Inductance Ontology

# Inductance Ontology — Flow Algebra

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

FLOW InductanceOntology {

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

  PURPOSE:
    Represent inductance as a measurable electromagnetic quantity describing magnetic flux linkage associated with electric current, including self-inductance, mutual inductance, induced voltage, magnetic energy storage, geometry and permeability dependence, AC behaviour, units, dimensional structure, measurement methods, uncertainty, and distinctions from magnetic flux, reactance, impedance and resistance.

  ENTITY Inductance {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: L
    DIMENSION: M * L^2 * T^-2 * I^-2
    SI_UNIT: henry
    SI_SYMBOL: H

    LINEAR_DEFINITION:
      L = lambda_B / I
      WHEN I != 0 AND linear_magnetic_context

    FLUX_LINKAGE_RELATION:
      lambda_B = L*I

    DIFFERENTIAL_INDUCTANCE:
      L_d = d(lambda_B)/dI

    PROPERTIES:
      is_scalar_in_defined_lumped_coil_context
      has_value
      has_unit
      has_dimension
      depends_on_geometry
      depends_on_permeability
      may_depend_on_current
      may_depend_on_frequency
      may_depend_on_temperature
      may_be_nonlinear
      may_have_uncertainty
  }

  ENTITY MagneticFluxLinkage {
    SYMBOL: lambda_B
    SI_UNIT: weber_turn
    RELATION:
      lambda_B = N*Phi_B
      WHEN each_turn_links_same_flux
  }

  ENTITY MagneticFlux {
    SYMBOL: Phi_B
    SI_UNIT: weber
    SI_SYMBOL: Wb
  }

  ENTITY ElectricCurrent {
    SYMBOL: I
    SI_UNIT: ampere
    SI_SYMBOL: A
  }

  ENTITY Voltage {
    SYMBOL: V
    SI_UNIT: volt
    SI_SYMBOL: V
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: henry
      symbol: H
      equivalence:
        1 H = 1 Wb/A
        1 H = 1 V*s/A
        1 H = 1 ohm*s
    }

    COMMON_ALTERNATIVES:
      millihenry
      microhenry
      nanohenry

    CONVERSION_RULE:
      inductance_value(target_unit)
        = inductance_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by_coupling:
      self_inductance
      mutual_inductance

    by_behaviour:
      linear_inductance
      nonlinear_inductance
      static_inductance
      differential_inductance

    by_component:
      air_core_inductance
      magnetic_core_inductance
      parasitic_inductance
      leakage_inductance

    by_distribution:
      lumped_inductance
      distributed_inductance
  }

  SELF_INDUCTANCE_MODEL {
    LINEAR:
      lambda_B = L*I

    CONSTANT_L:
      v_L = L*dI/dt
      UNDER passive_sign_convention

    FARADAY_CONTEXT:
      induced_emf = -d(lambda_B)/dt
      according_to_loop_orientation

    RULE:
      voltage_sign depends_on polarity_and_orientation_convention
  }

  MUTUAL_INDUCTANCE_MODEL {
    ENTITY MutualInductance {
      SYMBOL: M
      SI_UNIT: henry
    }

    RELATION:
      lambda_21 = M_21*I_1

    INDUCED_VOLTAGE:
      v_2 = M_21*dI_1/dt
      with_sign_determined_by_winding_orientation

    RECIPROCITY:
      M_12 = M_21
      UNDER reciprocal_linear_passive_conditions

    RULE:
      winding_orientation_and_dot_convention MUST be preserved
  }

  COUPLING_MODEL {
    coupling_coefficient:
      k = M/sqrt(L_1*L_2)

    IDEAL_PASSIVE_RANGE:
      0 <= abs(k) <= 1

    RELATION:
      M = k*sqrt(L_1*L_2)
  }

  SOLENOID_MODEL {
    IDEAL_LONG_SOLENOID:
      L = mu*N^2*A/l

    PARAMETERS:
      mu = permeability
      N = turns
      A = cross_section_area
      l = magnetic_path_length

    CONDITIONS:
      approximately_uniform_field
      linear_material
      negligible_leakage_and_fringing
      l != 0
  }

  MAGNETIC_CIRCUIT_MODEL {
    RELUCTANCE:
      R_m = l/(mu*A)

    IDEAL_LINEAR_COIL:
      L = N^2/R_m

    RULE:
      magnetic_reluctance_and_electrical_resistance
      are_analogous_but_not_semantically_identical
  }

