# Element Reference

## Passives

ACME.resistorFunction
resistor(r)

Creates a resistor obeying Ohm’s law. The resistance r has to be given in Ohm.

Pins: 1, 2

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ACME.capacitorFunction
capacitor(c)

Creates a capacitor. The capacitance c has to be given in Farad.

Pins: 1, 2

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ACME.inductorMethod
inductor(l)

Creates an inductor. The inductance l has to be given in Henri.

Pins: 1, 2

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ACME.inductorMethod
inductor(Val{:JA}; D, A, n, a, α, c, k, Ms)

Creates a non-linear inductor based on the Jiles-Atherton model of magnetization assuming a toroidal core thin compared to its diameter. The parameters are set using named arguments:

parameterdescription
DTorus diameter (in meters)
ATorus cross-sectional area (in square-meters)
nWinding's number of turns
aShape parameter of the anhysteretic magnetization curve (in Ampere-per-meter)
αInter-domain coupling
cRatio of the initial normal to the initial anhysteretic differential susceptibility
kamount of hysteresis (in Ampere-per-meter)
Mssaturation magnetization (in Ampere-per-meter)

A detailed discussion of the parameters can be found in D. C. Jiles and D. L. Atherton, “Theory of ferromagnetic hysteresis,” J. Magn. Magn. Mater., vol. 61, no. 1–2, pp. 48–60, Sep. 1986 and J. H. B. Deane, “Modeling the dynamics of nonlinear inductor circuits,” IEEE Trans. Magn., vol. 30, no. 5, pp. 2795–2801, 1994, where the definition of c is taken from the latter. The ACME implementation is discussed in M. Holters, U. Zölzer, "Circuit Simulation with Inductors and Transformers Based on the Jiles-Atherton Model of Magnetization".

Pins: 1, 2

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ACME.transformerMethod
transformer(l1, l2; coupling_coefficient=1, mutual_coupling=coupling_coefficient*sqrt(l1*l2))

Creates a transformer with two windings having inductances. The primary self-inductance l1 and the secondary self-inductance l2 have to be given in Henri. The coupling can either be specified using coupling_coefficient (0 is not coupled, 1 is closely coupled) or by mutual_coupling, the mutual inductance in Henri, where the latter takes precedence if both are given.

Pins: primary1 and primary2 for primary winding, secondary1 and secondary2 for secondary winding

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ACME.transformerMethod
transformer(Val{:JA}; D, A, ns, a, α, c, k, Ms)

Creates a non-linear transformer based on the Jiles-Atherton model of magnetization assuming a toroidal core thin compared to its diameter. The parameters are set using named arguments:

parameterdescription
DTorus diameter (in meters)
ATorus cross-sectional area (in square-meters)
nsWindings' number of turns as a vector with one entry per winding
aShape parameter of the anhysteretic magnetization curve (in Ampere-per-meter)
αInter-domain coupling
cRatio of the initial normal to the initial anhysteretic differential susceptibility
kamount of hysteresis (in Ampere-per-meter)
Mssaturation magnetization (in Ampere-per-meter)

A detailed discussion of the parameters can be found in D. C. Jiles and D. L. Atherton, “Theory of ferromagnetic hysteresis,” J. Magn. Magn. Mater., vol. 61, no. 1–2, pp. 48–60, Sep. 1986 and J. H. B. Deane, “Modeling the dynamics of nonlinear inductor circuits,” IEEE Trans. Magn., vol. 30, no. 5, pp. 2795–2801, 1994, where the definition of c is taken from the latter. The ACME implementation is discussed in M. Holters, U. Zölzer, "Circuit Simulation with Inductors and Transformers Based on the Jiles-Atherton Model of Magnetization".

Pins: 1 and 2 for primary winding, 3 and 4 for secondary winding, and so on

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## Independent Sources

ACME.voltagesourceFunction
voltagesource(; rs=0)
voltagesource(v; rs=0)

Creates a voltage source. The source voltage v has to be given in Volt. If omitted, the source voltage will be an input of the circuit. Optionally, an internal series resistance rs (in Ohm) can be given which defaults to zero.

