# דף נוסחאות מבוא למעגלים

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1.1V '

. Vth

VOC.I

3. 3.

3r (t 1) r (3t 3) t

0 1t 1 3t 3 t

q [c A ]sec

n

I SC

3r (t 1) 3 u (t ' 1) d (t ' 1)

] 3 [ c / m ] [ c / m] 2A [m ]v [ m / sec ] 3V [ m ] V [ joul / c Volt ] U [ N m joul ] W [ joul

]E [ N / c V / m ]B [Tesla N / A m ]I [c / sec A ] 2J [ A / m ]K [ A / m ] L [(Volt sec) / A H ] C [c / Volt Farad

1 1 RT n Rn n

CT Cn "

1

n 1 CT n Cn

RT Rn

)1 3(t 1) u(t 1) (3t 3) u(t - )r ( a t ) r ( a t b 3 0 t 0 3 1 t 0 (( Unit( - u -0 1(:

2

u(t 3)

) U (t ) (t

1 1 LT n Ln

LT olt tesla m VLn n sec

: " .KVL , 2V1 V 1 2 LI .2 . : " .KCL , . . ( (:

(: - (Impulse / Delta 0 t ) dU (t (t ) ) (t )dt 1 (t )dt U (t dt 0

] [ joul / c Volt ]R [Volt / A n

]) [ siemens / m 1/( m ] [ m ] P [ Joul / sec WattN

21m mily 103 micro 106 nano 10 9 pico 10

(t )

0 t 0 else

a

1 ) (t )dt 1 (a t ) a (t a

0 8.85 12 [c 2 / Nm 2 ] 0 4 7 01 01 B Bg [Weber ] uB A rr E E d a Qin2

m T A 1

1 02

B

2

U

0 t t (t t0 ) 0 elsed ) 1 (t ) (t dt

t0 a

02

B

u r

2

dv

t0 a

1 (t t )dt 0

0

] [ Nm / c

1 uE 0 E 2 U u dv E 2

:

= DC . : I s (t ) 0 (Open Circuit (OC

R Vn Vs n R

(:Pulse( - p

p (t ) p (t )

. ( :

In Is I1 I s 2

G2R R

Gn

R

G

1

the other ]RC [sec

0 0t 1 1/ 0 t P (t )dt 0 t) u (t ) u (t

: Vs (t ) 0 (Short Cirtcuit (SC : - V I R I V G : () ) V (0 ) V (0 VC (t ) 1 1 ' I C dt ' VC 0 c I C dt c 0 dvC dt . ( - (DC . (+0( .t t

2L I L I 0 (t )g 3L2 L

:

I C (t ) c

. " ( ) ',

) 0f (t ) (t t0 )dt f (t )0( f (t ) (t )dt f (0) (t )dt f

-

'

KVL,KCL

) f (t ) ( )d f ( ) (t )d f (t

: () ) I (0 ) I (0 I L (t ) 1 1 ' VL dt ' I L 0 L VL dt L 0 dI L dtt t

""

R 1 ] [ L sec 2^ s '

H(s(=out/in

)0( ) f (t ) ( n ) (t )dt (1) n f ( n

VL (t ) L

( (

s2

2d , 2 dt

s

d dtZIR, ZSR

P V I I 2 R

(y(t

(""(

1 : R: SL : CS (" ("G

: . " ". :

2V : watt R 0 - P . 0 - P .( ,' (

. . (+0( . .: . ' = 0. ()Kirchoff :KCL . (' 1-( N :KVL . (' (1-(N(-B B' ( , / ( : - KCL , . 2. = - "-" - "+". - KVL .

1 0 Im(Y ) Im( ) z

W

] Pdt V (t ) I (t ) dt [ w

t

t

:

t :s

WC

21 ]cv( t ) [ w 2:

y ( s ) y (t ) e dt st 0

1 ]WL LI (2t ) [ w 2 :

1. 3. 4.

Vs I s g s R

:

2) L f ( t )1 f ( t )2 F( s )1 F( s

: :

Vs

(k ) )0( L f ((t n ) S n F( s ) S n 1k f) ' )0( L f (''t ) S 2 F( s ) S f (0) f 0k

Rs

+

Is1n

+

Rs

" " / : : ( ( Rth Rn" , ( (. 2. : 1. . 2. .

(, ) , ( ).

L

1 f d S Ft 0 ) (

1.

)(s

, , . 6. 7. " .

5.

) L f ( t ) e s F( s1

:

) R(t ) U (t ) U (t ) (t

(,(( Ramp (Step( r-(:

1.1V :

2 s1,2 n n 2 1 n j n 1 n j d

y yZSR yZIR yP H yH y & ) p y q y h (t ***** : - ZSR 3 : - .ZSR

) L e at f ( t ) F( s a ) lim f ( t ) lim S F( s0t s

:

': 0 n 2 ( (. " .

:

': 0 n 2 1 - Over Damped : 2 . 1 - Critial Damped : . 1 - Under Damped : 0 . 0 : .

1. 2. 3. 4.

& 0 p y q y )0 (t ? y (0 )

1. 2. ZIR . :0

) lim f ( t ) lim S F( st 0s

:

" :

0

(

)dt

) L f ( t / a ) a F( as ) L a f ( at ) F( s / aL t f ( t ) d ) F( s ds

:

y (0 )

h p - ******.ZSR

:

3. 1.

: ZSR : - ) f ( t ) g ( t : : . ..

:

s j

: " :

. - 0 - . Q, 0 , 2. ": " KCL " v" KVL " .i :ZIR 1. / :2 0 P( s ) s 2 2 s 0

1. 3.

1.

