HW7_Soln - Escuti/Masnari 2007 ECE200 Fall 2007 Homework 7...

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Unformatted text preview: Escuti/Masnari 2007 ECE200 Fall 2007 Homework 7 Solutions Periodic Signals In Frequency Domain, Amplifiers Page 1 of 14 Problem 1: [16 pts total, 8 part a, 4 part b, 4 part c] a) Draw the magnitude, phase, and power spectra (using both W and dBW scales) of the following signal. (This means four plots.) b) Find the total signal power. Hint: the total power can always be found as the sum of the powers in the power spectrum (in units of Watts). c) Find the RMS value of this signal. Hint: this is easily calculated from the answer to the previous question. Solution: Frequency (Hz) Amplitude (V) Phase (radian) Power (W) Power (dBW) 0 10 0 100 20.00 1000 8 /4 32 15.05 2000 6 - /4 18 12.55 3000 4 3 /4 8 9.03 Escuti/Masnari 2007 ECE200 Fall 2007 Homework 7 Solutions Periodic Signals In Frequency Domain, Amplifiers Page 2 of 14 Phase Spectrum 0.25-0.25 0.75-0.4-0.2 0.2 0.4 0.6 0.8 1000 2000 3000 Frequency (Hz) Phase ( ! radian) Escuti/Masnari 2007 ECE200 Fall 2007 Homework 7 Solutions Periodic Signals In Frequency Domain, Amplifiers Page 2 of 14 Phase Spectrum 0.25-0.25 0.75-0.4-0.2 0.2 0.4 0.6 0.8 1000 2000 3000 Frequency (Hz) Phase ( ! radian) Escuti/Masnari 2007 ECE200 Fall 2007 Homework 7 Solutions Periodic Signals In Frequency Domain, Amplifiers Page 3 of 14 Escuti/Masnari 2007 ECE200 Fall 2007 Homework 7 Solutions Periodic Signals In Frequency Domain, Amplifiers Page 4 of 14 Problem 2: [8 pts] Given the power spectrum shown below, construct an equation for the signal v ( t ) (i.e. in the time domain). Assume = 0 for a ll peaks. Hint: note that there will be five terms in the expression. Solution: For DC signal, 2 DC V P = 1 . Using dbW P = 10logP => dBW P 10 P = 10 we could find the power at other frequency. Then, we find the amplitude at each frequency by realizing, For f = 0, 2 DC V P = 1 For other frequency, 2 2 RMS V amplitude 1 P = = 1 2 1 ! From which we can find the amplitude at each frequency. The results of these calculations are shown below. Frequency (Hz) Power (dBW) Power (W) Amplitude (V) 0 20 100.00 10 100 30 1000.00 44.72 200 20 100.00 14.14 400 10 10.00 4.47 600 5 3.16 2.51 Since all phase angles are assumed to be zero, the waveform can be written as: ( ) 10 44.72cos(2 100 ) 14.14cos(2 200 ) 4.47cos(2 400 ) 2.51cos(2 600 ) v t t t t t ! ! ! ! = + + + + Escuti/Masnari 2007 ECE200 Fall 2007 Homework 7 Solutions Periodic Signals In Frequency Domain, Amplifiers Page 5 of 14 Problem 3: [10 pts] An amplifier with a voltage gain of 1500 is used to amplify the electrical signals generated by a microphone. The amplified signal is fed to an 4 audio speaker....
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This homework help was uploaded on 03/20/2008 for the course ECE 200 taught by Professor Escuti during the Fall '07 term at N.C. State.

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HW7_Soln - Escuti/Masnari 2007 ECE200 Fall 2007 Homework 7...

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