RLCModel

An electrical circuit model featuring an inductor in series with a parallel resistor-capacitor combination, driven by a constant voltage source.

This model represents an electrical circuit where an inductor (L) is connected in series with a parallel arrangement of a resistor (R) and a capacitor (C). This L-(R||C) configuration is subjected to a constant voltage provided by a voltage source. The key dynamics are governed by Kirchhoff's laws. Initial conditions are specified for $i_L(0) = 0A$ and $v_C(0) = 10V$. The system is expected to reach a steady state where $v_C = V_{sig} = 30V$.

Usage

RLCModel()

Behavior

\[ \begin{equation} \left[ \begin{array}{c} \mathtt{signal.y}\left( t \right) = \mathtt{source.V}\left( t \right) \\ \mathrm{connect}\left( source_{+}n, inductor_{+}p \right) \\ \mathrm{connect}\left( inductor_{+}n, resistor_{+}n, capacitor_{+}n \right) \\ \mathrm{connect}\left( resistor_{+}p, ground_{+}g, capacitor_{+}p, source_{+}p \right) \\ \mathtt{resistor.v}\left( t \right) = - \mathtt{resistor.n.v}\left( t \right) + \mathtt{resistor.p.v}\left( t \right) \\ \mathtt{resistor.i}\left( t \right) = \mathtt{resistor.p.i}\left( t \right) \\ \mathtt{resistor.p.i}\left( t \right) + \mathtt{resistor.n.i}\left( t \right) = 0 \\ \mathtt{resistor.v}\left( t \right) = \mathtt{resistor.R} \mathtt{resistor.i}\left( t \right) \\ \mathtt{capacitor.v}\left( t \right) = \mathtt{capacitor.p.v}\left( t \right) - \mathtt{capacitor.n.v}\left( t \right) \\ \mathtt{capacitor.i}\left( t \right) = \mathtt{capacitor.p.i}\left( t \right) \\ \mathtt{capacitor.p.i}\left( t \right) + \mathtt{capacitor.n.i}\left( t \right) = 0 \\ \mathtt{capacitor.C} \frac{\mathrm{d} \mathtt{capacitor.v}\left( t \right)}{\mathrm{d}t} = \mathtt{capacitor.i}\left( t \right) \\ \mathtt{inductor.v}\left( t \right) = - \mathtt{inductor.n.v}\left( t \right) + \mathtt{inductor.p.v}\left( t \right) \\ \mathtt{inductor.i}\left( t \right) = \mathtt{inductor.p.i}\left( t \right) \\ \mathtt{inductor.p.i}\left( t \right) + \mathtt{inductor.n.i}\left( t \right) = 0 \\ \mathtt{inductor.L} \frac{\mathrm{d} \mathtt{inductor.i}\left( t \right)}{\mathrm{d}t} = \mathtt{inductor.v}\left( t \right) \\ \mathtt{signal.y}\left( t \right) = \mathtt{signal.k} \\ \mathtt{source.v}\left( t \right) = - \mathtt{source.n.v}\left( t \right) + \mathtt{source.p.v}\left( t \right) \\ \mathtt{source.i}\left( t \right) = \mathtt{source.p.i}\left( t \right) \\ \mathtt{source.p.i}\left( t \right) + \mathtt{source.n.i}\left( t \right) = 0 \\ \mathtt{source.v}\left( t \right) = \mathtt{source.uV} \mathtt{source.V}\left( t \right) \\ \mathtt{ground.g.v}\left( t \right) = 0 \\ \end{array} \right] \end{equation} \]

Source

# An electrical circuit model featuring an inductor in series with a parallel resistor-capacitor combination, driven by a constant voltage source.
#
# This model represents an electrical circuit where an inductor (L) is connected in series with a parallel arrangement of a resistor (R) and a capacitor (C).
# This L-(R||C) configuration is subjected to a constant voltage provided by a voltage source.  The key dynamics are governed by Kirchhoff's laws.
# Initial conditions are specified for $i_L(0) = 0A$ and $v_C(0) = 10V$. The system is expected to reach a steady state where $v_C = V_{sig} = 30V$.
example component RLCModel
  # Resistor subcomponent with a resistance value of 100 Ohms.
  resistor = Resistor(R=100) [{
    "Dyad": {
      "placement": {"diagram": {"x1": 850, "y1": 450, "x2": 950, "y2": 550, "rot": -90}}
    }
  }]
  # Capacitor subcomponent with a capacitance value of 1 milliFarad.
  capacitor = Capacitor(C=1m) [{
    "Dyad": {
      "placement": {"diagram": {"x1": 550, "y1": 450, "x2": 650, "y2": 550, "rot": -90}}
    }
  }]
  # Inductor subcomponent with an inductance value of 1 Henry.
  inductor = Inductor(L=1) [{
    "Dyad": {
      "placement": {"diagram": {"x1": 375, "y1": 250, "x2": 475, "y2": 350, "rot": 0}}
    }
  }]
  # Constant signal generator block providing an output value of 30.
  signal = BlockComponents.Constant(k=30) [{"Dyad": {"placement": {"icon": {"x1": 0, "y1": 450, "x2": 100, "y2": 550}}}}]
  # Voltage source subcomponent providing the electromotive force.
  source = VoltageSource() [{
    "Dyad": {
      "placement": {"diagram": {"x1": 200, "y1": 450, "x2": 300, "y2": 550, "rot": -90}}
    }
  }]
  # Ground subcomponent providing the reference potential (0V).
  ground = Ground() [{
    "Dyad": {
      "placement": {"diagram": {"x1": 550, "y1": 800, "x2": 650, "y2": 900, "rot": 0}}
    }
  }]
relations
  initial inductor.i = 0
  initial capacitor.v = 10
  connect(signal.y, source.V) [{"Dyad": {"edges": [{"S": 1, "E": 2}]}}]
  connect(source.n, inductor.p) [{"Dyad": {"edges": [{"S": 1, "M": [{"x": 250, "y": 300}], "E": 2}]}}]
  connect(inductor.n, resistor.n, capacitor.n) [{
    "Dyad": {
      "edges": [
        {"S": 1, "E": -1},
        {"S": 2, "M": [{"x": 900, "y": 300}], "E": -1},
        {"S": 3, "E": -1}
      ],
      "junctions": [{"x": 600, "y": 300}]
    }
  }]
  connect(resistor.p, ground.g, capacitor.p, source.p) [{
    "Dyad": {
      "edges": [
        {"S": 1, "M": [{"x": 900, "y": 700}], "E": -1},
        {"S": 2, "E": -1},
        {"S": 3, "E": -1},
        {"S": -1, "M": [{"x": 250, "y": 700}], "E": 4}
      ],
      "junctions": [{"x": 600, "y": 700}]
    }
  }]
metadata {
  "Dyad": {
    "labels": [
      {
        "label": "RLC Model",
        "x": 800,
        "y": 100,
        "layer": "diagram",
        "attrs": {"font-size": "100"}
      }
    ],
    "tests": {
      "case1": {
        "stop": 10,
        "expect": {"initial": {"capacitor.v": 10}, "final": {"capacitor.v": 30}}
      }
    }
  }
}
end