0L 0( t t0 ) e st L 1( t ) 1/ S ) L e at f ( t ) F( s a S 2S2 2 L sin( t ) 2S 1 L e at 1( t ) S a !n 1L t n 1( t ) n S L cos( t ) L 1( t a ) 1( t ( a ))

:

2. :

2. : ) 0f (t t ) 0. g ( t t ) dg (t ) df (t . 3.: dt dt

S1,2 2

2 0

3. :

' f (t ')dt0

t

: ' . g (t ')dt0

4.

:

1(

t

2,1S :

) 2 G (af1 (t ) bf 2 (t )) aG ( f1 ) bG ( f

5. :

e as 1 e s S RC, RL

:

2. 3. 5.

0 Q 1 / 2 ; y y H Ae S1t Be S2tt

- ) 0( . VC (0 ) VC

- ) I L (0 ) LL (0 :

** ", => KVL" KCL" : " KCL, KVL ". ( :)ZIR )Zero Input Response) 1. ( , ( = ( (. 2. . s t y( t ) Ke

2(

- ZSR- ) u( t -.ZIR

2,1S :

L 4. ; RC ; . [sec] LC R- :ZSR (" - .(t 6. " .

1. 2.

y Q 1/ 2 ; 0 ; S1 S2 A

y H Ae t Bte t

& y s y 0 y (0 ) K

t

RCL, CL

:

3(

:

0

: . - 0 . - 0 .

) d y( t2

2

2,1S 0 Q 1/ 2 ; :y

dt 0y (0 ) y

2

) dy(t

dt 0y(0 ) y

2 ) 0 y( t ) f (t

2 B d 0 2 ; S1,2 j d

ke tt

y H e t ( A sin( d t ) B cos( d t )) 2 ) Ke t cos( d t T

d

:

4(

2,1S 0 Q ; 0 ; S1,2 y j y H A sin( 0 t ) B cos( 0 t ) ) K cos( 0 t . + , . t :

1 sec rad - 0 . sec 0 - Q " 2. 2 .: Q - , , . "

( :)ZSR )Zero State Response ) ** 1. . 2. . 3. + .

3.

& y s y f ( t ) ZSR yU ) y ( t ) ( yP H ) (t y (0 ) 0 - ZIR :

4. 5.

Ne st yH

) d 2 y( t

4. 4.

2 dt 0y (0 ) y

2 n

) dy( t

dt & & 0y (0 ) y

2 ) n y( t ) f ( t

:

) sin(0 t ) cos( 0 t :

. .- " 2.

n 1 / sec

) y p A cos( 0 t ) B sin( 0 t :

- 2 a t

y p b t 2 c t d. - " ( (., . . . 4. :

( :ZSR -s ( ( ( - .ZIR 2. . 2

1.

2 d n 1 :

0 s 2 2n s n 2

1.1V1 1 V I cos( R V R I ) Re V I * 2 2 2 1 2 1 I Re Z V Re Y 2 2 Pav Im V , Veff m 2 2 ) Pav I eff eff cos( R V R I V I eff :

= .

2. 1I

"

0

0 " . RLC .

3.

3. . .

. (+0( ZSR . .

4. 5.

- Q: , . :

1 S V I 2:Power Factor

Q

IC IS

IL IS RLC : 1. - Yin ( - Z in (.

' ZIR . " " - , .

5. : y y ZSR yZIR: / " y H e" .t s t

P P P.F cos 1 S V I 2 " RLC:

2. " , .

0 : Bandpass h

Vc''

1 'R 1 Vc Vc VS L LC LC R 1 1 I '' I ' 'I Vs L LC L" RLC:

1 3. LC

d 1 : - S @ @ dt S V( t ) R I ( t ) RI 0 e S t:

RLC l Band Pass

V ''

1 1 1 V ' ' V Is RC LC C 1 1 1 I '' L I 'L IL Is RC LC LC:

(- DC (. 2. ( (. 3. . .

1. 4.

1 1 : ) I ( t V( t ) / = sc sc : ) V( t ) SLI ( t / = SL " " :S 1. / , " ". 2." . 3. : 4. . , ( t S ( ".

h , l

3dB Pass Band:

H 2 /1

1 ) ( 1 tan 2 x 1 dW 2 f 2 , P T dttan 1 ( x )

5.

" - : y ( x) P )g ( x y ( x) P , y ( x ) H x s ( s 0,1, 2...) y ( x) P . )g ( x :

" " :S 1. . (( Z S

2.

H ( j )

XdBnormal

) H ( j 20 log H MAX

t .( e S ( e 3. " :

V( t ) I ( t ) Z I 0 e st Z: " - .S , . (z(

pn ( x) a0 a1 x ... an xy ( x) P

n

: . .

] x s [ A0 A1 x ... An x n

) H ( j 3dB 20 log H MAX H ( j ) H MAX

MAX 1 ] l , h [ rad / sec 2

MAX H

dH 0 d , H MAX

z Am cos( t ) Re A e jt A Am e A x jyj

H ( j ) H ( j )

:

y

(Im(z [ fR

T

2

1 T f c

x (Re(z

/ 1 ] Hz ] [ meter ] T [sec sec

2 T

'

2 fk

k

2

0 1 0 0 0 H ( j ) 1

tan 1 -LPF

Im( A) y

Re( A) x

2 Am x 2 y: x- .y

-HPF : ((, . Z , Y .

/

T

2 / T 2 /

ck

P( t ) v( t ) i( t )

-BPF 0 :

, ": 1. . 2. , . 3. . 4.: - 2 : 1.- - . 2.- -

1 1 ) V I cos(R V R I ) V I cos(2 t R V R I 2 2: . :

1 j Zc , Yc jwc j c c