This paper presents a 24 GHz dual-mode frequency synthesizer fabricated in a 55-nm CMOS process that supports both Doppler radar and frequency modulated continuous wave (FMCW) radar applications. It provides differential local oscillation (LO) signals for the transmitter (TX) and quadrature LO signals for the 2-channel receiver (RX). The effects of chirp linearity and delta-sigma modulation (DSM) resolution on the RMS FM error is analyzed and a design procedure for the PLL loop bandwidth and frequency step is developed. The prototype demonstrated a loop bandwidth of 350 kHz, a frequency step time interval of 2 us, and a voltage-controlled oscillator (VCO) tuning linearity of 26%. The achieved RMS FM error is 68.8 kHz over a 1.25 GHz chirp bandwidth in FMCW mode, and the free-running VCO can accurately generate the 24.125 GHz frequency for Doppler mode.