Is it possible to realize this transfer function using an op amp and passive R, L, and C elements? Analyse and explain.

(8)

2) If R is allowed to be negative, propose a circuit to realize this transfer function. (7)

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TOTAL: 100