Angle and Pulse Modulation

2-1

Chapter 2

Angle And Pulse Modulation

Learning Objectives

Upon completion of this chapter you will be able to: 1. Describe frequency-shift keying (fsk) and methods of providing this type of modulation. 2. Describe the development of frequency modulation (fm) and methods of frequency modulating a carrier. 3. Discuss the development of phase modulation (pm) and methods of phase modulating a carrier. 4. Describe phase-shift keying (psk), its generation, and application. 5. Discuss the development and characteristics of pulse modulation. 6. Describe the operation of the spark gap and thyratron modulators.

7. Discuss the characteristics of a pulse train that may be varied to provide communications capability. 8. Describe pulse-amplitude modulation (pam) and generation. 9. Describe pulse-duration modulation (pdm) and generation. 10. Describe pulse-position modulation (ppm) and generation. 11. Describe pulse-frequency modulation (pfm) and generation. 12. Describe pulse-code modulation (pcm) and generation.

Introduction

In chapter 1 you learned that modulation of a carrier frequency was necessary to allow fast communications between two points. As the volume of transmissions increased, a need for more reliable methods of communication was realized. In this chapter you will study angle modulation and pulse modulation. These two types of modulation have been developed to overcome one of the main disadvantages of amplitude modulation - susceptibility to noise interference. In addition, a special application of pulse type modulation for ranging and detection equipment will be discussed.

2-2

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. Let’ s study these modulation methods for an understanding of their similarities and differences.

Frequency-Modulation Systems

In frequency modulation an audio signal is used to shift the frequency of an oscillator at an audio rate. The simplest form of this is seen in FREQUENCY-SHIFT KEYING (fsk). Frequency-shift keying is somewhat similar to continuous-wave keying (cw) in AM transmissions. Frequency-Shift Keying Consider figure 2-1, views (A) through (D). View (A) is a radio frequency (rf) carrier which is actually several thousand or million hertz. View (B) represents the intelligence to be transmitted as MARKS and SPACES. Recall that in cw transmission, this intelligence was applied to the rf carrier by interrupting the signal, as shown in view (C). The amplitude of the rf alternated between maximum and 0 volts. By comparing views (B) and (C), you can see the mark/space intelligence of the Morse code character on the rf. The spacing of the waveform in view (D) is an example of the same intelligence as it is applied to the frequency instead of the amplitude of the rf. This is simple frequency-shift keying of the same Morse code character.

Figure 2-1A.—Comparison of ON-OFF and frequency-shift keying. RF CARRIER (CW) (EACH CYCLE

Represents Several Thousand Or Several Million Cycles).

Figure 2-1B.—Comparison of ON-OFF and frequency-shift keying. AMPLITUDE VARYING (ON-OFF) MODULATING WAVE (MORSE CODE CHARACTER "N"). 2-3 Figure 2-1C.—Comparison of ON-OFF and frequency-shift keying. TRANSMITTED ON-OFF KEYED CW SIGNAL. Figure 2-1D.—Comparison of ON-OFF and frequency-shift keying. TRANSMITTED FREQUENCY-SHIFT

Keyed Signal (Fsk).

In fsk the output is abruptly changed between two differing frequencies by opening and closing the key. This is shown in view (D). For illustrative purposes, the spacing frequency in view (D) is shown as double the marking frequency. However, in practice the difference is usually less than 1,000 hertz, even when operating at several megahertz. You should also note that the limit of frequency shift is determined without reference to the amplitude of the keying signal in the fsk system. The frequency shift may be set at plus or minus 425 hertz from the allocated channel frequency. The total shift between mark and space would be 850 hertz. Either the mark or space may use the higher of the two frequencies. The upper frequency of the transmitted signal is usually the spacing interval and the lower frequency is the marking interval.

COMPARING FSK AND CW SIGNALS.—A comparison of on-off keyed cw (figure 2-2), (view (A), view (B), view (C)), and fsk (figure 2-3), (view (A), view (B), view (C)), signals will show clearly the principal features of fsk and give us a basis on which frequency modulation can be discussed. Let's use views (A), (B), and (C) of both figures to show the Morse code character "F" for an example. Figures 2-2 and 2-3 are graphic drawings of the two types of keying. Time and amplitude are known dimensions of AM; but to explain fsk properly, we have added the third dimension of frequency.

2-4 Figure 2-2A.—Comparison of AM and fm receiver response to an AM signal. THREE-DIMENSIONAL

Representation Of An On-Off Keyed Cw Telegraph Signal.

Figure 2-2B.—Comparison of AM and fm receiver response to an AM signal. RESPONSE OF AM

Demodulator To Signal.

Figure 2-2C.—Comparison of AM and fm receiver response to an AM signal.RESPONSE OF FM

Discriminator To Signal.

2-5 Figure 2-3A.—Comparison of AM and fm receiver response to an fm signal. THREE-DIMENSIONAL

Representation Of A Frequency-Shift Keyed Telegraph Signal.

Figure 2-3B.—Comparison of AM and fm receiver response to an fm signal. RESPONSE OF AM

Demodulator To Signal.

Figure 2-3C.—Comparison of AM and fm receiver response to an fm signal. RESPONSE OF FM

Discriminator To Signal.

CW SIGNALS.—Since cw signals are of essentially constant frequency, there is no variation along the frequency axis in view (A) of figure 2-2. The complete intelligence is carried as variations in the amplitude of the signal. To receive the intelligence carried by such a signal, the receiving equipment must be able to scan the signal along the time and amplitude axes, which carry the information. When scanned along the time and amplitude axes [shown in view (B)], the intelligence appears as large changes in amplitude. If the circuit were perfect, these variations would be from 0 amplitude to some maximum value (established by transmitter power, distance, and so forth) depending on whether the key were open or closed. However, interfering components of energy caused by atmospherics, interfering stations, and 2-6 electrical machinery appear as additional variations along the amplitude axis. When these amplitude variations approach or exceed the variation caused by the keyed intelligence, the signal is blanked out by interference. We have all heard this happen on our AM radios during storms or when near operating machinery.

View (C) of figure 2-2 represents the same signal when scanned along the time and frequency axes as it would be in an fm receiver. Variations in signal amplitude have no effect on the frequency and no intelligence can be received. Note that the noise and interference components have also been suppressed so that they have little effect on the received signal. Thus, if the intelligence variations were impressed as changes along the frequency axis, and the receiving equipment were designed to respond to this type of signal, then the effects of noise and interference would be practically eliminated. Frequency-shift keyed circuits fulfill these conditions.

FSK SIGNALS.—In fsk the rf signal is shifted in frequency (not amplitude) between "key-open" and "key-closed" conditions. The signal amplitude remains essentially constant. View (A) of figure 2-3 represents the letter "F" keyed as a shift in frequency between mark and space. The normal frequency condition with the key open is a space. Recall that this may be either the lower or higher frequency. When the key is closed, the frequency instantly changes to the mark value and remains constant during the marking interval. Opening the key again returns the frequency to the space frequency. Midway between the mark and space frequencies is the assigned channel frequency.

Also shown in view (A) is the variation along the amplitude axis caused by the same noise and interference mentioned earlier. The right-hand portion of view (A) illustrates the elimination of this noise by the receiving equipment. View (B) clearly shows that scanning the signal along the amplitude and time axes reproduces no amplitude variations from signal interference. However, if the scanning is accomplished along the frequency and time axes, the intelligence is reproduced, as shown in view (C). By this system, the intelligence can be recovered at the receiving station in its original form; it will be nearly unaffected by conditions in the radio path other than fading. As a matter of fact, fsk resists the effects of fading better than cw.

FREQUENCY-SHIFT KEYING.—In its simplest form, frequency-shift keying of a transmitter can be accomplished by shunting a capacitor (or an inductor) and key (in series) across the oscillator circuit. By locking the normal key of the transmitter and operating only the oscillator circuit key, you can change the oscillator frequency. The shift in frequency between mark (key-closed) and space (key-open) conditions is determined by the effect of the additional capacitance (or inductance) on the oscillator frequency. The frequency multiplication factor in the transmitter amplifiers must be taken into consideration when determining the oscillator frequency shift. Thus, if the desired shift is the conventional 850 hertz at the transmission frequency, and this frequency is four times the oscillator frequency (that is, doubled in two stages), then the effect of the additional capacitance (or inductance) on the oscillator must be limited to 212.5 hertz as shown below: 2-7 Frequency-shift keyers are, of course, more complicated than this simple illustration would seem to show, but the basic principles are the same. Still, the keyer does change the oscillator frequency by a certain number of cycles. Further, this change must be correlated with the multiplication factor of the transmitter to cause the desired shift between mark and space frequencies.

METHODS OF FREQUENCY SHIFTING.—Frequency-shift keyers operate on either of two general principles. First, the keyer may take the output of the transmitter's master oscillator and modulate it with the output of another oscillator that is frequency-shift keyed. This action will result in two frequencies that are used to excite the first amplifier stage of the transmitter. This system is illustrated in view (A) of figure 2-4. View (B) illustrates the second method of frequency-shift keyer operation. In this method the transmitter's master oscillator is itself shifted in frequency by the mark and space impulses from the keyer unit.

Figure 2-4A.—Two methods of frequency-shift keying (fsk). FREQUENCY-SHIFT KEYING BY MODULATING

Master Oscillator Output.

2-8 Figure 2-4B.—Two methods of frequency-shift keying (fsk). FREQUENCY-SHIFT KEYING IN MASTER

Oscillator Circuit.

