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Examples.Modulation.md

Examples.Modulation ​

Demonstrates amplitude modulation (AM) and frequency modulation (FM) using the variable-frequency/amplitude sine and cosine sources.

Mirrors Modelica.Blocks.Examples.Modulation. The carrier frequency is 100 Hz and the message (modulating) frequency is 2 Hz:

  • sine.y is the unmodulated 100 Hz carrier reference, sin(2π·100·t).

  • sinAM.y / cosAM.y are amplitude modulated with a constant 100 Hz carrier and a time-varying amplitude 1 + 0.5·sin(2π·2·t).

  • sinFM.y / cosFM.y are frequency modulated with a constant amplitude of 1 and an instantaneous frequency 100 + 50·sin(2π·2·t).

The SineVariableFrequencyAndAmplitude / CosineVariableFrequencyAndAmplitude blocks always read both amplitude and frequency from input ports, so the constant carrier frequency (AM) and constant carrier amplitude (FM) are supplied by Constant sources.

Usage ​

BlockComponents.Examples.Modulation()

Behavior ​

julia
using BlockComponents #hide
using ModelingToolkit #hide
@named sys = BlockComponents.Examples.Modulation() #hide
let eqs = full_equations(sys); Base.length(eqs) > 25 ? nothing : eqs end #hide
<< @example-block not executed in draft mode >>

Source ​

dyad
"""
Demonstrates amplitude modulation (AM) and frequency modulation (FM) using the
variable-frequency/amplitude sine and cosine sources.

Mirrors `Modelica.Blocks.Examples.Modulation`. The carrier frequency is 100 Hz and
the message (modulating) frequency is 2 Hz:

- `sine.y` is the unmodulated 100 Hz carrier reference,
  `sin(2π·100·t)`.
- `sinAM.y` / `cosAM.y` are amplitude modulated with a constant 100 Hz carrier and a
  time-varying amplitude `1 + 0.5·sin(2π·2·t)`.
- `sinFM.y` / `cosFM.y` are frequency modulated with a constant amplitude of 1 and an
  instantaneous frequency `100 + 50·sin(2π·2·t)`.

The `SineVariableFrequencyAndAmplitude` / `CosineVariableFrequencyAndAmplitude`
blocks always read both `amplitude` and `frequency` from input ports, so the constant
carrier frequency (AM) and constant carrier amplitude (FM) are supplied by `Constant`
sources.
"""
example component Modulation
  "Unmodulated 100 Hz carrier reference"
  sine = BlockComponents.Sources.Sine(amplitude = 1, frequency = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 350, "y1": 30, "x2": 450, "y2": 130, "rot": 0}
      },
      "tags": []
    }
  }
  "AM amplitude signal: 1 + 0.5*sin(2π*2*t)"
  am_amplitude = BlockComponents.Sources.Sine(amplitude = 0.5, frequency = 2, offset = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 390, "y1": 610, "x2": 490, "y2": 710, "rot": 0}
      },
      "tags": []
    }
  }
  "Constant 100 Hz carrier frequency for the AM blocks"
  carrier_frequency = BlockComponents.Sources.Constant(k = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 390, "y1": 820, "x2": 490, "y2": 920, "rot": 0}
      },
      "tags": []
    }
  }
  "Constant unit carrier amplitude for the FM blocks"
  carrier_amplitude = BlockComponents.Sources.Constant(k = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 360, "y1": 210, "x2": 460, "y2": 310, "rot": 0}
      },
      "tags": []
    }
  }
  "FM frequency signal: 100 + 50*sin(2π*2*t)"
  fm_frequency = BlockComponents.Sources.Sine(amplitude = 50, frequency = 2, offset = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 370, "y1": 370, "x2": 470, "y2": 470, "rot": 0}
      },
      "tags": []
    }
  }
  "Amplitude-modulated sine"
  sinAM = BlockComponents.Sources.SineVariableFrequencyAndAmplitude() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": 610, "x2": 800, "y2": 710, "rot": 0}
      },
      "tags": []
    }
  }
  "Amplitude-modulated cosine"
  cosAM = BlockComponents.Sources.CosineVariableFrequencyAndAmplitude() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": 830, "x2": 800, "y2": 930, "rot": 0}
      },
      "tags": []
    }
  }
  "Frequency-modulated sine"
  sinFM = BlockComponents.Sources.SineVariableFrequencyAndAmplitude() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 690, "y1": 360, "x2": 790, "y2": 460, "rot": 0}
      },
      "tags": []
    }
  }
  "Frequency-modulated cosine"
  cosFM = BlockComponents.Sources.CosineVariableFrequencyAndAmplitude() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 680, "y1": 200, "x2": 780, "y2": 300, "rot": 0}
      },
      "tags": []
    }
  }
relations
  connect(am_amplitude.y, sinAM.amplitude) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 610, "y": 660}, {"x": 610, "y": 632}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(am_amplitude.y, cosAM.amplitude) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 610, "y": 660}, {"x": 610, "y": 854}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(carrier_frequency.y, sinAM.frequency) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 560, "y": 870}, {"x": 560, "y": 683}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(carrier_frequency.y, cosAM.frequency) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 560, "y": 870}, {"x": 560, "y": 903}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(fm_frequency.y, sinFM.frequency) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 530, "y": 420}, {"x": 530, "y": 433}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(fm_frequency.y, cosFM.frequency) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 530, "y": 420}, {"x": 530, "y": 273}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(sinFM.amplitude, carrier_amplitude.y) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 565, "y": 382}, {"x": 565, "y": 260}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(cosFM.amplitude, carrier_amplitude.y) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 565, "y": 224}, {"x": 565, "y": 260}], "E": 2}],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "icons": {"default": "dyad://BlockComponents/Example.svg"},
    "tests": {
      "case1": {"stop": 1, "signals": ["sine.y", "sinAM.y", "cosAM.y", "sinFM.y", "cosFM.y"]}
    }
  }
}
end
Flattened Source
dyad
"""
Demonstrates amplitude modulation (AM) and frequency modulation (FM) using the
variable-frequency/amplitude sine and cosine sources.

