transformers in electrical netwrork analysis, Summaries of Electrical Network Analysis

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Transformers

By Muhammad Abdul Majid

Mutual Inductance

• When two coils are wound on same ferromagnetic core and are physical close to each other, the magnetic flux generated in one coil links - Itself (where it is generated) - Other coil as well This situation results in the concept of mutual inductance as follows

Mutual Inductance

• In this diagram
• Φ11= Flux produced due to i and linking coil 1
• Φ21= Flux produced due to i and linking coil 2
• Φ1 = Φ11 + Φ21(Total Flux)
• We know Φ = P Ni

Mutual Inductance

• Φ1 = Φ11 + Φ21(Total Flux)
• We know Φ = P Ni
• There fore
• P 1 N1 i1 = P11 N1 i +

P21 N1 i

Mutual Inductance

Transformer equivalent circuit

Transformer equivalent circuit

Transformer equivalent circuit

The last expression is the secondary reflected impedance

Question

• 1. A linear transformer has following parameters R1= 100 ohm, R2= 40 ohm L1= 500mH, L2= 125mH and K= 0.4. It couples a load consisting of a 360 ohm resistor in series with a 0.25 H inductor to a sinusoidal voltage source, The voltage source has an internal impedance 184 ohms of and a maximum voltage of 245.20 V, and it is operating at 800 rad/sec. Calculate (a) the reflected impedance;
• (b) the primary current; and (c) the secondary current.

solution

• Find out circuit parameters and draw circuit diagram first

solution

solution

• Correction
• Use Z22 instead of R22 on LHS

solution

solution

• Correction
• i2 = 0.08 cos(800t - 0 o )