94 BELL SYSTEM TECHNICAL JOURNAL 



these two readings, namely, 0.1 mw, and the signal-to-noise ratio of 

 the actual system is 3 times, or 4.8 db worse than its best possible 

 value with a given signal. These data may be expressed in terms of an 

 equivalent input resistance which has the advantage that the ampli- 

 fying properties of the tube have been taken into account. This 

 leaves for the engineer only the problem of selecting a tube having an 

 input capacity of such a value that the construction of a relatively 

 high impedance input circuit is possible. 



So far, the discussion has been based upon the properties of amplifiers 

 only, no mention being made of the effects of modulators, detectors, 

 frequency converters, and other nonlinear devices on the signal-to- 

 noise ratio. A detailed discussion of the noise in such devices is 

 beyond the scope of this paper, but the relations in the most commonly 

 used ones may be indicated and their general properties outlined. 



First, consider a system composed of a radio frequency amplifier 

 followed by a detector and a pair of headphones. A certain amount of 

 noise will be heard in the phones if the gain of the amplifier is great 

 enough. This noise is caused by the various components of the radio 

 frequency noise beating together in the detector to form audio fre- 

 quency components. Next, suppose that an unmodulated carrier is 

 introduced into the amplifier. It will be observed that the audio 

 noise in the phones increases. The increase in audio noise is produced 

 by the radio frequency carrier beating with the radio frequency noise 

 components and this increase is proportional to the strength of the 

 carrier. 



If a small percentage of modulation is added to the carrier, the audio 

 signal-to-noise ratio in the phones will be determined by the properties 

 of the amplifier in the same way as though the system were a straight 

 amplifier without any detector. Comparison of the actual system 

 with the ideal may be made by introducing the carrier into one of the 

 amplifier stages subsequent to the input, and then measuring the audio 

 noise with the input circuit in its normal condition and again with 

 the input circuit short-circuited. The ratio of these two energy values 

 gives the ratio of the equivalent input resistance of the actual system 

 to the equivalent input resistance of the noisy amplifier alone. The 

 ratio of the ideal signal-to-noise ratio to the actual one may be found 

 by dividing the difference between the two audio energy readings by 

 the reading taken with the input circuit in its normal condition. 



If the percentage of modulation of the carrier is large, the system 

 will be noisier because there will be appreciable audio noise components 

 caused by beats between the side bands and the radio frequency noise 

 components. Again, if the carrier level is not large compared with 



