Department of Electrical and Electronic Engineering
ELEN30009 Electrical Network Analysis and Design
Semester 2 Assessment, 2022
Question 1 (4+10 = 14 marks)
Consider the second-order circuit shown in Fig. 1. The switch has been in the closed position for a long time, and then it opens at t = 0.
Fig. 1.
(a) Determine the initial conditions
(b) Find the expressions of v1 (t) and v2 (t) for t ≥ 0 using the time-domain method, i.e., you MAY NOT use Laplace transform. for this question.
Question 2 (2+8+6 = 16 marks)
Consider the circuit shown in Fig. 2 with a current source input is (t) and the output io (t) as the current through the inductor.
Fig. 2.
(a) Show that the impulse response of the circuit is A.
(b) Use the convolution integral to compute the output response when the input is given by:
(c) Now, consider is (t) = cos(10t)u(t) A. Derive the expressions for Io (s) and io (t).
Question 3 (4+3+6+2+5 = 20 marks)
Consider the circuit shown in Fig. 3 with input vi (t) and output vo (t).
Fig. 3.
(a) Show that the frequency response of this circuit can be written as
where w1 = 1/(R1c1) and w2 = 1/(R2c2).
(b) Using R1 = 2 kΩ, design this circuit to provide a voltage gain of 40 dB in the passband with a low- frequency 3-dB point at 200 Hz and a high-frequency 3-dB point at 200 kHz.
(c) Plot the Bode magnitude and phase response of this filter.
(d) A sinusoidal input vi (t) = A cos(wt + φ) is applied to this filter with the following parameters:
• Magnitude: 2 V.
• Frequency: 10 kHz.
• Phase: 45。.
Determine the steady-state output voltage of the filter.
(e) Design an active cascaded broadband bandpass filter to achieve the same specifications in (b). Use 0.4 μF capacitors. Draw the circuit diagram of your final design and label all component values.
Question 4 (6+4+2=12 Marks)
You are in the process of completing a circuit for on-farm sensing application that will need to amplify signals in the frequency range of 0-80 MHz. However, when you were testing this circuit, you realise that the VHF radio transmitting tower nearby is causing a strong interfering signal around 95-105 MHz and saturates your amplifiers in the circuit.
You are now required to complete the design of a passive band-reject filter of the form shown in Fig. 4 with following specifications:
• Centre frequency = 100MHz
• Bandwidth = 10 MHz
• You may assume that the antenna and the amplifier circuits will not load this filter circuits as you plan to use buffer amplifiers to ensure this is the case.
Fig. 4.
(a) Obtain the transfer function H(s) that relates output voltage Vo (s) to Vi (s) of the band-reject filter form. shown in Fig. 4. Identify the parts of the transfer function that determines the centre frequency and the bandwidth of the filter.
(b) To set the centre frequency at 100 MHz, select first a value for inductance (L) from the available collection of 1μH, 100 μH, 1 mH, and 100 mH and then calculate the capacitance (c).
(c) Determine the value of the resistance (R) to achieve the required bandwidth of 10 MHz.
Question 5 (2+4+2+6+4=18 Marks)
Two engineers are attempting to fix a circuit attached to a sensor device. After closely examining the circuit elements and their interconnections, they come up with an equivalent circuit shown in Fig. 5 and now they are trying to understand the function of this circuit. You are required to help them with the analysis.
The circuit has been in the unpowered state for a long time and thus can be assumed to be free from any stored charge.
(a) Assuming the operational amplifier is ideal, determine the current through the positive and the negative terminal of the operational amplifier.
(b) By applying suitable circuit laws, derive the expression for describing the time domain description of the output voltage vo (t) as a function of vi (t), assuming there are no initial conditions, i.e., vi (t = 0) = 0 and vo (t = 0) = 0.
(c) Based on the expression obtained in (b), describe the function of the circuit.
(d) You realise that the circuit is built with a real operational amplifier with a finite gain A. Derive an expression for the output voltage Vo (s) in frequency domain by taking this into account.
(e) Identify two imperfections or limitations of real operational amplifiers and discuss how they will impact the function of the circuit.
Question 6 (4+6+4+3+3=20 Marks)
You are working with a circuit shown in Fig. 6b where two identical two-port circuits (as shown in Fig. 6a) are used to connect the signal source Vs = 80∠0。mV with a source resistance fRs = 50Ω to a load with resistance of RL = 50 Ω.
You have no knowledge of internal makeup of the circuit. However, it is known to have no frequency dependence over the frequency range of interest.
To model the two-port circuit shown in Fig. 6a using its A-matrix, the following two sets of measurements are made to help you with the determination of the circuit’s a-parameters. The results are summarised below.
Fig. 6.
(a) Using the measurements, derive the a-parameters of the two-port circuit.
(b) Using the a-parameters obtained in (a) for the two-port circuit of Fig 6a, determine equivalent a- parameters for the combination of two identical two port circuits.
(c) Determine the output voltage Vo across the load RL produced by the input source Vs = 80∠0。mV.
(d) Determine the power delivered to the load.
(e) Determine the power delivered by the source.