I am an older EE and I have used the old tried and true methods of circuit analysis like KVL, KCL and some Signal Flow Graph methods. Recently I have been reading about methods that were originally used for solving larger circuit analysis problems by computer methods using "state variable analysis".

I was reading in the textbook "Computer methods for circuit analysis and design" by Vlach, that "Since the disadvantages of state variable formulation far outweigh its advantages, it is no longer used in computer applicatons".

Is the above really true with respect to circuit analysis?

Before you say "just use pspice, etc" please remember that spice methods provide an answer to a specific problem without providing much "insight" into the circuit in question. Of course I have used spice for years after I have gained a fundamental understanding of what I really want the circuit to accomplish and how I need to implement it.

Thank You Tom


1 Answer 1


I assume that by the State Variable Formulation you mean dx/dt= Ax + Bu, where A is the state matrix and B is the input matrix.

The State Variable Formulation is not popular with programmers. For better or worse, a more popular circuit analysis method today is Modified Nodal Analysis, which is used in simulators.

The difference between these two approaches are confined to the details of how the matrix math is written. For lumped, linear elements, they all analyze the same state variables of the circuit. When these solvers work, they provide the same answers. The challenge is to write the matrix in a way that:

  • Is not too difficult to understand and create
  • Can be fed to a solver that provides useful solutions
  • \$\begingroup\$ Also formally known as State-space. We did not learn this for circuit analysis, however, we did learn it for use in control systems. I thought State Space was fairly knew though (introduced in the 1960s during the space programs and replaced transfer functions in control systems) so it doesn't seem to make sense to me how it fits into the circuit analysis timeline since I thought KVL and mesh analysis were much older than this, and still used. \$\endgroup\$
    – DKNguyen
    Commented Nov 24, 2019 at 7:44
  • \$\begingroup\$ Nodal and mesh analysis are still in use and still taught. They are not used much for general purpose computer simulations of large circuits, which is the topic of the question. Modified nodal is used instead because it can handle controlled sources, voltage and current sources all in the same formulation. \$\endgroup\$ Commented Apr 2, 2020 at 7:12

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