https://github.com/ttwag/p12_spice_simulator

A SPICE-like circuit simulator
https://github.com/ttwag/p12_spice_simulator

Last synced: 9 days ago
JSON representation

A SPICE-like circuit simulator

• Host: GitHub
• URL: https://github.com/ttwag/p12_spice_simulator
• Owner: ttwag
• Created: 2024-08-17T20:26:43.000Z (3 months ago)
• Default Branch: main
• Last Pushed: 2024-09-16T18:29:18.000Z (about 2 months ago)
• Last Synced: 2024-09-16T22:55:10.920Z (about 2 months ago)
• Language: Python
• Size: 33.2 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

        
# P12_Circuit_Simulator

 A SPICE-like circuit simulator.

## Circuit Notation

For a circuit with n nodes and m voltage sources and k independent current source:

| Circuit Component | Symbol |

| --:|--:|

| Ground | 0 |

| Node | 1 $\to$ n |

| Nodal Voltage | v_1 $\to$ v_n |

| Independent Voltage Source | V1 $\to$ Vm |

| Current through Independent Voltage Source | i_1 $\to$ i_m|

| Independent Current Source | I1 $\to$ Ik |

## Modified Nodal Analysis (MNA)

MNA will reduce circuits that only have passive components and independent voltage or current sources into the form:

$$\mathbf{Ax} = \mathbf{z}$$

For a circuit with n nodes and m voltage sources:

### $\mathbf{A}$ matrix

* Size: $(n + m) \times (n + m)$

* Contains **4 sub-matrices**: the conductance matrix ($\mathbf{G}$), the voltage source matrices ($\mathbf{B}$ and $\mathbf{C}$), and the dependent source matrix ($\mathbf{D}$).

$$

\begin{bmatrix}

\mathbf{G} &  \mathbf{B}\\

\mathbf{C} & \mathbf{D} \\

\end{bmatrix}

$$

* The $\mathbf{G}$ matrix:

    * Size: $(n \times n)$

    * Each diagonal term is equal to the sum of the conductance of elements connected to the corresponding node. EX: The first diagonal term is the sum of conductances connected to node 1.

    * Each off-diagonal term is the negative conductance of the element connected to the pair of corresponding nodes. EX: A resistor connected to nodes 2 and 3 will go into $\mathbf{G}$ matrix position (2, 3) and (3, 2).

* The $\mathbf{B}$ matrix 

    * Size: $(n \times m)$

    * Contains only the value, -1, 0, 1.

    * If the nth node is connected to the mth voltage source's positive terminal, then the element at (n, m) is 1.

    * If the nth node is connected to the mth voltage source's negative terminal, then the element at (n, m) is -1.

    * Otherwise, the entry is 0.

    

* The $\mathbf{C}$ matrix

    * $(m \times n)$

    * Transpose of the $\mathbf{B}$ matrix.

* The $\mathbf{D}$ matrix

    * $(m \times m)$

    * Contains all 0.

### $\mathbf{x}$ vector

* Size: $(n + m) \times 1$

* Contains **2 vectors**: $\mathbf{v}$ and $\mathbf{j}$

$$

\mathbf{x} = 

\begin{bmatrix}

\mathbf{v} \\

\mathbf{j} \\

\end{bmatrix}

$$

* The $\mathbf{v}$ vector

    * Each entry of the vector is the node voltage of the nth node (No entry for ground, node 0).

    * EX: 

    

$$

\mathbf{v} = 

\begin{bmatrix}

v_1 \\

\vdots\\

v_n \\

\end{bmatrix}

$$

* The $\mathbf{j}$ vector 

    * Each entry of the vector is the current flowing into the mth voltage source.

    * EX: 

    

$$

\mathbf{j} = 

\begin{bmatrix}

\ i_1 \\

\ \vdots\\

\ i_m \\

\end{bmatrix}

$$

### $\mathbf{z}$ vector:

* Size: $(n + m) \times 1$

* Contains **2 vectors**: $\mathbf{i}$ and $\mathbf{e}$

$$

\mathbf{z} = 

\begin{bmatrix}

\mathbf{i} \\

\mathbf{e} \\

\end{bmatrix}

$$

* The $\mathbf{i}$ vector

    * Size: $(n \times 1)$

    * The nth element is the sum of the current source into the nth node (Node 0 isn't included). If no current source is connected to the nth node, (n, 1) = 0.

 * The $\mathbf{e}$ vector

    * Size: $(m \times 1)$

    * The mth entry contains the value of the mth voltage source