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Source: SWITCHMODE POWER SUPPLY HANDBOOK

CHAPTER 5

OPTIMUM 150-W TRANSFORMER DESIGN EXAMPLE USING NOMOGRAMS

5.1 INTRODUCTION
The following example will demonstrate the rapid optimization possible using the various nomograms shown in Chap. 4. The transformer is a self-oscillating half-bridge square-wave DC-to-DC converter operating at 20 kHz and producing 150 W. To minimize leakageinductance and skin effects, a sandwiched construction as shown in Fig. 3.4.8c is to be used. The transformer is required to meet UL and VDE safety requirements, and will have two grounded safety screens. The input voltage is 200 V, and the output is to be 25 V at 6 A, using bridge rectification. The temperature rise is to be 30°C in free air cooling conditions.

5.2 CORE SIZE AND OPTIMUM FLUXDENSITY SWING
For an output power of 150 W at 20 kHz with a 30°C temperature rise, for halfbridge or push-pull applications, the nomogram shown in Fig. 3.4.3 indicates an EC41 core with a flux density swing of 330 mT for optimum efficiency. (The example is shown on the nomogram.)

5.2.1 Use of Nomogram 3.4.3
Step 1. Enter the nomogram on the right-hand side with the required power (150 W), and atthe top with the required operating frequency (20 kHz), as shown in the example drawn on the nomogram. Step 2. The horizontal line from the intersection of the frequency and power lines gives the area product AP (left) and some examples of standard switchmode cores 3.108
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OPTIMUM 150-W TRANSFORMER DESIGN EXAMPLE USING NOMOGRAMS 5. OPTIMUM 150-W TRANSFORMER DESIGN 3.109

(right). In this example, AP=2.2, and suitable cores would be EC41 or ETD34/17/11. Choose one of the recommended cores, or select a different core type using the area product value. In this example,the EC41 (FX 3730) core is chosen. Step 3. The vertical projection from the intersection of the power line with the frequency line to the lower flux density swing scale indicates a B value of 330 mT. Hence, for this example, an EC41 core with a flux density swing of 330 mT is chosen.

5.3 CORE AND BOBBIN PARAMETERS
Core type=EC41 Area product of EC41 (core)=2.6 cm4 Window area of bobbin=134 mm2of core=215 mm2 Width of bobbin=24 mm Effective core area=121 mm2 Topology factor K´ (from App. 4.A)=0.164 Total weight (cores)=52 g Optimum flux density swing ∆B from Fig. 3.4.3=330 mT Frequency=20 kHz Half period=25 µs

5.4 CALCULATE PRIMARY TURNS
The converter is in square-wave full-conduction-angle operation, so the maximum “on” period for each drive device is a half cycle, or 25 µs. (Thistype of converter is sometimes referred to as a DC transformer; see Part 2, Chap. 17.) A single halfperiod square pulse gives the maximum primary volt-seconds stress; hence the turns can be established from a single half cycle using the volt-seconds approach. From Faraday’s law of induction,

where Np=primary turns V=primary voltage (200 V) t=“on” period (25 µs) ∆B=flux density swing (0.33 T)Ae=effective core area (121 mm2) Hence

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OPTIMUM 150-W TRANSFORMER DESIGN EXAMPLE USING NOMOGRAMS 3.110 PART 3

5.5 CALCULATE PRIMARY WIRE SIZE
The bobbin window area Awfor the EC41 is 134 mm2. Kub, the bobbin window copper utilization factor, is 50% (Appendix 4.A). For equal primary and secondary loss, 25% will be used for each winding. Hence 25% of Aw is used for the primary winding window Awp. The rest is used for insulation and screens. Hence primary window area Awp is

The area available for each turn is

Although round wire, which would normally...