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The discontinuous conduction mode (DCM) is usually studied in single-diode and single-inductor converters, where only one DCM exists. However, multiple DCMs can appear in multidiode and multi-inductor topologies and the methodology to identify and characterize these multiple modes is not evident. In this article, a general method to study multiple DCMs is presented. The first step of the method consists in finding out the number <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>, which is the number of diodes conducting current passing exclusively through inductors when the transistor turns <sc>off</sc>. For a given <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> value, <inline-formula><tex-math notation="LaTeX">$2^{n}$</tex-math></inline-formula> possible conduction modes are expected: 1 continuous mode and <inline-formula><tex-math notation="LaTeX">$2^{n}-1$</tex-math></inline-formula> DCMs. The second step is to create an <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-dimensional space called &#x201C;<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-space.&#x201D; In the <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-space, the converter operation describes a straight line when the load changes. This straight line called &#x201C;converter trajectory&#x201D; passes through different <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-dimensional enclosures. Each one of these enclosures represents a different conduction mode. The third step is to determine the borders between conduction modes which are subspaces of <inline-formula><tex-math notation="LaTeX">$(n-1)$</tex-math></inline-formula> dimensions. This method must be followed for both control strategies (i.e., open- and closed-loop controls). The proposed method is applied to the versatile buck&#x2013;boost converter. Experimental results verify the theoretical analysis for all the identified conduction modes.

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A General Method to Study Multiple Discontinuous Conduction Modes in DC&#x2013;DC Converters With One Transistor and Its Application to the Versatile Buck&#x2013;Boost Converter