Frequency Modulation

In frequency modulation, the instantaneous frequency of the radio-frequency wave varies with the modulation signal. As mentioned in NEETS, module 12, the amplitude is kept constant. The number of times per second that the instantaneous frequency varies 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:

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.)

The amplitude and frequency of the signal used to modulate the carrier will determine both the number of significant sidebands (shown in fig. 5-19) and the amplitude of the sidebands (shown in fig. 5-20). Both the number of significant sidebands and the bandwidth increase as the frequency of the modulating signal increases.

Figure 5-19. - Distribution of sidebands.

Figure 5-20. - Spectrum distribution for a modulation index of 2.

NEETS, module 12, should be consulted for an in-depth discussion of frequency-modulation principles.

Q.6 What happens to an fm signal as you increase the frequency of the modulating signal?

PULSED WAVES

An ideal pulsed radar signal is made up of a train of rf pulses with a constant repetition rate, constant pulse width and shape, and constant amplitude. To receive the energy reflected from a target, the radar receiver requires almost ideal pulse radar emission characteristics. By observing the spectra of a pulsed radar signal, you can easily and accurately measure such characteristics as pulse width, duty cycle, and peak and average power. The principles of radar are covered in NEETS, Module 18, Radar Principles, which can be consulted for an explanation of pulsed waves.

Rectangular Pulse

A rectangular wave is used to pulse-modulate the constant frequency rf carrier to produce the pulse radar output. The rectangular wave is made up of a fundamental frequency and its combined odd and even harmonics. Figure 5-21 shows the development of a rectangular wave.

Figure 5-21. - Rectangular pulse.

Pulsed Wave Analysis

In amplitude modulation, sidebands are produced above and below the carrier frequency. A pulse is also produced above and below the carrier frequency, but the pulse is made up of many tones. These tones produce multiple sidebands that are commonly referred to as SPECTRAL LINES, or RAILS, on the spectrum analyzer display. Twice as many rails will be in the pulse-modulated output of the radar as there are harmonics contained in the modulating pulse (upper and lower sidebands), as shown in figure 5-22. In the figure, the pulse repetition frequency (prf) is equal to the pulse interval of 1/T. The actual spectrum analyzer display would show the lower lobes (shown below the reference line in the figure) on top because the spectrum analyzer does not retain any polarity information. Changing the pulse interval, or pulse width, of the modulation signal will change the amount of rails (prf), or number of lobe minima, as illustrated in figure 5-23.

Figure 5-22. - Pulsed radar output.

Figure 5 - 23. - Pulsed radar changes caused by modulating signal changes.

ANALYZING THE SPECTRUM PATTERN

The leading and trailing edges of the radiated pulse-modulated signal must have a sharp rise time and decay time and a constant amplitude between them. Incorrect pulse shape will cause frequency spread and pulling, which results in less available energy at the frequency to which the receiver is tuned. The primary reason for analyzing the spectrum is to determine the exact amount of amplitude and frequency modulation present. The amount of amplitude modulation determines the increase in the number of sidebands within the applied pulse spectrum; an increase in frequency modulation increases the amplitude of the side-lobe frequencies. In either case, the energy available to the main spectrum lobe is decreased.

SPECTRUM ANALYZER OPERATION

The information desired from the spectra to be analyzed determines the SPECTRUM ANALYZER requirements. Real-time analysis is used if a particular point in the frequency spectrum is to be analyzed, such as a line spectra display. Continuous- or swept-frequency analysis, which is the most common mode of observation, is used to display a wider portion of the frequency spectrum or (in some cases) the entire range of the spectrum analyzer in use. Changing the spectrum analyzer setting from one mode to another is accomplished by varying the scan time and the bandwidth of the spectrum analyzer or a combination of the two. Most real-time spectrum analyzers, however, are preceded by mechanical filters, which limit the input bandwidth of the spectrum analyzer to the desired spectra to be analyzed. Tunable- or swept-spectrum analyzers function basically the same as heterodyne receivers, the difference being that the local oscillator is not used but is replaced by a voltage-controlled oscillator (vco). The vco is swept electronically by a ramp input from a sawtooth generator. The output of the receiver is applied to a crt, which has its horizontal sweep in synchronization with the vco. The lower frequency appears at the left of the crt display. As the trace sweeps to the right, the oscillator increases in frequency. Figure 5-24 is a block diagram of a heterodyne spectrum analyzer.

Figure 5-24. - Block diagram of a heterodyne spectrum analyzer.

Before the frequency of a signal can be measured on a spectrum analyzer, it must be RESOLVED. Resolving a signal means distinguishing it from other signals near it. Resolution is limited by the narrowest bandwidth of the spectrum analyzer because the analyzer traces out its own IF bandwidth shape as it sweeps through a signal. If the narrowest bandwidth is 1 kilohertz, the nearest any two signals can be, and still be resolved, is 1 kilohertz. Reducing the IF bandwidth indefinitely would obtain infinite resolution except that the usable IF bandwidth is limited by the stability of the spectrum analyzer. The smaller the IF bandwidth, the greater the capability of the analyzer to resolve closely spaced signals of unequal amplitudes. Modern spectrum analyzers have been refined to the degree that IF bandwidths are less than 1 hertz.

It is important that the spectrum analyzer be more stable in frequency than the signals being measured. The stability of the analyzer depends on the frequency stability of its vco. Scan time of the spectrum analyzer must be long enough, with respect to the amplitude of the signal to be measured, to allow the IF circuitry of the spectrum analyzer to charge and recover. This will prevent amplitude and frequency distortion.

Q.7 When referring to spectrum analyzers, what is meant by the term resolving signals?