Equivalent Models of Linear Transformers(Magnetically Coupled Coils)

1. Linear Transformer

The transformer is said to be linear if the coils are wound on a magnetcially linear material - a material for which the magnetic permeability is constant. Such materials include air, plastic, Bakelite, and wood. In fact, most materials are magnetically linear. Linear transformers are sometimes called air-core transformers, although not all of them are necessarily air-coire.

Fig 1. Linear Transformer

 

2. Equivalent models

 

Fig 2. Determining the equivalent circuit of a linear transformer

 

voltage-current relationships for the primary and secondary coils :

 

 

 

 

 

matrix inversion :

 

 

 

 

 

 

 

 

 

 

① T (or Y) network

Fig 3. An equivalent T circuit

 

 

 

 

 

 

 →

 

 

 

 

② π (or △) network

Fig 4. An equivalent π circuit

 

 

 

 

 

 

 

 

 

 

 →

 

 

 

 

 

 

 

 

3. More on Magnetically Coupled Coils and Ideal Transformers

 

NilssonAppC.pdf