This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 0.250.25 0.750.40.2 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 0.250.25 0.750.40.2 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....
View
Full
Document
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.
 Fall '07
 Escuti
 Amplifier, Frequency

Click to edit the document details