.

()

, .

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)