Statistical studies of 1/f noise from carbon resistors

J. J.

Brophy

, , ().

F. N.

Hooge

and

A. M. H.

Hoppenbrouwers

, , ().

J. J.

Brophy

, , ().

L. J.

Greenstein

and

J. J.

Brophy

, , ().

J. J.

Brophy

, , ().

J. J.

Brophy

, , ().

W. E.

Purcell

, , ().

R. A.

Dell

, Jr.,

M.

Epstein

, and

C. R.

Kannewurf

, , ().

H.

Nyquist

, , ().

See for example: T. W. Anderson, Introduction to Multivariate Statistical Analysis (Wiley, New York, 1958).

See for example, C. A. Weatherburn, A First Course in Mathematical Statistics (Cambridge U.P., New York, 1968).

See for example, M. Fisz, Probability Theory and Mathematical Statistics (Wiley, New York, 1963).

M. Fisz, Probability Theory and Mathematical Statistics (Wiley, New York, 1963), p. 343ff.

It is often pointed out that measurements made using electronics that respond to dc signals (i.e., when no low‐frequency cutoff filter is present) result in a noise variance which is determined by the measuring time and hence leads to an infinite noise energy content as the measuring time goes to infinity. That is, the time window of width T produces a crude low‐frequency filter whose cutoff frequency $ω1$ varies as 1/T. Then $σ2≈Clog(ω2T).$ The variance then increases logarithmically to infinity as the measurement time increases to infinity. This apparent “catastrophe,” however, produces no serious problem, since the 1/f noise is only present when bias current is maintained constant in the device. This bias current produces an energy dissipation in the device which increases as the measurement time T. The fraction of the total energy appearing as noise then varies as $(1/T)log(ω2T),$ which diminishes to zero as T approaches infinity. Therefore a catastrophe is, in fact, not present.

R. A. Dell, Jr., Ph.D. dissertation (Northwestern Univ., 1971) (unpublished).