6.31(b). The inductor voltage w-, capacitor current if--, and dc source current are given by

= - (6.39)

With the assumption that the converter operates in the continuous conduction mode, with small inductor current ripple and small capacitor voltage ripple, the magnetizing current / and output capacitor voltage v can be approximated by their dc components, / and V, respectively. Equation (6.39) then becomes

ic = - (6,40)

During the second subiutervah the transistor is in die off-state, and the ditjde conducts. The equivalent circuit of Fig. 6.3i(c) is obtained. The primary-side magnetizing inductance vohage v the capacitor current ifn, and the dc source current forthis subinterval are:

ic-i- (6.41)

h is important to consistently define vt) on the same side of the transformer for all subintervals. Upon making the small-ripple approximation, one obtains

: -I V (6.42)

c - n fi

The vjit), if4t), and i{f) waveforms are sketched in Fig. 6.32 for continuous conduction mode operation.

Application of the principle of volt-second balance to the primary-side magnetizing inductance

yields

Solution for the conversion ratio then leads to

MiD] = = n§ (6,44)

So the conversion ratio of the flyback converter is similar to that of the buck-boost converter, but contains an added factor of n.

Apphcation ofthe principle of charge balance to the output capacitor С leiids to

Fig. 6J2 Flyback ciinvcricr WEiveforms, cotidmious coiidjcticm mode.

Conducting ; devices:]

Solution for / vield.s

-V/R

DT

1/n - V/R

(6.46)

This is the dc component of the magnetizing current, referred to the primary. The dc component of the

source current l is

(6.47)

An equivalent circuit that models the dt components of the flyback converter waveform.4 can now be constructed. Circuits corresponding to tlie inductor loop equation (6.43) and to node equations (6.45) and (6.47) are illustrated in Fig. 6.33(a). By replacing the dependent sources with ideal dc transformers, one obtains Fig. 6.33(b). This кч the dc equivalent circuit of the flyback converter. It contains a 1:D buck-type conversion ratio, followed by a D.l boo.st-type conversion ratio, and an added factor of l:rt atising from the flyback transformer turns ratio. By use of the method developed m Chapter 3, the model can be refined to account for losses and to predict the converter efficiency. The flyback converter can also be operated in the discontinuous conduction mode; analysis is left as a homework problem. Tlie results are similar to the DCM buck-boost converter results tabulated in Chapter 5, but are generalized to account for the turns ratio 1: .

The flyback converter is commonly used at the 50 to 1(X) W power range, as well as in high-voltage power supplies for televisions and computer monitors. It has the advantage of very low parts

s n

1 :D

ki ii*

Fig. 6.33 Flybatk converter equiviilent circuit mrtdei, CCM: (a) circuits correspundiiig to Eqs. (6.43). (6.45), and <6,47); (b) equivalent circuit containing ideal dc transformers.

count. Multiple outputs can be obtained using a minimum number of parts: each additional output requires only an additional winding, diode, and capacitor. However, in comparison with the full-bridge, half-bridge, or two-transistor forward converters, the flyback converter has the disadvantages of high transistor voltage stress and poor cross-regulation. The peak transistor voltage is equal to the dc input voltage V, plus the retlected load voltage V/ir, in practice, additional voltage is observed due to ringing associated with the transformer leakage inductance. Rigorous comparison of the utilization of the flyback transformer with the transformers of buck-derived circuits is difficult because ofthe different functions performed by these elements. The magnetizing current of the flyback transformer is unipolar, and hence no more than half of the core material В-Я loop can be utilized. The magnetizing current must contain a significant dc component. Yet, tiie size of the flyback transformer is quite small in designs intended to operate in the discontinuous conduction mode. However, DCIVI operation leads to increased peak currents in the transistor, diode, and filter capacitors. Continuous conduction mode designs require larger values of L, and hence larger flyback transformers, but the peak currents in the power stage elements are lower.

6.3.5

Boost-Deriveil bolateil Converters

Transformer-isolated boost converters can be derived by inversion ofthe source and load of buck-derived isolated converters. A number of configurations are known, and two of these are briefly discussed here. These converters find some employment in high-voltage power supplies, as well as in low-harmonic rec-tlFier applications.

A full-bridge configuration is diagrammed in Fig. 6.34, and waveforms for the continuous conduction mode are illustrated in Fig. 6.35. The circuit topologies during the first and second subintervals are equivalent to those ofthe basic nonisolated boost converter, and when the turns ratio is 1:1, the inductor current lit} and output current i(t) waveforms are identical to the inductor current and diode current waveforms of the nonisolated boost converter.

During subinterval 1, all four traii.sistois operate in the on state. This comiects the inductor L across the dc input source V, and causes diodes and Dj to be reverse-biased. The inductor current j(f)