Circuits

Generate, visualize and analyze electrical networks.

Creating a circuit

The simplest way to create a circuit is through the @circuit macro. As an example, here a square network is generated with two named (a and b) and two unnamed (or rather not explicitly named) nodes, one voltage source, a resistor and a capacitor in series and a capacitor and an inductor in parallel:

c = @circuit begin
    b:(0,0) --> VSource(3) --> (1,0) --> Resistor(4) --> Inductor(2) --> (1,1) --> a:(0,1)
    :a --> Capacitor(1) // Inductor(4) --> :b
end

Visualizing a circuit

The normal show method for Circuits just prints a brief summary (number of nodes, number of sources, number of impedors (which is what I call RCL components... if you're an electrical engineer and know a better word lmk)).

To see the entire circuit, a method show(io::IO,::MIME"text/circuitikz",c::Circuit) is implemented. If you use this method to print to a file, and then \input that file inside a tikzpicture in a LaTeX document with circuitikz loaded, it will draw the circuit.

show(io,mime,c,shownodes=true) will also show the node labels, which is useful while modifying or analyzing the circuit.

Simplifying a network

A Parallel will happily contain any collection of Impedors, except Parallels which will be expanded during construction (Parallel(a,Parallel(b,c)) = Parallel(a,b,c)). And vice versa for Series. But for calculations, a series or parallel coupling of the same type of component can be simplified by either addition or reciprocal addition of their characteristic parameters. simplify(n::Network) will walk through the tree and combine the components like this, until you are left with a single component, a Series of RCL components and Parallels, a Parallel of RCL components and Series, a Short or an Open.

Analyzing a network

For an Impedor (Series, Parallel, RCL component, Short or Open) i, voltageDivision(i,s) returns א such that component with index k has a voltage drop א[k]·V₀ if i has a total voltage drop V₀. s is the complex frequency. By default this is 0 (DC voltage).

For the network above, opening the voltage source and going from the node at (1,1) to b, (i.e. n = Series(Resistor(4),Inductor(2),Parallel(Capacitor(1),Inductor(4)))), voltageDivision(n) == [1.0, 0.0, [0.0, 0.0]] by which we can read that the resistor experiences a voltage drop of V₀, and the rest of the components none (as expected for DC voltage). voltageDivision(n,1im) == [0.97 - 0.16im, 0.081 + 0.48im, [-0.054 - 0.32im, -0.054 - 0.32im]] (so at 1 frequency unit, those are the respective responses in each component).

Current division works the same: currentDivision(n) == [1, 1, [0.0, NaN]] (the NaN is from an Inf/Inf, a good symbolic package will probably fix this, but for now I mostly read those as 1s. currentDivision(n,1im) == [1, 1, [1.33 + 0.0im, -0.33 - 0.0im]]. That's probably right? Idk.

To do

• Connect to LightGraphs.jl?
• Function to extract Network from Circuit (at specific nodes)
• More recursion in simplify. MOAR
• Circuit to matrix for computer circuit analysis
• Bode diagrams
• Power calculations
• Get rid of some NaNs in current and voltage division
• ...