任意非線形整流素子の一般的な不規則応答解析

抄録

We are well aware of the fact that various types of non-linear system elements are widely used and the sensitivity of measurements is finally limited by random noise in most physical in-struments. More explicitly, when many correlative random physical processes are passed through non-linear circuit elements such as detectors or rectifiers and the output random fluctuations are considered, the probability variables defined over positive region are fundamental quantities in the statistical physical engineering.
First, a general expression of multi-dimensional probability density distribution function in the form of orthogonal series such as statistical Hermite expansion is introduced. This probability expression is more general than the well-known expansion expression due to Gram Charlier, because it includes the latter one.
Then, for the special case of interest when many correlative physical quantities fluctuating only probability in positive region as mentioned in the above are treated, an explicit representation of joint density function in the form of statistical Laguerre expansion series is also presented.
Further, it has been pointed out that the latter method using a statistical Laguerre expansion is closely connected with the statistical Hermite expansion method under a squaring non-linear transformation.
We must call our attention to the fact that the statistical meaning (i.e., the random property) is reflected in each expansion coefficient.
Finally, the detailed experimental considerations enough to corroborate the above theories are given in the following two cases:
(a) a squaring rectifier with non-Gaussian random excitation,
(b) a non-squaring rectifier with Gaussian random excitation.
The statistical method described in this paper is also applicable to other wide fields of mea-surement on the random phenomena, since the probability variables defined only in positive region are fundamental in applied physics.