Pins: + and - with v being measured from + to -

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ACME.currentsourceFunction
currentsource(; gp=0)
currentsource(i; gp=0)

Creates a current source. The source current i has to be given in Ampere. If omitted, the source current will be an input of the circuit. Optionally, an internal parallel conductance gp (in Ohm⁻¹) can be given which defaults to zero.

Pins: + and - where i measures the current leaving source at the + pin

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## Probes

ACME.voltageprobeFunction
voltageprobe()

Creates a voltage probe, providing the measured voltage as a circuit output. Optionally, an internal parallel conductance gp (in Ohm⁻¹) can be given which defaults to zero.

Pins: + and - with the output voltage being measured from + to -

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ACME.currentprobeFunction
currentprobe()

Creates a current probe, providing the measured current as a circuit output. Optionally, an internal series resistance rs (in Ohm) can be given which defaults to zero.

Pins: + and - with the output current being the current entering the probe at +

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## Semiconductors

ACME.diodeFunction
diode(;is=1e-12, η = 1)

Creates a diode obeying Shockley's law $i=I_S\cdot(e^{v/(\eta v_T)}-1)$ where $v_T$ is fixed at 25 mV. The reverse saturation current is has to be given in Ampere, the emission coefficient η is unitless.

Pins: + (anode) and - (cathode)

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ACME.bjtFunction
bjt(typ; is=1e-12, η=1, isc=is, ise=is, ηc=η, ηe=η, βf=1000, βr=10,
ile=0, ilc=0, ηcl=ηc, ηel=ηe, vaf=Inf, var=Inf, ikf=Inf, ikr=Inf)

Creates a bipolar junction transistor obeying the Gummel-Poon model

$i_f = \frac{\beta_f}{1+\beta_f} I_{S,E} \cdot (e^{v_E/(\eta_E v_T)}-1)$
$i_r = \frac{\beta_r}{1+\beta_r} I_{S,C} \cdot (e^{v_C/(\eta_C v_T)}-1)$
$i_{cc} = \frac{2(1-\frac{V_E}{V_{ar}}-\frac{V_C}{V_{af}})} {1+\sqrt{1+4(\frac{i_f}{I_{KF}}+\frac{i_r}{I_{KR}})}} (i_f - i_r)$
$i_{BE} = \frac{1}{\beta_f} i_f + I_{L,E} \cdot (e^{v_E/(\eta_{EL} v_T)}-1)$
$i_{BC} = \frac{1}{\beta_r} i_r + I_{L,C} \cdot (e^{v_C/(\eta_{CL} v_T)}-1)$
$i_E = i_{cc} + i_{BE} \qquad i_C=-i_{cc} + i_{BC}$

where $v_T$ is fixed at 25 mV. For

$I_{L,E}=I_{L,C}=0,\quad V_{ar}=V_{af}=I_{KF}=I_{KR}=∞,$

this reduces to the Ebers-Moll equation

$i_E = I_{S,E} \cdot (e^{v_E/(\eta_E v_T)}-1) - \frac{\beta_r}{1+\beta_r} I_{S,C} \cdot (e^{v_C/(\eta_C v_T)}-1)$
$i_C = -\frac{\beta_f}{1+\beta_f} I_{S,E} \cdot (e^{v_E/(\eta_E v_T)}-1) + I_{S,C} \cdot (e^{v_C/(\eta_C v_T)}-1).$

Additionally, terminal series resistances are supported.

