Exact analysis of maximum available gain and unilateral gain including phase angle of S21

Exact formulae are presented for both maximum available gain (Gma) and unilateral gain (U), which include both the magnitude and phase angle of the S21 parameter. The result for Gma is not unique since there are many possible solutions to simultaneously match S11 and S22 when k>1. For the phase angle of U, the result tends to become 180 degree when using the topology of a variable coupler, a line stretcher, and a feedback amplifier. From the verifications, an amplifier using the unilateralizing technique will achieve 4-6 dB higher gain than that of the Gma amplifier.