ACME.jl - Analog Circuit Modeling and Emulation for Julia

ACME is a Julia package for the simulation of electrical circuits, focusing on audio effect circuits. It allows to programmatically describe a circuit in terms of elements and connections between them and then automatically derive a model for the circuit. The model can then be run on varying input data.

ACME is based on the method described in M. Holters, U. Zölzer, "A Generalized Method for the Derivation of Non-Linear State-Space Models from Circuit Schematics".

If you have not done so already, download and install Julia. (Any version starting with 1.4 should be fine; earlier ACME versions support Julia starting with version 0.3.)

To install ACME, start Julia and run:

Pkg.add("ACME")

This will download ACME and all of its dependencies.

We will demonstrate ACME by modeling a simple diode clipper. The first step is to load ACME:

using ACME

Now we create the circuit description:

circ = @circuit begin
    j_in = voltagesource()
    r1 = resistor(1e3)
    c1 = capacitor(47e-9)
    d1 = diode(is=1e-15)
    d2 = diode(is=1.8e-15)
    j_out = voltageprobe()
    j_in[+] ⟷ r1[1]
    j_in[-] ⟷ gnd
    r1[2] ⟷ c1[1] ⟷ d1[+] ⟷ d2[-] ⟷ j_out[+]
    gnd ⟷ c1[2] ⟷ d1[-] ⟷ d2[+] ⟷ j_out[-]
end

The first six lines inside the begin/end block instantiate circuit elements. Specifying a voltagesource() sets up a voltage source as an input, i.e. the voltage it sources will be specified when running the model. Alternatively, one can instantiate a constant voltage source for say 9V with voltagesource(9). The resistor and capacitor calls take the resistance in ohm and the capacitance in farad, respectively, as arguments. For the diode, one may specify the saturation current is as done here and/or the emission coefficient η. Finally, desired outputs are denoted by adding probes to the circuit; in this case a voltageprobe() will provide voltage as output.

The remaining four lines specify connections, either among element pins as in j_in[+] ⟷ r1[1], which connects the + pin of the input voltage to pin 1 of the resistor, or among pins and named nets as in j_in[-] ⟷ gnd, which connects the - pin of the input voltage source to a net named gnd. Note that naming nets is only for the sake of readability; there is nothing special about them and the names are arbitrary. As can be seen in the last two lines, multiple pins can be connected at once.

It is also possible to specify connections following the element definition (separated by commas), in which case the element name may be omitted. However, one can only connect to elements defined before. Thus, above circuit could also be entered as:

circ = @circuit begin
    j_in = voltagesource(), [-] ⟷ gnd
    r1 = resistor(1e3), [1] ⟷ j_in[+]
    c1 = capacitor(47e-9), [1] ⟷ r1[2], [2] ⟷ gnd
    d1 = diode(is=1e-15), [+] ⟷ r1[2], [-] ⟷ gnd
    d2 = diode(is=1.8e-15), [+] ⟷ gnd, [-] ⟷ r1[2]
    j_out = voltageprobe(), [+] ⟷ r1[2], [-] ⟷ gnd
end

Now that the circuit has been set up, we need to turn it into a model. This could hardly be any easier:

model = DiscreteModel(circ, 1/44100)

The second argument specifies the sampling interval, the reciprocal of the sampling rate, here assumed to be the typical 44100 Hz.

Now we can process some input data. It has to be provided as a matrix with one row per input (just one in the example) and one column per sample. So for a sinusoid at 1 kHz lasting one second, we do

y = run!(model, [sin(2π*1000/44100*n) for c in 1:1, n in 0:44099])

The output y now likewise is a matrix with one row for the one probe we have added to the circuit and one column per sample.

In the likely event that you would like to process real audio data, take a look at the WAV package for reading writing WAV files.

Note that the solver used to solve the non-linear equation when running the model saves solutions to use as starting points in the future. Model execution will therefore become faster after an initial learning phase. Nevertheless, ACME is at present more geared towards computing all the model matrices than to actually running the model. More complex circuits may run intolerably slow or fail to run altogether.

There is some documentation available for how to use ACME. Additionally, you can take a look at the examples that can be found in the examples directory below Pkg.dir("ACME").

If you would like to extend and improve ACME, that's great! But unfortunately, there is no developer documentation as of now, so you will to delve into the source code to figure out how things work, or try to ask on gitter.