Artificial parameter homotopy methods for the dc operating point problem

A simulation method executed by a computer for simulating the operation of a circuit comprising the steps of:

• forming in a computer a circuit design of said circuit with a set of equations, F(x)=0 which corresponds to F.sub.1 (x)=0, F.sub.2 (x)=0, F.sub.3 (x)=0 . . . F.sub.i (x)=0 where each F(x)=0 represents the current relationship at node i of the circuit, x is the set of node voltages of the circuit, and F(x) represents the function that relates the node voltages to the currents at node i, with that function accepting nonlinearities that have a defined and continuous first and second derivative at all values of interest of the voltages x,
• developing in a computer a representation of a modified circuit design that includes a normalized control parameter, t, G(x,t)=G.sub.1 (x,t)+G.sub.2 (x,t), where F.sub.2 (x,1)=F(x) and where G.sub.1 (x,0) is a modified representation of said circuit that allows for simplified determination of voltages x that satisfy the relationship G.sub.1 (x,0,a)=0 and where a is a set of randomizing parameters that are selected to prevent bifurcation points in the trajectory of dc operating point of the modified circuit as a function of the control parameter, t;
• setting said control parameter to 0 and evaluating the dc operating state of said modified circuit, corresponding to G(x,1)=0;
• modifying said control parameter by a step size of preselected magnitude, in a direction of transforming said modified circuit to its original configuration, F(x);
• determining the dc operating point of said modified circuit;
• returning to said step of modifying said control parameter at least as long as said control parameter has not reached the level 1;
• and
• outputting said circuit design when the control parameter has reached the level 1.

A method for manufacturing a circuit comprising the steps of:

• creating a design of said circuit;
• verifying said design of the circuit against a selected set of criteria to form a verified circuit design;
• and
• manufacturing the circuit in accordance with said verified circuit design,
• wherein said step of verifying said design of the circuit includes the steps of
• forming a circuit description of said circuit with a set of equations, F(x)=0 which corresponds to F.sub.1 (x)=0, F.sub.2 (x)=0, F.sub.3 (x)=0 . . . F.sub.i (x)=0 where each F(x)=0 represents the current relationship at node i of the circuit, x is the set of node voltages of the circuit, and F(x) represents the function that relates the node voltages to the currents at node i, with that function accepting nonlinearities that have a defined and continuous first and second derivative at all values of interest of the voltages x,
• developing a representation of a modified circuit that includes a normalized control parameter, t, G(x,t,a)=G.sub.1 (x,t,a)+G.sub.2 (x,t), where G.sub.2 (x,1)=F(x) and where G.sub.1 (x,0,a) is a modified representation of said circuit that allows for simplified determination of voltages x that satisfy the relationship F.sub.1 (x,0,a)=0 and where a is a set of randomizing parameters that are selected to prevent bifurcation points in the trajectory of dc operating point of the modified circuit as a function of the control parameter, t;
• setting said control parameter to 0 and evaluating the dc operating state of said modified circuit, corresponding to G(x,t)=0;
• modifying said control parameter by a step size of preselected magnitude, in a direction of transforming said modified circuit to its original configuration, F(x);
• determing the dc operating point of said modified circuit;
• and
• returning to said step of modifying said control parameter at least as long as said control parameter has not reached the level 1.