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Symbolic linear circuit analysis

Project description

Lcapy is a Python package for linear circuit analysis. It uses SymPy for symbolic mathematics.

Run tests and checks Binder Documentation

Lcapy can symbolically analyse circuits described with netlists or by series/parallel combinations of components. It can also manipulate continuous-time and discret-time expressions.

Comprehensive documentation can be found at

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 run-time. 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)
 Rₐ + R_b
>>> cct.Ra.I(t)
Rₐ + R_b
>>> cct.Ra.V(s)
s⋅(Rₐ + R_b)

One-port networks

One-port networks can be created by series and parallel combinations of other one-port networks. The primitive one-port 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 s-domain 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 open-circuit impedance
  • Ysc short-circuit admittance
  • Voc open-circuit voltage
  • Isc short-circuit 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 s-domain open circuit voltage across the network can be printed with:

>>> a.V(s)

The time domain open circuit voltage is given by:

>>> a.V(t)

The s-domain 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)

If you want units displayed:

>>> state.show_units=True
>>> a.Isc(t)

Two-port networks

One-port networks can be combined to form two-port 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'))


  1. Non-linear components cannot be modelled (apart from a linearisation around a bias point).

  2. High order systems can go crazy.

  3. Some two-ports generate singular matrices.


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 (open-circuit) and W denotes a wire (short-circuit). The drawing hints are separated from the netlist arguments by a semicolon. They are a comma separated list of key-value 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 . These include:


For comprehensive documentation, see (alternatively, the documentation can be viewed in a web browser after running 'make doc' in the top-level directory).

For release notes see

For another view on Lcapy see


To cite Lcapy in publications use

Hayes M. 2022. Lcapy: symbolic linear circuit analysis with Python. PeerJ Computer Science 8:e875

A BibTeX entry for LaTeX users is

 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 = {2376-5992},
 url = {},
 doi = {10.7717/peerj-cs.875}

Copyright 2014--2022 Michael Hayes, UCECE

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