lab1-1 - Boise State University Department of Electrical...

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Unformatted text preview: Boise State University Department of Electrical and Computer Engineering ECE 212L – Circuit Analysis and Design Lab Experiment #1: Waveform Measurements 1 Objectives The objectives of this laboratory experiment are: • to review and apply the definitions of performance measures of periodic waveforms. 2 Theory min V max V o t +T o t t 2T T v(t) Figure 1: Example of a Periodic Waveform Consider the above periodic waveform with period T in seconds. Recall that the period is equal to the smallest time interval over which the waveform repeats itself. The period also includes any dead time when the waveform is equal to zero. Mathematically, f ( t + T ) = f ( t ) for any time t (1) The frequency f of this waveform is equal to the number of cycles over one second. Mathematically, the frequency of a periodic waveform is equal to the reciprocal of the period and it has units of cycles per second (cps) or Hertz (Hz). Thus, f = 1 T (2) The angular frequency of the waveform is equal to ω = 2 πf = 2 π T (3) and has units of radians per second (rad/s). Note that θ = ωT = 2 π = 360 o (4) 1 over a period T. The zero-to-peak or peak value V p of this waveform is defined as the largest absolute value (peak absolute value) of this waveform. Mathematically, V p = max {| V max | , | V min |} (5) The peak-to-peak value V pp of this waveform is equal to the range of this waveform between its maximum and minimum values. Mathematically, V pp = V max- V min (6) The average value of a periodic waveform is defined as V avg = 1 T ∫ T v ( t ) dt ⇐⇒ TV avg = ∫ T v ( t ) dt (7) Using the relationship on the right, this average value can be interpreted as the value of a constant (DC) waveform that covers the same area between itself and the time axis over a period. Note that the area under the original waveform is counted positively if the waveform is positive and negatively if the waveform is negative. Thus, a sine waveform has zero average value over a period as the positive area cancels the negative area under the sine wave.as the positive area cancels the negative area under the sine wave....
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lab1-1 - Boise State University Department of Electrical...

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