Patent ID: 7332974

Claim:
A computer-implemented method of computing a steady state of a voltage controlled oscillator, the method comprising the steps of: generating a set of one or more differential algebraic equations representative of the of an electronic circuit, for analysis of the voltage controlled oscillator, the set of one or more differential algebraic equations including a known period or a known frequency of oscillation of the voltage controlled oscillator and an unknown control voltage of the voltage controlled oscillator that generates the period or the frequency of oscillation; modifying the set of one or more differential algebraic equations to obtain a set of one or more matrix equations corresponding to the differential algebraic equations; and obtaining a solution to the set of one or more matrix equations using a Krylov subspace method, the solution including the control voltage of the voltage controlled oscillator in steady state, wherein the set of one or more differential algebraic equations is in the form of: ⅆ q ⁡ ( x ) ⅆ t + f ⁡ ( x ) + b + ce = 0 , where x represents a steady state solution, t represents time, q(x) and f(x) represent parameters of the voltage controlled oscillator that are functions of the steady state solution, b represents an independent source of the voltage controlled oscillator except a control source, and ce represents the control source of the voltage controlled oscillator wherein c is a control voltage scalar and e is a vector with one or two nonzero entries that are either 1 or −1.