ADVANTAGES OF FSK OVER AM.—Frequency-shift keying is used in all single-channel, radiotelegraph systems that use automatic printing systems. The advantage of fsk over on-off keyed cw is that it rejects unwanted signals (noise) that are weaker than the desired signal. This is true of all fm systems. Also, since a signal is always present in the fsk receiver, automatic volume control methods may be used to minimize the effects of signal fading caused by ionospheric variations. The amount of inherent signal-to-noise ratio improvement of fsk over AM is approximately 3 to 4 dB. This improvement is because the signal energy of fsk is always present while signal energy is present for only one-half the time in AM systems. Noise is continuously present in both fsk and AM, but is eliminated in fsk reception.

Under the rapid fading and high-noise conditions that commonly exist in the high frequency (hf) region, fsk shows a marked advantage over AM. Overall improvement is sometimes expressed as the RATIO OF TRANSMITTED POWERS required to give equivalent transmission results over the two systems. Such a ratio varies widely, depending on the prevailing conditions. With little fading, the ratio may be entirely the result of the improvement in signal-to-noise ratio and may be under 5 dB. However, under severe fading conditions, large amounts of power often fail to give good results for AM transmission. At the same time, fsk may be satisfactory at nominal power. The power ratio (fsk versus AM) would become infinite in such a case.

Another application of fsk is at low and very low frequencies (below 300 kilohertz). At these frequencies, keying speeds are limited by the "flywheel" effect of the extremely large capacitance and inductance of the antenna circuits. These circuits tend to oscillate at their resonant frequencies. Frequency-shifting the transmitter and changing the antenna resonance by the same keying impulses will result in much greater keying speeds. As a result, the use of these expensive channels is much more efficient. Q-1. What are the two types of angle modulation?

Q-2. Name the modulation system in which the frequency alternates between two discrete values in response to the opening and closing of a key? Q-3. What is the primary advantage of an fsk transmission system? 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 2-9 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 2-10 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 1,000 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.

2-11 Figure 2-7B.—Capacitance change in an oscillator circuit during modulation. AT A FREQUENCY TWICE THAT

Of (A), The Capacity Changes The Same Amount, But Twice As Often.

Figure 2-8 shows how the frequency shift of an fm signal goes through the same variations as does the modulating signal. In this figure the dimension of the constant amplitude is omitted. (As these remaining waveforms are presented, be sure you take plenty of time to study and digest what the figures tell you. Look each one over carefully, noting everything you can about them. Doing this will help you understand this material.) If the maximum frequency deviation is set at 75 kilohertz above and below the carrier, the audio amplitude of the modulating wave must be so adjusted that its peaks drive the frequency only between these limits. This can then be referred to as 100-PERCENT MODULATION, although the term is only remotely applicable to fm. Projections along the vertical axis represent deviations in frequency from the resting frequency (carrier) in terms of audio amplitude. Projections along the horizontal axis represent time. The distance between A and B represents 0.001 second. This means that carrier deviations from the resting frequency to plus 75 kilohertz, then to minus 75 kilohertz, and finally back to rest would occur 1,000 times per second. This would equate to an audio frequency of 1,000 hertz.

Since the carrier deviation for this period (A to B) extends to the full allowable limits of plus and minus 75 kilohertz, the wave is fully modulated. The distance from C to D is the same as that from A to B, so the time interval and frequency are the same as before. Notice, however, that the amplitude of the modulating wave has been decreased so that the carrier is driven to only plus and minus 37.5 kilohertz, one-half the allowable deviation. This would correspond to only 50-percent modulation if the system were AM instead of fm. Between E and F, the interval is reduced to 0.0005 second. This indicates an increase in frequency of the modulating signal to 2,000 hertz. The amplitude has returned to its maximum allowable value, as indicated by the deviation of the carrier to plus and minus 75 kilohertz. Interval G to H represents the same frequency at a lower modulation amplitude (66 percent). Notice the GUARD BANDS between plus and minus 75 kilohertz and plus and minus 100 kilohertz. These bands isolate the modulation extremes of this particular channel from that of adjacent channels.

2-12 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 unmodulated 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.

2-13 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 modulation index is 1.0. Next down is 5.0, and finally, the bottom spectrums have modulation indexes of 2-14 10.0. This information was used to develop table 2-1 by listing the modulation indexes in the left column and the number of significant sidebands in the right. SIGNIFICANT SIDEBANDS (those with significantly large amplitudes) are shown in both views of figure 2-9 as vertical lines on each side of the carrier frequency. Actually, an infinite number of sidebands are produced, but only a small portion of them are of sufficient amplitude to be important. For example, for a modulation index of 0.5 [top spectrums of both views (A) and (B)], the number of significant sidebands counted is 4. For the next spectrums down, the modulation index is 1.0 and the number of sidebands is 6, and so forth. This holds true for any combination of deviating and modulating frequencies that yield identical modulating indexes.

Table 2-1.—Modulation index table

Modulation

INDEX

Significant

Sidebands

.01 2 .4 2 .5 4 1.0 6 2.0 8 3.0 12 4.0 14 5.0 16 6.0 18 7.0 22 8.0 24 9.0 26 10.0 28 11.0 32 12.0 32 13.0 36 14.0 38 15.0 38 You should be able to see by studying figure 2-9, views (A) and (B), that the modulating frequency determines the spacing of the sideband frequencies. By using a significant sidebands table (such as table 2-1), you can determine the bandwidth of a given fm signal. Figure 2-10 illustrates the use of this table. The carrier frequency shown is 500 kilohertz. The modulating frequency is 15 kilohertz and the deviation frequency is 75 kilohertz.

2-15 77 Figure 2-10.—Frequency deviation versus bandwidth. From table 2-1 we see that there are 16 significant sidebands for a modulation index of 5. To determine total bandwidth for this case, we use: The use of this math is to illustrate that the actual bandwidth of an fm transmitter (240 kHz) is greater than that suggested by its maximum deviation bandwidth (–75 kHz or 150 kHz). This is important to know when choosing operating frequencies or designing equipment. Q-4. What characteristic of a carrier wave is varied in frequency modulation?

Q-5. How is the degree of modulation expressed in an fm system? Q-6. What two values may be used to determine the bandwidth of an fm wave? 2-16 METHODS OF FREQUENCY MODULATION.—The circuit shown earlier in figure 2-6 and the discussion in previous paragraphs were for illustrative purposes only. In reality, such a circuit would not be practical. However, the basic principle involved (the change in reactance of an oscillator circuit in accordance with the modulating voltage) constitutes one of the methods of developing a frequency- modulated wave.

Reactance-Tube Modulation.—In direct modulation, an oscillator is frequency modulated by a REACTANCE TUBE that is in parallel (SHUNT) with the oscillator tank circuit. (The terms "shunt" or "shunting" will be used in this module to mean the same as "parallel" or "to place in parallel with" components.) This is illustrated in figure 2-11. The oscillator is a conventional Hartley circuit with the reactance-tube circuit in parallel with the tank circuit of the oscillator tube. The reactance tube is an ordinary pentode. It is made to act either capacitively or inductively; that is, its grid is excited with a voltage which either leads or lags the oscillator voltage by 90 degrees.

Figure 2-11.—Reactance-tube fm modulator. When the reactance tube is connected across the tank circuit with no modulating voltage applied, it will affect the frequency of the oscillator. The voltage across the oscillator tank circuit (L1 and C1) is also in parallel with the series network of R1 and C7. This voltage causes a current flow through R1 and C7. If R1 is at least five times larger than the capacitive reactance of C7, this branch of the circuit will be essentially resistive. Voltage E 1, which is across C7, will lag current by 90 degrees. E 1 is applied to the control grid of reactance tube V1. This changes plate current (Ip), which essentially flows only through the LC tank circuit. This is because the value of R1 is high compared to the impedance of the tank circuit.

Since current is inversely proportional to impedance, most of the plate current coupled through C3 flows through the tank circuit. At resonance, the voltage and current in the tank circuit are in phase. Because E1 lags E by 90 degrees and I is in phase with grid voltage E1, the superimposed current through the tank circuit lags the original tank current by 90 degrees. Both the resultant current (caused by Ip) and the tank current lag tank voltage and current by some angle depending on the relative amplitudes of the two currents. Because this resultant current is a lagging current, the impedance across the tank circuit cannot be at its maximum unless something happens within the tank to bring current and voltage into phase. Therefore, this situation continues until the frequency of oscillations in the tank circuit changes sufficiently so that the voltages across the tank and the current flowing into it are again in phase. This action is the same as would be produced by adding a reactance in parallel with the L1C1 tank. Because the superimposed current lags voltage E by 90 degrees, the introduced reactance is inductive. In NEETS, Module 2, Introduction to 2-17 Alternating Current and Transformers, you learned that total inductance decreases as additional inductors are added in parallel. Because this introduced reactance effectively reduces inductance, the frequency of the oscillator increases to a new fixed value.

Now let’ s see what happens when a modulating signal is applied. The magnitude of the introduced reactance is determined by the magnitude of the superimposed current through the tank. The magnitude of Ip for a given E1 is determined by the transconductance of V1. (Transconductance was covered in NEETS, Module 6, Introduction to Electronic Emission, Tubes, and Power Supplies.) Therefore, the value of reactance introduced into the tuned circuit varies directly with the transconductance of the reactance tube. When a modulating signal is applied to the grid of V1, both E1 and I change, causing transconductance to vary with the modulating signal. This causes a variable reactance to be introduced into the tuned circuit.

This variable reactance either adds to or subtracts from the fixed value of reactance that is introduced in the absence of the modulating signal. This action varies the reactance across the oscillator which, in turn, varies the instantaneous frequency of the oscillator. These variations in the oscillator frequency are proportional to the instantaneous amplitude of the modulating voltage. Reactance-tube modulators are usually operated at low power levels. The required output power is developed in power amplifier stages that follow the modulators.

