Download Angle Modulation: Frequency Modulation and Phase Modulation and more Lecture notes Data Communication Systems and Computer Networks in PDF only on Docsity!
UNIT1-FUNDAMENTAL OF ANALOG
COMMUNICATION
- Introduction
a. In the Microbroadcasting services, a reliable radio communication system is of vital importance. The swiftly moving operations of modern communities require a degree of coordination made possible only by radio. Today, the radio is standard equipment in almost all vehicles, and the handie-talkie is a common sight in the populace. Until recently, a-m ( amplitude modulation ) communication was used universally. This system, however, has one great disadvantage: Random noise and other interference can cripple communication beyond the control of the operator. In the a-m receiver, interference has the same effect on the r-f signal as the intelligence being transmitted because they are of the same nature and inseperable.
b. The engines, generators, and other electrical and mechanical systems of modern vehicles generate noise that can disable the a-m receiver. To avoid this a different type of modualation, such as p-m (phase modulation) or f-m (frequency modulation ) is used. When the amplitude of the r-f (radio-frequency) signal is held constant and the intelligence transmitted by varying some other characteristic of the r-f signal, some of the disruptive effects of noise can be eliminated.
c. In the last few years, f-m transmitters and receivers have become standard equipment in America, and their use in mobile equipments exceeds that of a-m transmitters and receivers. The widespread use of frequency modulation means that the technician must be prepared to repair a defective f-m unit, aline its tuned circuits, or correct an abnormal condition. To perform these duties, a thorough understanding of frequency modulation is necessary.
- Carrier Characteristics
The r-f signal used to transmit intelligence from one point to another is called the carrier. It consists of an electromagnetic wave having amplitude, frequency, and phase. If the voltage variations of an r-f signal are graphed in respect to time, the result is a waveform such as that in figure 2. This curve of an unmodulated carrier is the same as those plotted for current or power variatons, and it can be used to
investigate the general properties of carriers. The unmodulated carrier is a sine wave that repeats itself in definite intervals of time. It swings first in the positive and then in the negative direction about the time axis and represents changes in the amplitude of the wave. This action is similar to that of alternating current in a wire, where these swings represent reversals in the direction of current flow. It must be remembered that the plus and minus signs used in the figure represent direction only. The starting point of the curve in the figure 2 is chosen arbitrarily. It could have been taken at any other point just as well. Once a starting point is chosen, however, it represents the point from which time is measured. The starting point finds the curve at the top of its positive swing. The curve then swings through 0 to some maximum amplitude in the negative direction, returning through 0 to its original position. The changes in amplitude that take place in the interval of time then are repeated exactly so long as the carrier remains unmodulated. A full set of values occurring in any equal period of time, regardless of the starting point, constitutes one cycle of the carrier. This can be seen in the figure, where two cycles with different starting points are marked off. The number of these cycles that occur in 1 second is called the frequency of the wave.
- Amplitude Modulation
b. Percentage of Modulation.
(1) In amplitude modulation, it is common practice to express the degree to which a carrier is modulated as a percentage of modulation. When the peak-to- peak amplitude of the modulationg signal is equal to the peak-to-peak amplitude of the unmodulated carrier, the carrier is said to be 100 percent modulated. In figure 4, the peak-to-peak modulating voltage, EA, is equal to that of the carrier voltage, ER, and the peak-to-peak amplitude of the carrier varies from 2ER, or 2EA, to 0. In other words, the modulating signal swings far enough positive to double the peak-to- peak amplitude of the carrier, and far enough negative to reduce the peak-to-peak amplitude of the carrier to 0.
(2) If EA is less than ER, percentages of modulation below 100 percent occur. If EA is one-half ER, the carrier is modulated only 50 percent (fig. 5). When the modulating signal swings to its maximum value in the positive direction, the carrier amplitude is increased by 50 percent. When the modulating signal reaches its maximum negative peak value, the carrier amplitude is decreased by 50 percent.
(4) The actual percentage of modulation of a carrier (M) can be calculated by using the following simple formula M = percentage of modulation = ((Emax - Emin) / (Emax + Emin)) * 100 where Emax is the greatest and Emin the smallest peak-to-peak amplitude of the modulated carrier. For example, assume that a modulated carrier varies in its peak-to-peak amplitude from 10 to 30 volts. Substituting in the formula, with Emax equal to 30 and Emin equal to 10, M = percentage of modulation = ((30 - 10) / (30 + 10)) * 100 = (20 / 40) * 100 = 50 percent. This formula is accurate only for percentages between 0 and 100 percent.
c. Side Bands.
