11.1 Power and Energy Relations for a Simple RC Circuit

• Instantaneous Power

• Simple RC circuit

• Capacitor Charging Dynamics equation:

• Instantaneous Power for the RC circuit:

• Energy over period of 0 to T

• Total energy for the RC circuit:

10.7.4 A Static Memory Element

• The static memory element can store a value written into it indefinitely 
• Static memory element example using a trickle switch:

10.7.3 Design of the Digital Memory Element

• Circuit implementation of a memory element:

10.7.2 An Abstract Digital Memory Element

• An abstract one-bit memory element:

10.7 Digital Memory

10.7.1 The Concept of Digital State

• The value stored in memory is simply a digital state variable in a manner analogous to an analog state variable value stored on a capacitor

10.5.3 Zero-Input and Zero-State Response

• State variable allows us to solve transient problem by superposition
• Total response is the sum of the zero-input-response (ZIR) and the zero-state-response (ZSR)
• The particular solution and the homogeneous solution are terms which apply to a method of solving differential equations 
• Zero-input and zero-state responses arise from a particular way of partitioning the circuit problem into two simpler subproblems. The resulting subcircuits can be solved by finding the homogeneous solution and particular solution in each case.

10.5.2 Computer Analysis using the State Equation

• One advantage of state equation formulation is that even in the nonlinear case, the equations can be readily solved on a computer
• The value of state variable at time t + dt can be estimated by standard numerical method ie. Euler's method:

• The value of vC at time t = t + 2dt can be determined in like manner from the value of vC(t0+dt) and i(t0+dt) . Subsequent value of vC can be determined in same process
• By choosing small value of dt, a computer can determine the waveform of vC(t) to a certain degree of accuracy
• This process illustrates the fact that the initial state contains all the information that is necessary to determine the entire future behavior of the system from the initial state and subsequent input
• This procedure works even for circuits with many capacitors and inductors, linear or nonlinear, because these higher-order circuits can be formulated in term of a set of first order state equations, one for each energy storage element ( with an independent state variable) in the network