#### Transcript State-variable method, standard

```[Mathematical Circuit Theory and Analysis]
State-variable method,
standard-form state equations
Seo Yeon Youn
Contents
I. Capacitor and inductor
 Characteristic
II. State variable method
 Approach
 Simple example
III. Standard state form equation
State, state equation
Standard state form equation
Exercise
2
Capacitor and inductor
Capacitor
 An electrical/electronic device that can store energy in the electric field
between a pair of conductors
Protecting voltage changing

.


.
.
3
Capacitor and inductor
Inductor
 A circuit element that consist of a conducting wire usually in form of a coil.
 A Changing magnetic field produced a voltage that was proportional to the
time rate of change of the current that produced the magnetic field.

.

.

.
4
State variable method
Approach
 We want to expect time invariant circuits analysis which contain capacitor
and/ or inductor
 How can we expect this circuit?
State variable method
Express circuit equation by the variables of voltage across the capacitor
and/or current through the inductor. When we use state variable method, we
can solve the problems easily.
5
State variable method
Simple example : state variable characterization of first- order networks
6
State variable method
Simple example : state variable characterization of first- order networks
7
Standard state form equation
What is “State”? “State equation”?
 A state of a lumped network at time t0 is any amount of information given at
time t0 adequate to characterize completely any chosen output function from
time t0 onward given any admissible input function from time t0 onward.
Choice of state is the concept of minimality.
 The equations relating the current state and output of a system to its current
input and past states are called the state equations.
 So in State variable method, we can get next state from state equation which
is formed by the variable of present state and input.
8
Standard state form equation
 Standard state form equation
 State equation in standard form (linear , time-invariant)
(state equation)
(input- state-output equation)
 x : state variable (vector)
 x(t) : state at time t
 x(t0) : initial condition to be the state at time t0
u(t) : input function (vector)
 y(t) : output function(vector)
 Alternate set of standard form state equations would dictate a different choice
for the state.
9
Standard state form equation
 Standard state form equation
 Extended form state equation (linear , time-invariant)
(state equation)
(input- state-output equation)
10
Standard state form equation
Exercise
 Solve
by state variable method.
11
Standard state form equation
Exercise
12
Standard state form equation
Exercise
13
Question
Q&A
Thank You
 In state variable method, mathematical skill is important
 Reference :
-Circuit Theory : An introduction to the state variable approach, R.A. Rohrer
-Basic engineering circuit analysis, J.David Irwin
- www.wikipedia.org
```