Symbolic linear circuit analysis
Project description
Lcapy is a Python package for linear circuit analysis. It uses SymPy for symbolic mathematics.
Lcapy can symbolically analyse circuits described with netlists or by series/parallel combinations of components. It can also manipulate continuoustime and discrettime expressions.
Comprehensive documentation can be found at https://lcapy.readthedocs.io/en/latest/
Circuit analysis
The circuit is described using netlists, similar to SPICE, with arbitrary node names (except for the ground node which is labelled 0). The netlists can be loaded from a file or created at runtime. For example:
>>> from lcapy import Circuit, s, t
>>> cct = Circuit("""
... Vs 2 0 {5 * u(t)}
... Ra 2 1
... Rb 1 0
... """)
The circuit can then be interrogated to determine branch currents, branch voltages, and node voltages (with respect to the ground node 0). For example:
>>> cct[1].V(t)
5⋅R_b⋅u(t)
──────────
Rₐ + R_b
>>> cct.Ra.I(t)
5⋅u(t)
────────
Rₐ + R_b
>>> cct.Ra.V(s)
5⋅Rₐ
────────────
s⋅(Rₐ + R_b)
Oneport networks
Oneport networks can be created by series and parallel combinations of other oneport networks. The primitive oneport networks are the following ideal components:
 V independent voltage source
 I independent current source
 R resistor
 C capacitor
 L inductor
These components are converted to sdomain models and so capacitor and inductor components can be specified with initial voltage and currents, respectively, to model transient responses.
The components have the following attributes:
 Zoc opencircuit impedance
 Ysc shortcircuit admittance
 Voc opencircuit voltage
 Isc shortcircuit current
The component values can be specified numerically or symbolically using strings, for example,
>>> from lcapy import Vdc, R, L, C, s, t
>>> R1 = R('R_1')
>>> L1 = L('L_1')
>>> a = Vdc(10) + R1 + L1
Here a is the name of the network formed with a 10 V DC voltage source in series with R1 and L1.
The sdomain open circuit voltage across the network can be printed with:
>>> a.V(s)
10/s
The time domain open circuit voltage is given by:
>>> a.V(t)
10
The sdomain short circuit current through the network can be printed with:
>>> a.Isc(s)
10/(L_1*s**2 + R_1*s)
The time domain short circuit current is given by:
>>> a.Isc(t)
10/R_1
If you want units displayed:
>>> state.show_units=True
>>> a.Isc(t)
10/R_1.A
Twoport networks
Oneport networks can be combined to form twoport networks. Methods are provided to determine transfer responses between the ports.
Here's an example of creating a voltage divider (L section)
>>> from lcapy import *
>>> a = LSection(R('R_1'), R('R_2'))
Limitations

Nonlinear components cannot be modelled (apart from a linearisation around a bias point).

High order systems can go crazy.

Some twoports generate singular matrices.
Schematics
LaTeX schematics can be generated using circuitikz from the netlist. Additional drawing hints, such as direction and size are required.
>>> from lcapy import Circuit
>>> cct = Circuit("""
... P1 1 0; down
... R1 1 3; right
... L1 3 2; right
... C1 3 0_1; down
... P2 2 0_2; down
... W 0 0_1; right
... W 0_1 0_2; right""")
>>> cct.draw(filename='pic.tex')
In this example, P denotes a port (opencircuit) and W denotes a wire (shortcircuit). The drawing hints are separated from the netlist arguments by a semicolon. They are a comma separated list of keyvalue pairs except for directions where the dir keyword is optional. The symbol label can be changed using the l keyword; the voltage and current labels are specified with the v and i keywords. For example,
>>> from lcapy import Circuit
>>> cct = Circuit("""
... V1 1 0; down
... R1 1 2; left=2, i=I_1, v=V_{R_1}
... R2 1 3; right=2, i=I_2, v=V_{R_2}
... L1 2 0_1; down, i=I_1, v=V_{L_1}
... L2 3 0_3; down, i=I_1, v=V_{L_2}
... W 0 0_3; right
... W 0 0_1; left""")
>>> cct.draw(scale=3, filename='pic2.svg')
The drawing direction is with respect to the positive node; i.e., the drawing is performed from the positive to the negative node. Since lower voltages are usually lower in a schematic, then the direction of voltage sources and ports is usually down.
By default, component (and current) labels are drawn above horizontal components and to the right of vertical components. Voltage labels are drawn below horizontal components and to the left of vertical components.
Node names containing a dot or underscore are not displayed.
Jupyter notebooks
Lcapy can be used with Jupyter Notebooks. For a number of examples see https://github.com/mph/lcapy/tree/master/doc/examples/notebooks . These include:
Documentation
For comprehensive documentation, see http://lcapy.readthedocs.io/en/latest (alternatively, the documentation can be viewed in a web browser after running 'make doc' in the toplevel directory).
For release notes see http://lcapy.readthedocs.io/en/latest/releases.html
For another view on Lcapy see https://blog.ouseful.info/2018/08/07/aneasierapproachtoelectricalcircuitdiagramgenerationlcapy/
Citation
To cite Lcapy in publications use
Hayes M. 2022. Lcapy: symbolic linear circuit analysis with Python. PeerJ Computer Science 8:e875 https://doi.org/10.7717/peerjcs.875
A BibTeX entry for LaTeX users is
@article{10.7717/peerjcs.875,
title = {Lcapy: symbolic linear circuit analysis with {Python}},
author = {Hayes, Michael},
year = 2022,
month = Feb,
keywords = {Linear circuit analysis, symbolic computation, Python},
pages = {e875},
journal = {PeerJ Computer Science},
issn = {23765992},
url = {https://doi.org/10.7717/peerjcs.875},
doi = {10.7717/peerjcs.875}
}
Copyright 20142022 Michael Hayes, UCECE
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