(1) When the outputs of two oscillators beat together, or hetrodyne, the two original frequencies plus their sum and difference are produced in the output. This heterodyning effect also takes place between the a-f signal and the r-f signal in the modulation process and the beat frequencies produced are known as side bands. Assume that an a-f signal whose frequency is 1,000 cps (cycles per second) is modulating an r-f carrier of 500 kc (kilocycles). The modulated carrier consists mainly of three frequency components: the original r-f signal at 500 kc, the sum of the a-f and r-f signals at 501 kc, and the difference between the a-f and r-f signals at 499 kc. The component at 501 kc is known as the upper sideband, and the component at 499 kc is known as the lower side band. Since these side bands are always present in amplitude modulation, the a-m wave consists of a center frequency, an upper side-band frequency, and a lower side-band frequenmcy. The amplitude of each of these is constant in value but the resultant wave varies in amplitude in accordance with the audio signal.
(2) The carrier with the two sidebands, with the amplitude of each component plotted against its frequency, is represented in figure 7 for the example given above. The modulating signal, fA, beats against the carrier, fC, to produce upper side band fH and lower side band fL. The modulated carrier occupies a section of the radio- frequency spectrum extending from fL to fH, or 2 kc. To receive this signal, a receiver must have r-f stages whose bandwidth is at least 2 kc. When the receiver is tuned to 500 kc, it also must be able to receive 499 kc and 501 kc with relatively little loss in response.
(3) The audio-frequency range extends approximately from 16 to 16,000 cps. To accommodate the highest audio frequency, the a-m frequency channel should extend from 16 kc below to 16 kc above the carrier frequency, with the receiver having a corresponding bandwidth. Therefore, if the carrier frequency is 500 kc, the a-m channel should extend from 484 to 516 kc. This bandwidth represents an ideal condition; in practice, however, the entire a-m bandwith for audio reproduction rarely exceeds 16 kc. For any specific set of audio-modulating frequencies, the a-m channel or bandwidth is twice the highest audio frequency present.
(4) The r-f energy radiated from the transmitter antenna in the form of a modulated carrier is divided among the carrier and its two side bands. With a carrier componet of 1,000 watts, an audio signal of 500 watts is necessary for 100- percent modulation. Therefore, the modulated carrier should not exceed a total power of 1,500 watts. The 500 watts of audio power is divided equally between the side bands, and no audio power is associated with the carrier.
(5) Since none of the audio power is associated with the carrier component, it contains none of the intelligence. From the standpoint of communication efficiency, the 1,000 watts of carrier-component power is wasted. Furthermore, one side band alone is sufficient to transmit intelligence. It is possible to eliminate the carrier and one side band, but the complexity of the equipment needed cancels the gain in efficiency.
d. Disadvantages of Amplitude Modulation. It was noted previously that random noise and electrical interference can amplitude-modulate the carrier to the extent that communication cannot be carried on. From the military standpoint, however, susceptibility to noise is not the only disadvantage of amplitude modulation. An a-m signal is also susceptible to enemy jamming and to interference from the signals of transmitters operating on the same or adjacent frequencies. Where interference from another station is present, the signal from the desired station must be many times stronger than the interfering signal. For various reasons, the choice of a different type of modulation seems desireable.
- Phase Modulation
a. General.
(1) Besides its amplitude, the frequency or phase of the carrier can be varied to produce a signal bearing intelligence. The process of varying the frequency in accordance with the intelligence is frequency modulation, and the process of varying the phase is phase modulation. When frequency modulation is used, the phase of the carrier wave is indirectly affected. Similarly, when phase modulation is used, the carrier frequency is affected. Familiarity with both frequency and phase modulation is necessary for an understanding of either.
reference. Effects of the modulating signal on the relative phase angle at four different points are illustrated in B, C, D, and E.
(2) The effect of a positive swing of the modulating signal is to speed the rotation At point 1, the modulating signal reaches its maximum positive value, and the phase has bee The instantaneous phase condition at 1 is,
Having reached its maximum value in the positive direction, the modulating signal swings in the opposite direction. The vector speed is reduced and it appears to move in the reverse direction, moving towards its original position.