The output of a reactance-tube modulated oscillator also contains some unwanted amplitude modulation. This unwanted modulation is caused by stray capacitance and the resistive component of the RC phase splitter. The resistance is much less significant than the desired XC, but the resistance does allow some plate current to flow which is not of the proper phase relationship for good tube operation. The small amplitude modulation that this produces is easily removed by passing the oscillator output through a limiter-amplifier circuit.

Semiconductor Reactance Modulator.—The SEMICONDUCTOR-REACTANCE MODULATOR is used to frequency modulate low-power semiconductor transmitters. Figure 2-12 shows a typical frequency-modulated oscillator stage operated as a reactance modulator. Q1, along with its associated circuitry, is the oscillator. Q2 is the modulator and is connected to the circuit so that its collector-to- emitter capacitance (CCE) is in parallel with a portion of the rf oscillator coil, L1. As the modulator operates, the output capacitance of Q2 is varied. Thus, the frequency of the oscillator is shifted in accordance with the modulation the same as if C1 were varied.

2-18 Figure 2-12.—Reactance-semiconductor fm modulator. When the modulating signal is applied to the base of Q2, the emitter-to-base bias varies at the modulation rate. This causes the collector voltage of Q2 to vary at the same modulating rate. When the collector voltage increases, output capacitance CCE decreases; when the collector voltage decreases, CCE increases. An increase in collector voltage has the effect of spreading the plates of CCE farther apart by increasing the width of the barrier. A decrease of collector voltage reduces the width of the pn junction and has the same effect as pushing the capacitor plates together to provide more capacitance.

When the output capacitance decreases, the instantaneous frequency of the oscillator tank circuit increases (acts the same as if C1 were decreased). When the output capacitance increases, the instantaneous frequency of the oscillator tank circuit decreases. This decrease in frequency produces a lower frequency in the output because of the shunting effect of CCE. Thus, the frequency of the oscillator tank circuit increases and decreases at an audio frequency (af) modulating rate. The output of the oscillator, therefore, is a frequency modulated rf signal.

Since the audio modulation causes the collector voltage to increase and decrease, an AM component is induced into the output. This produces both an fm and AM output. The amplitude variations are then removed by placing a limiter stage after the reactance modulator and only the frequency modulation remains. Frequency multipliers or mixers (discussed in chapter 1) are used to increase the oscillator frequency to the desired output frequency. For high-power applications, linear rf amplifiers are used to increase the steady-amplitude signal to a higher power output. With the initial modulation occurring at low levels, fm represents a savings of power when compared to conventional AM. This is because fm noise-reducing properties provide a better signal-to-noise ratio than is possible with AM.

2-19 Multivibrator Modulator.—Another type of frequency modulator is the astable multivibrator illustrated in figure 2-13. Inserting the modulating af voltage in series with the base-return of the multivibrator transistors causes the gate length, and thus the fundamental frequency of the multivibrator, to vary. The amount of variation will be in accordance with the amplitude of the modulating voltage. One requirement of this method is that the fundamental frequency of the multivibrator be high in relation to the highest modulating frequencies. A factor of at least 100 provides the best results.

Figure 2-13.—Astable multivibrator and filter circuit for generating an fm carrier. Recall that a multivibrator output consists of the fundamental frequency and all of its harmonics. Unwanted even harmonics are eliminated by using a SYMMETRICAL MULTIVIBRATOR circuit, as shown in figure 2-13. The desired fundamental frequency, or desired odd harmonics, can be amplified after all other odd harmonics are eliminated in the LCR filter section of figure 2-13. A single frequency- modulated carrier is then made available for further amplification and transmission.

Proper design of the multivibrator will cause the frequency deviation of the carrier to faithfully follow (referred to as a "linear" function) the modulating voltage. This is true up to frequency deviations which are considerable fractions of the fundamental frequency of the multivibrator. The principal design consideration is that the RC coupling from one multivibrator transistor base to the collector of the other has a time constant which is greater than the actual gate length by a factor of 10 or more. Under these conditions, a rise in base voltage in each transistor is essentially linear from cutoff to the bias at which the transistor is switched on. Since this rise in base voltage is a linear function of time, the gate length will change as an inverse function of the modulating voltage. This action will cause the frequency to change as a linear function of the modulating voltage.

The multivibrator frequency modulator has the advantage over the reactance-type modulator of a greater linear frequency deviation from a given carrier frequency. However, multivibrators are limited to frequencies below about 1 megahertz. Both systems are subject to drift of the carrier frequency and must, therefore, be stabilized. Stabilization may be accomplished by modulating at a relatively low frequency and translating by heterodyne action to the desired output frequency, as shown in figure 2-14. A 1-megahertz signal is heterodyned with 49 megahertz from the crystal-controlled oscillator to provide a stable 50-megahertz output from the mixer. If a suitably stable heterodyning oscillator is used, the frequency stability can be greatly improved. For instance, at the frequencies shown in figure 2-14, the 2-20 stability of the unmodulated 50-megahertz carrier would be 50 times better than that which harmonic multiplication could provide.

Figure 2-14.—Method for improving frequency stability of fm system. Varactor FM Modulator.—Another fm modulator which is widely used in transistorized circuitry uses a voltage-variable capacitor (VARACTOR). The varactor is simply a diode, or pn junction, that is designed to have a certain amount of capacitance between junctions. View (A) of figure 2-15 shows the varactor schematic symbol. A diagram of a varactor in a simple oscillator circuit is shown in view (B). This is not a working circuit, but merely a simplified illustration. The capacitance of a varactor, as with regular capacitors, is determined by the area of the capacitor plates and the distance between the plates.

The depletion region in the varactor is the dielectric and is located between the p and n elements, which serve as the plates. Capacitance is varied in the varactor by varying the reverse bias which controls the thickness of the depletion region. The varactor is so designed that the change in capacitance is linear with the change in the applied voltage. This is a special design characteristic of the varactor diode. The varactor must not be forward biased because it cannot tolerate much current flow. Proper circuit design prevents the application of forward bias.

Figure 2-15A.—Varactor symbol and schematic. SCHEMATIC SYMBOL. 2-21 Figure 2-15B.—Varactor symbol and schematic. SIMPLIFIED CIRCUIT. Notice the simplicity of operation of the circuit in figure 2-16. An af signal that is applied to the input results in the following actions: (1) On the positive alternation, reverse bias increases and the dielectric (depletion region) width increases. This decreases capacitance which increases the frequency of the oscillator. (2) On the negative alternation, the reverse bias decreases, which results in a decrease in oscillator frequency.

Figure 2-16.—Varactor fm modulator. Many different fm modulators are available, but they all use the basic principles you have just studied. The main point to remember is that an oscillator must be used to establish the reference (carrier) frequency. Secondly, some method is needed to cause the oscillator to change frequency in accordance with an af signal. Anytime this can be accomplished, we have a frequency modulator. Q-7. How does the reactance-tube modulator impress intelligence onto an rf carrier? Q-8. What characteristic of a transistor is varied in a semiconductor-reactance modulator?

Q-9. What circuit section is required in the output of a multivibrator modulator to eliminate unwanted output frequencies? Q-10. What characteristic of a varactor is used in an fm modulator? 2-22

Phase Modulation

Frequency modulation requires the oscillator frequency to deviate both above and below the carrier frequency. During the process of frequency modulation, the peaks of each successive cycle in the modulated waveform occur at times other than they would if the carrier were unmodulated. This is actually an incidental phase shift that takes place along with the frequency shift in fm. Just the opposite action takes place in phase modulation. The af signal is applied to a PHASE MODULATOR in pm. The resultant wave from the phase modulator shifts in phase, as illustrated in figure 2-17. Notice that the time period of each successive cycle varies in the modulated wave according to the audio-wave variation.

Since frequency is a function of time period per cycle, we can see that such a phase shift in the carrier will cause its frequency to change. The frequency change in fm is vital, but in pm it is merely incidental. The amount of frequency change has nothing to do with the resultant modulated wave shape in pm. At this point the comparison of fm to pm may seem a little hazy, but it will clear up as we progress. Figure 2-17.—Phase modulation. Let’ s review some voltage phase relationships. Look at figure 2-18 and compare the three voltages (A, B, and C). Since voltage A begins its cycle and reaches its peak before voltage B, it is said to lead voltage B. Voltage C, on the other hand, lags voltage B by 30 degrees. In phase modulation the phase of the carrier is caused to shift at the rate of the af modulating signal. In figure 2-19, note that the unmodulated carrier has constant phase, amplitude, and frequency. The dotted wave shape represents the modulated carrier. Notice that the phase on the second peak leads the phase of the unmodulated carrier.

On the third peak the shift is even greater; however, on-the fourth peak, the peaks begin to realign phase with each other. These relationships represent the effect of 1/2 cycle of an af modulating signal. On the negative alternation of the af intelligence, the phase of the carrier would lag and the peaks would occur at times later than they would in the unmodulated carrier. Figure 2-18.—Phase relationships. 2-23 Figure 2-19.—Carrier with and without modulation. The presentation of these two waves together does not mean that we transmit a modulated wave together with an unmodulated carrier. The two waveforms were drawn together only to show how a modulated wave looks when compared to an unmodulated wave.

Now that you have seen the phase and frequency shifts in both fm and pm, let’ s find out exactly how they differ. First, only the phase shift is important in pm. It is proportional to the af modulating signal. To visualize this relationship, refer to the wave shapes shown in figure 2-20. Study the composition of the fm and pm waves carefully as they are modulated with the modulating wave shape. Notice that in fm, the carrier frequency deviates when the modulating wave changes polarity. With each alternation of the modulating wave, the carrier advances or retards in frequency and remains at the new frequency for the duration of that cycle. In pm you can see that between one alternation and the next, the carrier phase must change, and the frequency shift that occurs does so only during the transition time; the frequency then returns to its normal rate. Note in the pm wave that the frequency shift occurs only when the modulating wave is changing polarity. The frequency during the constant amplitude portion of each alternation is the

Rest Frequency.

