If a system has two or more input variables and two or more output variables, simultaneous equations for the output variables can be written. In general, when the number of inputs and outputs is large, the simultaneous equations are written in matrix form.
Electric circuit theory is often divided into special topics, either on the basis of how the voltages and currents in the circuit vary with time (direct-current, alternating-current, nonsinu-soidal, digital, and transient circuit theory) or by the arrangement or configuration of the electric current paths (series circuits, parallel circuits, series-parallel circuits, networks, coupled circuits, open circuits, and short circuits). Circuit theory can also be divided into special topics according to the physical devices forming the circuit, or the application and use of the circuit (power, communication, electronic, solid-state, integrated, computer, and control circuits).
Fortunately, most of these transistors occur in pairs, such as the npn and the pnp bipolar junction transistors, or the n-channel and the p-channel MOSFETs, allowing designers to work symmetrically with positive and negative signals and sources. This statement may be clarified by noting that transistors can be characterized by graphs of output current i versus output voltage v that are parametrized by an input current (in the case of the bipolar junction transistor) or input voltage (in the MOSFET and JFET cases). Typically, the curves for an npn bipolar junction transistor or an n-channel field-effect transistor are used in the first quadrant of the output i-v plane, while for a pnp bipolar junction transistor or a p-channel field-effect transistor the same curves show up in the third quadrant. Mathematically, if i = f(v) for an npn bipolar junction transistor or n-channel field-effect device, then i = -f(-v) for a pnp bipolar junction transistor or p-channel field-effect device when the controlling parameters are also changed in sign.
Circuit diagrams show connectors between components and the locations of connectors and lead-ins; such diagrams also illustrate methods of laying out, mounting, and fastening conductors, cables, and piping. Others show external connections to other articles; such diagrams are used for the installation and operation of complex units. Diagrams showing the principal parts of a complex and the interconnections between subassemblies when the complex is installed and operated are designed primarily to give a general representation of the complex. Layout diagrams show the relative spatial arrangement of components.