Voltage regulation—the change in secondary voltage from no-load to full-load—is affected by copper loss. High copper loss increases voltage drop under load, causing poor regulation. Optimized winding resistance and conductor sizing minimize copper loss, improving voltage stability. OEM audio and lighting transformers must maintain tight regulation to ensure consistent sound quality or LED brightness.

    Voltage regulation and copper loss are intrinsically linked through the internal impedance of the transformer, primarily its winding resistance. The handbook explains this relationship clearly.

  1. Definitions:

    • Voltage Regulation (VR): The change in secondary output voltage from no-load to full-load, expressed as a percentage of the full-load voltage. $VR% = \frac{V_{no-load} – V_{full-load}}{V_{full-load}} \times 100%$. A lower VR indicates a “stiffer” power supply.

    • Copper Loss ($P_{cu}$): The $I^2R$ loss in the windings under load.

  2. The Direct Relationship:
    For a resistive-inductive load, the simplified formula for voltage regulation is: $VR% \approx \frac{I R \cos\phi + I X \sin\phi}{V} \times 100%$, where:

    • I is the load current.

    • R is the total equivalent resistance referred to the secondary.

    • X is the total equivalent leakage reactance.

    • cosφ is the load power factor.

    • V is the rated output voltage.

    • The term I R \cosφ is the resistive voltage drop, directly caused by the winding resistance.

  3. How Copper Loss Affects Voltage Regulation:

    • High Copper Loss implies High Winding Resistance (R). A high R leads to a larger resistive voltage drop (I * R) when load current flows.

    • This larger voltage drop directly translates into a greater decrease in output voltage from no-load to full-load, resulting in poorer (higher) voltage regulation.

    • For purely resistive loads (cosφ = 1), the relationship is most direct: VR% ∝ I * R. Since P_cu = I^2 R, it’s clear that for a given current, higher copper loss (higher R) causes worse regulation.

  4. Practical Implications from the Handbook:

    • Design Trade-off: To achieve good voltage regulation (low VR%), the winding resistance R must be minimized. This requires using larger wire (lower current density), which reduces copper loss but increases cost and size.

    • Load Dependency: Both copper loss and voltage regulation worsen with increasing load current (I), but copper loss worsens with $I^2$, while the resistive part of VR worsens with I.

    • Diagnostic Tool: Measuring a transformer’s voltage regulation under test load provides indirect insight into the magnitude of its winding resistance and, by extension, its designed copper loss.

Key Insight: Copper loss and voltage regulation are two sides of the same coin—the winding resistance. You cannot independently optimize one without affecting the other. A transformer designed for high efficiency (low copper loss) will inherently have good voltage regulation. The handbook stresses that target specifications for both must be considered simultaneously in the design process.