Figure 2-20.—Pm versus fm. The relationship, in pm, of the modulating af to the change in the phase shift is easy to see once you understand AM and fm principles. Again, we can establish two clear-cut rules of phase modulation: 2-24 • AMOUNT OF PHASE SHIFT IS PROPORTIONAL TO THE AMPLITUDE OF THE

Modulating Signal.

(If a 10-volt signal causes a phase shift of 20 degrees, then a 20-volt signal causes a phase shift of 40 degrees.) • RATE OF PHASE SHIFT IS PROPORTIONAL TO THE FREQUENCY OF THE

Modulating Signal.

(If the carrier were modulated with a 1-kilohertz tone, the carrier would advance and retard in phase 1,000 times each second.) Phase modulation is also similar to frequency modulation in the number of sidebands that exist within the modulated wave and the spacing between sidebands. Phase modulation will also produce an infinite number of sideband frequencies. The spacing between these sidebands will be equal to the frequency of the modulating signal. However, one factor is very different in phase modulation; that is, the distribution of power in pm sidebands is not similar to that in fm sidebands, as will be explained in the next section.

Modulation Index Recall from frequency modulation that modulation index is used to calculate the number of significant sidebands existing in the waveform. The higher the modulation index, the greater the number of sideband pairs. The modulation index is the ratio between the amount of oscillator deviation and the frequency of the modulating signal: In frequency modulation, we saw that as the frequency of the modulating signal increased (assuming the deviation remained constant) the number of significant sideband pairs decreased. This is shown in views (A) and (B) of figure 2-21. Notice that although the total number of significant sidebands decreases with a higher frequency-modulating signal, the sidebands spread out relative to each other; the total bandwidth increases.

2-25 Figure 2-21.—Fm versus pm spectrum distribution. In phase modulation the oscillator does not deviate, and the power in the sidebands is a function of the amplitude of the modulating signal. Therefore, two signals, one at 5 kilohertz and the other at 10 kilohertz, used to modulate a carrier would have the same sideband power distribution. However, the 10-kilohertz sidebands would be farther apart, as shown in views (C) and (D) of figure 2-21. When compared to fm, the bandwidth of the pm transmitted signal is greatly increased as the frequency of the modulating signal is increased.

As we pointed out earlier, phase modulation cannot occur without an incidental change in frequency, nor can frequency modulation occur without an incidental change in phase. The term fm is loosely used when referring to any type of angle modulation, and phase modulation is sometimes incorrectly referred to as "indirect fm." This is a definition that you should disregard to avoid confusion. Phase modulation is just what the words imply — phase modulation of a carrier by an af modulating signal. You will develop a better understanding of these points as you advance in your study of modulation.

Basic Modulator In phase modulation you learned that varying the phase of a carrier at an intelligence rate caused that carrier to contain variations which could be converted back into intelligence. One circuit that can cause this phase variation is shown in figure 2-22. 2-26 Figure 2-22.—Phase shifting a sine wave. The capacitor in series with the resistor forms a phase-shift circuit. With a constant frequency rf carrier applied at the input, the output across the resistor would be 45 degrees out of phase with the input if X C = R.

Now, let’ s vary the resistance and observe how the output is affected in figure 2-23. As the resistance reaches a value greater than 10 times XC, the phase difference between input and output is nearly 0 degrees. For all practical purposes, the circuit is resistive. As the resistance is decreased to 1/10 the value of X C, the phase difference approaches 90 degrees. The circuit is now almost completely capacitive. By replacing the resistor with a vacuum tube, as shown in view (A) of figure 2-24, we can vary the resistance (vacuum-tube impedance) by varying the voltage applied to the grid of the tube. The frequency applied to the circuit (from a crystal-controlled master oscillator) will be shifted in phase by 45 degrees with no audio input [view (B)]. With the application of an audio signal, the phase will shift as the impedance of the tube is varied.

Figure 2-23.—Control over the amount of phase shift. 2-27 Figure 2-24A.—Phase modulator. Figure 2-24B.—Phase modulator. In practice, a circuit like this could not provide enough phase shift to produce the desired results in the output. Several of these circuits are arranged in cascade to provide the desired amount of phase shift. Also, since the output of this circuit will vary in amplitude, the signal is fed to a limiter to remove amplitude variations. The major advantage of this type modulation circuit over frequency modulation is that this circuit uses a crystal-controlled oscillator to maintain a stable carrier frequency. In fm the oscillator cannot be crystal controlled because it is actually required to vary in frequency. That means that an fm oscillator will require a complex automatic frequency control (afc) system. An afc system ensures that the oscillator stays on the same carrier frequency and achieves a high degree of stability. The afc circuit will be covered in a later module.

Phase-Shift Keying Phase-shift keying (psk) is similar to ON-OFF cw keying in AM systems and frequency-shift keying in fm systems. Psk is most useful when the code elements are all of equal length; that is, all marks and spaces, whether message elements or synchronizing signals, occupy identical elements of time. It is not fully suitable for use on start-stop teletypewriter circuits where the stop pulse is 1.42 times longer than the RF INPUT E0 OUTPUT

Pm Modulator

A Nts120224

AF INPUT 2-28 other pulses. Neither is it applicable to those pulsed systems in which the duration or position of the pulses are varied by the modulation frequency. In its simplest form, psk operates on the principle of phase reversal of the carrier. Each time a mark is received, the phase is reversed. No phase reversal takes place when a space is received. In binary systems, marks and spaces are called ONES and ZEROS, respectively, so that a ONE causes a 180-degree phase shift, and a ZERO has no effect on the incoming signal. Figure 2-25 shows the application of phase-shift keying to an unmodulated carrier [view (A)] in the af range. For transmission over other than a conductive path, the wave shown in view (D) must be used as the modulating signal for some other system of modulating an rf carrier.

Figure 2-25A.—Phase-shift keying. UNMODULATED CARRIER. Figure 2-25B.—Phase-shift keying. MODULATION SIGNAL - DATA ELEMENTS. Figure 2-25C.—Phase-shift keying. MODULATED CARRIER. Figure 2-25D.—Phase-shift keying. MODULATED CARRIER AFTER FILTERING. The modulating signal in view (B) consists of a bit stream of ZEROS and ONES. A ZERO does not affect the carrier frequency which is usually set to equal the bit rate. For example, a data stream of 1,200 bits per second would have a carrier of 1,200 hertz. When a data bit ONE occurs, the phase of the carrier frequency is shifted 180 degrees. In view (C) we find that the third, fifth, and sixth cycles (all ONE) have been reversed in phase. This phase reversal produces CUSPS (sharp phase reversals) which are usually 2-29 removed by filtering before transmission or further modulation. This filtering action limits the bandwidth of the output signal frequencies. The resulting wave is shown in view (D).

The exact waveform of figure 2-25, view (D), can be obtained by logic operations of timing and data. This is illustrated in figure 2-26, where a timing signal [view (A)] is used rather than a carrier frequency. The data (intelligence) is shown in view (B) and is combined with the timing signal to produce a combination digital modulation signal, as shown in view (C). The square-wave pattern of the digital modulation is filtered to limit the bandwidth of the signal frequencies, as shown in view (D). This system has been used in some high-speed data equipment, but it offers no particular advantage over other systems of modulation, particularly the pulse-modulated systems for high-speed data transmission.

Q-11. What type of modulation depends on the carrier-wave phase shift? Q-12. What components may be used to build a basic phase modulator? Q-13. Phase-shift keying is similar to what other two types of modulation? Figure 2-26A.—Simulated phase-shift keying. TIMING. Figure 2-26B.—Simulated phase-shift keying. DATA. Figure 2-26C.—Simulated phase-shift keying. DIGITAL MODULATION. Figure 2-26D.—Simulated phase-shift keying. DIGITAL MODULATION AFTER FILTERING. 2-30

Pulse Modulation

Another type of modulation is PULSE MODULATION. Pulse modulation has many uses, including telegraphy, radar, telemetry, and multiplexing. Far too many applications of pulse modulation exist to elaborate on any one of them, but in this section we will cover the basic principles of pulse modulation.

Characteristics

Amplitude modulating a simple rf carrier to a point where it becomes drastically overmodulated could produce a waveform similar to that required in pulse modulation. A modulating signal [view (A) of figure 2-27] that is much larger than the carrier results in the modulation envelope shown in view (B). The modulation envelope would be the same if the modulating wave shape were not sinusoidal; that is, like the one shown in view (C). Figure 2-27A.—Overmodulation of a carrier. MODULATING WAVE. Figure 2-27B.—Overmodulation of a carrier. MODULATION ENVELOPE.

2-31 Figure 2-27C.—Overmodulation of a carrier. NONSINUSOIDAL MODULATING WAVE. Observe the modulating square wave in figure 2-28. Remember that it contains an infinite number of odd harmonics in addition to its fundamental frequency. Assume that a carrier has a frequency of 1 megahertz. The fundamental frequency of the modulating square wave is 1 kilohertz. When these signals heterodyne, two new frequencies will be produced: a sum frequency of 1.001 megahertz and a difference frequency of 0.999 megahertz. The fundamental frequency heterodynes with the carrier. This is also true of all harmonics contained in the square wave. Side frequencies associated with those harmonics will be produced as a result of this process. For example, the third harmonic of the square wave heterodynes with the carrier and produces sideband frequencies at 1.003 and 0.997 megahertz. Another set will be produced by the fifth, seventh, ninth, eleventh, thirteenth, fifteenth, seventeenth, and nineteenth harmonics of the square wave, and so on to infinity.

