Experiment5 - - Department of Electrical & Computer...

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- Department of Electrical & Computer Engineering Course ECSE-291 EXPERIMENT 5 Frequency Response 2003-2004 -1- Objective: To study the frequency response of simple RLC circuits. Preparation: 1. Determine the transfer function H(jw) = V o /V i for the circuit shown in Fig. 1. (a) The magnitude and phase of H(jw), viewed as functions of frequency, together specify the frequency response of the circuit. Note particularly that if the amplitude of the input sinusoid V, is held constant as its frequency w is varied, in the steady state the output sinusoidal amplitude will be linearly proportional to |H(jw)|. In graphical presentation, the magnitude of H(jw) is usually plotted as 20log 10 |H(jw)| versus log 10 w, where the unit for 20log 10 |H(jw)| is the decibel (dB). -- See Section 14.2 in Ref. 1. (b) Find the relationship for : (i) the cutoff frequency and the time constant, and (ii) the DC gain and the steady state of the unit step response. (c) If the input v i (t) = 0.3sin(500 Π t + θ ) volts, where θ is constant, what is v o (t)? (d) Consider an input v i (t) consisting of two additive components: a sinusoidal signal of 250 Hz and an unwanted sinusoidal component (noise) of 25 kHz. If both components have an amplitude of 0.30 volts, then v i (t) = 0.30sin(500 π t + θ 1 ) + 0.30sin(50 000 π t + θ 2 ) volts where θ 1 and θ 2 are constants. By using the Principal of Superposition show that v o (t) is approximately equal to the low-frequency component. 2. Determine the transfer function H(jw) = V o /V i of the circuit shown in Fig. 2. Plot the amplitude and phase frequency response, showing the cutoff frequency in Hz. Find the relationship between the time constant of the circuit and the cutoff frequency. 3. Determine the transfer function H(jw) = V o /V i of the circuit shown in Fig. 3. 4.
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This note was uploaded on 12/22/2010 for the course ECSE ECSE 291 taught by Professor Khazaka during the Winter '03 term at McGill.

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Experiment5 - - Department of Electrical & Computer...

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