Chapter 13. Sinusoidal Alternating Waveforms

Chapter 13. Sinusoidal Alternating Waveforms

1. 13.2 SINUSOIDAL ac VOLTAGE CHARACTERISTICS AND DEFINITIONS

   • The sinusoidal waveform with its additional notation will now be used as a model in defining a few basic terms. These terms, however, can be applied to any alternating waveform. It is important to remember, as you proceed through the various definitions, that the vertical scaling is in volts or amperes and the horizontal scaling is in units of time.

2. 13.3 FREQUENCY SPECTRUM

   • Using a log scale, a frequency spectrum from 1 Hz to 1000 GHz can be scaled off on the same axis. A number of terms in the various spectrums are probably familiar to you from everyday experiences.

3. 13.5 GENERAL FORMAT FOR THE SINUSOIDAL VOLTAGE OR CURRENT

   • The basic mathematical format for the sinusoidal waveform is: Am*sin(wt). where Am is the peak value of the waveform and wt is the unit of measure for the horizontal axis.

4. 13.4 THE SINUSOIDAL WAVEFORM

   • The sinusoidal waveform is the only alternating waveform whose shape is unaffected by the response characteristics of R, L, and C elements.

5. 13.10 APPLICATIONS

   • Safety Concerns (High Voltages and dc versus ac), (120 V at 60 Hz) versus (220 V at 50 Hz),

6. 13.8 EFFECTIVE (rms) VALUES

   • The equivalent dc value of a sinusoidal current or voltage is or 0.707 of its peak value.

7. 13.6 PHASE RELATIONS

   • The terms leading and lagging are used to indicate the relationship between two sinusoidal waveforms of the same frequency plotted on the same set of axes. In Fig. 13.29, the cosine curve is said to lead the sine curve by 90°, and the sine curve is said to lag the cosine curve by 90°. The 90° is referred to as the phase angle between the two waveforms. In language commonly applied, the waveforms are out of phase by 90°.

8. 13.7 AVERAGE VALUE

   • The average value of any current or voltage is the value indicated on a dc meter. In other words, over a complete cycle, the average value is the equivalent dc value. In the analysis of electronic circuits to be considered in a later course, both dc and ac sources of voltage will be applied to the same network.

9. 13.9 ac METERS AND INSTRUMENTS

   • It is important to note whether the DMM in use is a true rms meter or simply a meter where the average value is calibrated to indicate the rms level. A true rms meter reads the effective value of any waveform and is not limited to only sinusoidal waveforms. For example, an oscilloscope displays only those signals generated elsewhere and connected to the input terminals of the oscilloscope. The absence of an external signal will simply result in a horizontal line on the screen of the scope. an ohmmeter cannot be used to measure the ac reactance or impedance of an element or system even though reactance and impedance are measured in ohms.