162 BELL SYSTEM TECHNICAL JOURNAL 



by a very simple example. Consider a resonant circuit consisting of a 

 capacitance C, an inductance L and a resistance Rq , all in parallel. The 

 resistive component of the impedance across this circuit is 



R = 



1 + Q 



2 I 03 C0o\ (11) 



(Oi _ COoV 

 Wo w/ 



Q = i^ocooC = i^o/cooL (12) 



coo = l/VZC. (13) 



Here coo is the resonant frequency of the circuit and Q has its usual meaning. 



From (1) we see that as Rq , the resistance at resonance (co = coo) is made 

 higher, the noise voltage for frequencies near resonance increases. How- 

 ever, if we regard coo and C in (12) as fixed, we see that as Rq is increased 

 the Q of the circuit is increased, the frequency range over which R is high is 

 decreased, and R actually becomes lower far from resonance. (9) tells us 

 that the mean square noise voltage integrated over all frequencies remains 

 constant as Rq is changed. 



It is found that for a high Q circuit, the noise is much like a carrier of 

 frequency coo modulated by low-frequency noise. If we let the radian fre- 

 quency of this ''noise modulation" be (co — coo), then the mean square 

 ampHtude of the noise modulation varies with frequency about as R given 

 by (11) varies with (co — coo). 



II. ScHOTTKY Noise or Shot Noise 



In 1918 Schottky^ described the ''Schrot-Effekt": the noise in vacuum 

 tubes due to the corpuscular nature of the electron convection current. 

 This is commonly known as ''shot noise." The magnitude of this noise is 

 usually derived by means quite different from those used here. 



Johnson noise is necessarily associated with any electrical resistance, 

 whatever its nature. Now, consider a close spaced planar diode shown in 

 Fig. 3 consisting of two opposed emitting cathodes, each emitting a current 

 /o . Suppose the whole diode is held at the same temperature. There are 

 no batteries or other sources of power aside from thermal energy; the only 

 electrical energy flow must then be Johnson noise, ascribable to the re- 

 sistance of the diode. 



Assume that the cathodes both have the same uniform work function. 

 Then when the diode is short circuited, each electron emitted from cathode 1 

 will reach cathode 2, and each electron emitted from cathode 2 will reach 

 cathode 1 .* If cathode 2 were made negative, all the electrons from 2 would 



* It is here assumed that /© is small enough so that depression of potential due to space 

 charge is avoided. 



