# The Switch Matrix

Historical example of a physical switch matrix used for telephone relay stations.

We already know that some switches will lie between an electrical source and a load. There might be just one switch, or perhaps a large group. In any case, there is a complexity limit. If a converter has m inputs and n outputs, even the densest possible collection of switches would have a single switch between each input line and each output line. The m X n switches in the circuit can be arranged according to their connections. The pattern suggests a matrix.

Power electronic circuits are of two types:

1. Direct switch matrix circuits. In these circuits, any energy storage elements are connected to the matrix only at the input and output terminals. The storage elements effectively become part of the source or load. A full-wave rectifier with external low-pass filter is an example of a direct switch matrix circuit. In the literature, these circuits are sometimes just called matrix converters.
2. Indirect switch matrix circuits, also termed embedded converters. These circuits, like the polarity reverser example, have energy storage elements connected within the matrix structure. There are usually very few storage elements in such a case, and indirect switch matrix circuits are often analyzed as a cascade connection of two direct switch matrix circuits with the storage in between.

The switch matrices in realistic applications are usually small. For example, a typical source has two connections, as does a typical load. a two-by-two switch matrix is just about as complicated as it gets in this situation. A rectifier example is illustrated below. The source and the load have two connections each. More generally, these represent a source and a load with a 2 X 2 matrix in between. The matrix is commonly drawn as the H-bridge. In contrast, a half-wave rectifier uses just one input and one output line – a single switch forms its “matrix”. A more complicated example is the three-phase AC-DC converter. There are three possible inputs, and two terminals of the DC circuit provide outputs, to give a 3 X 2 switch matrix.

Another example is similar to that in a personal computer power supply. In this case, there are five separate DC loads, and the switch matrix is 2 X 10. There are very few practical converters with more than about 24 switches, and most designs used fewer than 12 switches.

A switch matrix provides a clear way to organize devices for a given application. It also helps to focus the effort into three major problem areas. Each of these areas must be addressed effectively in order to produce a useful power electronic system.

• The Hardware problem $\rightarrow$ Build a switch matrix.
• The Software problem $\rightarrow$ Operate the matrix to achieve the desired conversion.
• the Interface problem $\rightarrow$ Add energy storage elements to provide the filters or intermediate storage necessary to meet the application requirements.

In a generic circuit, we must decide what electronic parts to use, how to operate them, and how best to filter the output to satisfy the needs of the load.

As a first stem, replace the switches in the general rectifier with diodes. One choice of diode directions gives the full-wave bridge rectifier circuit shown below.

A basic full wave diode bridge rectifier circuit is one circuit described by a 2X2 switch matrix.

Other devices would be used if the objective were an inverter or a controlled rectifier. We will look at consistent choices of device types throughout our study of power electronics. The diode directions must be consistent with circuit laws and must provide the intended energy flow. The choice of diodes gives one solution to the hardware problem, while the choice of diode directions in effect represents a solution of the software problem for a rectifier circuit. Let us consider the issues of circuit laws, first, and examine how they affect switch matrices.