HW7_Soln - Escuti/Brickley Fall 2008 ECE200 Fall 2008...

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Escuti/Brickley Fall 2008 ECE200 – Fall 2008 – Homework 7 Periodic Signals In Frequency Domain, Amplifiers Page 1 of 9 PROBLEM 1 The magnitude and phase spectra of a signal are given below. Find the expression for the time domain signal, v ( t ). v ( t ) = (15 V ) + (10 V )cos 2 π 2000 t + /6 () + (5 V )cos 2 5000 t + /2 ( ) Note that the phase angle in degrees must be converted to radians. PROBLEM 2 Plot the magnitude and phase spectra (on separate graphs!) of the following signals: Note: Remember to put them in the standard form. a. v ( t ) = (1 V ) + (2 V )cos(2 100 t ) + (3 V )cos(2 200 t + /5) This is already in standard cosine form. b. v ( t ) = (4 V ) + (6 V )cos(2 250 t ) + V )cos(2 500 t ) V )cos(2 1000 t ) The standard cosine form for this function is v ( t ) = V ) + (6 V )cos(2 250 t ) + V )cos(2 500 t ) + V )cos(2 1000 t + )
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Escuti/Brickley Fall 2008 ECE200 – Fall 2008 – Homework 7 Periodic Signals In Frequency Domain, Amplifiers Page 2 of 9 c. v ( t ) = ( 10 V ) + (5 V )sin(2 π 60 t ) + (20 V )cos 2 (2 60 t ) Note that (20 V 2 (2 60 t ) = (10 V ) + V )cos(2 120 t ) . The standard cosine form for this function is therefore v ( t ) = (5 V )cos(2 60 t /2) + V )cos(2 120 t ) PROBLEM 3 A multiplier is an electronic instrument that multiplies two analog signals, v 1 ( t ) and v 2 ( t ) and the output is given as v out ( t ) = v 1 ( t )* v 2 ( t ). Let the input signals to the multiplier be v 1 ( t ) = 5 V + (2 V )cos(2 200 t ) v 2 ( t ) = (2 V )cos(2 1000 t ) a. Find the multiplier output signal v out ( t ) (in time domain) where each term has only one cosine. Hint: You may find the following identity useful: cos( A )cos( B ) = 1 2 cos( A B ) + 1 2 cos( A + B ) The output is found by multiplying the signals and keeping the output units as volts: v ( t ) = v 1 ( t ) v 2 ( t ) = 5 + 2cos(2 200 t ) () 2cos(2 1000 t ) = 10cos(2 1000 t ) + 4cos(2 200 t )cos(2 1000 t and then, using the identity above… v ( t ) = 10cos(2 1000 t ) + 2cos(2 800 t ) + 2cos(2 1200 t b. Find and sketch the magnitude spectrum of the multiplier output signal.
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Escuti/Brickley Fall 2008 ECE200 – Fall 2008 – Homework 7 Periodic Signals In Frequency Domain, Amplifiers Page 3 of 9 PROBLEM 4 Plot the power spectra of the signals in Problem 2.
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This note was uploaded on 03/10/2009 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/Brickley Fall 2008 ECE200 Fall 2008...

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