Impedance Ontology

# Impedance Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/electromagnetic-measurements/impedance-ontology.html

FLOW ImpedanceOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Electromagnetic Measurements
    -> Impedance Ontology

  PURPOSE:
    Represent electrical impedance as a complex frequency-dependent quantity describing the relationship between sinusoidal voltage and current in linear AC systems, including resistance, reactance, magnitude, phase, admittance, capacitive and inductive behaviour, series and parallel networks, complex power, units, measurement conditions, uncertainty, and distinctions from resistance, reactance and conductance.

  ENTITY Impedance {
    TYPE: ComplexDerivedElectromagneticQuantity
    SYMBOL: Z
    SI_UNIT: ohm
    SI_SYMBOL: ohm

    PHASOR_DEFINITION:
      Z = V_phasor / I_phasor
      WHEN I_phasor != 0

    RECTANGULAR_FORM:
      Z = R + jX

    POLAR_FORM:
      Z = |Z| * exp(j*phi)

    MAGNITUDE:
      |Z| = sqrt(R^2 + X^2)

    PHASE:
      phi = atan2(X, R)

    PROPERTIES:
      is_complex_quantity
      has_real_component
      has_imaginary_component
      has_magnitude
      has_phase
      has_unit
      depends_on_frequency
      may_depend_on_temperature
      may_depend_on_operating_point
      may_have_uncertainty
  }

  ENTITY Resistance {
    TYPE: RealElectricalQuantity
    SYMBOL: R
    SI_UNIT: ohm

    RELATION:
      R = real_part(Z)
      IN common_linear_AC_representation
  }

  ENTITY Reactance {
    TYPE: ImaginaryElectricalQuantity
    SYMBOL: X
    SI_UNIT: ohm

    RELATION:
      X = imaginary_part(Z)
  }

  ENTITY Admittance {
    TYPE: ComplexDerivedElectromagneticQuantity
    SYMBOL: Y
    SI_UNIT: siemens
    SI_SYMBOL: S

    RELATION:
      Y = 1/Z
      WHEN Z != 0
  }

  ENTITY VoltagePhasor {
    SYMBOL: V_phasor
    SI_UNIT: volt
  }

  ENTITY CurrentPhasor {
    SYMBOL: I_phasor
    SI_UNIT: ampere
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: ohm
      symbol: ohm
      equivalence:
        1 ohm = 1 V/A
    }

    COMMON_ALTERNATIVES:
      milliohm
      kiloohm
      megaohm

    RULE:
      complex_impedance_components_and_magnitude
      share_ohm_unit_but_have_distinct_semantic_roles
  }

  CLASSIFICATION {
    by composition:
      purely_resistive_impedance
      inductive_impedance
      capacitive_impedance
      mixed_impedance

    by representation:
      rectangular_impedance
      polar_impedance

    by network:
      series_impedance
      parallel_equivalent_impedance
      input_impedance
      output_impedance
      characteristic_impedance
      transfer_impedance

    by frequency:
      frequency_dependent_impedance
      broadband_impedance
      resonance_impedance
  }

  RESISTIVE_MODEL {
    IDEAL_RESISTOR:
      Z_R = R

    PHASE:
      phi = 0

    CONDITION:
      ideal_frequency_independent_resistor_model
  }

  INDUCTIVE_MODEL {
    IDEAL_INDUCTOR:
      Z_L = j*omega*L

    REACTANCE:
      X_L = omega*L

    PHASE:
      +pi/2

    FREQUENCY:
      omega = 2*pi*f
  }

  CAPACITIVE_MODEL {
    IDEAL_CAPACITOR:
      Z_C = 1/(j*omega*C)

    EQUIVALENT:
      Z_C = -j/(omega*C)

    REACTANCE:
      X_C = -1/(omega*C)

    PHASE:
      -pi/2

    CONDITIONS:
      omega != 0
      C != 0
  }

  SERIES_MODEL {
    GENERAL:
      Z_eq = sum(Z_i)

    RLC_SERIES:
      Z = R + j*(omega*L - 1/(omega*C))

    CONDITIONS:
      lumped_linear_components
      common_series_current
  }

  PARALLEL_MODEL {
    GENERAL:
      Y_eq = sum(Y_i)

    THEN:
      Z_eq = 1/Y_eq
      WHEN Y_eq != 0

    TWO_IMPEDANCE_FORM:
      Z_eq = (Z_1*Z_2)/(Z_1 + Z_2)
      WHEN denominator != 0
  }

  RESONANCE_MODEL {
    IDEAL_SERIES_RLC:
      omega_0 = 1/sqrt(L*C)

    AT_RESONANCE:
      X_L + X_C = 0
      Z = R

    CONDITIONS:
      L > 0
      C > 0
      ideal_lumped_RLC_model

    RULE:
      practical_resonance MAY shift_due_to_losses_parasitics_and_frequency_dependent_parameters
  }

