Low-power power transformer design and its examples - Database & Sql Blog Articles

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In this article, we won't go into the detailed application formulas, but rather aim to provide a practical example that readers can use to achieve similar results in their own designs.

1. Calculate Secondary Output Power (P2)

The maximum output voltage in "Li" is 24V. Assuming a rated output current of 1A, and considering a voltage drop of 3V across the K790 tube of the regulator, with negligible power consumption from the voltage doubler rectifier circuit, the secondary output power can be calculated as:

P2 = (24 + 3) × 1 = 27W

2. Calculate Primary Power (P1)

Assuming a transformer efficiency (η) of 0.75, the primary power can be determined as:

P1 = 27W / 0.75 = 36W

Note: Transformer efficiency varies slightly depending on the output power. Typically, for transformers below 100W, the efficiency ranges between 0.7 and 0.8, while for those between 100W and 1000W, it ranges between 0.8 and 0.9. In practice, lower output power usually corresponds to a smaller efficiency value.

3. Calculate Wire Diameter for Primary and Secondary Coils (d)

The formula for calculating wire diameter is:

Where I is the operating current, and J is the current density (usually taken as 3–3.5 A/mm²).

3.1 Primary Winding Wire Diameter

Primary winding current I1 = 36W / 220V = 0.164A

3.2 Secondary Winding Wire Diameter

Secondary winding current I2 = 1A × 1.17 = 1.17A

The 1.17 factor is the rectification coefficient of the AC current on the secondary side of the transformer.

Since 0.67mm is not available in standard enameled wire sizes, we use 0.7mm instead.

Typically, the current density of the secondary coil is kept slightly lower to reduce internal resistance and temperature rise in the power supply.

4. Calculate Core Cross-sectional Area

We use an empirical formula to calculate the core cross-sectional area (S):

Where K is a coefficient related to the output power of the transformer. For output power below 100W, K is typically between 1.25 and 1.1 (with higher values for larger power). In this case, K = 1.15, so:

While theoretically, the tongue width and stack thickness of the core can be adjusted arbitrarily, in practice, factors such as manufacturing process, uniformity, and leakage reactance must be considered. Generally, the tongue width is about 1.5 to 2 times the stack thickness. In this example, an EI core with a tongue width of 66mm and a stack thickness of 2.7cm was selected.

5. Calculate Primary and Secondary Winding Turns

5.1 Number of Turns per Volt (W0)

The formula is:

Where f is the AC frequency (Hz), B is the magnetic flux density (T), and S is the core cross-sectional area (in cm²).

The B value depends on the core material. For example, H23 silicon steel sheets have a B value of 1.42.

5.2 Primary Turns (W1)

W1 = 220 × W0 = 1160 turns

5.3 Secondary Turns (W2)

The 1.2 factor accounts for the rectified and filtered capacitor, while 1.12 compensates for voltage drop due to winding impedance under load. Usually, the secondary turns should be increased by 5% to 25%, especially for smaller output powers.

At this point, the basic design of the transformer is complete, and further optimization or adjustments may be needed based on specific requirements and testing.