DUBLIN INSTITUTE OF TECHNOLOGY KEVIN STREET, DUBLIN 8 Diploma in Applied Electronics YEAR II SUMMER EXAMINATIONS 1999 ELECTRIC CIRCUITS MR. P. Tobin MR. C. Bruce DATE Attempt FIVE questions with a maximum of three questions selected from Section A or Section B Laplace/Z Transform Tables
2 SECTION A 1. (a) Draw the circuit diagram, and derive the transfer function, for a simple first order low-pass RC filter. Sketch the asymptotic amplitude response. Explain the terms: cut-off frequency and roll-off rate. [12 marks] (b) Show how this circuit can be modified to ensure a constant attenuation at high frequencies. Determine the component values for this modified circuit if the two cut-off frequencies are 10 khz and 100 khz using a 10 nf capacitor. 2. (a) Develop an appropriate Thévenin equivalent circuit for the circuit shown in Figure1. Calculate a value for the load Z L connected across AB for the condition of maximum power transfer. [12 marks] (b) Use the Thévenin equivalent circuit to obtain a Norton equivalent circuit. R1 = 5 Ω, R2 = 3 Ω, XL1 = j4 Ω, XL2 = j5 Ω, V1 = 10 V RMS. Figure 1 3. (a) Apply mesh analysis to the circuit shown in Figure 2 and write the resultant equations in matrix form. Hence solve for the current in R2 using determinant algebra. [14 marks] (b) Write a set of equations for the node voltages v1, v2, and v3 expressing the equations in matrix form (Do not solve for any node voltages). R1 = 1 Ω, R2 = 2 Ω, X c1 = -j1 Ω, X c2 = -j0.25 Ω, X c3 = -j0.25 Ω, X L1 = j4 Ω, V1 = 5 60 V.
3 Figure 2 4. A single-tuned RF amplifier stage, using a self-biased common source JFET, is required to operate at a centre frequency of 1 MHz and with a bandwidth of 50 khz. Sketch the circuit diagram and briefly explain the circuit operation. [7 marks] For this amplifier, calculate i) The loaded Q-factor of the circuit ii) The source bias resistance value, iii) The inductance value for resonance, iv) The ac resistance of the coil, and v) The maximum voltage gain. The transconductance of the transistor is g m = 2 ms. It may be assumed that the total tuning capacitance is 100 pf and the unloaded Q-factor of the coil is 50. The quiescent drain-source current I dsq is 2 ma with V gsq = 2 V. Justify any assumptions made in the analysis. [13 marks] SECTION B 5. The output signal from digital filters can be characterised according to the equation: = m a( x( k = 0 k = 1 L b( Use this definition to classify FIR and IIR type filters. Give a simple block diagram using a first-order representation for each filter. Obtain the system function H(Z) for the DSP system represented in block diagram form as shown in Figure 3. Plot the pole-zero map and state with justification, whether the system is BIBO stable. a = -0.5, b =- 0.75 [12 marks]
4 Figure 3 6. (a) Obtain the Z - transform for the step function f( = u( if the unilateral Z transform is defined as: f ( z) = f (. Z n= 0 (b) A difference function for a system is given as: = x( + 0.5x( n 1) + 0.25 n 1) + 0.75 n 2) Draw a block diagram representation and derive the system function H(Z). (c) Outline a graphical technique for obtaining the frequency response of a system using the pole-zero map. 7. (a) Explain the importance of digital convolution. [4 marks] (b) Discrete convolution of an input signals x( and the impulse response of a system h( is related by the equation: = m k = 0 n x( h( Using the convolution sum, obtain the output response for a system if a input signal x( shown in Figure 4 is applied. The impulse response h( is identical to x(. [10 marks] (c) Verify that the output Y(Z) is the product of the individual Z- transforms of x(and h(. Figure 4
5 8. (a) The circuit shown in Figure 5 has a 1V step applied at time t=0 seconds. Redraw the circuit in the s-domain and show how initial conditions are represented. (b) Obtain an expression for the current I(t) in the circuit before the switch is closed. (c) Obtain a value for the current at t = 0.2 seconds if the switch is closed at time t = 0.1 seconds. The initial conditions at t = 0 seconds are zero. R1 = R2 = 5 Ω, L = 2 H, V1 = 1 V. Figure 5