This brief reports a mode-switching dual-core multi-coil voltage-controlled oscillator (VCO) with improved frequency tuning range (FTR) and phase noise (PN). Specifically, our VCO utilizes the head transformer (HT) and source center-tap inductor to enable dual-mode operation for FTR extension. Besides, the multi-coil VCO features two-port configuration, where the inherent boosted transformer voltage gain help reducing the PN injection. We also propose a compact HT layout to aid eliminating the parasitic common mode (CM) inductance. The tiny mode-selection switches at the drain terminal introduce negative resistance at the desired mode, averting the oscillation state ambiguity. The VCO fabricated in 65-nm CMOS occupies a core area of 0.098 mm2 while dissipating 16.8 mW at a 0.7-V supply. The measured PN peaks to -129.1 dBc/Hz at 10-MHz offset throughout the entire FTR of 58% (12.9 to 24 GHz) with the corresponding peak FoMT of 199.2 dBc/Hz.