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ELEC S201F Basic Electronics There are TWO sections in this paper

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ELEC S201F Basic Electronics

There are TWO sections in this paper. You should answer altogether NINE (9) questions in this paper.

You should attempt ALL SIX (6) questions in Section A (50 marks). Answer ALL THREE (3) questions in Sections B (50 marks).

SECTION A:

This section carries 50% of the total marks and you should attempt ALL SIX questions.

Question 1 (6 marks)

Consider the circuit in Figure Q1, a load resistor R_Lis connected to a d.c. voltage source V_Swith an internal resistance R_S.

When R_L= 4 k:, the load voltage V_L= 15V.

When R_L= 2 k:, the load voltage is dropped to V_L= (12 + 0.2 × X8) V. e.g. if X8 = 4, V_L= 12 + 0.2 × 4 = 12.8 V.

Using voltage divider to find the open-circuit voltage V_Sand the internal resistance R_Sof the source as shown in Figure Q1.

(6 marks)

Figure Q1

Question 2 (10 marks)

For the circuit shown in Figure Q2, a resistor R, a capacitor C = 5 × 10^-9F and an inductor L = 0.1 H.

X7 k: if your X7 z 0 ^{R ®}¯10 k: if your X7 0

e.g. if X7 = 0, R = 10 k:.

The input voltage

V_in(t) = 12 cos(2 × 10⁴t + 30q) V.

Figure Q2

(a) Redraw the circuit in Figure Q2 using phasors.

(2 marks) (b) Find the equivalent input impedance of the circuit.

(4 marks) (a) Find the output voltage V_out(t).

(4 marks)

Question 3 (8 marks)

Showing all working carry out the following. Consider the 3-digit number 1ab, where

a = X5 and b = X6

e.g. if X5 = 3, X6 = 5, your 3-digit number is 135₁₀

(i) Convert your 3-digit number into an octal number.

(2 marks)

(ii) Find the 2’s complement of your 3-digit number

(2 marks)

A logic circuit has three inputs A, B, and C, and produces the outputs X where,

X A?CB?C?D A?B?C

Using only INVERTERs, AND-gates and OR-gates, draw a logic diagram of a circuit that generates X. Clearly label the output of each gate with the variable or term that it generates.

(4 marks)

Question 4 (6 marks)

Consider the circuit shown in Figure Q4(a). The transformer is assumed to have no losses with a turn ratio of N:1 and the diode is ideal.

X5u5 if your X5 z 0 where N ®¯ 50 if your X5 ₀

Figure Q4(a)

The input V_in(t) is a square wave with an amplitude of 10 V and a frequency of 10 Hz, as shown in Figure Q4(b).

(a) Sketch the waveform of the voltage V_a(t) at the output of the transformer.

(3 marks) (b) Sketch the waveform of the voltage V_out(t) after passing through the diode.

(3 marks)

(

)

(

)

Question 5 (15 marks)

The switch in the circuit in Figure Q5 has been closed (in position A) for a long time. The switch opens at t = 0 (The switch changes from position A to position B).

Given: V_S= 5V, R₁= 2 ?, R₂= 4 ?, R₃= 4 ? and L = 2 H.

(

)

(a) Redraw the circuit in Figure Q5 for the cases: t < 0 and t t 0.

(2 marks) (b) Find the current i_L(t) for t < 0.

(4 marks) (c) Find the current i_L(t) for t t 0.

(9 marks)

Question 6 (5 marks)

Consider the circuit in Figure Q6, V₁= 6V, V₂= 3V, resistors R₁= 4 k: and

10X8 k: if your X8 z 0 ^R² ^®¯ 20 k: if your X8 0

e.g. if X8 = 4, R₂= 10 + 4 = 14 k:

Assuming an ideal op-amp, find the output voltage V_out.

Hint: you should use the two Golden rules for the ideal op-amp.

Figure Q6

(5 marks)

End of Section A

SECTION B:

This section carries 50% of the total marks and you should attempt ALL THREE (3) questions.

Question 7 (20 marks)

Consider the circuit in Figure Q7. You are going to find the Thevenin equivalent circuit between terminals A and B.

Given an ideal current source I_S2= 2 mA, resistors R₁= 3 k?, R₂= 6 k?, R₃= 4 k?, R₄= 2 k? and an ideal voltage source V_S1, where

?7 V if your ?7 0

^?^?110 V if your ?7 0

e.g. if X7 = 0, V_S1= 10V.

Use nodal voltage analysis to find the open-circuit voltage V_OCbetween terminals A and B.

(11 marks)

Find the Thevenin equivalent resistance R_Tof the circuit by removing all the sources.

