Tài liệu Circuits & Electronics P14 pptx

6.002 Fall 2000 Lecture
1
14
6.002
CIRCUITS
AND
ELECTRONICS
State and Memory
6.002 Fall 2000 Lecture
2
14
C
+
–
C
v
I
v
+
–
R
1
Recall
Reading: Sections 10.3, 10.5, and 10.7
Review
Vv
II
0t
≥
=
for

()
RC
t
IIC
eVVv
−
−+=
()
C
v 0
()
C
v 0
6.002 Fall 2000 Lecture
3
14
t
I
v
0
t
C
v
0
I
V
( )
0
C
v

I
v
I
V
This lecture will dwell on the
memory property of capacitors.
For the RC circuit in the previous slide
Notice that the capacitor voltage for is
independent of the form of the input voltage
before . Instead, it depends only on the
capacitor voltage at , and the input voltage
for .
0t
≥
0t
≥
0t
=
0t
=
0t
≥
()
RC
t
IIC
eVVv
−
−+=
()

C
v
0
6.002 Fall 2000 Lecture
4
14
VCq
=
for linear capacitors,
capacitor voltage
V
is also state variable
state variable, actually
State
:
summary of past inputs relevant
to predicting the future
State
6.002 Fall 2000 Lecture
5
14
()()
RC
t
ICIC
eVvVv
−
−+= 0
1
Back to our simple RC circuit

( ) ( )( )
tvvfv
ICC
,0
=
State
Summarizes the past input relevant
to predicting future behavior
6.002 Fall 2000 Lecture
6
14
We are often interested in circuit
response for

zero state
v
C
(0) = 0

zero input
v
I
(
t
) = 0

zero input response or
ZIR
()
RC

t
CC
evv
−
= 0
RC
t
IIC
eVVv
−
−=
Correspondingly,

zero state response or
ZSR
2
3
State