⚡ Circuit Analyzer

An interactive desktop simulator for linear electric circuits based on the Laplace transform.

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📖 Description

Circuit Analyzer is a Python desktop application that bridges the gap between circuit theory and hands-on analysis. It lets you draw an electrical schematic using a drag-and-drop interface, then automatically derives symbolic equations in the operator (Laplace) domain, computes numerical values, and plots transient responses — all without manual algebraic manipulation.

Why does it exist? Analyzing RLC circuits with inductors, capacitors, and resistors by hand requires solving systems of integro-differential equations, which is tedious and error-prone. Circuit Analyzer automates exactly that pipeline:

1. Build a schematic visually.
2. Get symbolic equations in the Laplace domain instantly.
3. Evaluate any variable numerically at a chosen moment in time.
4. Plot the full transient waveform.

How it works under the hood: The solver uses Modified Nodal Analysis (MNA) in operator form — the same method used by industrial SPICE simulators. Passive elements are replaced by their operator impedances (R, Lp, 1/Cp), and the resulting matrix equation A(p)·X(p) = Z(p) is solved symbolically via SymPy. The inverse Laplace transform is then applied analytically (where possible) or numerically via FFT-based methods to recover the time-domain signal.

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🎯 Usage Examples

🔋 Scenario 1 — Simple RLC Series Circuit

Place a Voltage Source, Resistor, Inductor, and Capacitor in series. Hit Analyse to get the symbolic expression for current I(p) and plot the transient response showing whether the circuit is over-, under-, or critically damped.

🔀 Scenario 2 — Parallel RC Branch

Connect a capacitor and resistor in parallel, driven by a constant EMF through an inductor. The tool computes node voltages and branch currents symbolically, verifies Kirchhoff's laws automatically, and outputs expressions ready for further analysis.

〰️ Scenario 3 — Sinusoidal Source & Switch

Use an AC voltage source with configurable amplitude A, angular frequency ω, and phase φ. Toggle a switch (modelled as a near-zero / near-infinite resistance) to simulate circuit make/break events and observe the resulting transient current waveform.

📐 Scenario 4 — Two-Loop Mutual Circuit

Build a two-loop circuit with shared reactive elements (as in classical textbook problems). The MNA engine handles the coupled equations automatically and returns individual loop currents as rational functions of p.

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🚀 Installation & Usage

Prerequisites

• Python 3.9+
• pip

1. Clone the repository

git clone https://github.com/Ulaykss/Circuit-Analyzer.git
cd Circuit-Analyzer

2. Install dependencies

pip install -r requirements.txt

Key packages: PyQt5, sympy, numpy, matplotlib.

3. Run the application

cd src
python main.py

Or, on Windows, run the pre-built executable:

dist/main.exe

4. Build a circuit & analyse

1. Drag components from the left panel onto the canvas.
2. Right-click a component to rotate, flip, or edit its properties.
3. Draw wires by dragging from one terminal (green dot) to another.
4. Open Settings → Voltage Source Type to choose DC or AC.
5. Click Analyse in the toolbar.
6. Switch between the Symbolic Analysis, Numerical Analysis, and Graphs tabs on the right panel.

🎬 Demo Video

demo.mp4

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🛠️ Technologies Used

Technology	Role
Python 3.9+	Core language
PyQt5	GUI framework (canvas, dialogs, event loop)
SymPy	Symbolic algebra, LU solve, inverse Laplace transform
NumPy	Numerical arrays, FFT-based inverse Laplace
Matplotlib	Transient waveform plots embedded in Qt
JSON	.circuit file format for saving/loading schematics
Union-Find (DSU)	Netlist topology construction
MNA (Modified Nodal Analysis)	Core circuit equation assembly

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✅ Validation

The symbolic results produced by Circuit Analyzer have been verified against analytical solutions from classical electrical engineering problems:

• Example 1 (RLC series, DC source): The operator expression for source current I_E1 matches the hand-derived result exactly (up to a common factor of C₁ before simplification).
• Task №70 (RL circuit, sinusoidal source with switch): The program outputs a generalized expression valid for arbitrary switch resistance K₁. Taking the limit K₁ → ∞ (open switch) reproduces the textbook formula identically:

$$i(p) = \frac{u_0(\omega\cos\psi + p\sin\psi)}{(p^2 + \omega^2)(Lp + R_1 + R_2)}$$

Both cases confirm that the MNA engine, symbolic solver, and operator-form source models work correctly.

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⚠️ Known Limitations & Contribution Ideas

The project is functional but has room for improvement. Here are concrete areas where your contribution would be welcome:

🐢 Performance

• Python's interpreted nature makes analysis of complex multi-loop circuits noticeably slow.
• Idea: Implement the MNA matrix assembly and LU solver as a native shared library (dll / .so) in C or C++, called from Python via ctypes or cffi. This could yield a 10–100× speedup for large netlists.

🔢 Numerical inverse Laplace

• The current FFT-based method (Tallon–Stieltjes) can be inaccurate for stiff systems or very long time windows.
• Idea: Integrate the Weeks method or de Hoog algorithm for more robust numerical inversion.

📦 Component library

• Currently supports R, L, C, voltage source, and switch only.
• Idea: Add current sources, dependent sources (VCVS, CCCS), transformers, and transmission lines.

💾 Export

• Simulation results cannot be saved.
• Idea: Add export to CSV / PDF report, and SPICE netlist export for cross-validation with LTspice.

🧪 Unit tests

• The codebase lacks automated tests.
• Idea: Add a tests/ directory with pytest cases covering netlist construction, MNA stamping, and known analytical solutions.

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📄 License

This project is licensed under the MIT License — see the LICENSE file for details.

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👤 Authors & Contacts

Yaroslav Obukhov — developer, author of the bachelor's thesis underlying this project.

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Made with ❤️ and lots of Laplace transforms  ·  Irkutsk State University, 2026