Noise Suppression Effects of FM: Noise is interference generated by lightning, motors, automotive ignition systems, and any power line switching that produces transient signals. Such noise is typically narrow spikes of voltage with very high frequencies. They add to a signal and interfere with it. The potential effect of such noise on an FM signal is shown in Fig. 5-11. If the noise signals were strong enough, they could completely obliterate the information signal. FM signals, however, have a constant modulated carrier amplitude, and FM receivers contain limiter circuits that deliberately restrict the amplitude of the received signal.

Any amplitude variations occurring on the FM signal are effectively clipped off, as shown in Fig. 5-11. This does not affect the information content of the FM signal, since it is contained solely within the frequency variations of the carrier. Because of the clipping action of the limiter circuits, noise is almost completely eliminated. Even if the peaks of the FM signal itself are clipped or flattened and the resulting signal is distorted, no information is lost. In fact, one of the primary benefits of FM over AM is its superior noise immunity. The process of demodulating or recovering an FM signal actually suppresses noise and improves the signal-to-noise ratio.

The noise amplitude added to an FM signal introduces a small frequency variation, or phase shift, which changes or distorts the signal. Fig. 5-12 shows how this works. The carrier signal is represented by a fixed-length (amplitude) phasor S. The noise is usually a short duration pulse containing many frequencies at many amplitudes and phases according to Fourier theory. To simplify the analysis, however, we assume a single high-frequency noise signal varying in phase. In Fig. 5-12(a), this noise signal is represented as a rotating phasor N. The composite signal of the carrier and the noise, labeled C, is a phasor whose amplitude is the phasor sum of the signal and noise and a phase angle shifted from the carrier by an amount ϕ. If you imagine the noise phasor rotating, you can also imagine the composite signal varying in amplitude and phase angle with respect to the carrier. The maximum phase shift occurs when the noise and signal phasors are at a right angle to each other, as illustrated in Fig. 5-12(b). This angle can be computed with the arcsine or inverse sine according to the formula

It is possible to determine just how much of a frequency shift a particular phase shift produces by using the formula

Figure 5-12 How noise introduces a phase shift.

Since there is 57.3° per radian, this angle is ϕ = 19.47/57.3 = 0.34 rad. The frequency deviation produced by this brief phase shift can be calculated as

δ = 0.34(800) = 271.8 Hz

Just how badly a particular phase shift will distort a signal depends on several factors. Looking at the formula for deviation, you can deduce that the worst-case phase shift and frequency deviation will occur at the highest modulating signal frequency. The overall effect of the shift depends upon the maximum allowed frequency shift for the application. If very high deviations are allowed, i.e., if there is a high modulation index, the shift can be small and inconsequential. If the total allowed deviation is small, then the noise-induced deviation can be severe. Remember that the noise interference is of very short duration; thus, the phase shift is momentary, and intelligibility is rarely severely impaired. With heavy noise, human speech might be temporarily garbled, but so much that it could not be understood. Assume that the maximum allowed deviation is 5 kHz in the example above. The ratio of the shift produced by the noise to the maximum allowed deviation is

This is only a bit more than a 5 percent shift. The 5-kHz deviation represents the maximum modulating signal amplitude. The 271.8-Hz shift is the noise amplitude. Therefore, this ratio is the noise-to-signal ratio N/S. The reciprocal of this value gives you the FM signal-to-noise ratio:

For FM, a 3:1 input S/N translates to an 18.4:1 output S/N.

Example 5-6 The input to an FM receiver has an S/N of 2.8. The modulating frequency is 1.5 kHz. The maximum permitted deviation is 4 kHz. What are (a) the frequency deviation caused by the noise and (b) the improved output S/N?

Noise can interfere with an FM signal, and particularly with the high-frequency components of the modulating signal. Since noise is primarily sharp spikes of energy, it contains a lot of harmonics and other high-frequency components. These frequencies canbelarger in amplitude than the high-frequency content of the modulating signal, causing frequency distortion that can make the signal unintelligible. Most of the content of a modulating signal, particularly voice, is at low frequencies. In voice communication systems, the bandwidth of the signal is limited to about 3 kHz, which permits acceptable intelligibility. In contrast, musical instruments typically generate signals at low frequencies but contain many high-frequency harmonics that give them their unique sound and must be passed if that sound is to be preserved. Thus a wide bandwidth is needed in high-fidelity systems. Since the high-frequency components are usually at a very low level, noise can obliterate them. To overcome this problem, most FM systems use a technique known as pre-emphasis that helps offset high-frequency noise interference. At the transmitter, the modulating signal is passed through a simple network that amplifies the high- frequency components more than the low-frequency components. The simplest form of such a circuit is a simple high-pass filter of the type shown in Fig. 5-13(a).

Specifications dictate a time constant t of 75 μs, where t 5 RC. Any combination of resistor and capacitor (or resistor and inductor) giving this time constant will work.

Such a circuit has a cutoff frequency of 2122 Hz; frequencies higher than 2122 Hz will be linearly enhanced. The output amplitude increases with frequency at a rate of 6 dB per octave. The pre-emphasis circuit increases the energy content of the higher frequency signals so that they become stronger than the high-frequency noise components. This improves the signal-to-noise ratio and increases intelligibility and fidelity. The pre-emphasis circuit also has an upper break frequency fu, at which the signal enhancement flattens out [see Fig. 5-13(b)], which is computed with the formula

The value of fu is usually set well beyond the audio range and is typically greater than 30 kHz. To return the frequency response to its normal, “flat” level, a de-emphasis circuit, a simple low-pass filter with a time constant of 75 μs, is used at the receiver [see Fig. 5-13(c)]. Signals above its cutoff frequency of 2123 Hz are attenuated at the rate of 6 dB per octave. The response curve is shown in Fig. 5-13(d). As a result, the pre-emphasis at the transmitter is exactly offset by the de-emphasis circuit in the receiver, providing a flat frequency response. The combined effect of pre-emphasis and de-emphasis is to increase the signal-to-noise ratio for the high- frequency components during transmission so that they will be stronger and not masked by noise. Fig. 5-13(e) shows the overall effect of pre-emphasis and de emphasis.

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