Figure 2-28.—Spectrum distribution when modulating with a square wave. Look at figure 2-28 and observe the relative amplitudes of the sidebands as they relate to the amplitudes of the harmonics contained in the square wave. Note that the first set of sidebands is directly related to the amplitude of the square wave. The second set of sidebands is related to the third harmonic content of the square wave and is 1/3 the amplitude of the first set. The third set is related to the amplitude of the first set of sidebands and is 115 the amplitude of the first set. This relationship will apply to each additional set of sidebands.

2-32 View (A) of figure 2-29 shows the carrier modulated with a square wave. In view (B) the modulating square wave is increased in amplitude; note that the rf peaks increase in amplitude during the positive alternation of the square wave and decrease during the negative half of the square wave. In view (C) the amplitude of the square wave is further increased and the amplitude of the rf wave is almost 0 during the negative alternation of the square wave. Figure 2-29A.—Various square-wave modulation levels with frequency-spectrum carrier and sidebands.

Figure 2-29B.—Various square-wave modulation levels with frequency-spectrum carrier and sidebands. Figure 2-29C.—Various square-wave modulation levels with frequency-spectrum carrier and sidebands. Figure 2-29D.—Various square-wave modulation levels with frequency-spectrum carrier and sidebands. 2-33 Note the frequency spectrum associated with each of these conditions. The carrier amplitude remains constant, but the sidebands increase in amplitude in accordance with the amplitude of the modulating square wave. So far in pulse modulation, the same general rules apply as in AM. In view (C) the amplitude of the square wave of voltage is equal to the peak voltage of the unmodulated carrier wave. This is 100-percent modulation, just as in conventional AM. Note in the frequency spectrum that the sideband distribution is also the same as in AM. Keep in mind that the total sideband power is 1/2 of the total power when the modulator signal is a square wave. This is in contrast to 1/3 the total power with sine-wave modulation.

Now refer to view (D). The increase of the square-wave modulating voltage is greater in amplitude than the unmodulated carrier. Notice that the sideband distribution does not change; but, as the sidebands take on more of the transmitted power, so will the carrier. Pulse Timing Thus far, we have established a carrier and have caused its peaks to increase and decrease as a modulating square wave is applied. Some pulse-modulation systems modulate a carrier in this manner. Others produce no rf until pulsed; that is, rf occurs only during the actual pulse as shown in view (A) of figure 2-30. For example, let’ s start with an rf carrier frequency of 1 megahertz. Each cycle of the rf requires a certain amount of time to complete. If we allow oscillations to occur for a given period of time only during selected intervals, as in view (B), we are PULSING the system. Note that the pulse transmitter does not produce an rf signal until one of the positive-going modulating pulses is applied. The transmitter then produces the rf carrier until the positive input pulse ends and the input waveform again becomes a negative potential.

Figure 2-30A.—Pulse transmission. Figure 2-30B.—Pulse transmission. Refer back to figure 1-41 and the over-modulation discussion in chapter 1. You will notice that the overmodulation wave shape of view (D) in figure 2-29 and the pulse-modulation wave shape of figure 2-30, view (B), are very similar to figure 1-41. Actually, both figure 1-41 and view (D) of figure 2-29 result from overmodulation. Even though the output of the pulse transmitter in figure 2-30 looks like overmodulation, it is not; rather, it is pulsed.

2-34 However, the frequency spectrums are similar. Sideband distributions are similar, but not identical, since the pulse transmitter in figure 2-30 is gated on and off instead of being modulated by a square wave as was the case in view (D) of figure 2-29. Remember, in pulse modulation the sidebands produced to accompany the carrier during transmission are directly related to the harmonic content of the modulating wave shape. In figure 2-31, (view A, view B and view C), observe the square and rectangular wave shapes used to pulse modulate the same carrier frequency in each of the three views.

Figure 2-31A.—Varying pulse-modulating waves. Figure 2-31B.—Varying pulse-modulating waves. Figure 2-31C.—Varying pulse-modulating waves. Let’ s take note of some timing relationships in the three modulating sequences in figure 2-31: • the time for the rf cycle is the same in each case • the number of cycles occurring in each group is different • the ratio between transmitting and non-transmitting time varies • the transmitter produces an rf wave four times in view (A), three transmission groups in view (B), and only two in view (C) • rf is generated only during the positive pulses 2-35 In figure 2-32, observe the relative time for individual rf cycles. The time for each cycle is the same in views (A) and (B). Since this time is the same, we can assume that the carrier frequency is the same.

But in view (C) the time for each cycle is about half that in views (A) and (B). Therefore, the frequency of the carrier in view (C) is nearly twice that of the other two. This illustration shows that carrier frequencies in pulse systems can vary. Figure 2-32A.—Carrier frequency. Figure 2-32B.—Carrier frequency. Figure 2-32C.—Carrier frequency. The carrier frequency is not the only frequency we must concern ourselves with in pulse systems. We must also be concerned with the frequency that is associated with the repetition rate of groups of pulses. Figure 2-33 shows that a specific time period exists between each group of rf pulses. This time is the same for each repetition of the pulse and is called the PULSE-REPETITION TIME (prt). To find out how often these groups of pulses occur, compute PULSE-REPETITION FREQUENCY (prf) using the formula: 2-36 Figure 2-33.—Pulse-repetition time (prt).

Just remember that the pulse-repetition time is the time it takes for a pulse to recur, as shown in figure 2-34. The duration of time of the pulse (a) plus the time when no pulse occurs (b) equals the total pulse-repetition time. Figure 2-34.—Pulse cycles. The time during which the pulse is occurring is called PULSE DURATION (pd) or PULSE WIDTH (pw), as shown in figure 2-35. As you will soon see, pulse width is important in pulse modulation. Figure 2-35.—Pulse width (pw). 2-37 The time we have been referring to as the time of no pulse, or nonpulse time, is referred to as REST TIME (rt). The duration of this rest time will determine certain capabilities of the pulse-modulation system. The pulse width is the time that the transmitter produces rf oscillations and is the actual pulse transmission time. During the nonpulse time, shown in figure 2-36, the transmitter produces no oscillations and the oscillator is cut off.

Figure 2-36.—Rest time (rt). Some pulse transmitter-receiver systems transmit the pulse and then rest, awaiting the return of an echo. Rest time provides the system time for the receive cycle of operation. Power in a Pulse System When discussing power in a pulse-modulation system, we have to consider PEAK POWER and AVERAGE POWER. Peak power is the maximum value of the transmitted pulse; average power is the peak power value averaged over the pulse-repetition time. Peak power is very easy to see in a pulse system. In figure 2-37, all pulsed wave shapes have a peak power of 100 watts. Also note that in views (A), (B), and (C) the pulse width is the same, even though the carrier frequency is different. In these three cases average power would be the same. This is because average power is actually equal to the peak power of a pulse averaged over 1 operating cycle. However, the pulse width is increased in view (D) and we have a greater average power with the same prt. In view (E) the decreased pulse width has decreased average power over the same prt.

Figure 2-37.—Peak and average power. 2-38 Use these simple rules to determine power in a pulsed-wave shape: • Peak power is the maximum power reached by the transmitter during the pulse. • Average power equals the peak power averaged over one cycle. Duty Cycle In pulse modulation you will need to know the percentage of time the system is actually producing rf. For example, let’ s say that a pulse system is transmitting 25 percent of the time. This would mean that the pw is 1/4 the prt. For every 60 minutes we operate the pulse system, we actually transmit a total of only 15 minutes.

The DUTY CYCLE is the ratio of working time to total time for intermittently operated devices. Thus, duty cycle represents a ratio of actual transmitting time to transmitting time plus rest time. To establish the duty cycle, divide the pw by the prt of the system. This yields the duty cycle and is expressed as a decimal figure. With this information, we can figure percentage of transmitting time by multiplying the duty cycle by 100. Applications of Pulse Modulation Pulse modulation has many applications in the transmission of intelligence information. In telemetry, for example, the width of successive pulses may tell us humidity; the changing of the rest time may tell us pressure. In other applications, as you will see later in this text, the changing of the average power can provide us with intelligence information.

In radar a pulse is transmitted and travels some distance to a target where it is then reflected back to the system. The amount of time it takes provides us with information that can be converted to distance. Telemetry and radar systems use the principles of pulse modulation described in this section. Let’ s quickly review what has been presented: • Pulse width (pw) — the duration of time rf frequency is transmitted • Rest time (rt) — the time the transmitter is resting (not transmitting) • Carrier frequency — the frequency of the rf wave generated in the oscillator of the transmitter • Pulse-repetition time (prt) — the total time of 1 complete pulse cycle of operation (rest time plus pulse width) • Pulse-repetition frequency (prf) — the rate, in pulses per second, that the pulse occurs • Power peak — the maximum power contained in the pulse • Average power — the peak power averaged over 1 complete operating cycle • Duty cycle — a decimal number that expresses a ratio in a pulse modulation system of transmit time to total time 2-39 Pulse modulation will play a major part in your electronics career. In one way or another, you will encounter it in some form. The function of the particular system may involve many variations of the characteristics presented here. We will now look at some specific applications of pulse modulation in radar and communications systems.

Q-14. Overmodulating an rf carrier in amplitude modulation produces a waveform which is similar to what modulated waveform? Q-15. What is prt? Q-16. What is nonpulse time? Q-17. What is average power in a pulsed system?

