LIMITS TO AMPLIFICATION 



87 



very effectively and it sets a lower limit to the possibility of amplifying 

 electrical impulses of any kind. Any signal much smaller than the 

 thermal noise would be masked hopelessly. The only factor under 

 control in the noise equation is the frequency range F, which should 

 be no greater than is needed for the transmission of the signal. 



An example will illustrate the magnitude involved in this limit to 

 amplification. When the signal is speech requiring a frequency band 

 of 6,000 cycles, then the apparent power generated at the input of 

 the amplifier by thermal agitation is 0.985 X 10~" watts, which is 

 about 138 db below the common reference level of 0.006 watts. (The 

 level of 10~^® instead of 0.006 watts is being considered as a reference 

 point for the decibel scale in communication circuits. This is approxi- 

 mately the level of thermal noise in a 6,000-cycle channel.) If the 

 input resistance were one megohm the corresponding r.m.s. noise 

 voltage would be 9.94 ^uv. 



A signal represents a certain amount of available power, and when 

 this is so small that it is near the thermal noise level it must be used 

 efficiently to produce voltage at the grid of the amplifier tube.''- ^ 

 Let the signal be supplied by a generator of voltage E and internal 

 resistance Ri which delivers power to a load resistance R^, the combina- 

 tion forming the input circuit of the amplifier as shown in Fig. 1. 

 The mean-square signal voltage on the grid of the amplifier tube is 



F 2 — i^ 



RiRi 



Ri + R2 



(4) 



However, the resistance required by equation 2 for the noise is the 



I 77.:::-.- 1 



AMPLIFIER 



Fig. 1 — Schematic diagram of a vacuum tube amplifier showing equivalent 



input circuit. 



combination of Ri and R^ in parallel, so that the mean-square noise 

 voltage on the grid of the amplifier tube is, from equations 2 and 3 



V,^WR=W{^;) 



(5) 