  ENERGY_MODEL {
    LINEAR_INDUCTOR:
      U = 0.5*L*I^2

    EQUIVALENT:
      U = 0.5*lambda_B*I

    GENERAL_NONLINEAR:
      energy_or_coenergy requires_integral_over_magnetic_state

    RULE:
      linear_energy_formula MUST_NOT be assumed_for_strongly_nonlinear_or_hysteretic_core
  }

  AC_MODEL {
    INDUCTIVE_REACTANCE:
      X_L = omega*L

    IMPEDANCE:
      Z_L = j*omega*L

    FREQUENCY:
      omega = 2*pi*f

    CONDITIONS:
      ideal_linear_inductor
      sinusoidal_steady_state

    RULE:
      inductance != inductive_reactance
      inductance != impedance
  }

  SERIES_PARALLEL_MODEL {
    UNCOUPLED_SERIES:
      L_eq = sum(L_i)

    UNCOUPLED_PARALLEL:
      1/L_eq = sum(1/L_i)

    RULE:
      significant_mutual_coupling requires_coupled_inductor_analysis
  }

  MATERIAL_MODEL {
    PERMEABILITY:
      mu = mu_0*mu_r
      UNDER linear_isotropic_context

    NONLINEAR_EFFECTS:
      saturation
      hysteresis
      remanence
      core_loss

    FREQUENCY_EFFECTS:
      permeability_dispersion
      eddy_current_loss
      skin_effect
      proximity_effect

    RULE:
      measured_inductance MAY depend_on frequency_current_temperature_and_core_state
  }

  RL_TIME_MODEL {
    time_constant:
      tau = L/R
      WHEN R != 0

    CURRENT_GROWTH:
      I(t) = I_final*(1 - exp(-t*R/L))
      UNDER ideal_step_response

    CURRENT_DECAY:
      I(t) = I_0*exp(-t*R/L)
      UNDER ideal_source_free_RL_decay
  }

  RELATIONSHIPS {
    Inductance -> RELATES -> FluxLinkageAndCurrent
    Inductance -> HAS_DIMENSION -> M*L^2*T^-2*I^-2
    Inductance -> MEASURED_IN -> Henry
    Inductance -> DEPENDS_ON -> Geometry
    Inductance -> DEPENDS_ON -> Permeability
    Inductance -> STORES -> MagneticFieldEnergy
    Inductance -> DETERMINES -> InductiveReactance
    Inductance -> CONTRIBUTES_TO -> CircuitImpedance
    MutualInductance -> RELATES -> CoupledCircuits
    TimeVaryingCurrent -> PRODUCES -> InducedVoltage
  }

  SEMANTIC_EQUIVALENCE {
    "inductance" ~= electrical_inductance
    "henry" ~= "H"
    "weber per ampere" ~= "Wb/A"
    "volt second per ampere" ~= "V*s/A"

    inductance != magnetic_flux
    inductance != flux_linkage
    inductance != inductive_reactance
    inductance != impedance
    inductance != resistance
    self_inductance != mutual_inductance
  }

  CONSTRAINTS {
    dimensional_formula = M*L^2*T^-2*I^-2
    SI_unit = H
    lambda_over_I_requires_nonzero_current = true
    inductance_and_magnetic_flux_are_not_semantically_equivalent = true
    inductance_and_reactance_are_not_semantically_equivalent = true
    inductance_and_impedance_are_not_semantically_equivalent = true
    static_and_differential_inductance_must_be_distinguished_for_nonlinear_devices = true
    winding_orientation_must_be_preserved_for_mutual_inductance = true
    frequency_current_temperature_and_material_state_may_be_required = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Inductance

    COMMON_INSTRUMENTS:
      LCR_meter
      impedance_analyser
      inductance_bridge
      network_analyser
      oscilloscope_plus_signal_source

    METHODS:
      direct_LCR_measurement
      impedance_frequency_inference
      voltage_current_phase_measurement
      transient_RL_time_constant_inference
      flux_linkage_current_measurement

    RECORD:
      numerical_value
      unit
      component_or_winding
      terminal_definition
      test_frequency
      test_current
      DC_bias
      temperature
      core_material
      winding_turns
      geometry
      self_or_mutual_inductance
      coupling_coefficient_when_relevant
      measurement_method
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_inductance = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF flux_linkage_known AND current_known AND current != 0
      AND linear_inductance_context
      THEN inductance = flux_linkage/current

    IF inductance_known AND current_known
      AND linear_inductance_context
      THEN flux_linkage = inductance*current

    IF constant_inductance_known AND current_time_derivative_known
      THEN inductor_voltage = inductance*current_time_derivative
      UNDER passive_sign_convention

