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Exact formulae are presented for both maximum available gain (G/sub ma/) and unilateral gain (U), which include both the magnitude and phase angle of the S/sub 21/ parameter. The result for G/sub ma/ is not unique since there are many possible solutions to simultaneously match S/sub 11/ and S/sub 22/ when k>1. For the phase angle of U, the result tends to become 180/spl deg/ 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 G/sub ma/ amplifier.