Small Microwave Signals

We will start our consideration of the microwave signal influence upon the Josephson junction with the simplest case of a small signal. According to the discussion of Section 2.4, the signal is represented by an ac current Ĩ(t) with sufficiently small amplitude I_ω (the exact conditions on the amplitude will be specified later). For the small signal, one can expand its effects to the Taylor series with respect to I_ω and consider consequently the linear (∝ I_ω), quadratic https://www.w3.org/1998/Math/MathML">(∝ Iω2)https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141572/0ba78ca1-05bc-4a29-bdf3-856e8fbc4b17/content/eq920.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and higher-order effects. The first-order (linear) effects are, of course, the most significant ones at I_ω → 0.