A transformer is a device that is based on magnetic coupling.

Transformers are used in both communication and power circuits.

In communication circuits, the transformer is used to match impedances and

eliminate dc signals from portions of the system.

In power circuits, transformers are used to establish ac voltage levels that

facilitate the transmission, distribution, and consumption of electrical power.

𝑴 = 𝒌 𝑳𝟏𝑳𝟐 , 𝒌: 𝒄𝒐𝒖𝒑𝒍𝒊𝒏𝒈 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕

The self-impedance of the mesh containing the secondary

winding is

𝒁𝒓 =𝝎𝑴

𝒁𝟐𝟐

𝟐

𝒁𝟐𝟐∗ 𝒁𝒂𝒃 = 𝑹𝟏 + 𝒋𝝎𝑳𝟏 + 𝒁𝒓

𝒁𝒓 =𝝎𝑴

𝒁𝟏𝟏

𝟐

𝒁𝟏𝟏∗ 𝒁𝒄𝒅 = 𝑹𝟐 + 𝒋𝝎𝑳𝟐 + 𝒁𝒓

• The magnitude of the volts per turn is the same for each coil

• The magnitude of the ampere-turns is the same for each coil

Voltage relationship for

an ideal transformer

Current relationship for

an ideal transformer