The equivalent winding resistance, when referred to the primary side, is found by summing the primary winding resistance and the secondary winding resistance referred to the primary.
Here's a breakdown:
Understanding Equivalent Winding Resistance
The equivalent winding resistance simplifies transformer circuit analysis by combining the resistances of both the primary and secondary windings into a single value. This allows calculations to be performed as if all the resistance is concentrated on one side of the transformer (usually the primary).
Calculation
The formula for equivalent resistance referred to the primary side (R01) is:
R01 = R1 + R2'
Where:
- R01 = Equivalent resistance referred to the primary side
- R1 = Resistance of the primary winding
- R2' = Resistance of the secondary winding referred to the primary side.
Referring Secondary Resistance to the Primary
To refer the secondary resistance (R2) to the primary side, you need to divide it by the square of the turns ratio (a). The turns ratio is defined as the number of turns in the primary winding (N1) divided by the number of turns in the secondary winding (N2):
a = N1 / N2
Therefore:
R2' = R2 / a2 = R2 / (N1/N2)2
Complete Formula
Substituting the value of R2', we get:
R01 = R1 + R2 / (N1/N2)2
*R01 = R1 + R2 (N2/N1)2**
Why is this useful?
Using the equivalent winding resistance simplifies calculations for:
- Voltage regulation: Determining the voltage drop across the transformer under load.
- Efficiency: Calculating the copper losses (I2R losses) in the transformer.
- Overall transformer performance: Analyzing the overall performance of the transformer circuit.
By transferring all the resistance to one side, calculations become easier because you only need to deal with one resistance value.