The parameters are set using named arguments:

parameterdescription
typEither :npn or :pnp, depending on desired transistor type
isReverse saturation current in Ampere
ηEmission coefficient
iscCollector reverse saturation current in Ampere (overriding is)
iseEmitter reverse saturation current in Ampere (overriding is)
ηcCollector emission coefficient (overriding η)
ηeEmitter emission coefficient (overriding η)
βfForward current gain
βrReverse current gain
ilcBase-collector junction leakage current in Ampere
ileBase-emitter junction leakage current in Ampere
ηclBase-collector junction leakage emission coefficient (overriding η)
ηelBase-emitter junction leakage emission coefficient (overriding η)
vafForward Early voltage in Volt
varReverse Early voltage in Volt
ikfForward knee current (gain roll-off) in Ampere
ikrReverse knee current (gain roll-off) in Ampere
reEmitter terminal resistance
rcCollector terminal resistance
rbBase terminal resistance

Pins: base, emitter, collector

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ACME.mosfetFunction
mosfet(typ; vt=0.7, α=2e-5, λ=0)

Creates a MOSFET transistor with the simple model

$i_D=\begin{cases} 0 & \text{if } v_{GS} \le v_T \\ \alpha \cdot (v_{GS} - v_T - \tfrac{1}{2}v_{DS})\cdot v_{DS} \cdot (1 + \lambda v_{DS}) & \text{if } v_{DS} \le v_{GS} - v_T \cap v_{GS} > v_T \\ \frac{\alpha}{2} \cdot (v_{GS} - v_T)^2 \cdot (1 + \lambda v_{DS}) & \text{otherwise.} \end{cases}$

The typ parameter chooses between NMOS (:n) and PMOS (:p). The threshold voltage vt is given in Volt, α (in A/V²) is a constant depending on the physics and dimensions of the device, and λ (in V⁻¹) controls the channel length modulation.

Optionally, it is possible to specify tuples of coefficients for vt and α. These will be used as polynomials in $v_{GS}$ to determine $v_T$ and $\alpha$, respectively. E.g. with vt=(0.7, 0.1, 0.02), the $v_{GS}$-dpendent threshold voltage $v_T = 0.7 + 0.1\cdot v_{GS} + 0.02\cdot v_{GS}^2$ will be used.

Pins: gate, source, drain

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## Integrated Circuits

ACME.opampMethod
opamp(;maxgain=Inf, gain_bw_prod=Inf)

Creates a linear operational amplifier as a voltage-controlled voltage source. The input current is zero while the input voltage is mapped to the output voltage according to the transfer function

$H(f) = \frac{A_\text{max}}{\sqrt{A_\text{max}^2-1} i \frac{f}{f_\text{UG}} + 1}$

where $f$ is the signal frequency, $A_\text{max}$ (maxgain) is the maximum open loop gain and $f_\text{UG}$ (gain_bw_prod) is the gain/bandwidth product (unity gain bandwidth). For gain_bw_prod=Inf (the default), this corresponds to a frequency-independent gain of maxgain. For maxgain=Inf (the default), the amplifier behaves as a perfect integrator.

For both maxgain=Inf and gain_bw_prod=Inf, i.e. just opamp(), an ideal operational amplifier is obtained that enforces the voltage between the input pins to be zero while sourcing arbitrary current on the output pins without restricting their voltage.

Note that the opamp has two output pins, where the negative one will typically be connected to a ground node and has to provide the current sourced on the positive one.

Pins: in+ and in- for input, out+ and out- for output

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ACME.opampMethod
opamp(Val{:macak}, gain, vomin, vomax)

Creates a clipping operational amplifier where input and output voltage are related by

$v_\text{out} = \frac{1}{2}\cdot(v_\text{max}+v_\text{min}) +\frac{1}{2}\cdot(v_\text{max}-v_\text{min})\cdot \tanh\left(\frac{g}{\frac{1}{2}\cdot(v_\text{max}-v_\text{min})}\cdot v_\text{in}\right).$

The input current is zero, the output current is arbitrary.

Note that the opamp has two output pins, one of which will typically be connected to a ground node and has to provide the current sourced on the other output pin.

Pins: in+ and in- for input, out+ and out- for output

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