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The amplitude of the audio-modulating voltage can also be determined from amplitude variations in the envelope pattern. Notice that the peak-to-peak variations in envelope amplitude (emax - e min) is equal to 400 volts on the scale. Note then that the peak amplitude of the audio voltage is 200 volts. If these rf and audio voltage values are inserted into the equation, the pattern in figure 1-42 is found to represent 50-percent modulation. If Em and Ec in the equation are assumed to represent peak-to-peak values, the following formula results:
Since the peak-to-peak value of E m in figure 1-42 is emax - emin, we can substitute as follows:
Also, since the peak-to-peak value of the carrier Ec is 2 times eo, we can subsititute 2eo for Ec as follows:
Linear vertical distance represents voltage on the screen of a cathode-ray tube. Vertical distance units can be used in place of voltage in equations. Thus, if only the percent of modulation is required, the oscilloscope need not be calibrated and the actual circuit voltages are not required. In figure 1-42, emax represents 600 volts (3 large divisions); emin is 200 volts (1 division); and eo is 400 volts (2 divisions). Using the equation and the dimensions of the screen pattern, you can figure the percent of modulation as follows:
When eo of the equation is difficult to measure, an alternative solution can be obtained with the equation below:
VECTOR ANALYSIS OF AN AM WAVE. - You studied earlier in this chapter that the modulation envelope results when the instantaneous sums of the carrier and sideband voltages are plotted with respect to time. An attempt to add these three voltages, point-by-point, would prove to be a huge task. The same end result can be obtained by using a rotating vector to represent each of the three frequencies in the composite envelope. In the following analysis, vectors will be scaled to indicate the peak voltage value of the frequencies they represent. The analysis has been simplified further by using a frequency of 8 hertz to represent the carrier frequency. Each cycle of the carrier then requires 1/8 of a second to complete 360 degrees. The carrier will be 100-percent modulated by a sine wave having a frequency of 1 hertz, thereby producing sideband frequencies of 7 and 9 hertz. Envelope Development from Vectors. - The modulating signal, upper sideband, carrier, and lower sideband waveforms are illustrated in views (A) through (D), respectively, in figure 1-43. Notice that the vertical lines passing through the figure divide each waveform into segments of 1/8 of a second each. These lines also coincide with the starting and ending points of each cycle of the carrier wave. Figure 1-43. - Formation of the modulation envelope by the addition of vectors representing the carrier and sidebands.
During the first 1/8 of a second (T1 to T2), the carrier wave completes exactly 1 cycle, or 360 degrees, as shown in view (C). The upper sideband, which has a frequency of 9 hertz, will complete each cycle in less than 1/8 of a second. Therefore, during the time required for the carrier to complete 1 cycle of 360 degrees, the upper sideband [view (B)] is able to complete 1 cycle of 360 degrees plus an additional 45 degrees of the next cycle, for a total of 405 degrees. The lower sideband [view (D)] has a frequency of 7 hertz and cannot complete an entire cycle in 1/8 of a second. During the time interval required for the carrier wave to progress through 360 degrees, the lower sideband frequency of 7 hertz can complete only 315 degrees, 45 degrees short of a full cycle. Keeping these factors in mind, you should be able to see that the phase angles between the two sideband frequencies, and between each sideband frequency and the carrier frequency, will continually shift. At an instant in time (T3), the carrier and sidebands will be in phase [view (E)], causing the envelope amplitude [view (F)] to be twice the amplitude of the carrier. At another instant in time (T7), the sidebands are out of phase with the carrier [view (E)], causing complete cancellation of the rf voltage. The envelope amplitude will become 0 at this point. You should see that, although the carrier and sideband frequencies have constant amplitudes, the ever-changing phase differences between them causes the modulation envelope to vary continuously in amplitude. The vector analysis of the modulation envelope will be developed with the aid of figure 1-44. In figure 1-44, view (A), a vertical vector (C) has been drawn to represent the carrier wave in figure 1-43. At T1 in figure 1-43, the upper and lower sideband frequencies are of opposite phase with respect to each other, and 90 degrees out of phase with respect to the carrier. This condition is illustrated in figure 1-44, view (A), by sideband vectors U and L drawn in opposite directions along the horizontal axis. Since the upper sideband U is equal in amplitude but opposite in phase to lower sideband L, the two sideband voltages cancel one another; the amplitude of the envelope at T1 is equal to the amplitude of the carrier. The same vector diagram is shown on a smaller scale in figure 1-43, view (E). Figure 1-44A. - Vector diagrams for T1 and T2.
During the 1/8 of a second time interval between T1 and T2, all three vectors rotate in a counterclockwise direction at a velocity determined by their respective frequencies. The vector representing the carrier, for example, has made one complete rotation of 360 degrees and is back in its original position, as shown in figure 1-44, view (B). The upper sideband frequency, however, will complete 405 degrees in this same 1/8 of a second. Notice in view (B) that vector U has made one complete counterclockwise rotation of 360 degrees, plus an additional 45 degrees for a total rotation of 405 degrees. Vector L, representing the lower sideband, rotates at a velocity less than that of either the carrier or the upper sideband. In 1/8 of a second, vector L completes only 315 degrees, which is 45 degrees short of one complete rotation. At the end of 1/8 of a second, the three vectors have advanced to the positions shown in view (B). Figure 1-44B. - Vector diagrams for T1 and T2.
The resultant vector in view (B) is obtained by adding vector U to vector L. Since each sideband has one-half the amplitude of the carrier, and the two sidebands differ in phase by 90 degrees, the amplitude of the resultant vector can be computed. This computation (not shown) would show the resultant vector to have an amplitude that is approximately 70 percent that of the carrier. Thus, at T2 the amplitude of the modulation envelope is about 1.7 times the amplitude of the carrier. This condition is shown in figure 1-43, view (F). By a similar procedure, vector diagrams can be constructed for time intervals T3 through T9. This has been done in figure 1-43, view (E). From these nine individual vector diagrams, the complete modulation envelope in figure 1-43, view (F), can be constructed. Notice in particular the vector diagrams for T3 and T7. At T3, all three waves, and therefore all three vectors, are in phase. The modulation envelope at this instant must, therefore, be equal to twice the amplitude of the carrier since each sideband frequency has one-half the amplitude of the carrier. At T7, the two sideband frequencies are in phase with each other but 180 degrees out of phase with the carrier. This causes the combined sideband voltage to cancel the carrier voltage, and the modulation envelope becomes 0 at that instant. Note that for the transmitter output to be 0 at T7, both the carrier and sideband frequencies must be present. If any one of these three frequencies were missing, complete cancellation would not occur and rf energy would be present in the output. Although this vector analysis was made for frequencies of 7, 8, and 9 hertz, the same description could be applied to the frequencies actually present at the output of a transmitter. Modulation Level of an AM Wave As stated earlier, the modulating signal can be introduced into any active element of a tube. In addition to the various arrangements possible within a single stage, the modulating signal can also be applied to any of the rf stages in the transmitter. For example, the modulating signal could be applied to the control grid or plate of one of the intermediate power amplifiers. A modulator circuit is usually placed into one of two categories, high- or low-level modulation. Circuits are categorized according to the level of the carrier wave at the point in the system where the modulation is applied. The FCC defines HIGH-LEVEL MODULATION in the Code of Federal Regulations as "modulation produced in the plate circuit of the last radio stage of the system." This same document defines LOW-LEVEL MODULATION as "modulation produced in an earlier stage than the final." Q.36 What is percent of modulation? |
 
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