The polynomial form of the input impedance of a CMOS cross-coupled amplifier with NMOS only active inductor are proposed. The formula of polynomial form and novel coefficients are programmed in Scilab and MATLAB so that the pole position of the fourth order polynomial can be found. From experience of a simple cross coupled oscillator design, the proposed circuit diagram may not oscillate as a triangular wave signal because the two poles are complex (underdamped case) but its real part could not be minimized to 0.001 so that it has a stable amplitude and additional two poles are real poles. The impulse sensitivity function (ISF) of the proposed circuit is derived for the first time so that it may be used to derive phase noise in the future.