SLIDE 1
Seriesrlciuits
Second
- rder
transient
response
current-voltagerelations.hr#
Component
symbol
i - v
relation1-
RResistor
a-WhoOr
= in . R + Or- I
capaoi.r.IE#=cdI
Inductor
terrors
K
= L did + q- dt
Seriesrlciuits order Second transient response - - PowerPoint PPT Presentation
Seriesrlciuits order Second transient response - - PowerPoint PPT Presentation
Seriesrlciuits order Second transient response current-voltagerelations.hr# capaoi.r.IE#=cdI 1- i - v Component symbol relation R = in Resistor a- Who . R Or + - Or I terrors L did Inductor K = + q - dt R L - m -
SLIDE 2
SLIDE 3 R L
- m-mm
¥
- v. =
KVL
: i R tk
+ Vc =- v. =L dd÷
i
= c daff⇒ [
iCtsdt
=Ck
⇒
acct)
= I #idtt
Vo⇒
- i. R t
t
Vo = SLIDE 4
Differentiate
withrespect
to 't
' .- i. R t
i dt
t
Vo =- R
d- i dt
at
+ I i =Divide
by
' L 'da÷+Ed÷+ziT
SLIDE 5
SOLVE
Differential
→ddI÷
+Eddie
+ Ici =- equation
ict )
=ke
then
ddI
=Ks
' estand
ddt
= Ks est⇒
Ks- est
t Ry
Ks est t t k est = O⇒
5-ies-tc-fcheghauE.int?
SLIDE 6
Sot
'
: s't Res t # = o s =- Eh
±
LC=
=- iz
±
→
Fixate:&:Ygeae
⇒
- T
c
- r complex
Define
Wo = Resonantfrequency
Cracks )
÷÷±=¥÷÷÷÷¥z
X
=R
- 2L
attenuation
constant SLIDE 7 S
.
- d If
L>wo→Rootsarereal0VsEyRsDAMmPED
te
x=wo→Roa%segre;da¥atmFE¥
te
×<wo→RjgaEGmek×UN?7?amPED
*
SLIDE 8
DampedFreqnenoy#
B
- frequency
- f
damped
- scillations
f
- FF
radians
"h
"4
Per resonantattenuation second
frequency
constant
=2T(frequency
in Herty) .