Representing the switching action (open and close) of a switch mathematically | Unit Step Function
When writing KCL and KVL equations for circuits that include switches that are used to
connect or disconnect a voltage source from a circuit, the switching action (closing or
opening) can be represented mathematically by step functions. In this video, you will learn how to write the mathematical expressions that describe the opening and closing action of the switch.
Note: However, in an electric circuit or in reality, it is not possible to switch in zero-time (Vo cannot
go from Vo in 0V seconds), for this reason, we cannot turn on a switch with an (ideal) step
function. A more realistic shape of the step function is needed to describe the process when
Vo goes from 0V to Vo or Vo to 0V.
The step function that describes this process is the realistic step function, this step function
replaces the discontinuous jump with a ramp-like waveform with a rise time delta t. Thus, at
t grater than zero, it makes a discontinuous jump to Vo, and from there on forward it remains at V0.
However, we will assume this and not explicitly draw this ramp transition when dealing with
the unit step function.