Method and apparatus for substantially improving the throughput of circuit simulators

An apparatus for modeling an operation of a periodic piece-wise linear system to a predetermined accuracy;

• comprising:
• first input means for accepting and setting up a specific topology for each switched subinterval occurring in each cycle of operation of the periodic piece-wise linear system;
• second input means for accepting an initial value of a state vector for the periodic piece-wise linear system at the beginning of a cycle of operation of the periodic piece-wise linear system;
• means for simulating a single cycle of operation of the periodic piece-wise linear system to obtain a final value of the state vector for the wise linear system to obtain a final value of the state vector for the periodic piece-wise linear system at the end of the cycle;
• means for comparing the initial and final values of the state vector to determine if a steady state operating condition has been achieved;
• wherein the improvement comprises;
• means for dividing each cycle into a plurality of subintervals for each switched subinterval of the periodic piece-wise linear system and computing a subinterval Jacobian matrix for each subinterval by computing a subinterval state transition matrix;
• and adding a correction square matrix to the subinterval state transition matrix to account for changes in subinterval time durations;
• means for computing a cycle Jacobian matrix by subtracting an identity matrix from a product of all computed subinterval Jacobian matrices;
• means for adjusting the value of the initial value of the state vector to a new value from the computed cycle Jacobian matrix through a truncated power-series procedure;
• means for repeating the above described opertions until the predetermined accuracy of steady state operation is achieved.

A method for simulating steady state operation of a periodic piece-wise switched linear system and where the switched linear system is modeled by k different switching topologies and the system being piece-wise linear in each individual topology, the method comprising the steps of:

• defining a cycle of operation of the switched system;
• defining k subintervals of the cycle in which different switched states in the switched linear system define a different system topology in the different subintervals;
• describing the system by a linear vector differential equation
• dx/dt=A.sub.k x+B.sub.k u
• and a linear vector algebraic equation
• Y=C.sub.k x+D.sub.k u
• for each of the k different topologies;
• selecting an initial state vector x.sub.i of the system for the beginning of a cycle of opertion of the system;
• simulating a single cycle of operation to calculate a final state vector x.sub.f of the system for the ending of a cycle of operation of the system;
• defining a change in the state vector over one switching cycle by defining the vector function
• F(x.sub.i)=x.sub.f -x.sub.i
• in terms of the initial state vector x.sub.i and the final state vector x.sub.f;
• wherein the improvement comprises:
• continuing with the following steps if x.sub.f does not equal x.sub.i:
• calculating an individual subinterval sensitivity matrix J.sub.k for each piece-wise linear subinterval of the cycle by computing a state transition matrix .omega.k(tk) and a correction square matrix r.sub.k and
• J.sub.k =.omega..sub.k (t.sub.k)+r.sub.k
• to account for variations in subinterval time durations;
• computing a steady-state Jacobian matrix J(x.sub.i) by the operation
• J(x.sub.i)=J.sub.k J.sub.k -1 . . . J.sub.2 J.sub.1 -I;
• correcting the value of the initial state vector x.sub.i by the j operation
• x.sub. <x.sub.i -[J(x.sub.i ].sup.-1 F(x.sub.i);
• repeating the above step of simulating s single cycle of operation to calculate a final state vector x.sub.f of the system and continuing subsequent steps until x.sub.f substantially equal x.sub.i.

A circuit simulator for modeling the cyclic steady state operation of a piece-wise linear closed loop regulated switching mode power circuit having a plurality of switched states in each cycle each of which define a different topology of the circuit each topology being operative within a separate subinterval of the cycle, composing:

• a first input device for accepting values of the circuit system parameters,
• a second input device for accepting an initial value of a state vector for the circuit system at the beginning of a cycle of operation,
• a circuit system processor set up in the separate subintervals for the circuit system topologies of each separate subinterval whose operation is to be simulated over a cycle of operation, including;
• a steady state simulator operative for simulating steady state operation of the circuit system and for calculating a final state vector at an end of one periodic cycle of opertion of the circuit system, and having;
• means for computing a subinterval Jacobian matrix for each separate subinterval of the cycle by computing a subinterval state transition matrix;
• and adding a correction square matrix to the subinterval state transition matrix to account for changes in subinterval time durations;
• means for computing a cycle Jacobian matrix by subtracting an identity matrix from a product of all computed subinterval Jacobian matrices;
• a comparator for comparing the initial state vector and the final state vector as a means of determining if steady state simulation has been achieved,
• means for adjusting the value of the initial value of the state vector to a new value from the computed cycle Jacobian matrix through a truncated power-series precedure and applying the new value to simulate anew a cycle of operation of the circuit system.