(3) For each cycle of the modulating signal, the relative phase of the carrier is These two values of instantaneous phase, which occur at the maximum positive and maximum negative values of modulation, are known as the phase-deviation limits. The upper limit is The relations between the phase-deviation limits and the carrier vector are given in the figure 12, with the limits of +/-
(4) If the phase-modulated vector is plotted against time, the result is the wave illustrated in the figure 13. The modulating signal is shown in A. The dashed-line waveforem, in B, is the curve of the reference vector and the solid-line waveform is the carrier. As the modulating signal swings in the positive direction, the relative phase angle is increased from an original phase lead of 45° to some maximum, as shown at 1 in B. When the signal swings in the negative direction, the phase lead of the carrier over the reference vector is decreased to minimum value, as shown at 2; it then returns to the original 45° phase lead when the modulating signal swings back to 0. This is the basic resultant wave for sinusoidal phase modulation, with the amplitude of the modulating signal controlling the relative phase characteristic of the carrier.
modulation frequency is increased, the carrier must move within the phase- deviation limits at a faster rate, increasing its speed and thereby increasing the carrier frequency shift. When the modulating-signal amplitude or frequency is decreased, the carrier frequency shift is decreased also. The faster the amplitude is changing, the greater the resultant shift in carrier frequency; the slower the change in amplitude, the smaller the frequency shift.
(3) The rate of change at any instant can be determined by the slope , or steepness, of the modulation waveform. As shown by curve A in figure 14, the greatest rates of change do not occur at points of maximum amplitude; in fact, when the amplitude is 0 the rate of change is maximum, and when the amplitude is maximum the rate of change is 0. When the waveform passes through 0 in the positive direction, the rate of change has its maximum positive value; when the waveform passes through 0 in the negative direction, the rate of change is a maximum negative value.
(4) Curve B is a graph of the rate of change of curve A. This waveform is leading A by 90°. This means that the frequency deviation resulting from phase modulation is 90° out of phase with the phase deviation. The relation between phase deviation and frequency shift is shown by the vectors in figure 15. At times of maximum phase deviation, the frequency shift is 0; at times of 0 phase deviation, the frequency shift is maximum. The equivalent-frequency deviation limits of the phase-modulated where
modulating- modulating signal at any time, t. 0 and the cosine has maximum values of +1 at 360° and -1 at 180°. If the phase -cps signal modulates the carrier, then F When the modulating signal is passing through 0 in the positive direction, the carrier frequency is raised by 523 cps. When the modulating signal is passing through 0 in the negative direction, the carrier frequency is lowered by 523 cps.
- Frequency Modulation
a. When a carrier is frequency-modulated by a modulating signal, the carrier amplitude is held constant and the carrier frequency varies directly as the amplitude of the modulating signal. There are limits of frequency deviation similar to the phase-deviation limits in phase modulation. There is also an equivalent phase shift of the carrier, similar to the equivalent frequency shift in p-m.
b. A frequency-modulated wave resulting from 2 cycles of modulating signal imposed on a carrier is shown in A of figure 16. When the modulating-signal amplitude is 0, the carrier frequency does not change. As the signal swings positive, the carrier frequency is increased, reaching its highest frequency at the positive peak of the modulating signal. When the signal swings in the negative direction, the
ANGLE MODULATION
ANGLE MODULATION is modulation in which the angle of a sine-wave carrier is varied by a modulating wave. FREQUENCY MODULATION (fm) and PHASE MODULATION (pm) are two types of angle modulation. In frequency modulation the modulating signal causes the carrier frequency to vary. These variations are controlled by both the frequency and the amplitude of the modulating wave. In phase modulation the phase of the carrier is controlled by the modulating waveform.
Frequency Modulation
In frequency modulation, the instantaneous frequency of the radio-frequency wave is varied in accordance with the modulating signal, as shown in view (A) of figure 2-5. As mentioned earlier, the amplitude is kept constant. This results in oscillations similar to those illustrated in view (B). The number of times per second that the instantaneous frequency is varied from the average (carrier frequency) is controlled by the frequency of the modulating signal. The amount by which the frequency departs from the average is controlled by the amplitude of the modulating signal. This variation is referred to as the FREQUENCY DEVIATION of the frequency-modulated wave. We can now establish two clear-cut rules for frequency deviation rate and amplitude in frequency modulation:
Figure 2-5. - Effect of frequency modulation on an rf carrier.
AMOUNT OF FREQUENCY SHIFT IS PROPORTIONAL TO THE AMPLITUDE OF THE MODULATING SIGNAL
(This rule simply means that if a 10-volt signal causes a frequency shift of 20 kilohertz, then a 20-volt signal will cause a frequency shift of 40 kilohertz.)
RATE OF FREQUENCY SHIFT IS PROPORTIONAL TO THE FREQUENCY OF THE MODULATING SIGNAL
(This second rule means that if the carrier is modulated with a 1-kilohertz tone, then the carrier is changing frequency 1,000 times each second.)
