The quest for efficient and versatile microwave and optical isolators has recently spawned several novel space-time-modulated isolator structures. However, such space-time isolators suffer from a large profile and complex architecture caused by progressive nonreciprocal space-time coupling properties. To overcome these limitations, we propose a nonmagnetic phase-engineered temporal-loop-based isolator featuring large isolation levels, weak undesired time harmonics, and a low profile. The proposed isolator is composed of two temporal loops that provide desired constructive and destructive interferences of different time harmonics. Furthermore, these two loops are designed in a way to assure that the circulation and reflection of different time harmonics strengthen a low insertion loss unidirectional signal transmission. An experimental demonstration of the proposed time-modulated isolator at microwave frequencies is provided, featuring strong unidirectional wave transmission through the isolator with more than 27 dB contrast between the forward and backward waves across a fractional bandwidth of 14.3%. The proposed isolator outperforms the nonlinear-based and transistor-based isolators by featuring a highly linear response with OP 1dB of higher than 31 dBm, high power rating of more than 47 dBm, and a low noise figure of 3.4 dB.