Allowed lofLil power dissipation Winding fill factor Core IcKS exponent Core loss coefficient The core dimensions are expressed in cm: Core cross-secQonal area Core window area Mean length per turn Magnetic path length Peak ac flux density Wire areas

A ,.A.......

(W/tmV)

(cm)

(cm)

(cm)

Cfcsla)

(cm)

The use of centimeters rather than meters requires that appropriate factors be added to the design equations.

15.2.1 PrtKedure

1. Determine core size.

(15.19)

Choose a core that is large enough to satisfy this inequality. If necessary, it may be possible to use ai smaller core by choosing a core material having lower loss, i.e., smaller A;..

2. Evaluate peak ac flu.x density.

Afl =

P>.5L (MLT) 1

2K..

15+ 1,1

(15.20)

Checlc whether iB is greater than the core material saturation flux density. If the core operates with a flux dc bias, then the dc bias plus AB should not exceed the saturation flux density. Pioceed to die next step if adequate margins exist to prevent saturation. Otherwise, (1) repeat the procedure using a core material having greater core loss, or (2) use the A design method, in which the maximum flux density is specified.

3. Evaluate primary turns.

20.8A.

(i,5.21)

4. Choose nimihers of turns for other windings According to the desired turns ratios:

(15,22;

5. Evaluate fraction of window area allocated to each winding.

6. Evaluate wire sizes.

hi,.., 14I

(15,23)

(15.24)

Choose wire gauges to satisfy these criteria

A winding geometry can now be determined, and copper losses due to the proximity effect can be evaluated. If these losses are significant, it may be desirable to further optimize the design by reiterating the above steps, accounting for proximity losses by increasing the effective wire resistivity to the value Pig - PcacJtk where P. is the actual copper loss including proximity effects, and Pj is the copper ioss obtained when the proximity effect is negligible.

If desired, the power losses and transformer model parameters can now be checked. For the simple model of Fig. 15.4, the following parameters are estimated:

Magnetizing inductance, referred to winding 1:

) f.

Peak ac magnetizing current, referred to winding 1:

Fig. 1S,4 Computed elements of simpl& transformer model.

ЛЛг-

-ЛЛг-

Winding resistanees:

p ,{MLT)

The aire loss, topper k)ss, and total power loss can be determined using Eqs. (15.1), (15.7), and (15.8), respectively.

15J EXAIVIPLES

15.3.1 Example 1: Sittgle-Output Isoluled Cuk Converter

As an example, let us consider the design of a simple two-winding transformer forthe Cuk converter of Fig. 15.5. This transformer is to be optimized at the operating point shown, corresponding to D = 0.5. The steady-state converter solution is V, = V, V. = V. The desired transformer turns ratio is

+ Id*) - - +

25 V

© 4a

v.CO g +

20 a

j,(0 n:l (г(0 Fig. IS.S Isolated Cuk cottvertcr example.