Table of Contents

**The Principles of FM (Frequency Modulation**)

[ Frequency Modulation and Phase Modulation (PM)] the carrier amplitude remains constant and the carrier frequency is changed by the modulating signal. As the amplitude of the information signal varies, the carrier frequency shifts proportionately. As the modulating signal amplitude increases, the carrier frequency increases. If the amplitude of the modulating signal decreases, the carrier frequency decreases.

The reverse relationship can also be implemented. A decreasing modulating signal increases the carrier frequency above its center value, whereas an increasing modulating signal decreases the carrier frequency below its center value. As the modulating signal amplitude varies, the carrier frequency varies above and below its normal center, or resting, frequency with no modulation. The amount of change in carrier frequency produced by the modulating signal is known as the frequency deviation fd.

Maximum frequency deviation occurs at the maximum amplitude of the modulating signal. The frequency of the modulating signal determines the frequency deviation rate, or how many times per second the carrier frequency deviates above and below its center frequency. If the modulating signal is a 500-Hz sine wave, the carrier frequency shifts above and below the center frequency 500 times per second.

An FM signal is illustrated in Fig. 5-1(c). Normally the carrier [Fig. 5-1(a)] is a sine wave, but it is shown as a triangular wave here to simplify the illustration. With no modulating signal applied, the carrier frequency is a constant-amplitude sine wave at its normal resting frequency. The modulating information signal [Fig. 5-1(b)] is a low-frequency sine wave. As the sine wave goes positive, the frequency of the carrier increases proportionately.

The highest frequency occurs at the peak amplitude of the modulating signal. As the modulating signal amplitude decreases, the carrier frequency decreases. When the modulating signal is at zero amplitude, the carrier is at its center frequency point. When the modulating signal goes negative, the carrier frequency decreases. It continues to decrease until the peak of the negative half-cycle of the modulating sine wave is reached. Then as the modulating signal increases toward zero, the carrier frequency again increases. This phenomenon is illustrated in Fig. 5-1(c), where the carrier sine waves seem to be first compressed and then stretched by the modulating signal. Assume a carrier frequency of 150 MHz.

If the peak amplitude of the modulating signal causes a maximum frequency shift of 30 kHz, the carrier frequency will deviate up to 150.03 MHz and down to 149.97 MHz. The total frequency deviation is 150.03 − 149.97 = 0.06 MHz = 60 kHz. In practice, however, the frequency deviation is expressed as the amount of frequency shift of the carrier above or below the center frequency. Thus, the frequency deviation for the 150-MHz carrier frequency is represented as +- 30 kHz. This means that the modulating signal varies the carrier above and below its center frequency by 30 kHz.

Example 5-1 A transmitter operates on a frequency of 915 MHz. The maximum FM deviation is 612.5 kHz. What are the maximum and minimum frequencies that occur during modulation?

Note that the frequency of the modulating signal has no effect on the amount of deviation, which is strictly a function of the amplitude of the modulating signal. Frequently, the modulating signal is a pulse train or series of rectangular waves, e.g., serial binary data. When the modulating signal has only two amplitudes, the carrier frequency, instead of having an infinite number of values, as it would have with a continuously varying (analog) signal, has only two values. This phenomenon is illustrated in Fig. 5-2.

For example, when the modulating signal is a binary 0, the carrier frequency is the center frequency value. When the modulating signal is a binary 1, the carrier frequency abruptly changes to a higher frequency level. The amount of the shift depends on the amplitude of the binary signal. This kind of modulation, called frequency-shift keying (FSK), is widely used in the transmission of binary data in Bluetooth headsets, wireless speakers, and many forms of industrial wireless.

**Principles of Phase Modulation** **(AM)**

When the amount of phase shift of a constant-frequency carrier is varied in accordance with a modulating signal, the resulting output is a phase modulation (PM) signal [see Fig. 5-1(d)]. Imagine a modulator circuit whose basic function is to produce a phase shift, i.e., a time separation between two sine waves of the same frequency. Assume that a phase shifter can be built that will cause the amount of phase shift to vary with the amplitude of the modulating signal.

The greater the amplitude of the modulating signal, the greater the phase shift. Assume further that positive alternations of the modulating signal produce a lagging phase shift and negative signals produce a leading phase shift. If a constant-amplitude, constant-frequency carrier sine wave is applied to the phase shifter whose phase shift is varied by the intelligence signal, the output of the phase shifter is a PM wave.

As the modulating signal goes positive, the amount of phase lag, and thus the delay of the carrier output, increases with the amplitude of the modulating signal. The result at the output is the same as if the constant-frequency carrier signal had been stretched out, or had its frequency lowered. When the modulating signal goes negative, the phase shift becomes leading. This causes the carrier sine wave to be effectively speeded up, or compressed. The result is the same as if the carrier frequency had been increased.