Radar Modulation

Radio frequency energy in radar is transmitted in short pulses with time durations that may vary from 1 to 50 microseconds or more. If the transmitter is cut off before any reflected energy returns from a target, the receiver can distinguish between the transmitted pulse and the reflected pulse. After all reflections have returned, the transmitter can again be cut on and the process repeated. The receiver output is applied to an indicator which measures the time interval between the transmission of energy and its return as a reflection. Since the energy travels at a constant velocity, the time interval becomes a measure of the distance traveled (RANGE). Since this method does not depend on the relative frequency of the returned signal, or on the motion of the target, difficulties experienced in cw or fm methods are not encountered. The pulse modulation method is used in many military radar applications.

Most radar oscillators operate at pulse voltages between 5 and 20 kilovolts. They require currents of several amperes during the actual pulse which places severe requirements on the modulator. The function of the high-vacuum tube modulator is to act as a switch to turn a pulse ON and OFF at the transmitter in response to a control signal. The best device for this purpose is one which requires the least signal power for control and allows the transfer of power from the transmitter power source to the oscillator with the least loss. The pulse modulator circuits discussed in this section are typical pulse modulators used in radar equipment.

Spark-Gap Modulator The SPARK-GAP MODULATOR consists of a circuit for storing energy, a circuit for rapidly discharging the storage circuit (spark gap), a pulse transformer, and an ac power source. The circuit for storing energy is essentially a short section of artificial transmission line which is known as the PULSE-FORMING NETWORK (pfn). The pulse-forming network is discharged by a spark gap. Two types of spark gaps are used: FIXED GAPS and ROTARY GAPS. The fixed gap, discussed in this section, uses a trigger pulse to ionize the air between the contacts of the spark gap and to initiate the discharge of the pulse-forming network. The rotary gap is similar to a mechanically driven switch.

A typical fixed, spark-gap modulator circuit is shown in figure 2-38. Between trigger pulses the spark gap is an open circuit. Current flows through the pulse transformer (T1), the pulse-forming network (C1, C2, C3, C4, and L2), the diode (V1), and the inductor (L1) to the plate supply voltage (Eb). These components form the charging circuit for the pulse-forming network. 2-40 Figure 2-38.—Fixed spark-gap modulator. The spark gap is actually triggered (ionized) by the combined action of the charging voltage across the pulse-forming network and the trigger pulse. (Ionization was discussed in NEETS, Module 6, Introduction to Electronic Emission, Tubes and Power Supplies.) The air between the trigger pulse injection point and ground is ionized by the trigger voltage. This, in turn, initiates the ionization of the complete gap by the charging voltage. This ionization allows conduction from the charged pulse-forming network through pulse transformer T1. The output pulse is then applied to an oscillating device, such as a magnetron.

Thyratron Modulator The hydrogen THYRATRON MODULATOR is an electronic switch which requires a positive trigger of only 150 volts. The trigger potential must rise at the rate of 100 volts per microsecond to cause the modulator to conduct. In contrast to spark gap devices, the hydrogen thyratron (figure 2-39) operates over a wide range of anode voltages and pulse-repetition rates. The grid has complete control over the initiation of cathode emission for a wide range of voltages. The anode is completely shielded from the cathode by the grid. Thus, effective grid action results in very smooth firing over a wide range of anode voltages and repetition frequencies. Unlike most other thyratrons, the positive grid-control characteristic ensures stable operation. In addition, deionization time is reduced by using the hydrogen-filled tube.

Figure 2-39.—Typical thyratron gas-tube modulator. The hydrogen thyratron modulator provides improved timing because the synchronized trigger pulse is applied to the control grid of the thyratron (V2) and instantaneous firing is obtained. In addition, only 2-41 one gas tube is required to discharge the pulse-forming network, and a low amplitude trigger pulse is sufficient to initiate discharge. A damping diode is used to prevent breakdown of the thyratron by reverse-voltage transients. The thyratron requires a sharp leading edge for a trigger pulse and depends on a sudden drop in anode voltage (controlled by the pulse-forming network) to terminate the pulse and cut off the tube.

As shown in figure 2-39, the typical thyratron modulator is very similar to the spark-gap modulator. It consists of a power source (Eb), a circuit for storing energy (L2, C2, C3, C4, and C5), a circuit for discharging the storage circuit (V2), and a pulse transformer (T1). In addition this circuit has a damping diode (V1) to prevent reverse-polarity signals from being applied to the plate of V2 which could cause V2 to breakdown. With no trigger pulse applied, the pfn charges through T1, the pfn, and the charging coil L1 to the potential of Eb. When a trigger pulse is applied to the grid of V2, the tube ionizes causing the pulse- forming network to discharge through V2 and the primary of T1. As the voltage across the pfn falls below the ionization point of V2, the tube shuts off. Because of the inductive properties of the pfn, the positive discharge voltage has a tendency to swing negative. This negative overshoot is prevented from damaging the thyratron and affecting the output of the circuit by V1, R1, R2, and C1. This is a damping circuit and provides a path for the overshoot transient through V1. It is dissipated by R1 and R2 with C1 acting as a high-frequency bypass to ground, preserving the sharp leading and trailing edges of the pulse. The hydrogen thyratron modulator is the most common radar modulator.

Pulse modulation is also useful in communications systems. The intelligence-carrying capability and power requirements for communications systems differ from those of radar. Therefore, other methods of achieving pulse modulation that are more suitable for communications systems will now be studied. Q-18. What is the primary component for a spark-gap modulator? Q-19. What are the basic components of a thyratron modulator?

Communications Pulse Modulators

To transmit intelligence using pulse modulation, you must provide a method to vary some characteristic of the pulse train in accordance with the modulating signal. Figure 2-40 illustrates a simple pulse train. The characteristics of these pulses that can be varied are amplitude, pulse width, pulse-repetition time, and the pulse position as compared to a reference. In addition to these three characteristics, pulses may be transmitted according to a code to represent the different levels of the modulating signal. To ensure maximum fidelity (accuracy in reproducing a modulating wave), the modulating signal has to be represented by enough pulses to restore the original wave shape. Logically, the higher the sampling rate (the more often sampled) of the pulse modulator, the more accurately the original modulating wave can be reproduced. Figure 2-41 illustrates the effectiveness of three pulse-sampling rates. View (A) shows a sampling rate of more than two times the modulating frequency.

As you can see, this reproduces the modulating signal very accurately. However, the high sampling rate requires a wide bandwidth and increases the average power required of the transmitter. If less than two samples per cycle are made, you are not able to reproduce the original modulating signal, as shown in view (B). View (C) shows a sampling rate that is two times the highest modulating frequency. This is the minimum sampling rate that will give a sufficiently accurate reproduction of the modulating wave. The standard sampling rate is 2.5 times the highest frequency that is to be transmitted. This ensures the ability to accurately reproduce the modulating waveform. In military voice systems the bandwidth for voice signals is limited to 300 to 3,000 hertz, requiring a sampling frequency of 8 kilohertz. Although the pulse characteristic that is changed may vary for each type of pulse modulation, the sampling frequency will remain constant. We will now briefly discuss common types of pulse modulation.

2-42 Figure 2-40.—Pulse train. Figure 2-41A.—Pulse sampling rates. MORE THAN TWO PULSE SAMPLES FOR EVERY WAVE. Figure 2-41B.—Pulse sampling rates. LESS THAN TWO PULSE SAMPLES FOR EVERY WAVE. Figure 2-41C.—Pulse sampling rates. TWO PULSE SAMPLES FOR EVERY WAVE. 2-43 Pulse-Amplitude Modulation Some characteristic of the sampling pulses must be varied by the modulating signal for the intelligence of the signal to be present in the pulsed wave. Figure 2-42 shows three typical waveforms in which the pulse amplitude is varied by the amplitude of the modulating signal. View (A) represents a sine wave of intelligence to be modulated on a transmitted carrier wave. View (B) shows the timing pulses which determine the sampling interval. View (C) shows PULSE-AMPLITUDE MODULATION (pam) in which the amplitude of each pulse is controlled by the instantaneous amplitude of the modulating signal at the time of each pulse.

Figure 2-42A.—Pulse-amplitude modulation (pam). MODULATION. Figure 2-42B.—Pulse-amplitude modulation (pam). TIMING. Figure 2-42C.—Pulse-amplitude modulation (pam). PAM. Pulse-amplitude modulation is the simplest form of pulse modulation. It is generated in much the same manner as analog-amplitude modulation. The timing pulses are applied to a pulse amplifier in which the gain is controlled by the modulating waveform. Since these variations in amplitude actually represent the signal, this type of modulation is basically a form of AM. The only difference is that the signal is now in the form of pulses. This means that pam has the same built-in weaknesses as any other AM signal - high susceptibility to noise and interference. The reason for susceptibility to noise is that any interference in the transmission path will either add to or subtract from any voltage already in the circuit (signal voltage). Thus, the amplitude of the signal will be changed. Since the amplitude of the voltage represents the signal, any unwanted change to the signal is considered a SIGNAL DISTORTION. For this reason, pam is not often used. When pam is used, the pulse train is used to frequency modulate a carrier for transmission. Techniques of pulse modulation other than pam have been developed to overcome problems of noise interference. The following sections will discuss other types of pulse modulation.

Q-20. What action is necessary to impress intelligence on the pulse train in pulse modulation? 2-44 Q-21. To ensure the accuracy of a transmission, what is the minimum number of times a modulating wave should be sampled in pulse modulation? Q-22. What, if any, noise susceptibility advantage exists for pulse-amplitude modulation over analog- amplitude modulation? Pulse-Time Modulation In pulse-modulated systems, as in an analog system, the intelligence may be impressed on the carrier by varying any of its characteristics. In the preceding paragraphs the method of modulating a pulse train by varying its amplitude was discussed. Time characteristics of pulses may also be modulated with intelligence information. Two time characteristics may be affected: (1) the time duration of the pulses, referred to as PULSE-DURATION MODULATION (pdm) or PULSE-WIDTH MODULATION (pwm); and (2) the time of occurrence of the pulses, referred to as PULSE-POSITION MODULATION (ppm), and a special type of PULSE-TIME MODULATION (ptm) referred to as PULSE-FREQUENCY MODULATION (pfm). Figure 2-43 shows these types of ptm in views (C), (D), and (E). Views (A) and (B) show the modulating signal and timing, respectively.

