Electronic Circuit Simulation - Static Analysis Implementation (part 3) [Python] by drifter1

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Electronic Circuit Simulation - Static Analysis Implementation (part 3) [Python]
<html>
https://i.postimg.cc/3rpy62Ww/circuit-sim-series.jpg<br>
[Custom Thumbnail]<br>
All the Code of the series can be found at the <strong>Github repository</strong>:
https://github.com/drifter1/circuitsim
<hr>
<h1>Introduction</h1>&nbsp;&nbsp;&nbsp;&nbsp;Hello it's a me again @drifter1! Today we continue with the <strong>Electronic Circuit Simulation series</strong>, a tutorial series where we will be implementing a full-on electronic circuit simulator (like SPICE) studying the whole concept and mainly physics behind it! In this article we continue with the <strong>Implementation of a complete simulator for Static Analysis</strong>. In this third and final step we will loop through the components list of the last article(s) to fill the MNA Matrices and solve the MNA System...
<h2>Requirements:</h2>
<ul>
<li>Physics and more specifically <strong>Electromagnetism Knowledge</strong></li>
<li>Knowing <strong>how to solve Linear Systems</strong> using Linear Algebra</li>
<li>Some understanding of the <strong>Programming Language Python</strong></li>
</ul>
<h2>Difficulty:</h2>Talking about the <strong>series in general</strong> this series can be rated:
<ul><li>Intermediate to Advanced</li></ul>
<strong>Today's topic(s)</strong> can be rated:
<ul><li>Intermediate</li></ul>
<hr>
<h1>Actual Tutorial Content</h1>
<h2>Fill MNA Matrices</h2>&nbsp;&nbsp;&nbsp;&nbsp;In the <strong>Modified Nodal Analysis</strong> (MNA) articles I talked you through the whole mathematics that give us the linear system, which <strong>solves Electronic Circuits for Node potentials and currents through Group 2 components</strong>. The final linear system that we got for Static Analysis is:<br>
<img src="https://steemitimages.com/640x0/https://quicklatex.com/cache3/66/ql_332e2ef426bbb259ea8cb0faacaf4966_l3.png"><br><br>
As we showed in this article, the <strong>A-matrix</strong> contains 4 matrices:<br>
<ul>
<li><strong>G</strong> β†’ Conductance matrix:</li>
<ul>
<li>each line and row corresponds to a specific node</li>
<li>diagonal is positive and containing the total "self" conductance of each node</li>
<li>the non-diagonal are negative and containing the mutual conductance between nodes</li>
</ul>
<li><strong>B</strong> β†’ Group 2 component incidence matrix:</li>
<ul>
<li>each column corresponds to a specific Group 2 component (voltage source)</li>
<li>'1' when node connected to '+' pole, '-1' when node connected to '-' pole and '0' when not incident</li>
</ul>
<li><strong>C</strong> β†’ Transpose of B</li>
<li><strong>D</strong> β†’ All-zero when only independent sources are considered</li>
</ul><br>
&nbsp;&nbsp;&nbsp;&nbsp;The <strong>b-matrix</strong> on the other hand contains the constant output of all independent sources (current and voltage), with the current values following the logic:<br>
<ul>
<li>positive when entering the node</li>
<li>negative when leaving the node</li>
</ul>
<h3>FIlling Procedure</h3>In our Code we will have to:<br>
<ol>
<li><strong>Calculate</strong> the number of Group 2 components and the Matrix size</li>
<li><strong>Define the matrices</strong> as numpy arrays (A is two-dimensional, b is one-dimensional)</li>
<li><strong>Define a variable that keeps track of the current Group 2 component index</strong> to help us fill the correct spot in the Matrices</li>
<li><strong>Loop through all the components</strong> and <strong>fill the Matrices</strong> depending on their type:</li>
<ul>
<li>Resistance affect the G-matrix of A</li>
<li>Capacitance is an open circuit in Static Analysis</li>
<li>Inductance works like an closed circuit with 0 resistance and 0 voltage affecting the B and C matrices of A and the b-matrix with a value of '0'</li>
<li>Voltage sources affect the B and C matrices of A and the b-matrix with their value</li>
<li>Current sources only affect the b-matrix with negative impact on the high node and negative impact on the low node</li>
</ul>
</ol>
<h3>Python Code</h3>The Code looks like this:<br>
<pre><code>def <strong>calculateMatrices</strong>(components, nodeCount):<br>
    # use global scope variables for component counts
    global voltageCount, inductorCount<br>
    # <strong>calculate g2 components</strong>
    g2Count = voltageCount + inductorCount
    print("Group 2 count:", g2Count)<br>
    # <strong>calculate matrix size</strong>
    matrixSize = nodeCount + g2Count - 1
    print("Matrix size:", matrixSize, "\n")<br>
    # <strong>define Matrices</strong>
    A = np.zeros((matrixSize, matrixSize))
    b = np.zeros(matrixSize)<br>
    # <strong>Group 2 component index</strong>
    g2Index = matrixSize - g2Count<br>
    # <strong>loop through all components</strong>
    for component in components:
        # store component info in temporary variable
        high = component.high
        low = component.low
        value = component.value<br>