# An electrical circuit model featuring an inductor in series with a parallel resistor-capacitor combination, driven by a constant voltage source.
#
# This model represents an electrical circuit where an inductor (L) is connected in series with a parallel arrangement of a resistor (R) and a capacitor (C).
# This L-(R||C) configuration is subjected to a constant voltage provided by a voltage source.  The key dynamics are governed by Kirchhoff's laws.
# Initial conditions are specified for $i_L(0) = 0A$ and $v_C(0) = 10V$. The system is expected to reach a steady state where $v_C = V_{sig} = 30V$.
example component RLCModel
  # Resistor subcomponent with a resistance value of 100 Ohms.
  resistor = Resistor(R=100) [{
    "Dyad": {
      "placement": {"diagram": {"x1": 850, "y1": 450, "x2": 950, "y2": 550, "rot": -90}}
    }
  }]
  # Capacitor subcomponent with a capacitance value of 1 milliFarad.
  capacitor = Capacitor(C=1m) [{
    "Dyad": {
      "placement": {"diagram": {"x1": 550, "y1": 450, "x2": 650, "y2": 550, "rot": -90}}
    }
  }]
  # Inductor subcomponent with an inductance value of 1 Henry.
  inductor = Inductor(L=1) [{
    "Dyad": {
      "placement": {"diagram": {"x1": 375, "y1": 250, "x2": 475, "y2": 350, "rot": 0}}
    }
  }]
  # Constant signal generator block providing an output value of 30.
  signal = BlockComponents.Constant(k=30) [{"Dyad": {"placement": {"icon": {"x1": 0, "y1": 450, "x2": 100, "y2": 550}}}}]
  # Voltage source subcomponent providing the electromotive force.
  source = VoltageSource() [{
    "Dyad": {
      "placement": {"diagram": {"x1": 200, "y1": 450, "x2": 300, "y2": 550, "rot": -90}}
    }
  }]
  # Ground subcomponent providing the reference potential (0V).
  ground = Ground() [{
    "Dyad": {
      "placement": {"diagram": {"x1": 550, "y1": 800, "x2": 650, "y2": 900, "rot": 0}}
    }
  }]
relations
  initial inductor.i = 0
  initial capacitor.v = 10
  connect(signal.y, source.V) [{"Dyad": {"edges": [{"S": 1, "E": 2}]}}]
  connect(source.n, inductor.p) [{"Dyad": {"edges": [{"S": 1, "M": [{"x": 250, "y": 300}], "E": 2}]}}]
  connect(inductor.n, resistor.n, capacitor.n) [{
    "Dyad": {
      "edges": [
        {"S": 1, "E": -1},
        {"S": 2, "M": [{"x": 900, "y": 300}], "E": -1},
        {"S": 3, "E": -1}
      ],
      "junctions": [{"x": 600, "y": 300}]
    }
  }]
  connect(resistor.p, ground.g, capacitor.p, source.p) [{
    "Dyad": {
      "edges": [
        {"S": 1, "M": [{"x": 900, "y": 700}], "E": -1},
        {"S": 2, "E": -1},
        {"S": 3, "E": -1},
        {"S": -1, "M": [{"x": 250, "y": 700}], "E": 4}
      ],
      "junctions": [{"x": 600, "y": 700}]
    }
  }]
metadata {
  "Dyad": {
    "labels": [
      {
        "label": "RLC Model",
        "x": 800,
        "y": 100,
        "layer": "diagram",
        "attrs": {"font-size": "100"}
      }
    ],
    "tests": {
      "case1": {
        "stop": 10,
        "expect": {"initial": {"capacitor.v": 10}, "final": {"capacitor.v": 30}}
      }
    }
  }
}
end

Test Cases

Test Case case1

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