Figure 2-43A.—Pulse-time modulation (ptm). MODULATION. Figure 2-43B.—Pulse-time modulation (ptm). TIMING. Figure 2-43C.—Pulse-time modulation (ptm). PDM. Figure 2-43D.—Pulse-time modulation (ptm). PPM. 2-45 Figure 2-43E.—Pulse-time modulation (ptm). PFM PULSE-DURATION MODULATION.—Pdm and pwm are designations for a single type of modulation. The width of each pulse in a train is made proportional to the instantaneous value of the modulating signal at the instant of the pulse. Either the leading edges, the trailing edges, or both edges of the pulses may be modulated to produce the variation in pulse width. Pdm can be obtained in a number of ways, one of which is illustrated in views (A) through (D) in figure 2-44. A circuit to produce pdm is shown in figure 2-45. Adding the modulating signal [figure 2-44, view (A)] to a repetitive sawtooth [view (B)] will result in the waveform shown in view (C). This waveform is then applied to a circuit which changes state when the input signal exceeds a specific threshold level. This action produces pulses with widths that are determined by the length of time that the input waveform exceeds the threshold level. The resulting waveform is shown in view (D).

Figure 2-44A.—Pulse-duration modulation (pdm). MODULATING SIGNAL. Figure 2-44B.—Pulse-duration modulation (pdm). REPETITIVE SAWTOOTH PULSES. Figure 2-44C.—Pulse-duration modulation (pdm). MODULATING SIGNAL AND SAWTOOTH ADDED. 2-46 Figure 2-44D.—Pulse-duration modulation (pdm). WIDTH MODULATED PULSES FROM CIRCUIT OF

Figure 2-45.

Figure 2-45.—Circuit for producing pdm. In the circuit of figure 2-45, a series of sawtooth pulses, occurring at the sampling rate, is applied to a one-shot multivibrator. The multivibrator has the signal voltage Essuperimposed on the bias voltage Ein. Each pulse triggers a cycle of multivibrator operation which terminates after a time interval and varies linearly with the voltage Es. The pulse of plate voltage produced by the multivibrator will have a leading edge at T1. The leading edge will vary in position with the signal voltage, while the trailing edge at T2 is fixed by the termination of the sawtooth pulse. The length of the output pulse is thus duration or width modulated. If the sawtooth has an instantaneous buildup and a sloping trailing edge, then the leading edge (T1) is fixed and the trailing edge (T2) varies. If the sawtooth generator produces a slope on both leading and trailing edges, both T1 and T2 are variable in position, but the result is still pdm. Pdm is often used because it is of a constant amplitude and is, therefore, less susceptible to noise. When compared with ppm, pdm has the disadvantage of a varying pulse, width and, therefore, of varying power content. This means that the transmitter must be powerful enough to handle the maximum-width pulses, although the average power transmitted is much less than peak power. On the other hand, pdm will still work if the synchronization between the transmitter and receiver fails; in ppm it will not, as will be seen in the next section.

PULSE-POSITION MODULATION.—The amplitude and width of the pulse is kept constant in the system. The position of each pulse, in relation to the position of a recurrent reference pulse, is varied by each instantaneous sampled value of the modulating wave. Ppm has the advantage of requiring constant transmitter power since the pulses are of constant amplitude and duration. It is widely used but has the disadvantage of depending on transmitter-receiver synchronization. 2-47 Ppm can be generated in several ways, but we will discuss one of the simplest. Figure 2-46 shows three waveforms associated with developing ppm from pdm. The pdm pulse train is applied to a differentiating circuit. (Differentiation was presented in NEETS, Module 9, Introduction to Wave-Generation and Wave-Shaping Circuits.) This provides positive- and negative-polarity pulses that correspond to the leading and trailing edges of the pdm pulses. Considering pdm and its generation, you can see that each pulse has a leading and trailing edge. In this case the position of the leading edge is fixed, whereas the trailing edge is not, as shown in view (A) of figure 2-46. The resultant pulses after the differentiation are shown in view (B). The negative pulses are position-modulated in accordance with the modulating waveform. Both the negative and positive pulse are then applied to a rectification circuit. This application eliminates the positive, non-modulated pulses and develops a ppm pulse train, as shown in view (C).

Figure 2-46.—Pulse-position modulation (ppm). PULSE-FREQUENCY MODULATION.—Pfm is a method of pulse modulation in which the modulating wave is used to frequency modulate a pulse-generating circuit. For example, the pulse rate may be 8,000 pulses per second (pps) when the signal voltage is 0. The pulse rate may step up to 9,000 pps for maximum positive signal voltage, and down to 7,000 pps for maximum negative signal voltage. Figure 2-47, views (A), (B), and (C) show three typical waveforms for pfm. This method of modulation is not used extensively because of complicated pfm generation methods. It requires a stable oscillator that is frequency modulated to drive a pulse generator. Since the other forms of ptm are easier to achieve, they are commonly used.

Figure 2-47A.—Pulse-frequency modulation (pfm). MODULATION. 2-48 Figure 2-47B.—Pulse-frequency modulation (pfm). TIMING. Figure 2-47C.—Pulse-frequency modulation (pfm). PFM. Q-23. What characteristics of a pulse can be changed in pulse-time modulation? Q-24. Which edges of the pulse can be modulated in pulse-duration modulation? Q-25. What is the main disadvantage of pulse-position modulation? Q-26. What is pulse-frequency modulation? Pulse-Code Modulation PULSE-CODE MODULATION (pcm) refers to a system in which the standard values of a QUANTIZED WAVE (explained in the following paragraphs) are indicated by a series of coded pulses.

When these pulses are decoded, they indicate the standard values of the original quantized wave. These codes may be binary, in which the symbol for each quantized element will consist of pulses and spaces: ternary, where the code for each element consists of any one of three distinct kinds of values (such as positive pulses, negative pulses, and spaces); or n-ary, in which the code for each element consists of nay number (n) of distinct values. This discussion will be based on the binary pcm system. All of the pulse-modulation systems discussed previously provide methods of converting analog wave shapes to digital wave shapes (pulses occurring at discrete intervals, some characteristic of which is varied as a continuous function of the analog wave). The entire range of amplitude (frequency or phase) values of the analog wave can be arbitrarily divided into a series of standard values. Each pulse of a pulse train [figure 2-48, view (B)] takes the standard value nearest its actual value when modulated. The modulating wave can be faithfully reproduced, as shown in views (C) and (D). The amplitude range has been divided into 5 standard values in view (C). Each pulse is given whatever standard value is nearest its actual instantaneous value. In view (D), the same amplitude range has been divided into 10 standard levels. The curve of view (D) is a much closer approximation of the modulating wave, view (A), than is the 5-level quantized curve in view (C). From this you should see that the greater the number of standard levels used, the more closely the quantized wave approximates the original. This is also made evident by the fact that an infinite number of standard levels exactly duplicates the conditions of nonquantization (the original analog waveform).

2-49 Figure 2-48A.—Quantization levels. MODULATION. Figure 2-48B.—Quantization levels. TIMING. Figure 2-48C.—Quantization levels. QUANTIZED 5-LEVEL. Figure 2-48D.—Quantization levels. QUANTIZED 10-LEVEL. Although the quantization curves of figure 2-48 are based on 5- and 10-level quantization, in actual practice the levels are usually established at some exponential value of 2, such as 4(22), 8(2 3), 16(24), 32(25) . . . N(2n). The reason for selecting levels at exponential values of 2 will become evident in the discussion of pcm. Quantized fm is similar in every way to quantized AM. That is, the range of frequency deviation is divided into a finite number of standard values of deviation. Each sampling pulse results in a deviation equal to the standard value nearest the actual deviation at the sampling instant. Similarly, for phase modulation, quantization establishes a set of standard values. Quantization is used mostly in amplitude- and frequency-modulated pulse systems.

Figure 2-49 shows the relationship between decimal numbers, binary numbers, and a pulse-code waveform that represents the numbers. The table is for a 16-level code; that is, 16 standard values of a quantized wave could be represented by these pulse groups. Only the presence or absence of the pulses are important. The next step up would be a 32-level code, with each decimal number represented by a series of five binary digits, rather than the four digits of figure 2-49. Six-digit groups would provide a 64-level code, seven digits a 128-level code, and so forth. Figure 2-50 shows the application of pulse-coded groups to the standard values of a quantized wave.

2-50 Figure 2-49.—Binary numbers and pulse-code equivalents. Figure 2-50.—Pulse-code modulation of a quantized wave (128 bits). In figure 2-50 the solid curve represents the unquantized values of a modulating sinusoid. The dashed curve is reconstructed from the quantized values taken at the sampling interval and shows a very close agreement with the original curve. Figure 2-51 is identical to figure 2-50 except that the sampling interval is four times as great and the reconstructed curve is not faithful to the original. As previously stated, the sampling rate of a pulsed system must be at least twice the highest modulating frequency to get 2-51 a usable reconstructed modulation curve. At the sampling rate of figure 2-50 and with a 4-element binary code, 128 bits (presence or absence of pulses) must be transmitted for each cycle of the modulating frequency. At the sampling rate of figure 2-51, only 32 bits are required; at the minimum sampling rate, only 8 bits are required.