        if <strong>component.comp_type == 'R'</strong>:
            # affects G-matrix of A
            # diagonal self-conductance of node
            if high != 0:
                A[high - 1][high - 1] = A[high - 1][high - 1] + 1/value
            if low != 0:
                A[low - 1][low - 1] = A[low - 1][low - 1] + 1/value<br>
            # mutual conductance between nodes
            if high != 0 and low != 0:
                A[high - 1][low - 1] = A[high - 1][low - 1] - 1/value
                A[low - 1][high - 1] = A[low - 1][high - 1] - 1/value<br>
        # elif <strong>component.comp_type == 'C'</strong>:
            # Capacitance is an open circuit for Static Analysis<br>
        elif <strong>component.comp_type == 'L'</strong>:
            # closed circuit  in Static Analysis: 0 resistance and 0 voltage
            # affects the B and C matrices of A
            if high != 0:
                A[high - 1][g2Index] = A[high - 1][g2Index] + 1
                A[g2Index][high - 1] = A[g2Index][high - 1] + 1
            if low != 0:
                A[low - 1][g2Index] = A[low - 1][g2Index] - 1
                A[g2Index][low - 1] = A[g2Index][low - 1] - 1<br>
            # affects b-matrix
            b[g2Index] = 0<br>
            # increase G2 index
            g2Index = g2Index + 1<br>
        elif <strong>component.comp_type == 'V'</strong>:
            # affects the B and C matrices of A
            if high != 0:
                A[high - 1][g2Index] = A[high - 1][g2Index] + 1
                A[g2Index][high - 1] = A[g2Index][high - 1] + 1
            if low != 0:
                A[low - 1][g2Index] = A[low - 1][g2Index] - 1
                A[g2Index][low - 1] = A[g2Index][low - 1] - 1<br>
            # affects b-matrix
            b[g2Index] = value<br>
            # increase G2 counter
            g2Index = g2Index + 1<br>
        elif <strong>component.comp_type == 'I'</strong>:
            # affects b-matrix
            if high != 0:
                b[high - 1] = b[high - 1] - value
            if low != 0:
                b[low - 1] = b[low - 1] + value<br>
    return A, b</code></pre>
<br>
Don't forget to <strong>import the numpy library</strong> using:<br>
<pre><code>import numpy as np</code></pre>
<hr>
<h2>Solve MNA System</h2>&nbsp;&nbsp;&nbsp;&nbsp;To solve the MNA System we basically only have to call the "np.linalg.solve()" function. So, the <strong>Code</strong> for solving is:<br>
<pre><code>def solveSystem(A, b):
    x = np.linalg.solve(A, b)
    return x</code></pre>
<br>
Let's tweak the <strong>main function</strong> from last time...<br>
<pre><code># Initialize component counters
voltageCount = 0
currentCount = 0
resistorCount = 0
capacitorCount = 0
inductorCount = 0<br>
# Parse File
fileName = "example.spice"
print("Parsing file...\n")
components = parseFile(fileName)<br>
# Map nodes
print("Mapping nodes...\n")
components, hashtable = mapNodes(components)<br>
# Print Information
print("Circuit Info")
print("Component count: ", len(components))
print("Voltage count: ", voltageCount)
print("Current count: ", currentCount)
print("Resistance count: ", resistorCount)
print("Capacitance count: ", capacitorCount)
print("Inductance count: ", inductorCount)
print("Node count: ", hashtable.nodeCount)<br>
print("\nNodes are mapped as following:")
for key, val in hashtable.nodes.items():
    print("\"" + key + "\" :", val)<br>
print("\nCircuit Components:")
for i in range(0, len(components)):
    print(components[i])<br>
# Calculate and solve system
print("\nCalculating MNA Matrices...\n")
A, b = calculateMatrices(components, hashtable.nodeCount)
print("A:\n", A)
print("b:\n", b)<br>
print("\nSolving System...\n")
x = solveSystem(A, b)
print("x:\n", x)</code></pre>
<br>
&nbsp;&nbsp;&nbsp;&nbsp;The numpy arrays are printed out with maximum precision and scientific notation. To get rid of it and make them print out in a more"pretty" way, let's define the following <strong>print options</strong>:<br>
<pre><code>np.set_printoptions(precision=3, suppress=True)</code></pre>
<hr>
<h2>Running the Examples</h2>
<h3>Simple Example</h3>Suppose the simple circuit (that we used way to often):<br>
<img src="https://steemitimages.com/640x0/https://i.postimg.cc/rwDXGXsG/Untitled-1.jpg"><br><br>
Running our simulator for this simple example we get:<br>
<img src="https://i.postimg.cc/BZp9BcKF/image.png"><br><br>
&nbsp;&nbsp;&nbsp;&nbsp;You can see that the system got filled with the same values that we found in the article <a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-modified-nodal-analysis-part-2-python">Modified Nodal Analysis (part 2)</a>, which was:<br>
<img src="https://steemitimages.com/640x0/https://quicklatex.com/cache3/f6/ql_2a03bbd062a53d2b4ae667bf91d417f6_l3.png"><br><br>
&nbsp;&nbsp;&nbsp;&nbsp;Of course it also gives us the same solution that we got with "manual" Code! Having the same exact order in the solution was just random luck, as the <strong>nodes could have been mapped way differently</strong> giving us a mixed up solution! That's exactly what happens in more advanced circuits...
