conjugate match and K factor

For a simultaneous conjugate match amplifier design, is it a necessary condition to have K>1, delta<1?

It is best when amplifier have k>1. But it is not always possible. Be aware that additional microstrip between grounding and device makes such amplifier behave almost as perfect oscillator, because S11 probably can obtain negative resistance (S11>1). For example, some 1mm on source of FET makes it oscillate in my case, osscilation power even increases when gate phase is matched (conjugate).