Κυκλώματα - ΗΜΜΥ Πολυτεχνείο Κρήτης
-
Upload
xrhstoskoaksdokf -
Category
Documents
-
view
33 -
download
3
description
Transcript of Κυκλώματα - ΗΜΜΥ Πολυτεχνείο Κρήτης
-
.
-
()
, .
DC .
.
vs(t)=0
.
1. (voltage source)
: .
-
v
i
0
voltage
source
vs
+
vs-
is
+-
i-v .
-
, .
DC .
.
is(t)=0
o.
2. (current source)
: .
-
v
i
0
current
sourceis
+
vs-
is
i-v .
-
.
=
=
gm=
rm=
.
i1
-
.
.
.
()
-
1 2 1 2f x x f x f x
f ax a f x
(linear function): +
(homogeneous function):
(additive function):
-
v t R i t (linear), (time invariant):
v t R i i t
v t R t i t
v t R i,t i t
- (non-linear), (time-varying):
(time-varying):
- (non-linear):
v, i: .
-
v
i
+
v
-
i
0 v
i
0
diode ideal
diode
v
i
0
tunnel
diode
+
v
-
inegative
slope
1
qv t
kTsi t I e
,
.
: - .
(short-circuit).
v
i
0v
i
0v
i
slope=tan=1/R
0
(open-circuit).
(characteristics) -V:
dvr =di
(dynamic resistance):
-
- .
- .
-
(bilateral) i-v
(0,0) (v, i)
(-v, -i).
.
- /
.
: ,
.
( ): .
-
(capacitors)
( ) ( )dq
q t C v t Cdv
0
1( ) 0
tdq t dvi t i C v t v i d
d t d t C
v(0) = = & v(t) = +
i(t) , v(t) :
v(t) .
, : C v(0)
.
: q v.
- : q-v .
: q-v
.
(capacitance):
S=1/C: (elastance) v, i: .
-
i(0)
L
(inductors)
( ) ( )d
t = L i t L=di
0
1( ) 0
td d iv= v L i t i v d
d t d t L
i(0) = =
i(t) = +
v(t) , i(t) :
i(t) .
.
, :
: i.
=1/L:
(reciprocal inductance)
(inductance):
v, i: .
-
(hysteresis)
i
0
- : -i .
: -i
.
-
: .
v, i: .
-
o
t
ot
p t v t i t E t ,t v i d
to t
&
( ).
.
o
t t
o o o
- t
E(t)= v() i()d = E(t )+ v() i()d E(t )+E t ,t
:
-
(port) :
()
.
-
(equivalent one-ports) =
-.
2
(one-port) :
-
(passive) (
) : E(t)0 t
. 1 3 i-v
[: R0 & p(t) = v(t) x i(t) 0 t]
: (active)
t : (t)
-
/ :
(range) : , , ,
,
,
.
-
:
Ohm
Kirchhoff
-
Georg Simon Ohm 1827:
( )
.
v(t) = R i(t) R
Ohm
v, i R
( ), Ohm ().
, :
v(t)
i(t)
(.. ).
http://upload.wikimedia.org/wikipedia/en/d/de/OhmsLaw.svg
-
:
v(t)R =
i(t)
v(t) = R i(t) , R =
( -
):
:
- - (.
) :
v(t) = R(i) i(t) , R i
v(t)
i(t)
http://upload.wikimedia.org/wikipedia/en/d/de/OhmsLaw.svg
-
1848 Gustav Kirchhoff 2
:
Kirchhoff
-
Kirchhoff (KCL):
,
, .
O KCL t.
O KCL :
-, ,
.
KCL .
-
KCL :
1.
.
2. :
+
-
.
-
Kirchhoff (KCL).
1:
2:
( t)
( t) o:
(node equations)
-
Kirchhoff (KVL):
(loop) .
O KVL t.
O KVL :
-, ,
.
-
KVL :
1. .
2. .
3. :
+
-
.
-
Kirchhoff (KVL).
