A theory of valve and circuit noise

Noise spectrum of a diode with a retarding field

“…In figure 5 graphs are plotted of the true reduced potential distribution, V /V 1 = currents, one may usc eq 44 for obtaining an approximaLe potential distribution and thence calculating the noise spectrum. For the case of small plate cW'r ents, and large negativr anode voltages, the reduced potential distribution approaches a straight line of unit slop e, also graphed in fi gUTe 5 under th e label m= -11 1 j~I' Accordingly, the follo\\~ing sedion proceeds with th e calcula tion of Lb e noi se-power spectrum for the two cases, large pla te curren t (m 2 small ) and small plate CUTrent (m 2 Iarge).…”

“…In this section 5 will be derived an expreSSIOn for th e noise power generated by random emi ssion within a waveguide, or a transmission line. The latter is to be regarded as a special case of the former, in which the particular mod e propagated is the TEM mod e, and the word "guid e" will be used to designate both.…”

“…Since the pulses of energy are random, or statistically independent, the average power flow , by Campbell's Theorem [5], is …”

“…and since the resultant noise power due to uncorrelated noise sources is simply the sum of the powers of the individual sources [5], the resultant noise power spectrum due to all the electrons that r~turn to the cathode is…”

Model-based fit procedure for power-law-like spectra

“…A mathematical mechanism for producing 1/f α noise was proposed long ago by Bernamont [5], who observed that the superposition of many Lorentzian spectra with a certain distribution of different rates could produce a spectral density with a 1/f region. The Bernamont superposition argument can be made rigorous with a slight modification of the standard proof of Campbell's theorem [6], and it goes as follows. Take a signal x(t) originated by the linear superposition of many random pulses, i.e., pulses that are random in time and can be described by a memoryless process with a Poisson distribution, have random amplitude A drawn from a distribution with finite variance and probability density g A (A), and such that their pulse response function h(t, λ) = exp(−λt) (if t > 0, otherwise h(t, λ) = 0) is drawn from a distribution with probability density g λ (λ).…”