(3 marks)

Use OrCAD to find V_OCin (a). You need to submit your schematic and Output file in pdf format.

(6 marks)

Figure Q7

Question 8 (20 marks)

Figure Q8(a) shows an arrangement of 9 lamps. Of the many patterns that could be formed, a system only uses the 10 patterns shown in Figure Q8(b) where a filled circle indicates a lamp to be on; a lamp can only be on or off. Table Q8 shows a partially completed table describing the states of the lamp for the input codes (UVWX) used to generate the output patterns in Figure Q8(b) (the decimal equivalent of each code is marked against each pattern). A 0 in the output columns means that the lamp is off, a 1 means that the lamp is on, and an x represents a don't care state.

Figure Q8(a) and Q8(b)

		Inputs					Outputs to Lamps (ON = 1)
State	U	V	W	X	a	b	c	d	e	f	g	h	i
0	0	0	0	0	0	0	0		0	0	0	0
1	0	0	0	1	0	0	0		1	0	0	0
2	0	0	1	0	0	0	0		1	1	0	0
3	0	0	1	1	0	0	1		1	1	1	0
4	0	1	0	0	0	1	1		1	1	1	1
5	0	1	0	1	1	1	1		1	1	1	1
6	0	1	1	0	0	0	1		1	1	0	0
7	0	1	1	1	0	0	0		1	1	1	0
8	1	0	0	0	0	1	1		1	1	0	0
9	1	0	0	1	0	0	0		1	1	1	1
10	1	0	1	0	x	x	x		x	x	x	x
11	1	0	1	1	x	x	x		x	x	x	x
12	1	1	0	0	x	x	x		x	x	x	x
13	1	1	0	1	x	x	x		x	x	x	x
14	1	1	1	0	x	x	x		x	x	x	x
15	1	1	1	1	x	x	x		x	x	x	x

Table Q8

In your answer sheet construct a truth table giving the output states for lamps d and i.

(4 marks)

Write out a sum-of-minterms Boolean expression for lamp h by treating the don't care states as 0’s.

(2 marks) (c) A partially simplified Boolean expression for lamp g is,

g U?V?W U?W?X U?W ?X

Using only NAND gates, draw a circuit diagram that will produce g from the inputs U, V, W, X.

(3 marks)

Plot Karnaugh maps for outputs b and f. By treating each don’t care state as 0 or 1 as appropriate, find the simplest Boolean expressions for b and f.

(6 marks)

Use Quine-McCluskey (Tabular) method to find as simple a form as possible for the Boolean expression for c. Hint: you should make use of don’t care states.

(5 marks)

Question 9 (10 marks)

Consider the circuit in Figure Q9.

Figure Q9

Given a sinusoidal voltage source V_in, C₁= 3 PF, C₂= 3 nF, R₁= 250 ? and R₂= 1 k?, where

X6 V if your X6 0 Amplitude of ?_??10 V if your X6 0 e.g. if X6 = 5, amplitude of V_in= 5V.

Use OrCAD to build the circuit in Figure Q9. You must submit the schematic of your circuit in pdf format. Use OrCAD to simulate the frequency response of your circuit over the range of 1 Hz to 10 MHz, with 100 points per decade.

V^out

Obtain a plot of the magnitude of the transfer functionin dB vs frequency.

Vin

(6 marks)

V^out

Use the cursor to find the maximum value ofin dB from your plot.

Vin

(2 marks) (c) Find the 3-dB frequencies f_3dBof this circuit (i.e. the frequencies at which 3 dB below your maximum value in (b)).

(2 marks)

You must submit both the schematic and plot of your simulation results in pdf format.

END OF FINAL PROJECT

Appendix

KCL:	¦Iin ¦Iout
KVL:	¦V_i 0 in a loop i
v = iR,	i(t) C dv(t) , v(t) L di(t) dt dt
Impedance:	Z_C ¹and Z_L jZL , where Z = 2Sf jZC
Power:	P = V I

Impedance in series: Z = Z₁+ Z₂

Impedance in parallel: 1 ¹ ¹

Z Z1 Z2

Transformer: e² ^N²e1 N1

For the 1^storder ODE: _W^dx(t) x(t) A

dt

the general solution is: x(t) K₁exp(_W ^t) K₂, where K₁and K₂are constants.

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ELEC S201F Basic Electronics There are TWO sections in this paper

Electrical Engineering

Figure Q1

Figure Q2

Figure Q4(a)

Figure Q6

Figure Q7

Figure Q8(a) and Q8(b)

Table Q8

Figure Q9

Z Z1 Z2