Electric Transformer and Coupled Inductors

  • Sergey N. Makarov
  • Reinhold Ludwig
  • Stephen J. Bitar


Knowledge of complex arithmetic


Electric transformer (primary winding secondary winding circuit symbol isolation transformer instrumentation transformer current transformer clamp on ammeter potential transformer exciting current magnetizing current magnetizing inductance magnetizing reactance power conservation stored energy turns ratio step-up transformer step-down transformer high-voltage side low-voltage side transformer rating dot convention dotted terminals voltage polarity current reference directions summary of reference directions mechanical analogies) Ideal transformer model (ideal magnetic core ideal open-circuited transformer ideal transformer equations ideal transformer equations in phasor form power conservation stored energy model in terms of dependent sources) Ampere’s law (linked current for ideal magnetic core for multiwinding transformer) Referred (reflected) source network in the secondary Referred (reflected) load impedance in the primary Load reflection Source reflection Reflected resistance Reflected inductance Reflected capacitance Transformer as a matching circuit Matching real-valued impedances Matching arbitrary complex impedances Partial matching condition Power transfer via transformers (for fixed load voltage sending-end voltages for fixed source voltage) Autotransformer (step down step up circuit symbol ideal transformer equations) Multiwinding transformer (ideal circuit equations Ampere’s law telephone hybrid circuit) Center-tapped transformer (ideal transformer equations single-ended to differential transformation 180° power divider 180° power splitter) Real transformer (nonideal low-frequency model Steinmetz model Steinmetz parameters (magnetizing reactance core loss resistance primary leakage reactance secondary leakage reactance primary ohmic resistance secondary ohmic resistance) nonideal transformer model terminology/analysis voltage regulation transformer power efficiency nonideal high-frequency model) Model of two coupled inductors (equations circuit symbol circuit analysis solution for N coupled inductors stored energy conversion to T-network) Mutual inductance (definition of ideal transformer of two coaxial coils) Coupling coefficient (definition largest possible value trend) Wireless inductive power transfer (application basic model examples of) Mutual coupling for nearby magnetic radiators (arrays of magnetic radiators) Lenz’s law 

Supplementary material

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sergey N. Makarov
    • 1
  • Reinhold Ludwig
    • 2
  • Stephen J. Bitar
    • 3
  1. 1.ECE DepartmentWorcester Polytechnic InstituteWorcesterUSA
  2. 2.ECE DepartmentWorcester Polytechnic InstituteWorcesterUSA
  3. 3.Worcester Polytechnic InstituteWorcesterUSA

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