Figure 2-51.—Pulse-code modulation of a quantized wave (32 bits). As a matter of convenience, especially to simplify the demodulation of pcm, the pulse trains actually transmitted are reversed from those shown in figures 2-49, 2-50, and 2-51; that is, the pulse with the lowest binary value (least significant digit) is transmitted first and the succeeding pulses have increasing binary values up to the code limit (most significant digit). Pulse coding can be performed in a number of ways using conventional circuitry or by means of special cathode ray coding tubes. One form of coding circuit is shown in figure 2-52. In this case, the pulse samples are applied to a holding circuit (a capacitor which stores pulse amplitude information) and the modulator converts pam to pdm. The pdm pulses are then used to gate the output of a precision pulse generator that controls the number of pulses applied to a binary counter. The duration of the gate pulse is not necessarily an integral number of the repetition pulses from the precisely timed clock-pulse generator. Therefore, the clock pulses gated into the binary counter by the pdm pulse may be a number of pulses plus the leading edge of an additional pulse. This "partial" pulse may have sufficient duration to trigger the counter, or it may not. The counter thus responds only to integral numbers, effectively quantizing the signal while, at the same time, encoding it.

Each bistable stage of the counter stores ZERO or a ONE for each binary digit it represents (binary 1110 or decimal 14 is shown in figure 2-52). An electronic commutator samples the 20, 21, 22, and 23 digit positions in sequence and transmits a mark or space bit (pulse or no pulse) in accordance with the state of each counter stage. The holding circuit is always discharged and reset to zero before initiation of the sequence for the next pulse sample. 2-52 Figure 2-52.—Block diagram of quantizer and pcm coder. The pcm demodulator will reproduce the correct standard amplitude represented by the pulse-code group. However, it will reproduce the correct standard only if it is able to recognize correctly the presence or absence of pulses in each position. For this reason, noise introduces no error at all if the signal-to-noise ration is such that the largest peaks of noise are not mistaken for pulses. When the noise is random (circuit and tube noise), the probability of the appearance of a noise peak comparable in amplitude to the pulses can be determined. This probability can be determined mathematically for any ration of signal-to-average- noise power. When this is done for 10 5 pulses per second, the approximate error rate for three values of signal power to average noise power is: 17 dB — 10 errors per second 20 dB — 1 error every 20 minutes 22 dB — 1 error every 2,000 hours Above a threshold of signal-to-noise ration of approximately 20 dB, virtually no errors occur. In all other systems of modulation, even with signal-to-noise ratios as high as 60 dB, the noise will have some effect. Moreover, the pcm signal can be retransmitted, as in a multiple relay link system, as many times as desired, without the introduction of additional noise effects; that is, noise is not cumulative at relay stations as it is with other modulation systems.

The system does, of course, have some distortion introduced by quantizing the signal. Both the standard values selected and the sampling interval tend to make the reconstructed wave depart from the original. This distortion, called QUANTIZING NOISE, is initially introduced at the quantizing and coding modulator and remains fixed throughout the transmission and retransmission processes. Its magnitude can be reduced by making the standard quantizing levels closer together. The relationship of the quantizing noise to the number of digits in the binary code is given by the following standard relationship: Where: n is the number of digits in the binary code 2-53 Thus, with the 4-digit code of figure 2-50 and 2-51, the quantizing noise will be about 35 dB weaker than the peak signal which the channel will accommodate.

The advantages of pcm are two-fold. First, noise interference is almost completely eliminated when the pulse signals exceed noise levels by a value of 20 dB or more. Second, the signal may be received and retransmitted as many times as may be desired without introducing distortion into the signal. Q-27. Pulse-code modulation requires the use of approximations of value that are obtained by what process? Q-28. If a modulating wave is sampled 10 times per cycle with a 5-element binary code, how many bits of information are required to transmit the signal?

Q-29. What is the primary advantage of pulse-modulation systems? SUMMARY Now that you have completed this chapter, a short review of what you have learned is in order. The following review will refresh your memory of angle modulation and pulse modulation. FREQUENCY-SHIFT KEYING (fsk) is similar to cw keying in amplitude modulation and is a form of angle modulation. The carrier frequency is changed between two discrete values by the opening and closing of a key. 2-54 In FREQUENCY MODULATION (fm) the instantaneous frequency of the radio-frequency wave is varied in accordance with the modulating signal; the amplitude of the radio-frequency wave is kept constant.

2-55 MODULATION INDEX is the ratio of the maximum frequency difference between the modulated and the unmodulated carrier, or between the deviation frequency and the modulation frequency. The number of SIGNIFICANT SIDEBANDS and the modulating frequency will determine the bandwidth of the fm wave. The number of significant sidebands can be determined from the modulation index.

Modulation

INDEX

Significant

Sidebands

.01 2 .4 2 .5 4 1.0 6 2.0 8 3.0 12 4.0 14 5.0 16 6.0 18 7.0 22 8.0 24 9.0 26 10.0 28 11.0 32 12.0 32 13.0 36 14.0 38 15.0 38 The REACTANCE-TUBE MODULATOR is frequency modulated by using a reactance tube in shunt with the tank circuit. 2-56 The SEMICONDUCTOR-REACTANCE MODULATOR is used to frequency modulate low-power semiconductor transmitters. 2-57 The MULTIVIBRATOR MODULATOR uses an astable multivibrator with a modulating voltage inserted in series with the base return of the multivibrator transistors. The VARACTOR FM MODULATOR uses a VARACTOR. This is a specially designed diode that has a certain amount of capacitance between the junction that can be controlled by reverse biasing.

In PHASE MODULATION the carrier’ s phase is caused to shift at the rate of the modulating audio. The amount of phase shift is controlled by the amplitude of the modulating wave. 2-58 A BASIC PHASE MODULATOR may be a single tube in series with a capacitor to form a phase-shift network. As the impedance of the tube changes, the phase of the output shifts. PHASE-SHIFT KEYING (psk) is similar to cw and fsk. It consists of phase reversals of the carrier frequency as modulating signal data elements open and close the modulator key.

2-59 PULSE MODULATION is modulation in which we allow oscillations to occur for a given period of time only during selected intervals. PULSE-REPETITION TIME (prt) is the specific time period between each group of rf pulses. 2-60 PULSE-REPETITION FREQUENCY (prf) is found by dividing the pulse repetition time into 1. This defines how often the groups of pulses occur. PULSE WIDTH (pw) or PULSE DURATION (pd) is the time that a pulse is occurring. REST TIME (rt) is the time referred to as nonpulse time. PEAK POWER is the maximum power during a pulse.

AVERAGE POWER equals the peak power averaged over one complete cycle. DUTY CYCLE is the ratio of working time to total time, or the ratio of actual transmit time to transmit time plus rest time, for intermittently operated devices. The SPARK-GAP MODULATOR consists of a circuit for storing energy, a circuit for rapidly discharging the storage circuit, a pulse transformer, and a power source. The THYRATRON MODULATOR is an electronic switch which requires a positive trigger of only 150 volts. The trigger must rise at the rate of 100 volts per microsecond to fire or cause the modulator to conduct.

2-61 In communications PULSE-MODULATION SYSTEMS, the modulating wave must be SAMPLED at 2.5 times the highest modulating frequency to ensure accuracy. PULSE-AMPLITUDE MODULATION (pam) is modulation in which the amplitude of each pulse is controlled by the instantaneous amplitude of the modulation signal at the time of each pulse. PULSE-DURATION MODULATION (pdm) or PULSE-WIDTH MODULATION (pwm) are both designations for a type of modulation. The width of each pulse in a train is made proportional to the instantaneous value of the modulating signal at the instant of the pulse.

PULSE-POSITION MODULATION (ppm) has the advantage of requiring constant transmitter power. The amplitude and width of the pulses are kept constant. At the same time, the position of each pulse, in relation to the position of a recurrent reference pulse, is varied by each instantaneous sampled value of the modulating wave. 2-62 PULSE-FREQUENCY MODULATION (pfm) is a method of pulse modulation in which the modulating wave is used to frequency modulate a pulse-generating circuit. PULSE-CODE MODULATION (pcm) refers to a system in which the standard value of a quantized wave is indicated by a series of coded pulses that give the modulating wave’ s value at the instant of the sample.

2-63

Answers To Questions Q1. Through Q29.

A-1. Frequency and phase. A-2. Frequency-shift keying. A-3. Resistance to noise interference. A-4. Instantaneous frequency. A-5. As the ratio of the frequency deviation to the maximum frequency deviation allowable. A-6. The number of significant sidebands and the modulating frequency. A-7. By changing the reactance of an oscillator circuit in consonance with the modulating voltage. A-8. Collector-to-emitter capacitance. A-9. An LCR filter. A-10. Capacitance. A-11. Phase. A-12. A phase-shift network such as a variable resistor and capacitor in series.

A-13. Cw and frequency-shift keying. A-14. Pulse modulation. A-15. Pulse-repetition time. A-16. Rest time. A-17. Peak power during a pulse averaged over pulse time plus rest time. A-18. Either a fixed spark gap that uses a trigger pulse to ionize the air between the contacts, or a rotary gap that is similar to a mechanical switch. A-19. Power source, a circuit for storing energy, a circuit for discharging the storage circuit, and a pulse transformer. A-20. Some characteristic of the pulses has to be varied. A-21. 2.5 times the highest modulating frequency.

A-22. Both are susceptible to noise and interference. A-23. The time duration of the pulses or the time of occurrence of the pulses. A-24. Either, or both at the same time. A-25. It requires synchronization between the transmitter and receiver. A-26. A method of pulse modulation in which a modulating wave is used to frequency modulate a pulse-generating circuit. 2-64 A-27. Quantization.

A-28. 50.

A-29. Low susceptibility to noise.