Transformers

Question 1

Assumptions made when assuming an ideal transformer

Answer 1

• winding resistance are negligible
• no flux linkage (stays within iron core)
• core losses are negabile
• permeability of the core is infinite

Question 2

relationship between steps, voltage and current

Answer 2

V2 / V1 = N2 / N1 = I1 / I2

as they are induced by the same flux

Question 3

what are the two circuits involved in a transformer

Answer 3

primary (input) and secondary (output)

a magnetic flux φ induced in an iron core connects the two circuits

Question 4

reflected impedance Z_in

Answer 4

Z_in = Z_L / n^2
= (N1/N2)^2 V2 / L2

is the impedance of the secondary circuit referred to the primary side

n = N1 / N2

• Impedances in the secondary circuit may be referred to the primary
• Impedances in the primary circuit may be referred to the secondary

Question 5

steps to creating an equivalent circuit

Answer 5

• draw the ideal transformer, following assumptions
• add winding resistance,
• resistance in the primary winding (R1)
• resistance in the secondary winding (R2)
• add leakage reactance, the flux which links one winding without linking the other,
• flux leakage in the primary winding (X1)
• lux leakage in the secondary winding X2
• add magnetising reactance (Xm), accounts for the magnetising flux at no load due to the non-zero reluctance of the core.
• add core loss (Rm)
  total core loss (i.e. eddy current loss + hysteresis loss) can be represented with a parallel resistance
• The complete equivalent circuit
• I2’ is the effective value of the secondary current as seen from the primary side of the transformer.
• Io is the no-load current
• Im is the magnetising current component of the no-load current
• Ic is the core loss component of the no-load current
• Simplifying the equivalent circuit
• refer (move) R1 and X1 to the secondary
  a1’ = a1(N2/N1)^2
  (R and X can be in place of a)
• Rt2 = R2 + R1’ (same for X)