We present an ultra-low-power Bluetooth low-energy (BLE) transceiver (TRX) for the Internet of Things (IoT) optimized for digital 28-nm CMOS. A transmitter (TX) employs an all-digital phase-locked loop (ADPLL) with a switched current-source digitally controlled oscillator (DCO) featuring low frequency pushing, and class-E/F ₂ digital power amplifier (PA), featuring high efficiency. Low 1/ DCO noise allows the ADPLL to shut down after acquiring lock. The receiver operates in discrete time at high sampling rate (~10 Gsamples/s) with intermediate frequency placed beyond 1/ noise corner of MOS devices. New multistage multirate charge-sharing bandpass filters are adapted to achieve high out-of-band linearity, low noise, and low power consumption. An integrated on-chip matching network serves to both PA and low-noise transconductance amplifier, thus allowing a 1-pin direct antenna connection with no external band-selection filters. The TRX consumes 2.75 mW on the RX side and 3.7 mW on the TX side when delivering 0 dBm in BLE.