Mirrors `Modelica.Blocks.Examples.Modulation`. The carrier frequency is 100 Hz and
the message (modulating) frequency is 2 Hz:

- `sine.y` is the unmodulated 100 Hz carrier reference,
  `sin(2π·100·t)`.
- `sinAM.y` / `cosAM.y` are amplitude modulated with a constant 100 Hz carrier and a
  time-varying amplitude `1 + 0.5·sin(2π·2·t)`.
- `sinFM.y` / `cosFM.y` are frequency modulated with a constant amplitude of 1 and an
  instantaneous frequency `100 + 50·sin(2π·2·t)`.

The `SineVariableFrequencyAndAmplitude` / `CosineVariableFrequencyAndAmplitude`
blocks always read both `amplitude` and `frequency` from input ports, so the constant
carrier frequency (AM) and constant carrier amplitude (FM) are supplied by `Constant`
sources.
"""
example component Modulation
  "Unmodulated 100 Hz carrier reference"
  sine = BlockComponents.Sources.Sine(amplitude = 1, frequency = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 350, "y1": 30, "x2": 450, "y2": 130, "rot": 0}
      },
      "tags": []
    }
  }
  "AM amplitude signal: 1 + 0.5*sin(2π*2*t)"
  am_amplitude = BlockComponents.Sources.Sine(amplitude = 0.5, frequency = 2, offset = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 390, "y1": 610, "x2": 490, "y2": 710, "rot": 0}
      },
      "tags": []
    }
  }
  "Constant 100 Hz carrier frequency for the AM blocks"
  carrier_frequency = BlockComponents.Sources.Constant(k = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 390, "y1": 820, "x2": 490, "y2": 920, "rot": 0}
      },
      "tags": []
    }
  }
  "Constant unit carrier amplitude for the FM blocks"
  carrier_amplitude = BlockComponents.Sources.Constant(k = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 360, "y1": 210, "x2": 460, "y2": 310, "rot": 0}
      },
      "tags": []
    }
  }
  "FM frequency signal: 100 + 50*sin(2π*2*t)"
  fm_frequency = BlockComponents.Sources.Sine(amplitude = 50, frequency = 2, offset = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 370, "y1": 370, "x2": 470, "y2": 470, "rot": 0}
      },
      "tags": []
    }
  }
  "Amplitude-modulated sine"
  sinAM = BlockComponents.Sources.SineVariableFrequencyAndAmplitude() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": 610, "x2": 800, "y2": 710, "rot": 0}
      },
      "tags": []
    }
  }
  "Amplitude-modulated cosine"
  cosAM = BlockComponents.Sources.CosineVariableFrequencyAndAmplitude() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": 830, "x2": 800, "y2": 930, "rot": 0}
      },
      "tags": []
    }
  }
  "Frequency-modulated sine"
  sinFM = BlockComponents.Sources.SineVariableFrequencyAndAmplitude() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 690, "y1": 360, "x2": 790, "y2": 460, "rot": 0}
      },
      "tags": []
    }
  }
  "Frequency-modulated cosine"
  cosFM = BlockComponents.Sources.CosineVariableFrequencyAndAmplitude() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 680, "y1": 200, "x2": 780, "y2": 300, "rot": 0}
      },
      "tags": []
    }
  }
relations
  connect(am_amplitude.y, sinAM.amplitude) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 610, "y": 660}, {"x": 610, "y": 632}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(am_amplitude.y, cosAM.amplitude) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 610, "y": 660}, {"x": 610, "y": 854}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(carrier_frequency.y, sinAM.frequency) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 560, "y": 870}, {"x": 560, "y": 683}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(carrier_frequency.y, cosAM.frequency) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 560, "y": 870}, {"x": 560, "y": 903}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(fm_frequency.y, sinFM.frequency) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 530, "y": 420}, {"x": 530, "y": 433}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(fm_frequency.y, cosFM.frequency) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 530, "y": 420}, {"x": 530, "y": 273}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(sinFM.amplitude, carrier_amplitude.y) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 565, "y": 382}, {"x": 565, "y": 260}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(cosFM.amplitude, carrier_amplitude.y) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 565, "y": 224}, {"x": 565, "y": 260}], "E": 2}],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "icons": {"default": "dyad://BlockComponents/Example.svg"},
    "tests": {
      "case1": {"stop": 1, "signals": ["sine.y", "sinAM.y", "cosAM.y", "sinFM.y", "cosFM.y"]}
    }
  }
}
end


Test Cases ​

julia
using BlockComponents
using DyadInterface: TransientAnalysis, rebuild_sol, ODEAlg
using ModelingToolkit: toggle_namespacing, get_initial_conditions, @named
using CSV, DataFrames, Plots

snapshotsdir = joinpath(dirname(dirname(pathof(BlockComponents))), "test", "snapshots")
<< @setup-block not executed in draft mode >>

Test Case case1 ​

julia
@named model_case1 = BlockComponents.Examples.Modulation()
model_case1 = toggle_namespacing(model_case1, false)

model_case1 = toggle_namespacing(model_case1, true)
result_case1 = TransientAnalysis(; model = model_case1, alg = ODEAlg.Auto(), start = 0e+0, stop = 1e+0, abstol=1e-6, reltol=1e-6)
sol_case1 = rebuild_sol(result_case1)
<< @setup-block not executed in draft mode >>

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julia
<< @example-block not executed in draft mode >>