The rules for modified nodal analysis are given by: Consider the circuit shown below (Step 1 has already been applied) Apply step 2 (currents through the voltage sources with current from positive node to negative node): Apply step 3 (with positive currents out of the node): Apply step 4: Apply step 5: or Now all that is left is to solve the 5x5 set of equations (recall that the nodal analysis method resulted in just 1 equation, though we did some substitutions along the way).
Solving the 5x5 equation is difficult by hand, but not so with a computer.
Note also that the matrix size is 5x5 (in general (m n)(m n)).
For all of the circuits we will analyze (i.e., only passive elements and independent sources), these general observations about the A matrix will always hold.
MNA applied to a circuit with only passive elements (resistors) and independent current and voltage sources results in a matrix equation of the form: For a circuit with n nodes and m independent voltage sources: The circuit is solved by a simple matrix manipulation: Though this may be difficult by hand, it is straightforward and so is easily done by computer.