HW5_Soln - Masnari/Escuti/Brickley 2008 ECE200 Fall 2008...

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Unformatted text preview: Masnari/Escuti/Brickley 2008 ECE200 Fall 2008 Homework 5 Periodic Signals in the Time Domain Page 1 of 13 1. [16 pts total, 1/3 pts each part each quantity] Find the amplitude, peak-to-peak value, average (DC) value, frequency, period, and phase angle of the following sinusoidal waveforms: a. ) 8 / 50 2 cos( ) 8 ( 2 ) ( + = t V V t v b. ) 8 / 50 2 cos( ) 8 ( 2 ) ( = t V V t v c. ) 8 / 50 2 sin( ) 8 ( 2 ) ( + + = t V V t v d. ) 8 / 50 2 sin( ) 8 ( 2 ) ( + = t V V t v e. ] 8 / ) 50 / 2 cos[( ) 8 ( 2 ) ( + + = t V V t v f. )] 002 . ( 50 2 cos[ ) 8 ( 2 ) ( + + = t V V t v g. ) 50 2 ( cos ) 8 ( 2 ) ( 2 t V V t v = h. ) 50 2 ( sin ) 8 ( 2 ) ( 2 t V V t v + = a) ) 8 / 50 2 cos( ) 8 ( 2 ) ( + = t V V t v Amplitude = 8 V Peak-to-peak value = 16 V Average (DC) Value = 2 V Frequency = 50 Hz Period = 1/ (50 Hz) = 0.02 s = - /8 radians b) ) 8 / 50 2 cos( ) 8 ( 2 ) ( = t V V t v Amplitude = 8 V Peak-to-peak value = 16 V Average (DC) Value = -2 V Frequency = 50 Hz Period = 1/ (50 Hz) = 0.02 s = (- /8 + ) radians or (- /8 ) radians c) ) 8 / 50 2 sin( ) 8 ( 2 ) ( + + = t V V t v Amplitude = 8 V Peak-to-peak value = 16 V Average (DC) Value = 2 V Frequency = 50 Hz Period = 1/ (50 Hz) = 0.02 s To find the phase, we need to convert sine to a cosine. Consider the following identity: sin = cos( - /2) Thus, sin(2 50t + /8) = cos(2 50t + /8 - /2) = cos(2 50t - 3 /8) = -3 /8 radians Masnari/Escuti/Brickley 2008 ECE200 Fall 2008 Homework 5 Periodic Signals in the Time Domain Page 2 of 13 d) ) 8 / 50 2 sin( ) 8 ( 2 ) ( + = t V V t v Amplitude = 8 V Peak-to-peak value = 16 V Average (DC) Value = 2 V Frequency = 50 Hz Period = 1/ (50 Hz) = 0.02 s To find the phase, we first need to convert sine to a cosine, as above. Thus, -sin(2 50t + /8) = -cos(2 50t - 3 /8) Next, to get rid of the negative, we shift the cosine radians....
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HW5_Soln - Masnari/Escuti/Brickley 2008 ECE200 Fall 2008...

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