# Element Reference

## Passives

`ACME.resistor`

— Function`resistor(r)`

Creates a resistor obeying Ohm’s law. The resistance `r`

has to be given in Ohm.

Pins: `1`

, `2`

`ACME.capacitor`

— Function`capacitor(c)`

Creates a capacitor. The capacitance `c`

has to be given in Farad.

Pins: `1`

, `2`

`ACME.inductor`

— Method`inductor(l)`

Creates an inductor. The inductance `l`

has to be given in Henri.

Pins: `1`

, `2`

`ACME.inductor`

— Method`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:

parameter | description |
---|---|

`D` | Torus diameter (in meters) |

`A` | Torus cross-sectional area (in square-meters) |

`n` | Winding's number of turns |

`a` | Shape parameter of the anhysteretic magnetization curve (in Ampere-per-meter) |

`α` | Inter-domain coupling |

`c` | Ratio of the initial normal to the initial anhysteretic differential susceptibility |

`k` | amount of hysteresis (in Ampere-per-meter) |

`Ms` | saturation 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`

`ACME.transformer`

— Method`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

`ACME.transformer`

— Method`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:

parameter | description |
---|---|

`D` | Torus diameter (in meters) |

`A` | Torus cross-sectional area (in square-meters) |

`ns` | Windings' number of turns as a vector with one entry per winding |

`a` | Shape parameter of the anhysteretic magnetization curve (in Ampere-per-meter) |

`α` | Inter-domain coupling |

`c` | Ratio of the initial normal to the initial anhysteretic differential susceptibility |

`k` | amount of hysteresis (in Ampere-per-meter) |

`Ms` | saturation 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

## Independent Sources

`ACME.voltagesource`

— Function```
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 `-`

`ACME.currentsource`

— Function```
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

## Probes

`ACME.voltageprobe`

— Function`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 `-`

`ACME.currentprobe`

— Function`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 `+`

## Semiconductors

`ACME.diode`

— Function`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)

`ACME.bjt`

— Function```
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:

parameter | description |
---|---|

`typ` | Either `:npn` or `:pnp` , depending on desired transistor type |

`is` | Reverse saturation current in Ampere |

`η` | Emission coefficient |

`isc` | Collector reverse saturation current in Ampere (overriding `is` ) |

`ise` | Emitter reverse saturation current in Ampere (overriding `is` ) |

`ηc` | Collector emission coefficient (overriding `η` ) |

`ηe` | Emitter emission coefficient (overriding `η` ) |

`βf` | Forward current gain |

`βr` | Reverse current gain |

`ilc` | Base-collector junction leakage current in Ampere |

`ile` | Base-emitter junction leakage current in Ampere |

`ηcl` | Base-collector junction leakage emission coefficient (overriding `η` ) |

`ηel` | Base-emitter junction leakage emission coefficient (overriding `η` ) |

`vaf` | Forward Early voltage in Volt |

`var` | Reverse Early voltage in Volt |

`ikf` | Forward knee current (gain roll-off) in Ampere |

`ikr` | Reverse knee current (gain roll-off) in Ampere |

`re` | Emitter terminal resistance |

`rc` | Collector terminal resistance |

`rb` | Base terminal resistance |

Pins: `base`

, `emitter`

, `collector`

`ACME.mosfet`

— Function`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`

## Integrated Circuits

`ACME.opamp`

— Method`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

Missing docstring for `opamp(::Type{Val{:macak}}, gain, vomin, vomax)`

. Check Documenter's build log for details.