Frequency-modulated continuous wave (FMCW) radar is widely used in automotive and consumer electronics because of its range, velocity, and angle measurement functionality. In an FMCW radar system, the isolation between transmitting (Tx) and receiving (Rx) subsystems affects the sensitivity of the FMCW system, which directly impacts the system’s overall performance in target detection. The factors that affect system performance include transmitter-to-receiver on-chip coupling and Tx-to-Rx antenna coupling. The on-chip isolation performance is basically fixed once a radar chip is given, but the antenna isolation performance depends on a designed antenna array. Usually, a targeted antenna requirement is first specified, and then the corresponding Tx and Rx antenna array is designed. However, there is no general principle or criteria for specifying a proper antenna isolation requirement in the existing research. In this paper, first, we reveal that the antenna isolation requirement should be set to be almost the same as the given on-chip isolation value, which is very significant as a general guideline in setting a targeted antenna isolation requirement. All current antenna isolation methods cannot reach the level of on-chip isolation in a compactly designed radar system. We further propose a teardrop-based method to provide high antenna isolation. The principle of an antenna isolation requirement and a novel antenna design using teardrops are both analyzed and demonstrated based on a representative 24 GHz FMCW radar. Our teardrop-shaped structure in the mouth of the conventional Vivaldi antenna achieved greater than 50 dB isolation, while the distance between the Tx and Rx antennas could be reduced to 2.1 mm.