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The current voltage characteristics of Josephson junctions at finite temperatures under microwave irradiation are simulated in the resistively, capacitively, inductively shunted junction (RCLSJ) model including white noise. The simulated results as function of microwave power clearly show the appearance of Shapiro steps. It is shown that higher steps are suppressed for low microwave amplitudes. The rounding of the Shapiro steps observed experimentally has been reproduced by taking noise into consideration in RCLSJ model.

Josephson junction (JJ) is natural high frequency source tuneable up to terahertz. However the line width of single JJ is large and maximum power is small. The line width can be narrowed and power can be increased by using phase locked arrays of many nearly identical JJs. The single crystal and c-axis oriented CuO based high temperature superconductors (HTS) are natural stacks of JJs with the CuO2layer of 0.3 nm acting as superconducting electrodes and the Bi2O3 or Tl2O3 or Y2O3 or (Ba, Ca)O layers of approximately 1.0 nm acting as insulating barrier (intrinsic Josephson effect). The I-V characteristic of the intrinsic stacked Josephson junctions (ISJJ) as a function of magnetic field are simulated. ISJJ has been modelled as one dimensional series array of JJ. Each JJ of the series is considered as resistively shunted junction model in which the effect of capacitance, inductance and a current source producing white noise are included. The critical current of the ISJJ as function of magnetic field shows Fraunhoffer like pattern. The simulated results have been compared with the Tl2212 mesas experimental results. It has been found that the simulated results are in good agreement with the experimental one.