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电工学原理及应用electricalengineering经典双语详解
第1页
Introduction
Initial state and steady state
First-order RC Circuits
First-order RL Circuits
电工学原理及应用electricalengineering经典双语详解
第2页
t
E
New steady state
transient
C
Old steady state
K
R
E
+
_
Switch K is closed
Introduction
New steady state
R
Us
+
_
Conception of steady state and transient state
When t=0，uc(0)=0
When t=∞, uc(∞)=Us
Old steady state
电工学原理及应用electricalengineering经典双语详解
第3页
Why the transient response happens?
No transient
I
Resistive circuit
t = 0
E
R
+
_
I
K
Resistor is a energy-consumption element, current is proportional to voltage, no transient response will happen even if changing source
电工学原理及应用electricalengineering经典双语详解
第4页
Energy can not change instantly because of accumulating or decaying period.
Charging or discharging
Change gradually
Electric field energy
E
K
R
+
_
C
uC
E
t
电工学原理及应用electricalengineering经典双语详解
第5页
Magnetic field energy
Change gradually
K
R
E
+
_
t=0
iL
t
E/R
Energy can not change instantly because of accumulating or decaying period.
电工学原理及应用electricalengineering经典双语详解
第6页
The causes of transients
1. Energy storage elements
-inductors and capacitors
change gradually；
circuit, such as switching source.
电工学原理及应用electricalengineering经典双语详解
第7页
Transients
The time-varying currents and voltages resulting from the sudden application of sources, usually due to switching.
By writing circuit equations, we obtain integro-differential equations. These equations can be converted to pure differential equations by differentiating time.
The study of transients require us to solve differential equations .
电工学原理及应用electricalengineering经典双语详解
第8页
Initial state and steady state
Assume changing circuit when t=0, then t=0– is end point of old steady state; t=0+ is the start point of transient state.
From t=0–to t=0+,iL、uC can not change suddenly.
t=0
t
t=0-
t=0+
The law of changing circuit
(换路定则)
电工学原理及应用electricalengineering经典双语详解
第9页
Exa
Solu
(1)Brofore switch
We know that
By the law of
circuit changing
Knowns：before circuit changing，C、L have no energy; Find：the currents and voltages of all elements。
S
(a)
C
U
R2
R1
t=0
+
-
L
How to get initial value
电工学原理及应用electricalengineering经典双语详解
第10页