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T-10: Auto-Transformer

ECE 2207 — Explanation Answers (Sorted by Topic)

Topic Overview: This document compiles all semester final questions and explanation answers on Auto-Transformer from 7 years of exams (2017–2024). Repeated questions appear once with all exam appearances noted.

Q3(b): Copper saving in auto-transformer: detailed analysis

📋 Appeared in: 2018 Q3, 2020 Q3(b)

Why some power doesn't need to be "transformed"

In a step-down auto-transformer ( $k = V_{2} / V_{1} < 1$ ):

The output voltage $V_{2}$ is present across the common winding (the lower section of the single winding). The series winding (top section) has voltage $V_{1} - V_{2}$ across it.

The output current $I_{2}$ flows through the common winding. The series winding carries only $I_{1}$ (the primary current).

Power through the series winding: $P_{series} = (V_{1} - V_{2}) \times I_{1} = (1 - k) \times V_{1} I_{1} = (1 - k) S$

This is the power that must be transformed magnetically. The rest, $k S$ , is conducted directly.

The copper needed for the windings is proportional to the VA to be handled:

Series winding: Handles $(1 - k)$ fraction of full VA. Common winding: Current $(I_{2} - I_{1}) = I_{2} (1 - k)$ , voltage $V_{2}$ . VA $= V_{2} \times I_{2} (1 - k) = k S \times (1 - k) / k = (1 - k) S$ .

Total copper in auto-transformer $\propto 2 (1 - k) S$ . For ordinary transformer $\propto 2 S$ .

$\frac{W _{a u t o}}{W _{or d ina r y}} = 1 - k, Copper saved = k S \times (reference copper)$

Step-down and step-up autotransformer circuit schematics

Currents and voltages distribution in an autotransformer

When is auto-transformer best used? When $k$ is close to 1 (small voltage step). For $k = 0.9$ (e.g., 415V/380V), copper saved is 90%. For $k = 0.5$ (220V/110V), only 50% saved: still worthwhile. For $k = 0.1$ (large ratio), only 10% saved: not economical.

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