Method and system for steady state simulation and noise analysis of driven oscillators

A method for characterizing a driven oscillator circuit, comprising:

• providing, using one or more computer processors, a circuit description of the driven oscillator circuit, the driven oscillator circuit including an oscillator and a time-varying input signal coupled to the oscillator;
• forming a system of differential equations, using the one or more computer processors, for the driven oscillator circuit using information provided in the circuit description, the system of differential equations including a first differential operator in a time domain of the input signal and a product of a second differential operator in the time domain of the oscillator and a frequency variable that represents a frequency of the oscillator, wherein the frequency variable is independent of the time domain of the input signal;
• forming a Jacobian matrix for the driven oscillator circuit;
• forming a non-singular multitone phase noise vector (MPNV) for characterizing a phase noise in the driven oscillator circuit, wherein the multitone phase noise vector is based upon, at least in part, the Jacobian matrix and wherein the Jacobian matrix is an augmented Jacobian matrix including a static part and a dynamic part expressed in the frequency domain;
• and
• solving the system of differential equations, using the one or more computer processors, to obtain a waveform for characterizing the driven oscillator circuit.

A computer system for performing circuit simulation, the system comprising:

• a non-transitory computer-readable storage medium;
• one or more processors coupled to said non-transitory computer-readable storage medium;
• and
• computer code stored in said non-transitory computer-readable storage medium wherein said computer code, when retrieved from said non-transitory computer-readable storage medium and executed by said one or more processors, results in:
• retrieving from the non-transitory computer-readable storage medium information provided in a circuit description of a driven oscillator circuit having an oscillator coupled to a time-varying input signal;
• forming a Jacobian matrix for the driven oscillator circuit;
• forming a non-singular multitone phase noise vector (MPNV) for characterizing a phase noise in the driven oscillator circuit, wherein the multitone phase noise vector is based upon, at least in part, the Jacobian matrix and wherein the Jacobian matrix is an augmented Jacobian matrix including a static part and a dynamic part expressed in the frequency domain;
• forming with the one or more processors a frequency-domain harmonic balance equation for the driven oscillator circuit using the retrieved information provided in the circuit description of the driven oscillator circuit, the harmonic balance equation including a first differential operator in a frequency domain of the input signal and a product of a differential operator in a second frequency domain of the oscillator and a frequency variable of the oscillator, wherein the frequency variable is independent of the frequency domain of the input signal, wherein the harmonic balance equation in the frequency domain is described by:
• H(X)=(Ω1+ω2Ω2)Q+F=B,
• where
• X is a waveform of the oscillator,
• Q is a dynamic part of the driven oscillator circuit,
• F is a static part of the driven oscillator circuit,
• B is the injection signal in the frequency domain,
• Ω1 and Ω2 are frequency domain differential operators for t1 and t2, respectively, and
• ω2 is the frequency variable;
• and
• solving with the one or more processors the harmonic balance equation to obtain a waveform description of the driven oscillator circuit.

A non-transitory computer readable storage medium comprising computer code stored in said non-transitory computer-readable storage medium, wherein said computer code, when retrieved from said non-transitory computer-readable storage medium and executed by one or more computer processors, results in:

• retrieving from the non-transitory computer-readable storage medium information provided in a circuit description of a driven oscillator circuit having an oscillator coupled to a time-varying input signal;
• forming with the one or more computer processors a frequency-domain harmonic balance equation for the driven oscillator circuit using the retrieved information provided in the circuit description of the driven oscillator circuit, the harmonic balance equation including a first differential operator in a frequency domain of the input signal and a product of a differential operator in a second frequency domain of the oscillator and a frequency variable of the oscillator, wherein the frequency variable is independent of the frequency domain of the input signal;
• forming a Jacobian matrix for the driven oscillator circuit;
• forming a non-singular multitone phase noise vector (MPNV) for characterizing a phase noise in the driven oscillator circuit, wherein the multitone phase noise vector is based upon, at least in part, the Jacobian matrix and wherein the Jacobian matrix is an augmented Jacobian matrix including a static part and a dynamic part expressed in the frequency domain;
• and
• solving with the one or more computer processors the harmonic balance equation to obtain a waveform description of the driven oscillator circuit.

In a circuit simulation tool implemented in a computer system having one or more computer processors and a non-transitory computer-readable storage medium, a system for characterizing a driven oscillator circuit having an oscillator coupled to a time-varying input signal, the system comprising:

• means for retrieving from the non-transitory computer-readable storage medium information provided in a circuit description of the driven oscillator circuit;
• means for forming with one or more of the computer processors a frequency-domain harmonic balance equation for the driven oscillator circuit using the retrieved information provided in the circuit description of the driven oscillator circuit, the harmonic balance equation including a first differential operator in a frequency domain of the input signal and a product of a differential operator in a second frequency domain of the oscillator and a frequency variable of the oscillator, wherein the frequency variable is independent of the frequency domain of the input signal;
• means for forming a Jacobian matrix for the driven oscillator circuit;
• means for forming a non-singular multitone phase noise vector (MPNV) for characterizing a phase noise in the driven oscillator circuit, wherein the multitone phase noise vector is based upon, at least in part, the Jacobian matrix and wherein the Jacobian matrix is an augmented Jacobian matrix including a static part and a dynamic part expressed in the frequency domain;
• and
• means for solving with one or more of the computer processors the harmonic balance equation to obtain a waveform description of the driven oscillator circuit.