  ADMITTANCE_MODEL {
    Y = G + jB

    WHERE:
      G = conductance
      B = susceptance

    INVERSE:
      Y = 1/Z

    IF:
      Z = R + jX

    THEN:
      Y = (R - jX)/(R^2 + X^2)
      WHEN R^2 + X^2 != 0
  }

  PHASOR_MODEL {
    sinusoidal_voltage:
      v(t) represented_by V_phasor

    sinusoidal_current:
      i(t) represented_by I_phasor

    relation:
      V_phasor = Z*I_phasor

    REQUIRE:
      common_frequency
      consistent_RMS_or_peak_convention
      consistent_phase_reference

    RULE:
      phasor_values MUST_NOT be mixed_across_different_frequencies_or_amplitude_conventions
  }

  COMPLEX_POWER_MODEL {
    COMPLEX_POWER:
      S_complex = V_rms * conjugate(I_rms)

    FORM:
      S_complex = P + jQ

    APPARENT_POWER:
      |S_complex| = V_rms*I_rms

    POWER_FACTOR:
      PF = cos(phi)
      FOR simple_sinusoidal_voltage_current_phase_difference

    RELATION_TO_IMPEDANCE:
      phase_difference = arg(Z)
      under passive_linear_load_context

    RULE:
      impedance_phase MUST be interpreted_with_defined_current_voltage_polarity_and_sign_convention
  }

  FREQUENCY_MODEL {
    GENERAL:
      Z = Z(omega)

    possible_causes:
      capacitance
      inductance
      skin_effect
      dielectric_loss
      magnetic_loss
      parasitic_elements
      transmission_line_effects

    RULE:
      impedance_value_without_frequency
      MAY be semantically_incomplete
  }

  NONIDEAL_MODEL {
    resistor:
      may_include_parasitic_L_and_C

    capacitor:
      may_include_ESR
      leakage
      ESL
      dielectric_loss

    inductor:
      may_include_winding_resistance
      parasitic_capacitance
      core_loss

    RULE:
      real_component_and_imaginary_component
      MAY both_be_frequency_dependent
  }

  RELATIONSHIPS {
    Impedance -> RATIO_OF -> VoltagePhasorAndCurrentPhasor
    Impedance -> MEASURED_IN -> Ohm
    Impedance -> HAS_REAL_PART -> Resistance
    Impedance -> HAS_IMAGINARY_PART -> Reactance
    Impedance -> INVERSE_OF -> Admittance
    Inductance -> CONTRIBUTES_TO -> PositiveReactance
    Capacitance -> CONTRIBUTES_TO -> NegativeReactance
    Impedance -> DETERMINES -> VoltageCurrentPhaseRelationship
    Impedance -> MAY_DEPEND_ON -> Frequency
    Impedance -> CONTRIBUTES_TO -> AC_PowerBehaviour
  }

  SEMANTIC_EQUIVALENCE {
    "electrical impedance" ~= impedance
    "complex resistance" ~= impedance ONLY as informal_AC_description
    "ohm" ~= impedance_unit

    impedance != resistance
    impedance != reactance
    impedance != admittance
    impedance != conductance
    impedance != inductance
    impedance != capacitance
  }

  CONSTRAINTS {
    impedance_is_complex_in_general = true
    SI_unit = ohm
    phasor_ratio_requires_nonzero_current_phasor = true
    impedance_and_resistance_are_not_generally_semantically_equivalent = true
    impedance_and_reactance_are_not_semantically_equivalent = true
    impedance_and_admittance_are_inverse_not_synonyms = true
    frequency_context_is_required_for_frequency_dependent_impedance = true
    RMS_peak_and_phasor_conventions_must_be_preserved = true
    phase_reference_and_polarity_must_be_preserved = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      Impedance

    COMMON_INSTRUMENTS:
      LCR_meter
      impedance_analyser
      vector_network_analyser
      impedance_bridge
      oscilloscope_plus_signal_source
      source_measure_system

    METHODS:
      voltage_current_amplitude_phase_measurement
      bridge_measurement
      network_parameter_measurement
      frequency_sweep
      transient_model_inference

    RECORD:
      complex_value
      magnitude
      phase
      real_part
      imaginary_part
      unit
      frequency
      angular_frequency
      RMS_or_peak_convention
      voltage_level
      current_level
      DC_bias
      temperature
      component_or_network
      terminal_definition
      measurement_method
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_impedance =
        best_estimate_complex_value
        +/- magnitude_and_phase_or_component_uncertainty
  }

  REASONING_RULES {
    IF voltage_phasor_known AND current_phasor_known AND current_phasor != 0
      THEN impedance = voltage_phasor/current_phasor

    IF impedance_known
      THEN resistance_component = real_part(impedance)
      AND reactance_component = imaginary_part(impedance)

    IF resistance_and_reactance_known
      THEN impedance = resistance + j*reactance

