APPROXIMATE ANALYTIC EQUATIONS FOR SMALL SHAPIRO STEP JOSEPHSON-JUNCTIONS

Observation of Shapiro step is important for evaluation of the Josephson junction. This theoretical characteristic is given by a nonlinear differential equation with the normalized frequency Omega based on the current driven resistively shunted junction (RSJ) model as a parameter [14]. Although this model provides good agreement with the experimental results, the number of operations for the numerical solution of the equation is excessive. Hence, discussions of the experimental results by means of theoretical values are difficult. As a result, a proposal of a simple approximate equation which can describe the theoretical characteristics only with Omega is considered extremely useful. In the high temperature superconducting junction extensively studied recently, the I(c)R(n) product is large and Omega < 0.1 is expected. For Omega < 0.1, the current amplitude of Shapiro step decreases excessively. In practice, Shapiro steps are often not observed at a high-temperature superconducting junction. This is considered to be caused by the Omega < 0.1 measurement condition. It is important far evaluation of the junction to investigate this problem. No detailed analysis has been carried out for the region with Omega < 0.1. On the other hand, since Omega < 0.1 is the ideal operating condition of the Josephson mixer, understanding of the characteristics is important from the application point of view. In this paper, understanding of the theoretical characteristics for Omega < 0. 1, the derivation of the approximate equation and the condition in which Shapiro step cannot be observed are investigated. The analysis results and the experimental values are compared, and the effectiveness of the analysis is presented.