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 voltage controlled oscillator includes a variable capacitance circuit having a plurality of variable capacitance elements, each having a capacitance that is a function of a tuning voltage, two or more oscillator core circuits, each operable over a specified frequency band, and inductive elements connected between the variable capacitance circuit and the oscillator core circuits.

A dual-mode oscillator and a multi-phase oscillator includes a mode switching circuit to switch between two operating modes and obtain oscillation signals having two different bands. The dual-mode oscillator also includes two transformer-coupled oscillators with each having a step-up transformer. The step-up transformer multiplies a drain voltage swing of a first metal oxide semiconductor (MOS) transistor and then injects a voltage signal to a gate of a second MOS transistor to obtain a larger gate voltage swing without increasing a supply voltage of the oscillator. The dual-mode oscillators are coupled through multi-phase coupled circuits to form a Mobius loop.

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.

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 dual-mode oscillator and a multi-phase oscillator includes a mode switching circuit to switch between two operating modes and obtain oscillation signals having two different bands. The dual-mode oscillator also includes two transformer-coupled oscillators with each having a step-up transformer. The step-up transformer multiplies a drain voltage swing of a first metal oxide semiconductor (MOS) transistor and then injects a voltage signal to a gate of a second MOS transistor to obtain a larger gate voltage swing without increasing a supply voltage of the oscillator. The dual-mode oscillators are coupled through multi-phase coupled circuits to form a Mobius loop.

An oscillator circuit includes a total of N (N2) class-D oscillator circuits stacked together between a supply voltage node and a reference voltage node. The output ports of adjacent class-D oscillator circuits in the disclosed oscillator circuit are coupled together by capacitors to ensure frequency and phase synchronization for the frequency signals generated by the class-D oscillator circuits. Compared with a reference oscillator circuit formed of a single class-D oscillator circuit, the oscillation amplitude of each of the class-D oscillator circuits in the disclosed oscillator circuit is 1/N of that of the reference oscillator circuit, and the current consumption of the disclosed oscillator circuit is 1/N of that of the reference oscillator circuit.

A dual-mode oscillator and a multi-phase oscillator includes a mode switching circuit to switch between two operating modes and obtain oscillation signals having two different bands. The dual-mode oscillator also includes two transformer-coupled oscillators and a step-up transformer in the transformer-coupled oscillators where the step-up transformer multiplies a drain voltage swing of a first MOS transistor and then injects a voltage signal to a gate of a second MOS transistor to obtain a larger gate voltage swing without increasing a supply voltage of the oscillator. The dual-mode oscillators are connected through multi-phase coupled circuits to form a Mobius loop.

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 reconfigurable crystal oscillator and a method for reconfiguring a crystal oscillator are provided. The reconfigurable crystal oscillator includes a transconductance circuit, a feedback resistor, a crystal tank, an input-end capacitor and an output-end capacitor. Both of the feedback resistor and the crystal tank are coupled between an input terminal and an output terminal of the transconductance circuit. The input-end capacitor is coupled to the input terminal of the transconductance circuit, and the output-end capacitor is coupled to the output terminal of the transconductance circuit. In particular, the transconductance circuit is configured to provide a transconductance, and when an operation mode of the reconfigurable crystal oscillator is switched, an input-end capacitance of the input-end capacitor and an output-end capacitance of the output-end capacitor are switched, respectively.