Question

One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to be observed in this laboratory assignment are shown below. In all the examples A represents the amplitude of the signal and may be given as the measurement from 0 to the peak value A, Apk or can be given as the measurement between A and -A which defines a peak-to-peak value, ApTime increases from left to right. Time can be in seconds, milliseconds, or The signals shown above are over two periods of time. T is defined as the time necessary to complete one full cycle before the signal repeats. This T is related to frequency by taking the reciprocal of the other term, that is T is in time and f, frequency, is in Hertz or Hz which means cycle-per-second. As an example, a signal frequency of 1000Hz has a period, T, of 1 millisecond. Another relationship is 0, which is radians-per-second. A ω 2zf To explain phase, or a time shift, see the two signals below. The first is a reference cosine wave and is expressed as X, :: A cos(cot). The second signal shows the time shift (phase shift) of the signal or arbitrary sinusoid, X2-A cos(cot + φ). The time shift is. or X,-A cos(cot). The second signal shows the time shift (phase shift) of the signal or arbitrary sinusoid, X, A cos(cot + ф). The time shift is, or radian, or 360 T degrees, where a full cycle is 2 radians or 360 degrees for a complete circle. Phase shifts will be the subject or the next laboratory assignment. The relationship between a sine-wave and a cosine-wave can be expressed as A sin(ot)A cos(-2), Where the phase or time shift is 2 radians or-90 degrees, that is, toward the negative time direction or to the left if viewed on the time axis. VA All of the waveforms or signals are shown with the amplitude A symmetric around the reference value zero, 0. This zero, 0, is the same as reference ground in DC measurements. The average value of all these waveforms would be zero. However, these signals can have a more general expressed form. For example, a sine-wave with an expression given as X(t) =-6 + 2 sin(2a2000t + 6). This expression means that a sine-wave with a peak amplitude of 2 at a frequency of 2000Hz with a time shift of radian or 30 degrees to the right on the time axis, but it is the centered at -6 below the reference zero or ground. If x(t) is in voltage, the VAng of the sine-wave is -6V. The general expression for the average value is shown below. An example of this will be shown by the instructor. RMS value is the re of the signal. measurements. The average value of all these waveforms would be zero. However, these signals can have a more general expressed form. For example, a sine-wave with an expression given as x(t) =-6 + 2 sin( 2 2000e+ 6). This expression means that a sine-wave with a peak amplitude of 2 at a frequency of 2000Hz with a time shift of radian or 30 degrees to the right on the time axis, but it is the centered at -6 below the reference zero or ground. If x(t) is in voltage, the VAN of the sine-wave is -6V. The general expression An example of this will be shown by the instructor. for the average value is shown below. RMS value is the roots-means-square of the signal. The most familiar value for RMS is for the electrical power outlet. This value is normally 115 VAC. The general expression to find the RMS value is shown below. An example of this will be shown by the instructor Pre-Lab 4 Exercises Find V the average value of voltage, and V the RMS value of voltage from the voltage waveform shown below. What is the frequency? 21 Repeat the above exercise if the negative peak of the square-wave is offset to zero. The positive peak would be offset to 10V

Answer 1

ACt) 2 ava rmi v\ VYmS зу

lov 2 七. av MS 1 4. 0"1ト 0 4 て 3.03 V