    IF impedance_known AND impedance != 0
      THEN admittance = 1/impedance

    IF ideal_inductance_known AND frequency_known
      THEN inductive_impedance = j*2*pi*frequency*inductance

    IF ideal_capacitance_known AND frequency_known
      AND frequency != 0 AND capacitance != 0
      THEN capacitive_impedance =
        1/(j*2*pi*frequency*capacitance)

    IF series_impedances_known
      THEN equivalent_impedance = sum(series_impedances)

    IF parallel_admittances_known
      THEN equivalent_admittance = sum(parallel_admittances)

    IF R_L_C_known AND ideal_series_RLC_context
      THEN resonance_frequency =
        1/(2*pi*sqrt(inductance*capacitance))
  }

  NETWORK_MODEL {
    input_impedance:
      impedance_seen_at_defined_input_port

    output_impedance:
      impedance_seen_at_defined_output_port_under_defined_source_conditions

    characteristic_impedance:
      transmission_line_wave_ratio_quantity

    REQUIRE:
      port_definition
      termination_conditions
      frequency
      reference_direction

    RULE:
      different_impedance_types MUST_NOT be treated_as_interchangeable
  }

  TRANSMISSION_LINE_CONTEXT {
    characteristic_impedance:
      Z_0 = sqrt((R_prime + j*omega*L_prime)/(G_prime + j*omega*C_prime))

    CONDITIONS:
      distributed_parameter_transmission_line_model

    RULE:
      lumped_impedance_model MAY become_invalid_when_structure_size_is_not_small_relative_to_wavelength
  }

  UNCERTAINTY_MODEL {
    sources:
      amplitude_measurement
      phase_measurement
      frequency_accuracy
      calibration
      fixture_parasitics
      cable_and_connector_effects
      reference_plane
      temperature
      signal_level
      DC_bias
      noise
      model_assumptions

    PROPAGATION:
      complex_impedance_uncertainty
      <- magnitude_phase_or_real_imaginary_input_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    SI_unit_confidence: 1.00
    complex_representation_confidence: 1.00
    RLC_relationship_confidence: 1.00
    network_context_confidence: 0.98
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when frequency, phase convention,
      amplitude convention, port definition, reference plane,
      operating level, calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK unit_consistency
    CHECK complex_value_representation
    CHECK frequency_context
    CHECK RMS_peak_phasor_convention
    CHECK voltage_current_phase_reference
    CHECK impedance_vs_resistance_distinction
    CHECK impedance_vs_reactance_distinction
    CHECK impedance_vs_admittance_distinction
    CHECK series_parallel_topology
    CHECK ideal_vs_nonideal_component_model
    CHECK port_and_reference_plane_for_network_impedance
    CHECK lumped_vs_distributed_model
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_frequency
      identify_complex_representation
      identify_RMS_or_peak_convention
      identify_component_or_network
      identify_terminals_or_port
      attach_voltage_current_levels
      attach_DC_bias_when_relevant
      attach_temperature
      normalize_to_ohm
      preserve_original_representation
      attach_uncertainty
      update_impedance_state

    ON frequency_change:
      update_frequency
      recompute_reactance
      recompute_impedance
      update_phase_and_magnitude
      preserve_previous_frequency_state

    ON component_parameter_change:
      update_R_L_C_or_distributed_parameters
      recompute_network_impedance
      preserve_component_provenance

    ON topology_change:
      update_series_parallel_or_network_connections
      recompute_equivalent_impedance
      preserve_original_component_impedances

    ON calibration_revision:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Impedance
    canonical_symbol: Z
    canonical_SI_unit: ohm

    interpretation_order:
      identify_quantity
      identify_complex_value_or_magnitude_phase
      identify_unit
      identify_frequency
      identify_RMS_peak_or_phasor_convention
      identify_resistance_and_reactance_components
      identify_inductive_or_capacitive_context
      identify_series_parallel_or_network_topology
      identify_port_and_reference_plane
      identify_operating_level_bias_and_temperature
      identify_ideal_or_nonideal_model
      identify_measurement_method
      identify_uncertainty
      normalize_units
      infer_AC_network_relationships

    ambiguity_controls:
      distinguish_impedance_from_resistance
      distinguish_impedance_from_reactance
      distinguish_impedance_from_admittance
      distinguish_impedance_from_conductance
      distinguish_impedance_from_inductance
      distinguish_impedance_from_capacitance
      distinguish_magnitude_from_real_component
      distinguish_input_output_and_characteristic_impedance
      preserve_frequency_phase_and_reference_plane
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_electromagnetic_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Electromagnetic Measurements
      -> Impedance Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      units
      relationships
      constraints
      resistive_model
      inductive_model
      capacitive_model
      series_model
      parallel_model
      resonance_model
      admittance_model
      phasor_model
      complex_power_model
      frequency_model
      nonideal_model
      network_model
      transmission_line_context
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      complex_representation_changes
      RLC_model_changes
      frequency_model_changes
      network_topology_changes
      distributed_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW