10.5 State and State Variables

10.5.1 Concept of State

• Analysis of capacitor and inductor circuits based on their state/memory aspect is used when the circuit is non-linear or contains a large number of storage elements
• Voltage as a state variable:

• All of the relevant past history of the circuit prior to t1 is summarized in one value, q(t1)
• Variables that have this property are called state variables
• If we know the value of state variable at one time, and the value of input variable thereafter, we can find the value of the state variable for any subsequent time
• The first order differential equations for RC and RL circuits can be written as:

• Linear case: