A necessary condition for minimum of the phase shift vs. attenuation in a voltage controlled attenuator (VCA) is founded on the base of the linear system theory. The condition consists of equality of numerator and denominator polynomial degrees for the transfer function. Also the paper discloses details of the new VCA structure based on the cross-coupling circuits and discusses its performance. Its main difference from known consists in ultra wide band feature and large range of attenuation, where minimum of the phase shift is provided. As a result, the output parameters and adjusting parameters of diodes are founded.Index terms -Attenuator linear model, low phase shift, phase invariance, voltage controlled attenuator.