Note that it is the dynamic nature of the modulating signal that causes the frequency variation at the output of the phase shifter: FM is produced only as long as the phase shift is varying. To understand this better, look at the modulating signal shown in Fig. 5-3(a), which is a triangular wave whose positive and negative peaks have been clipped off at a fixed amplitude. During time t0, the signal is zero, so the carrier is at its center frequency. Applying this modulating signal to a frequency modulator produces the FM signal shown in Fig. 5-3(b). During the time the waveform is rising (t1), the frequency increases. During the time the positive amplitude is constant (t2), the FM output frequency is constant.

During the time the amplitude decreases and goes negative (t3), the frequency decreases. During the constant-amplitude negative alternation (t4), the frequency remains constant, at a lower frequency. During t5, the frequency increases. Now, refer to the PM signal in Fig. 5-3(c). During increases or decreases in amplitude (t1, t3, and t5), a varying frequency is produced. However, during the constant-amplitude positive and negative peaks, no frequency change takes place.

The output of the phase modulator is simply the carrier frequency that has been shifted in phase. This clearly illustrates that when a modulating signal is applied to a phase modulator, the output frequency changes only during the time that the amplitude of the modulating signal is varying. The maximum frequency deviation produced by a phase modulator occurs during the time when the modulating signal is changing at its most rapid rate. For a sine wave modulating signal, the rate of change of the modulating signal is greatest when the modulating wave changes from plus to minus or from minus to plus. As Fig. 5-3(c) shows,

the maximum rate of change of modulating voltage occurs exactly at the zero crossing points. In contrast, note that in an FM wave the maximum deviation occurs at the peak positive and negative amplitude of the modulating voltage. Thus, although a phase modulator does indeed produce FM, maximum deviation occurs at different points of the modulating signal.

In PM, the amount of carrier deviation is proportional to the rate of change of the modulating signal, i.e., the calculus derivative. With a sine wave modulating signal, the PM carrier appears to be frequency-modulated by the cosine of the modulating signal. Remember that the cosine occurs 90° earlier (leads) than the sine. Since the frequency deviation in PM is proportional to the rate of change in the modulating signal, the frequency deviation is proportional to the modulating signal frequency as well as its amplitude. This effect is compensated for prior to modulation.

**Relationship Between the Modulating Signal and Carrier Deviation**

In FM, the frequency deviation is directly proportional to the amplitude of the modulating signal. The maximum deviation occurs at the peak positive and negative amplitudes of the modulating signal. In PM, the frequency deviation is also directly proportional to the amplitude of the modulating signal. The maximum amount of leading or lagging phase shift occurs at the peak amplitudes of the modulating signal. This effect, for both FM and PM, is illustrated in Fig. 5-4(a).

Now look at Fig. 5-4(b), which shows that the frequency deviation of an FM signal is constant for any value of modulating frequency. Only the amplitude of the modulating signal determines the amount of deviation. But look at how the deviation varies in a PM signal with different modulating signal frequencies. The higher the modulating signal frequency, the shorter its period and the faster the voltage changes.

Higher modulating voltages result in greater phase shift, and this, in turn, produces greater frequency deviation. However, higher modulating frequencies produce a faster rate of change of the modulating voltage and thus greater frequency deviation. In PM, then, the carrier frequency deviation is proportional to both the modulating frequency (slope of modulating voltage) and the amplitude. In FM, frequency deviation is proportional only to the amplitude of the modulating signal, regardless of its frequency.

**Converting PM to FM**

To make PM compatible with FM, the deviation produced by frequency variations in the modulating signal must be compensated for. This can be done by passing the intelligence signal through a low-pass RC network, as illustrated in Fig. 5-5. This low-pass filter, called a frequency-correcting network, predistorter, or 1/f filter, causes the higher modulating frequencies to be attenuated. Although the higher modulating frequencies produce a greater rate of change and thus a greater frequency deviation, this is offset by the lower amplitude of the modulating signal, which produces less phase shift and thus less frequency deviation. The predistorter compensates for the excess frequency deviation caused by higher modulating frequencies. The result is an output that is the same as an FM signal. The FM produced by a phase modulator is called indirect FM

**Phase-Shift Keying**

PM is also used with binary signals, as Fig. 5-6 shows. When the binary modulating signal is 0 V, or binary 0, the PM signal is simply the carrier frequency. When a binary 1 voltage level occurs, the modulator, which is a phase shifter, simply changes the phase of the carrier, not its frequency. In Fig. 5-6, the phase shift is 180°. Each time the signal changes from 0 to 1 or 1 to 0, there is a 180° phase shift.

The PM signal is still the carrier frequency, but the phase has been changed with respect to the original carrier with a binary 0 input. The process of phase-modulating a carrier with binary data is called phase-shift keying (PSK) or binary phase-shift keying (BPSK). The PSK signal shown in Fig. 5-6 uses a 180° phase shift from a reference, but other phase-shift values can be used, for example, 45°, 90°, 135°, or 225°. The important thing to remember is that no frequency variation occurs. The PSK signal has a constant frequency, but the phase of the signal from some reference changes as the binary modulating signal occurs.

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