: :
( t) ( t)
o: (loop equations)
-
Kirchhoff:
.
:
, ,
.
-
v(t)
i(t) (
)
v(t) R:
: -v(t)
i(t)
+
-
v(t)
i(t) (
)
i(t) R:
:
-i(t)
v(t)
http://upload.wikimedia.org/wikipedia/en/d/de/OhmsLaw.svghttp://upload.wikimedia.org/wikipedia/en/d/de/OhmsLaw.svghttp://upload.wikimedia.org/wikipedia/en/d/de/OhmsLaw.svghttp://upload.wikimedia.org/wikipedia/en/d/de/OhmsLaw.svg
-
1 1 2
2 3 4
3 5 6 2
0
0
0
E V V
V V V
V V V E
Ohm KCL KVL:
1. KVL: :
1E
5V
1R
6R
5R
3R
2R 4R
2E
6V
4V
1V
2V
3V++ +
+
+
+
1
2
5
3
4 2. KCL:
1 3 4 2
3 1 5
4 5 2
0
0
0
I I I I
I I I
I I I
3. Ohm:
1 1 1 2 3 2 3 4 3
4 5 4 5 2 5 6 2 6
, , ,
, ,
V I R V I R V I R
V I R V I R V I R
4. 1, 2 R1, R2, R6 V1, V2, V3, V4, V5, V6 1,
2, 3, 4, 5 (1), (2) (3).
(1)
(2)
(3)
-
Tellegen
1
( ) ( ) 0n
j j
j
v t i t
n ,
t:
:
vj j (j=1,2,..n),
ij j (j=1,2,..n),
vj ij (j=1,2,..n)
KVL KCL, .
-
,
.
:
-, ,
.
Tellegen:
-
Tellegen:
v1=2V, v2= -1V, v3=1V, v4=4V, v5= -3V
i1=1A, i2=1A, i3= -3A, i4=2A, i5=2A
:
KVL: v1+v2=v3 v4+v5=v3
KCL: i1=i2, i4=i5, -i1-i3-i5=0 i2+i3+i4=0
KVL KCL:
Tellegen:
5
1
( ) ( ) 2 1 3 8 6 0j jj
v t i t
:
-
Kirchhoff = :
,
Kirchhoff,
.
= (variables) .
-
Kirchhoff
+ i-v
-
-
:
1o s o
s
v V R i i I vR
i-v
-
.
-
+
v
Io=Vo/Rs
-
-
.
- :
1
m
k
k
v v
1 2 mi i i ... i
:
:
-
si i
1
m
k
k
i i
1 2 mv v v ... v
ie
s
- v +
is
if e0 then v=e
else v=0
:
:
:
:
e = A x sin(t) t
v
0
e D
- v +
-
sv e
ie
s
- v +
is
:
:
-
i=i1+i2
v=e1+i1r1=e2+i2r2
v=v1+v2
i=i1+v1 / r2=i2+v2 / r1
- :
- :
-
:
nRRRR ......21
nRRRR
1......
111
21
:
:
i
iR
G1
: nGGGG ......21
(conductance)
-
1 2
1 1 1 1
nC C C C
1 2 nC C C C
:
1
0 0n
k
k
v v
:
:
: 1 20 0 0 0nv v v ... v
1
1
0
0
n
k k
kn
k
k
C v
v
C
:
:
C1 C2 Cn
iv(t)
+ -v1 + -v2 + -vn
+ -
C
i
v(t)+
-CC1 C2 Cn
i1 i2 in
-
nLLLL
1......
111
21
:
1
n
k
k
L L
1
1
0
0
n
k k
k
n
k
k
L i
i
L
:
: 10 0 0ni i ... i
:
:
1
0 0n
k
k
i i
:
L1 L2 Ln
+ -v1 + -v2 + -vn
i v(t)+ -
L
L1 L2 Ln
i1 i2 in
i
v(t)+
-L
-
(bridge)
: i1=i2=ib/2 i3=i4=ib/2 i5=0
(ladder network)
Vo
( Kirchhoff)