14.3 INTERFERENCE AND NOISE 655SNR=Pout
Nout=GPin
Gk(T+Ta)B=Pin
k(T+Ta)B(14.3.10)where the amplified signal power isPout=GPinin the numerator, which includes source and
amplifier noise given by Equation (14.3.9);Pinis the average power of the input signal; and the
denominatorNoutis the total output noise power given by Equation (14.3.9). Notice that the am-
plifier’s power gainGdoes not appear in the final result of the SNR. A large SNR indicates that the
signal is strong enough to mask the noise and possibly make the noise inconsequential. For exam-
ple, with SNR≥20 dB, intelligible voice communication results; otherwise, “static” in the voice
signal; with SNR≥50 dB, noisefree television image results; otherwise, “snowy” TV picture.
For a good system performance, Equation (14.3.10) suggests a large value ofPinand/or small
values forT+TaandB. However, one should be reminded here that the amplifier’s bandwidth
Bshould not be less than the signal bandwidthW. That simply means that with large-bandwidth
signals, one would expect noise to be more troublesome.
Frequency translation can be used effectively to reduce the effect of 1/fnoise by putting the
signal in a less noisy frequency band. Figure 14.3.8(a) shows the schematic implementation with
product modulation and demodulation, whereas Figure 14.3.8(b) illustrates the noise reduction in
terms of the areas under the noise power curve. The two multipliers in Figure 14.3.8(a) are normally
implemented by using a pair of synchronized switches. It turns out that the product modulation
requires bandwidthB= 2 W, and the synchronized product demodulation doubles the final SNR.
Another way of improving the SNR is bypreemphasisanddeemphasis filtering. Generally,
for low-frequency components of the message signal FM (frequency modulation) performs better,
and for high-frequency components PM (phase modulation) is a better choice. Hence, if one can
design a system that performs FM for low-frequency components of the message signal, and
Power
spectrumfAmplifier with 1/f noisefc(^0) W fc − W fc fc + W
Synchronized
switches
(b)
Low-pass
filter
(a)
Kx(t)
Figure 14.3.8(a)Schematic arrangement with frequency translation to reduce
the effect of 1/fnoise.(b)Noise power spectrum.