‫محاسبه مقاومتهای ورودی و خروجی در مدارهای مختلف‬
‫ امین شیخی‬:‫تهیه و تنظیم‬
‫ دکتر آشتیانی‬:‫مدرس‬
2 ‫ الکترونیک‬:‫درس‬
vgs = -R S I t
Vt = ro ( I t - g m vgs ) + R S I t  Vt = ro ( I t + g m R SI t ) + R SI t
 Vt = ( ro + R S + g m ro R S ) I t  R out =
Vt
= ro + R S + g m ro R S
It
Vt = -vgs
Vt = ro ( I t + g m vgs ) + R D I t  Vt = ro ( I t - g m v t ) + R D I t
 Vt (1 + g m ro ) = ( ro + R D ) I t  R in =
if g m ro >>1  R in
RD 
1 
1 +

gm 
ro 
1
Vt
r + RD
= o
It
1 + g m ro
v π = - ( R E rπ ) I t
(
)
Vt = ro (I t - g m v π ) + ( R E rπ ) I t  Vt = ro I t + g m ( R E rπ ) I t + ( R E rπ ) I t
(
)
 Vt = ro + ( R E rπ ) + g m ro ( R E rπ ) I t  R out =
Vt
= ro + ( R E rπ ) + g m ro ( R E rπ )
It
Vt = -v π






v
v 
V
V 
Vt = ro  I t + π + g m v π  + R C  I t + π   Vt = ro  I t - t - g m Vt  + R C  I t - t 
rπ
rπ 
rπ
rπ 









r
R 
1 R 
 Vt 1 + o + g m ro + C  = ( ro + R C ) I t  Vt 1 + ro  g m +  + C  = ( ro + R C ) I t
rπ
rπ 
rπ 
rπ 



1
β+1 1
gm +
=
= gm
rπ
rπ
α
 R in =
Vt
ro + R C
=
R
1
It
1 + g m ro + C
α
rπ
2
(
vπ = - R E
( rπ + R B ) ) I t ×
(
Vt = ro ( I t - g m v π ) + R E
rπ
R E rπ
=It
rπ + R B
R E + rπ + R B
( rπ + R B ) ) I t


R E rπ
 Vt = ro  I t + g m
I t  + R E ( rπ + R B ) I t
R E + rπ + R B 



R E rπ
 Vt =  ro + R E ( rπ + R B ) + g m ro
 It
R E + rπ + R B 

V
R E rπ
 R out = t = ro + R E ( rπ + R B ) + g m ro
It
R E + rπ + R B
(
(
)
)
(
)
VX = Vt - v π = Vt - rπ I t
KCL @ X node: I t + g m v π =
VX
V
VX
+ X  I t + g m rπ I t =
RE
ro
R E ro
(
)
 ( β + 1) ( R E ro ) I t = Vt - rπ I t  Vt = rπ + (β + 1) ( R E ro ) I t
 R in =
Vt
= rπ + ( β + 1) ( R E ro )
It
3
vπ = -
rπ
Vt
rπ + R B



v
v 
Vt = ro  I t + π + g m v π  + R C  I t + π 
rπ
rπ 






Vt
rπ
Vt 
 Vt = ro  I t - gm
Vt  + R C  I t 
rπ + R B
rπ + R B 
rπ + R B 



(β + 1) ro + R C  = r + R I
 Vt 1 +
 (o
C) t
rπ + R B
rπ + R B 

 R in =
Vt
=
It
ro + R C
(β + 1) ro + R C
1+
rπ + R B
rπ + R B
4
VX = Vt - v π = Vt - rπ I t



V
V 
Vt = rπ I t + ro  I t - X + g m v π  + R C  I t - X 
RE
RE 






V -r I
V -r I 
 Vt = rπ I t + ro  I t - t π t + g m rπ I t  + R C  I t - t π t 
RE
RE 






r + RC 
rπ I t 
rπ I t 
 Vt 1 + o
 = rπ I t + ro  ( β + 1) I t +
 + R C  It +

RE 
RE 
RE 



(β + 1) ro + R C  R = r + (β + 1) ro + R C R
V
 R in = t = rπ +
in
π
E
r + RC
It
R E + ro + R C
1+ o
RE
ro ,R C >> R E
if 
 R in
( β + 1) ro  R C
rπ +
( β + 1) R E
1+
5
RC
ro
:‫خالصه فرمولهای محاسبه مقاومتهای ورودی و خروجی در مدارهای مختلف‬
R out = ro + R s + g m ro R s
R in =
ro + R D
1 + g m ro
if g m ro >>1  R in
RD 
1 
1 +

gm 
ro 
R out = ro + ( R E rπ ) + g m ro ( R E rπ )
6
ro + R C
R in =
R
1
1 + g m ro + C
α
rπ
R out = ro + R E
R in =
( rπ + R B ) + g mro
R E rπ
R E + rπ + R B
ro + R C
(β + 1) ro + R C
1+
rπ + R B
rπ + R B
7
R in = rπ + (β + 1) ( R E ro )
R in = rπ +
(β + 1) ro + R C R
R E + ro + R C
ro ,R C >> R E
if 
 R in
β
+
1
r

R
(
)

o
C
8
E
rπ +
(β + 1) R E
1+
RC
ro