In a circuit simulation tool in a computer system having one or more computer processors and computer-readable storage, a method for characterizing a driven oscillator circuit having an oscillator coupled to a time-varying input signal includes retrieving information provided in a circuit description of the oscillator circuit. The method also includes forming a frequency-domain harmonic balance equation for the oscillator circuit using the retrieved information provided in the circuit description of the oscillator circuit. The harmonic balance equation includes 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. The frequency variable is independent of the frequency domain of the input signal. The method further includes solving the harmonic balance equation to obtain a waveform description of the oscillator circuit.