Modified Nodal Analysis Algorithm for real-time audio

This repository is just the implementation of the Modified Nodal Analysis for transient analysis of electronic circuit. This is a work in progress. At present, only linear components such as resistors, capacitors and inductors are supported. The aim is to create a functional program capable of loading a netlist in the form of a .txt file, where all the components of the circuit are referenced by their node connections, their values/caracteristics (Ohms, henrys, Farads...), and to simulate the behavior of the circuit for any input signal, and any location where we want to know the output voltage or current.

Documentation

The Modified Nodal Analysis Algorithm (MNA) is quite well documented over different books/papers as the following ones :

• Laurence W. Nagel - SPICE2: A computer program to simulate semiconductor circuits
• Lawrence T. Pillage, Ronald A. Rohrer, Chandramouli Visweswariah - Electronic Ciruit And System Simulation Methods
• Stefan Jahn, Michael Margraf, Vincent Habchi, Raimund Jacob - QUCS Technical Papers

Prerequisites

If you want to test/build this implementation, you will need to have:

• the Juce framework
• the Eigen library to perform linear algebra and matrix operations

Under the hood of the algorithm (from QUCS technical papers)

Many different kinds of network element are encountered in network analysis. For circuit analysis it is necessary to formulate equations for circuits containing as many different types of network elements as possible. There are various methods for equation formulation for a circuit. These are based on three types of equations found in circuit theory:

• equations based on Kirchhoff’s voltage law (KVL)
• equations based on Kirchhoff’s current law (KCL)
• branch constitutive equations

The equations have to be formulated (represented in a computer program) automatically in a simple, comprehensive manner. Once formulated, the system of equations has to be solved. There are two main aspects to be considered when choosing algorithms for this purpose: accuracy and speed. The MNA, has been proved to accomplish these tasks. MNA applied to a circuit with passive elements, independent current and voltage sources and active elements results in a matrix equation (linear system) of the form:

$$\mathbf{A}\cdot\mathbf{x} = \mathbf{b},$$

where $\mathbf{A}$ is a square Matrix, and where $\mathbf{x}$ and $\mathbf{b}$ are 1D column vectors (the way that both matrix and vectors are filled is really well documented in both 3 books that are referenced just above). The circuit can therefore be solved by a simple matrix manipulation:

$$\mathbf{x} = \mathbf{A}^{-1}\mathbf{b}$$

or LU decomposition for example. Though this may be difficult by hand, it is straightforward and so is easily done by computer.

Actually, this program use LU decomposition instead of computing the inverse as the computationnal cost to perform the LU decomposition is lower.