By Burns K., Dolgopyat D., Pesin Y. (eds.)

ISBN-10: 0821842862

ISBN-13: 9780821842867

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**Example text**

2) in general. For the convenience of application in different power electronic circuits, we will consider • Unipolar modulation: The carrier changes between 0 and a positive peak (Cm ); the reference is always positive; and the PWM output switches between 0 and 1; and 34 J. Sun • Bipolar modulation: The carrier is symmetric about zero, with a amplitude equal to Cm ; the reference is a sine wave without DC offset; and the PWM output switches between −1/2 and +1/2. The angular frequency of the carrier and the reference will be denoted ωc (= 2πfc ) and ω1 (= 2πf1 ), respectively, and will be used in place of fc and f1 when it is convenient.

1 Small-Signal Modelling of Constant-Frequency PWM A PWM-controlled converter can be described by a set of linear differential equations in each conduction state of the switches if all components are linear and the switches (including diodes) are assumed ideal. The number of possible conduction states depends on the number of switches and the operation pattern of the converter. 15 depicts three basic DC–DC converter circuits each of which uses one switch and one diode. In the continuous conduction mode (CCM) of operation [23], that is, when the inductor current flows continuously, the diode conducts whenever the switch is O FF , such that there are only two possible conduction states over a switching cycle: (a) the switch is O N and the diode is O FF ; (b) the switch is O FF and the diode is O N .

21c–d, respectively, to reduce either high-frequency current flow from the source or to the sink. 4 Summary Some relatively unknown, but interesting, DC–DC power converter topologies have been discussed in this chapter. The derivation of such converters and their relationships with fundamental converters have been discussed from a circuit-theoretic viewpoint. It is illustrated that current converters that may be useful for applications requiring current sources and sinks are derivable from fundamental voltage converters by using the principle of circuit duality or by using a proposed framework of a switching-capacitor cell.

### Geometric and Probabilistic Structures in Dynamics by Burns K., Dolgopyat D., Pesin Y. (eds.)

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