<h3>Advanced Circuit 1</h3>Running our simulator for the first Netlist of the previous article we get:<br>
<img src="https://i.postimg.cc/k5KL6xCB/image.png"><br>
<img src="https://i.postimg.cc/pTB7kRpv/image.png">
<h3>Advanced Circuit 2</h3>Running our simulator for the second Netlist of the previous article we get:<br>
<img src="https://i.postimg.cc/65qSLsws/image.png"><br>
<img src="https://i.postimg.cc/cJybSr3Z/image.png"><br><br>
The last two circuits would take much more time to solve "by hand"!<br><br>
&nbsp;&nbsp;&nbsp;&nbsp;And with that we are actually finished with the Implementation for Static Analysis, or are we? Well, the <strong>A matrix contains lots of zeros</strong> and so we are not really that memory optimized right now. To optimize our simulator we can use a so called <strong>Sparse matrix to store the two-dimensional array A</strong>, which is exactly what we will be doing next time!
<hr>
<h2>RESOURCES</h2>
<h3>References:</h3>
<ol>
<li>https://www.geeksforgeeks.org/python-numpy/</li>
</ol>
<br>
Mathematical Equations were made using <a href="https://www.quicklatex.com/">quicklatex</a>
<hr>
<h2>Previous parts of the series</h2>
<h3>Introduction and Electromagnetism Background</h3>
<ul>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-introduction-python">Introduction</a></li>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-electromagnetism-background-part-1-python">Electromagnetism Background (part 1)</a></li>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-electromagnetism-background-part-2-python">Electromagnetism Background (part 2)</a></li>
</ul>
<h3>Mesh and Nodal Analysis</h3>
<ul>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-mesh-analysis-python">Mesh Analysis</a></li>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-nodal-analysis-python">Nodal Analysis</a></li>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-modified-mesh-analysis-by-inspection-python">Modified Mesh Analysis by Inspection</a></li>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-modified-nodal-analysis-by-inspection-python">Modified Nodal Analysis by Inspection</a></li>
</ul>
<h3>Modified Nodal Analysis</h3>
<ul>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-incidence-matrix-and-modified-kirchhoff-laws-python">Incidence Matrix and Modified Kirchhoff Laws</a></li>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-modified-nodal-analysis-part-1-python">Modified Nodal Analysis (part 1)</a></li>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-modified-nodal-analysis-part-2-python">Modified Nodal Analysis (part 2)</a></li>
</ul>
<h3>Static Analysis</h3>
<ul>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-static-analysis-implementation-part-1-python">Static Analysis Implementation (part 1)</a></li>
<li><a href="https://steemit.com/utopian-io/@drifter1/electronic-circuit-simulation-static-analysis-implementation-part-2-python">Static Analysis Implementation (part 2)</a></li>
</ul>
<hr>
<h2>Final words | Next up on the project</h2>&nbsp;&nbsp;&nbsp;&nbsp;And this is actually it for today's post and I hope that you enjoyed it!<br><br>
&nbsp;&nbsp;&nbsp;&nbsp;Next time we will talk about Sparse Matrices, which will be used to optimize our Simulator for Memory, as we will not store 0 values anymore...<br><br>
So, see ya next time!
<hr>
<h2>GitHub Account:</h2>
https://github.com/drifter1<br>
https://steemitimages.com/0x0/https://media.giphy.com/media/ybITzMzIyabIs/giphy.gif
<br>
Keep on drifting! ;)
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