When you consider a single noise frequency. This could normally affect the output of a receiver only if it falls within its passband. In that case, the carrier and noise voltages will mix and the difference frequency, if audible, will interfere with the reception of the wanted signal.Considering the single noise voltage vectorially, the noise vector gets superimposed on the carrier, rotating about it with relative angular velocity (− x) as shown in Figure1.4. The maximum deviation in the resultant amplitude from the average value is whereas the maximum phase deviation is
= ¤¥O(/x). (1.58)
Figure1.4. Vector effect of noise on carrier.
Let the noise voltage amplitude be one-fourth of the carrier voltage amplitude. Then, for AM, the modulation H= /x= 8
" = 0.25 while the maximum phase deviation is =sin 0.25 /1 =14.5°. Let us also assume here that AM receiver responds only to amplitude channel and does not respond to phase changes.
We further assume that the FM receiver responds only to frequency changes and does not respond to amplitude changes since the amplitude limiter in FM receiver removes all the amplitude variations. We now proceed to assess the influence of phase changes on FM receiver and that of a amplitude changes on AM receiver.
We make this comparison under the most severe condition for FM. Let the modulating frequency be 15 kHz and let us assume for the sake of simplicity that the modulation index for both AM and FM be unity. Then in AM receiver noise-to-signal voltage ration will be 0.25/1 =0.25.
Concerning FM, we convert the modulation index from unity devices to radians. Thus the ration is14.5°/57.3° =0.253. Thus the noise-to-signal ration in FM is just slightly worse than in the case of AM.
We next study the performance when the modulation frequency has been altered from 15 kHz to the lowest value say 30 Hz. In AM, as the noise different frequency (− x)and the modulating frequency are reduced from 15 kHz to 30Hz, there appears no difference in the relative noise, carrier and the modulating voltage amplitudes. In order words, in AM variation in
157 the noise and modulating frequencies do not vary the noise-to signal ratio. In FM, on the other hand, since the ratio of noise to carrier voltage remains constant, the value of modulation index, i.e. maximum phase deviation due to noise also remains constant.
Thus, while the modulation index due to noise remains constant (as the noise sideband frequency is reduced), the modulation index caused by the signal goes on increasing in proportion to the reduction in modulation frequency. Hence in FM, the noise-to-signal ratio goes on reducing with modulation frequency. At the lowest modulation frequency of 30 Hz, the noise-to-signal ratio in FM is (0.253 x 30 /15000) =0.000505. Thus the noise-to-signal ratio reduces from 25.3 percent at 15 kHz to 0.05 per cent at 30 Hz.
We assume the noise frequency components to be evenly spread across the pass band of the receiver. Hence it is evident that the noise output from the receiver decreases uniformly with noise sideband frequency for FM. On the other hand, in AM it remains constant. Figure 3.13. (a) illustrates these noise sideband distributions for AM and FM. The triangular noise distribution for FM is referred as to the noise triangle. The noise sideband distribution for AM is a rectangle as shown in Figure 1.5a. From Figure 1.5a, we may conclude that the average voltage improvement for FM under these conditions is 3:1. Such a conclusion is valid for average audio frequency at which FM noise voltage appears to be half the AM noise voltage. In actual practice, however, the situation is more complex and the improvement obtainable in FM over AM is only a voltage ratio of √3: 1, i.e. power ratio of 3:1 or about 4.75 dB.
We have assumed in the beginning that the noise voltage is lower than the signal voltage. When two signals are simultaneously received, the amplitude limiter gets actuated by the stronger signal and it tends to reject the weaker signal. Accordingly if peak noise voltage exceeds the signal voltages, the signal will get excluded by the limiter. With very low signal-to-noise ratio, therefore, AM is superior to FM. The exact value of signal-to-noise voltage ratio at which FM becomes superior to AM depends on the value of FM modulation index. However, in general, FM becomes superior to AM when signal-to-noise voltage ratio becomes 4(12 dB) or more at the amplitude limiter level.
158 Figure 1.5. Noise sideband distribution in AM and FM.
3.9.2. Noise Triangle for ./ > 1
You must recall that in AM, the maximum permissible value of amplitude modulation is 1, i.e,H=1. In FM, there is no such limit. In FM, the limit is not the maximum frequency deviation. Thus for FM VHF broadcast, maximum frequency deviation is limited to 75 kHz.
Hence using even the highest modulation frequency of 15 kHz, the modulation index in FM broadcast is as high as 5. At lower modulating frequencies, the modulation index is correspondingly higher. Thus, with modulation frequency of 1kHz, HR is 75. The signal-to-noise voltage ratio in the output of the limiter in FM receiver will get increased in proportion to the modulation index. Thus, with HR=5 (the highest permitted HR¾Ã ¾4=15 kHz), the signal-to-noise improvement is 5:1 in voltages and 25:1 in power (14 dB). No such improvement is possible for AM. With sufficient signal-to-noise ratio at the receiver input as assumed earlier, overall improvement secured in FM over AM is (4.75+14) = 18.75 DB. Figure 1.5b shows the noise triangle forHR=5.
From the above considerations, it becomes evident that in FM, we may use reduced bandwidth and thereby achieve higher signal-to-noise ratio. Such a trading of bandwidth is not possible in AM. It may also be noticed that just the increase of deviation (and hence the system bandwidth) in FM, does not necessarily mean that more random noise will be admitted. In fact this extra random noise produces no effect if the noise sideband frequency lie output the pass band of the receiver. Hence from this consideration, the maximum deviation and hence bandwidth, may be increased without fear. Phase modulation also has all the properties of FM except the noise triangle. Noise now phase modulates the carrier but there is no improvement as modulating and noise sideband frequencies are lowered. Thus under identical conditions, FM will be 4.7 dB better than PM regarding noise. It is for this reason that frequency modulation is preferred to phase modulation in practical transmitters.
159 In practice, however, in FM, bandwidth and maximum deviation cannot be increased indefinitely. Thus when a pulse is applied to a turned circuit, its peak amplitude is proportional to the square root of the bandwidth of the circuit. Similarly when a noise impulse is applied to the tuned circuit in the IF amplifier of an FM receiver, a large noise pulse results because of the unduly large bandwidth needed to accommodate the high deviation. When the magnitudes of noise pulses exceed about one-half of the carrier amplitude at the amplitude limiter, then the limiter function fails. When the noise pulse magnitude exceeds the carrier amplitude, the noise so to say captures the signal. The maximum deviation of 75 kHz is a compromise between the two extreme conditions described above.
It may be proved that when impulse noise amplitude < 0.5 x, this impulse noise gets reduced in FM to the same extent as random noise. AM communication receivers use amplitude limiters.
Such a limiter does not limit random noise at all and limits impulse by about 10 dB. Thus the FM system is better than the AM system in this regard as well.