ELEN30009
Electrical Network Analysis and Design
Final Examination, Semester 1 2023
Question 1 (25 marks)
Consider the second-order circuit shown in Fig. 1. The switch has been in the open position for a long time, and then it closes at t = 0.
Fig. 1.
(a) [9 marks] Determine the initial conditions
(b) [16 marks] Find the expression of i(t) for t ≥ 0 using the time-domain method, i.e., you MAY NOT use Laplace transform. for this question.
Question 2 (30 marks)
Consider the circuit shown in Fig. 2 with input vi (t) and output vo (t).
Fig. 2.
(a) [11 marks] Show that the transfer function of this circuit is given by
Determine what kind of filter this circuit implements and calculate the cutoff frequency of the filter. You must give sufficient justification for your answer to receive marks.
(b) [9 marks] Consider vi (t) = 8 cos(2t)u (t) V. Derive the expressions for Vo (s) and vo (t).
(c) [10 marks] Use the convolution integral to compute the output response when the input is given by
vi (t) = u (t) 一 u(t 一 2) V
Question 3 (30 marks)
Consider the circuit shown in Fig. 3 with input vi and output vo taken across the capacitor.
Fig. 3.
(a) [13 marks] Design this circuit to obtain the following transfer function:
(b) [11 marks] Draw the Bode magnitude and phase plots ofthis circuit.
(c) [6 marks] Determine the steady-state output voltage of this circuit when
Question 4 (35 marks)
(a) [13 marks] Design a third-order broadband Butterworth bandpass op-amp filter with a lower cutoff frequency of 500 Hz and an upper cutoff frequency of 4500 Hz. The passband gain of the filter is 20 dB. Use 15 nF capacitors in the high-pass circuit and 10 kΩ resistors in the low-pass circuit.
(b) [7 marks] Draw a circuit diagram of the filter designed in (a) and label all the component values.
(c) [7 marks] Draw the Bode magnitude response of a third-order broadband cascaded bandpass op-amp filter with the same cutoff frequencies in (a). Discuss how the Bode plot would change for the third-order broadband Butterworth bandpass filter. Which one better approximates an ideal filter?
(d) [8 marks] Now, consider a student configures a filter as shown in Fig. 4. Determine the transfer function of this filter and discuss whether this circuit can be used as a second-order Sallen-Key filter.
Fig. 4.
Question 5 (40 marks)
Three two-port circuits, namely Circuit 1, Circuit 2, and Circuit 3, are interconnected in cascade. The input port of Circuit 1 is driven by a 6 A dc current source in parallel with an internal resistance of 30 Ω . The output port of Circuit 3 drives an adjustable load impedance ZL. The details of each circuit can be found below:
Circuit 1: The following dc measurements were made on the resistive network of Circuit 1.
Circuit 2: The inverse hybrid (g-parameter) matrix of Circuit 2 is given by:
Circuit 3: The circuit configuration of Circuit 3 with R1 = R2 = R3 = 10 Ω, is shown below.
Fig. 5
(a) [30 marks] Find the a-parameters of the cascaded network.
(Hint: Use y-parameter terminal equations for Circuit 3)
(a) [30 marks] Find the a-parameters of the interconnected cascaded network.
(Hint: Use y-parameter terminal equations for Circuit 3)
(a) [30 marks] Find the a-parameters of the cascaded network.
(Hint: Use y-parameter terminal equations for Circuit 3)
(b) [10 marks] Evaluate the maximum power that the cascaded two-port network can deliver to ZL.
(Hint: Source transform. current source and parallel internal resistance)
Question 6 (20 marks)
The electrical characteristics from the data sheet of a LM741 operational amplifier are shown below.
(a) [6 marks] The op-amp is used to build an inverting amplifier with gain, G = 4V/V. If an input voltage signal vin(t) is expected to be a pure sinusoidal signal, give an expression of vin(t) such that the output voltage vout(t) is not affected by any non-ideal characteristics of the op-amp. Consider an operating temperature condition TA of 25。C.
(b) [1 mark] The inverting op-amp from (a) has a feed-in resistor R1 = 100Ω and feedback resistor R2 = 400Ω . Based on the data sheet information, calculate the output dc offset voltage due to input offset voltage. Consider an operating temperature condition TA of 25。C. (Hint: Use the TYP value of VOS = 1 mV and you do not need to derive the equation for the output dc offset voltage)
(c) [1 mark] The inverting op-amp from (a) has a feed-in resistor R1 = 100Ω and feedback resistor R2 = 400Ω . Based on the data sheet information, calculate the output dc offset voltage due to input bias current. Consider an operating temperature condition TA of 25。C.
(d) [12 marks] To minimize output dc offset voltage due to input bias current, additional passive components(s) may be added to the inverting op-amp circuit of (a). Sketch this circuit configuration complete with component values. Show how the resulting output dc offset voltage is theoretically zero. Consider an operating temperature condition TA of 25。C.
(Hint: Use KVL around the negative input terminal of the op-amp, R2 and the output terminal of the op- amp)