ABSTRACT
To obtain an ideal voltage conversion ratio, Vo/Vi, for three converters, all circuit elements and the output ripple voltage are assumed to be ideal and zero, respectively. During the on state of the switch S in the buck converter, the voltage Vi – Vo is applied to the inductor winding, and –Vo is applied during the off state. Since the change in the inductor current during the on state is equal to that during the off state in the steady-state operation, the following equations are obtained:V V
L T
V L
Ti o on o off-= (2.2)V V
T T T
Doi onon off= + = (2.3) For the boost converter, the voltage Vi is applied to the inductor winding, and Vo – Vi is applied in the off state. ThenV
L T
V V L
Ti on o i off= - (2.4) VV T TT Doi on offoff= + = -11 (2.5) Similarly, the following equations are obtained for the buck-boost converter: V
L T
V L
Ti on o off= (2.6)V V
T T
D D
oi onoff= = -1 (2.7) A comparison of the voltage conversion ratios of the three types of the converters is illustrated in Fig. 2.3. Note that the operation of the converter can be divided into two modes, continuous inductor current mode (CCM) and discontinuous inductor current mode (DCM). The above analyses and results are in the case of CCM. In DCM, the inductor current in the off state reaches zero before the switch is turned on, and stays at zero until the next switching cycle. This mode may occur under the conditions of a small load current, a small inductance L, or a low switching frequency. Details of the voltage conversion ratio and dynamic characteristics in DCM are described in Chapter 4, Section 4.4.
