# Switched electrical circuits as computing systems

We can define computations as processes of working of electrical circuits which are associated with sequences of (meaningful) events. Let’s take these events as discrete, i.e. something that can be enumerated with integer indices.

We can then map sequences of events onto integer numbers, or indices. Events can be associated with the facts of the system reaching certain states. Or, in a more distributed view, individual variables of the system, reaching certain states or levels. Another view is that a component in the system’s model moving from one state to another.

To mark such events and enable them we need sensory or actuating properties in the system. Why not simply consider an element called “switch”:

Switch = {ON if CTRL= ACTIVE, OFF if CTRL = PASSIVE}

What we want to achieve is to be able to express the evolution of physical variables as functions of event indices.

Examples of such computing processes are:

• Discharging capacitance
• Charging a (capacitive) transmission line
• Switched cap converter
• VCO based on inverter ring, modelled by switched parasitic caps.

The goal of modelling is to find a way of solving the behaviour of computational electrical circuits using “switching calculus” (similar to Heaviside’s “operational calculus” used to solev differential equations in an efficient way).