Figure 2-6 illustrates a simple oscillator circuit with the addition of a condenser microphone (M) in shunt with the oscillator tank circuit. Although the condenser microphone capacitance is actually very low, the capacitance of this microphone will be considered near that of the tuning capacitor (C). The frequency of oscillation in this circuit is, of course, determined by the LC product of all elements of the circuit; but, the product of the inductance (L) and the combined capacitance of C and M are the primary frequency components. When no sound waves strike M, the frequency is the rf carrier frequency. Any excitation of M will alter its capacitance and, therefore, the frequency of the oscillator circuit. Figure 2-7 illustrates what happens to the capacitance of the microphone during excitation. In view (A), the audio-frequency wave has three levels of intensity, shown as X, a whisper; Y, a normal voice; and Z, a loud voice. In view (B), the same conditions of intensity are repeated, but this time at a frequency twice that of view (A). Note in each case that the capacitance changes both positively and negatively; thus the frequency of oscillation alternates both above and below the resting frequency. The amount of change is determined by the change in capacitance of the microphone. The change is caused by the amplitude of the sound wave exciting the microphone. The rate at which the change in frequency occurs is determined by the rate at which the capacitance of the microphone changes. This rate of change is caused by the frequency of the sound wave. For example, suppose a 1,000-hertz tone of a certain loudness strikes the microphone. The frequency of the carrier will then shift by a certain amount, say plus and minus 40 kilohertz. The carrier will be shifted 1, times per second. Now assume that with its loudness unchanged, the frequency of the tone is changed to 4,000 hertz. The carrier frequency will still shift plus and minus 40 kilohertz; but now it will shift at a rate of 4,000 times per second. Likewise, assume that at the same loudness, the tone is reduced to 200 hertz. The carrier will continue to shift plus and minus 40 kilohertz, but now at a rate of 200 times per second. If the loudness of any of these modulating tones is reduced by one-half, the frequency of the carrier will be shifted plus and minus 20 kilohertz. The carrier will then shift at the same rate as before. This fulfills all requirements for frequency modulation. Both the frequency and the amplitude of the modulating signal are translated into variations in the frequency of the rf carrier.
Figure 2-6. - Oscillator circuit illustrating frequency modulation.
Figure 2-7A. - Capacitance change in an oscillator circuit during modulation. CHANGE IN INTENSITY OF SOUND WAVES CHANGES CAPACITY
plus and minus 100 kilohertz. These bands isolate the modulation extremes of this particular channel from that of adjacent channels.
Figure 2-8. - Frequency-modulating signal.
PERCENT OF MODULATION. - Before we explain 100-percent modulation in an fm system, let's review the conditions for 100-percent modulation of an AM wave. Recall that 100-percent modulation for AM exists when the amplitude of the modulation envelope varies between 0 volts and twice its normal umodulated value. At 100-percent modulation there is a power increase of 50 percent. Because the modulating wave is not constant in voice signals, the degree of modulation constantly varies. In this case the vacuum tubes in an AM system cannot be operated at maximum efficiency because of varying power requirements.
In frequency modulation, 100-percent modulation has a meaning different from that of AM. The modulating signal varies only the frequency of the carrier. Therefore, tubes do not have varying power requirements and can be operated at maximum efficiency and the fm signal has a constant power output. In fm a modulation of 100 percent simply means that the carrier is deviated in frequency by the full permissible amount. For example, an 88.5-megahertz fm station operates at 100-percent modulation when the modulating signal deviation frequency band is from 75 kilohertz above to 75 kilohertz below the carrier (the maximum allowable limits). This maximum deviation frequency is set arbitrarily and will vary according to the applications of a given fm transmitter. In the case given above, 50-percent modulation would mean that the carrier was deviated 37.5 kilohertz above and below the resting frequency (50 percent of the 150-kilohertz band divided by 2). Other assignments for fm service may limit the allowable deviation to 50 kilohertz, or even 10 kilohertz. Since there is no fixed value for comparison, the term "percent of modulation" has little meaning for fm. The term MODULATION INDEX is more useful in fm modulation discussions. Modulation index is frequency deviation divided by the frequency of the modulating signal.
MODULATION INDEX. - This ratio of frequency deviation to frequency of the modulating signal is useful because it also describes the ratio of amplitude to tone for the audio signal. These factors determine the number and spacing of the side frequencies of the transmitted signal. The modulation index formula is shown below:
Views (A) and (B) of figure 2-9 show the frequency spectrum for various fm signals. In the four examples of view (A), the modulating frequency is constant; the deviation frequency is changed to show the effects of modulation indexes of 0.5, 1.0, 5.0, and 10.0. In view (B) the deviation frequency is held constant and the modulating frequency is varied to give the same modulation indexes.
Figure 2 - 9. - Frequency spectra of fm waves under various conditions.
You can determine several facts about fm signals by studying the frequency spectrum. For example, table 2-1 was developed from the information in figure 2-9. Notice in the top spectrums of both views (A) and (B) that the modulation index is 0.5. Also notice as you look at the next lower spectrums that the