    IF inductance_known AND current_known
      AND linear_inductor_conditions_apply
      THEN stored_energy = 0.5*inductance*current^2

    IF inductance_known AND frequency_known
      AND ideal_sinusoidal_AC_context
      THEN inductive_reactance = 2*pi*frequency*inductance

    IF permeability_turns_area_and_length_known AND length != 0
      AND ideal_solenoid_conditions_apply
      THEN inductance = permeability*turns^2*area/length

    IF L1_L2_and_coupling_known
      THEN mutual_inductance = coupling*sqrt(L1*L2)

    IF uncoupled_series_inductances_known
      THEN equivalent_inductance = sum(inductances)
  }

  NONIDEAL_MODEL {
    effects:
      winding_resistance
      interwinding_capacitance
      leakage_flux
      core_loss
      skin_effect
      proximity_effect
      self_resonance

    RULE:
      ideal_inductor_model MUST_NOT replace_nonideal_model
      when_parasitic_effects_are_material
  }

  UNCERTAINTY_MODEL {
    sources:
      test_frequency
      test_current
      DC_bias
      temperature
      core_permeability
      geometry
      winding_turn_count
      parasitic_capacitance
      winding_resistance
      instrument_resolution
      calibration_uncertainty
      model_assumptions

    PROPAGATION:
      derived_inductance_uncertainty
      <- measurement_geometry_material_and_model_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    flux_linkage_relationship_confidence: 1.00
    Faraday_relationship_confidence: 1.00
    geometry_material_relationship_confidence: 0.98
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when frequency, current, DC bias,
      temperature, geometry, core material, coupling,
      winding orientation, calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK nonzero_denominators
    CHECK self_vs_mutual_inductance
    CHECK linear_vs_nonlinear_inductance
    CHECK static_vs_differential_inductance
    CHECK inductance_vs_flux_distinction
    CHECK inductance_vs_reactance_distinction
    CHECK inductance_vs_impedance_distinction
    CHECK winding_orientation_and_dot_convention
    CHECK geometry_and_permeability_context
    CHECK frequency_current_bias_and_temperature
    CHECK coupling_for_series_parallel_combinations
    CHECK nonideal_effects_when_material
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_component_or_winding
      identify_self_or_mutual_inductance
      identify_measurement_method
      attach_test_frequency
      attach_test_current
      attach_DC_bias_when_relevant
      attach_temperature
      identify_core_material
      identify_geometry_and_turns
      normalize_to_henry
      preserve_original_value_and_unit
      attach_uncertainty
      update_inductance_state

    ON geometry_or_winding_change:
      update_turn_count
      update_area
      update_magnetic_path_length
      update_coupling_geometry
      recompute_inductance_when_valid
      preserve_previous_state

    ON material_change:
      update_permeability
      update_core_state
      update_hysteresis_or_saturation_model
      recompute_inductance_when_valid
      preserve_material_provenance

    ON frequency_current_or_temperature_change:
      update_operating_conditions
      recompute_inductance_when_model_available
      update_nonideal_parameters
      preserve_previous_operating_state

    ON coupling_change:
      update_mutual_inductance
      update_coupling_coefficient
      recompute_coupled_equivalent_inductance
      preserve_winding_orientation

    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: Inductance
    canonical_symbol: L
    canonical_dimension: M*L^2*T^-2*I^-2
    canonical_SI_unit: H

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_component_or_winding
      identify_self_or_mutual_inductance
      identify_flux_linkage_current_context
      identify_linear_or_nonlinear_behaviour
      identify_static_or_differential_inductance
      identify_geometry_turns_and_permeability
      identify_frequency_current_DC_bias_and_temperature
      identify_coupling_and_winding_orientation
      identify_AC_or_transient_context
      identify_nonideal_effects
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_circuit_and_field_relationships

    ambiguity_controls:
      distinguish_inductance_from_magnetic_flux
      distinguish_inductance_from_flux_linkage
      distinguish_inductance_from_inductive_reactance
      distinguish_inductance_from_impedance
      distinguish_inductance_from_resistance
      distinguish_self_from_mutual_inductance
      distinguish_static_from_differential_inductance
      distinguish_ideal_from_nonideal_inductor_behaviour
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_electromagnetic_quantity_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      self_inductance_model
      mutual_inductance_model
      coupling_model
      solenoid_model
      magnetic_circuit_model
      energy_model
      AC_model
      series_parallel_model
      material_model
      RL_time_model
      nonideal_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      flux_linkage_model_changes
      coupling_model_changes
      geometry_or_material_model_changes
      AC_or_transient_model_changes
      nonideal_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW