When you design a transformer for any power converter, you face several compromises. You must trade off core size against the number of primary turns and flux density. Another trade-off is the number of turns and winding resistance versus the associated losses. After making these trade-offs, you usually arrive at a good compromise that involves the primary and secondary turns. However, if the converter has more than one output, you face a new set of compromises. For high-power, low-output-voltage converters, the number of secondary turns is often very low. In a forward-converter topology, it is common for a 3.3 V transformer to have one turn in its main secondary winding. This one-turn configuration is ideal for lowering winding resistance and associated power losses.

For this design, the average output voltage is 3.3 V per turn. So, if you need another output from the converter, that output is a multiple of 3.3 V. For a multiple-output power converter, the ratio between the output voltages is often not a whole number (a problem known as “turns granularity”). Referring to this example, if the main output is 3.3 V and the desired auxiliary output is 5 V, two secondary turns yield 6.6 V – a 32% error. A linear regulator could drop 6.6 to 5 V but with the penalty of a power loss. Figure 1 shows an approach to solving the granularity problem if the regulation requirement is not particularly tight (5 to 15%).

Figure 1. |
A delta transformer eliminates the problem of turns-ratio granularity. |

Transformer T_{1} is a normal forward transformer. Each secondary winding has one turn. The control loop regulates the main output, V_{OUT1}, to 3.3 V. The objective is for the auxiliary output to be 5.5 V. With only one secondary turn, that output will also be 3.3 V. Consequently, you need a simple way to increase the voltage. You can add another transformer, T_{2}, dubbed a delta transformer, to the secondaries (Figure 1). The primary of the delta transformer is parallel with the V_{OUT1} winding, and the secondary of the delta transformer is in series with the V_{OUT2} winding. This connection has the effect of adding a portion of the main output voltage, V_{OUT1}, to the auxiliary output, V_{OUT2}. (The turns ratio determines the portion.) In the example above, suppose that the main transformer operates at a 50% duty cycle, and assume that the rectifiers have 0.6 V forward voltage drop. Then, the equation relating V_{OUT1} and the transformer secondary voltage, V_{T1}, during the on time is:

3.3 = (V_{T1} – 0.6)(0.5) – (0.6)(0.5).

Thus, V_{T1} = 7.8 V.

Now, you need to solve for the desired total V_{T} (V_{T2}) of the slave output, V_{OUT2} :

5 = (V_{T2} – 0.6)(0.5) – (0.6)(0.5).

Thus, V_{T2} = 11.2 V. V_{T2} is the sum of the main-transformer secondary voltage and the delta-transformer secondary voltage. The desired delta-transformer secondary voltage is 11.2 – 7.8 = 3.4 V. Because the primary voltage of the delta transformer is also 7.8 V, the turns ratio of the delta transformer must be 7.8/3.4 = 2.3. In this example, you can use 10 and 23 turns for the delta transformer. The main-transformer secondary output delivers current only during its on time, and an internal resistive-voltage drop exists in the secondary output. Therefore, the volt-time product of the main transformer's secondary output is not exactly zero, which is a required condition for the delta transformer's primary to reset. So, you should make the primary winding of the delta transformer resistive to add a small voltage drop in the forward direction or use a small core gap. You can use this approach in all buck regulators to fine-tune an auxiliary output.