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# Navy Electricity and Electronics Training Series (NEETS)Module 12—Modulation Principles Chapter 2:  Pages 2-11 through 2-20

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.

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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.

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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

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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

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.

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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?

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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 E1, which is across C7, will lag current by 90 degrees. E1 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

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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.

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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.

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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

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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.

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Introduction to Matter, Energy, and Direct Current, Introduction to Alternating Current and Transformers, Introduction to Circuit Protection, Control, and Measurement, Introduction to Electrical Conductors, Wiring Techniques, and Schematic Reading, Introduction to Generators and Motors, Introduction to Electronic Emission, Tubes, and Power Supplies, Introduction to Solid-State Devices and Power Supplies, Introduction to Amplifiers, Introduction to Wave-Generation and Wave-Shaping Circuits, Introduction to Wave Propagation, Transmission Lines, and Antennas, Microwave Principles, Modulation Principles, Introduction to Number Systems and Logic Circuits, Introduction to Microelectronics, Principles of Synchros, Servos, and Gyros, Introduction to Test Equipment, Radio-Frequency Communications Principles, Radar Principles, The Technician's Handbook, Master Glossary, Test Methods and Practices, Introduction to Digital Computers, Magnetic Recording, Introduction to Fiber Optics

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