A resonator circuit includes a transformer comprising a primary winding and a secondary winding. The primary winding is inductively coupled with the secondary winding. A primary capacitor is connected to the primary winding. The primary capacitor and the primary winding form a primary circuit. A secondary capacitor is connected to the secondary winding. The secondary capacitor and the secondary winding form a secondary circuit. The resonator circuit has a common mode resonance frequency at an excitation of the primary circuit in a common mode. The resonator circuit has a differential mode resonance frequency at an excitation of the primary circuit in a differential mode. The common mode resonance frequency is different from the differential mode resonance frequency.

The invention relates to a radio frequency oscillator, the radio frequency oscillator comprising a resonator circuit being resonant at an excitation of the resonator circuit in a differential mode and at an excitation of the resonator circuit in a common mode, wherein the resonator circuit has a differential mode resonance frequency at the excitation in the differential mode, and wherein the resonator circuit has a common mode resonance frequency at the excitation in the common mode, a first excitation circuit being configured to excite the resonator circuit in the differential mode to obtain a differential mode oscillator signal oscillating at the differential mode resonance frequency, and a second excitation circuit being configured to excite the resonator circuit in the common mode to obtain a common mode oscillator signal oscillating at the common mode resonance frequency.

The invention relates to a resonator circuit, the resonator circuit comprising a transformer comprising a primary winding and a secondary winding, wherein the primary winding is inductively coupled with the secondary winding, a primary capacitor being connected to the primary winding, the primary capacitor and the primary winding forming a primary circuit, and a secondary capacitor being connected to the secondary winding, the secondary capacitor and the secondary winding forming a secondary circuit, wherein the resonator circuit has a common mode resonance frequency at an excitation of the primary circuit in a common mode, wherein the resonator circuit has a differential mode resonance frequency at an excitation of the primary circuit in a differential mode, and wherein the common mode resonance frequency is different from the differential mode resonance frequency.

An oscillator is provided. The oscillator includes two reverse amplification elements, and each of the reverse amplification elements forms a self-feedback structure by using an inductor. Output ends of the two reverse amplification elements are coupled to each other by using one or more inductors, and input ends of the two reverse amplification elements are coupled to each other by using a capacitor. A capacitance value of the capacitor may be adjusted, to change an oscillation frequency of a differential output oscillation signal output by the oscillator.

An apparatus includes a digitally controlled oscillator (DCO), which includes an inductor coupled in series with a first capacitor. The DCO further includes a second capacitor coupled in parallel with the series-coupled inductor and first capacitor, a first inverter coupled in parallel with the second capacitor, and a second inverter coupled back-to-back to the first inverter. The DCO further includes a digital-to-analog-converter (DAC) to vary a capacitance of the first capacitor.

An apparatus includes a digitally controlled oscillator (DCO), which includes an inductor coupled in series with a first capacitor. The DCO further includes a second capacitor coupled in parallel with the series-coupled inductor and first capacitor, a first inverter coupled in parallel with the second capacitor, and a second inverter coupled back-to-back to the first inverter. The DCO further includes a digital-to-analog-converter (DAC) to vary a capacitance of the first capacitor.

An apparatus includes a digitally controlled oscillator (DCO), which includes an inductor coupled in series with a first capacitor. The DCO further includes a second capacitor coupled in parallel with the series-coupled inductor and first capacitor, a first inverter coupled in parallel with the second capacitor, and a second inverter coupled back-to-back to the first inverter. The DCO further includes a digital-to-analog-converter (DAC) to vary a capacitance of the first capacitor.

The invention relates to a resonator circuit, the resonator circuit comprising a transformer comprising a primary winding and a secondary winding, wherein the primary winding is inductively coupled with the secondary winding, a primary capacitor being connected to the primary winding, the primary capacitor and the primary winding forming a primary circuit, and a secondary capacitor being connected to the secondary winding, the secondary capacitor and the secondary winding forming a secondary circuit, wherein the resonator circuit has a common mode resonance frequency at an excitation of the primary circuit in a common mode, wherein the resonator circuit has a differential mode resonance frequency at an excitation of the primary circuit in a differential mode, and wherein the common mode resonance frequency is different from the differential mode resonance frequency.

Systems and methods are provided for hopping a digitally controlled oscillator (DCO) among a plurality of channels, wherein a gain of the DCO K.sub.DCO is a nonlinear function of frequency. A first normalized tuning word (NTW) corresponding to a first channel of the plurality of channels is generated. A first normalizing gain multiplier X is generated based on the nonlinear function of frequency, on an estimate of the nonlinear function of frequency, at a first frequency corresponding to the first channel. The first NTW is multiplied by the first X to obtain a first oscillator tuning word (OTW). The first OTW is input to the DCO to cause the DCO to hop to the first channel. A system for hopping among a plurality of channels at a plurality of respective frequencies comprises a phase-locked loop (PLL), a digitally controlled oscillator (DCO), a multiplexer, and an arithmetic module.

A resonant tank includes a first capacitor formed on a semiconductor substrate, a first inductor formed on the semiconductor substrate, a second capacitor formed on the semiconductor substrate, and a second inductor formed on the semiconductor substrate. The first capacitor, the first inductor, the second capacitor, and the second inductor are connected in a ring configuration, with each capacitor connected between a pair of the inductors and with each inductor connected between a pair of the capacitors. An amplifier circuit is coupled to the resonant tank and configured to amplify a signal in the resonant tank.