Two types of Si pnp punch-through BARITT diodes are fabricated and the d.c. and small-signal characteristics are studied both experimentally and theoretically. The d.c. solution of carrier-density and electric field distributions was numerically obtained with temperature- and field-dependent drift velocity for two types of diodes; uniform and non-uniform doping profiles. The calculated voltage-current curves were in good agreement with the measured ones from 210 K to 373 K. This agreement implies that the injection mechanism is not thermionic emission but diffusion-limited. Small-signal impedance was derived as functions of injection conductivity and transit-time-dependent space-charge impedance; the injection conductivity was given by perturbation of the d.c. solution and compared with other published theories. The present theory is applicable to a BARITT diode with non-uniform doping. The theory also succeeded in explaining the effect of self-heating. Because of neglect of the velocity-modulation and a.c. diffusion components, the theory overestimates the magnitude of negative resistance when a diode has low doping density (10¹⁵/cm³) in the emitter junction. Some predictions were made on effects of temperature, a doping profile and a velocity-field curve on the negative resistance by using the derived formula. As an example, the negative resistance of a GaAs BARITT diode is also predicted.

A concept of metric is defined in the set of labelled graphs. The concept is based on the idea that the extent of the difference in two graphs may be measured by the non-orthogonality of tie-set (loop) vectors of one graph to the cut-set vectors of the other. The meanings involved in the concept are discussed on the topics concerning flow and tension networks. Applications to electrical networks include the theorem that, for a non-reciprocal ⁿ-port network N which is realized by using λ_N controlled-sources, an inequality 1/2 rank (YY^T)D(g_c, g_v)λ_N holds where Y is the admittance matrix of N and D(g_c, g_v) is the distance between the corresponding current graph g_c and voltage graph g_v of N. An example for which the equalities hold in the above inequality is given.