A communications system comprising a processor, a variable oscillator, a radio frequency (RF) quadrature demodulator, a variable capacitor, a continuous-time, sigma-delta analog-to-digital converter (ADC), and a frequency divider, all integrated on a single semiconductor chip. The ADC samples the RF quadrature demodulator output. The processor sets the communications system frequency by controlling the oscillator, the frequency divider and the variable capacitor.