grzybek23/Podstawy_Elektroniki_-_tom_1/12... · ˚ˆ ˜ &)˛))’ ˝ ˇ ˇ ˘ ˘ ˙ ˘ ˘...
Transcript of grzybek23/Podstawy_Elektroniki_-_tom_1/12... · ˚ˆ ˜ &)˛))’ ˝ ˇ ˇ ˘ ˘ ˙ ˘ ˘...
*+
T T21E
T T21E
b)+8&&
5&
5&
5& 5
&
+8&&
8
8
5,
,
−8((
−8((
, 5,
8LU
−8 LU
8LV
8RU
8RU
,)) - ' !'
- U U Uir = −1 2
( ) 2/21 UUU is +=
(
. . !
I !& I
IR '
/
! ,
21 UU − irU
0 1U 2U
& 21 UU −= '.
.
!
$
,
orU
1 1U 2U $& 21 UU = '
!
1
2
! ∞→IR
!
2 ))!
*)
1U 2U
irU
isU
21 UUUir −= ( ) 2/21 UUU is += &))'
(!
-
±
±
±
± 1U 2U
(
*%+,(%-,-+.%(/$'""#$!$
3
ORU
IRU
))
T T21
&
&
(
(
&
&
+&&
−((
%(
%(
&
&
,
25
,)"
∞=IR (
)
IRBEBE UUUUU =−=− 2121 &)'
*
& ( & (
= =α α &)'
constIII EE ==+ 21 &)*'
4!56 TBEBE UU ϕ>>21,
( )( ) TBETBE
TBETBE
UES
UESE
UES
UESE
eIeII
eIeIIϕϕ
ϕϕ
//2
//1
22
11
1
1
≈−=≈−=
&)7'
&)'&)7'
( ) TIRTBEBE UUU
E
E eeI
I ϕϕ //
2
1 21 ≈= − &)8'
&)'&)*'&)8'
TIRUCe
II ϕ
α/
01 1 −+
≈ &)9'
TIRUCe
II ϕ
α/
02 1+
≈ &):'
&)9'&):' $)
-1-2-3-4 1 2 3 4
0,5
1,0
0
,&
,&
,
,
&
α
TIRU ϕ
,) 3
-
( )I I f UC IR T/ /α ϕ0 =
2
)
CCCCC
CCCCC
RIUU
RIUU
22
11
−=−=
&)'
,
( ) CCCCCOR RIIUUU 2121 −−=−= &))+'
; &)9'&):'&))+'
( )TIRCOR UIRU ϕα /tgh0−= &)))'
*
&)))'
)*
-1-2-3-4 1 2 3 4
1
0
-1
,5 7
ϕ
8 , 525 &
α
,)* 3
- ( )U f UOR IR=
) &)9' &):'
IRU & ±8<' IRU
+)+
=.>++; Tϕ >8< $ ))*< (!
! )* &)))' ( )IROR UfU =
( 1/ ≤TIRU ϕ
2 ( )IROR UfU =
0=IRU
CmCmrTCur RgRgIRk −=−=−= max0max 2/ ϕα &))'
-
mT
mr gI
g ==ϕ
α2
0max &))'
&))' maxmrg
0=IRU mg
I / 2
0 !1# '-)! '"
1)
-
orU 1cU
**
2cU $π
))! 1U 2U !
& ' isU
&' irU =
!
!
?
)7
-
0' =bbr 0=ceg (
& 10 >>β '
E
5&
5&
8F 8
F
J 8P E H
J 8P E H
JE H
JE H
, ,L E
= , ,L E
=
8E H
8E H
8
8RU
5 *, ,
=8H
8
,)7
%
IR
( ) ( )[ ]2'22'1'11' ebmebebmebIe ggUggURU +++= &))*'
(
( ) '0''0 1, ebebebm gggag α−==
mmebm gggg ≈
+=+
0'
11
β
&))*'
( )2'21'1 ebmebmIe UgUgRU +≈ &))7'
, ;$$ !
&))7'
*7
( ) ImebImebeeb RgURgUUUU 22'11'1'1 1 ++≈+= &))8'
( )ImebImebeeb RgURgUUUU 22'11'2'2 1++≈+= &))8!'
&))8' 1'ebU 2'ebU
$ 1U 2U
( )( ) Cm
Imm
ImCebmc Rg
Rgg
UURgURUgU 1
21
21211'11 1 ++
−+−≈−= &))9'
( )( ) Cm
Imm
ImCebmc Rg
Rgg
UURgURUgU 2
21
12122'22 1 ++
−+−≈−= &))9!'
21 ccor UUU −= &)):'
2
)( 21 ccos
UUU
+= &))'
( -
'#
( 0=isU
221irU
UU =−=
urk
( )( )[ ] C
Imm
Immmm
ir
orur R
Rgg
Rgggg
U
Uk
21
2121
12
4
++++
−== &)+'
rusk −
( )( )[ ]Imm
Cmm
ir
osrus Rgg
Rgg
U
Uk
21
21
14 ++−−==− &))'
( mmm ggg == 21 &)+'
&))' !
==
−==
− 0ir
osrus
Cmir
orur
U
Uk
RgU
Uk
&)'
*8
==
−==
2
2
22
11
Cm
ir
cur
Cm
ir
cur
Rg
U
Uk
Rg
U
Uk
&)'
!'#
( isUUU == 21 & 0=irU '
usk
( )( )[ ]Imm
Cmm
is
osus Rgg
Rgg
U
Uk
21
21
12 +++−== &)*'
surk −
( )( ) Imm
Cmm
is
orsur Rgg
Rgg
U
Uk
21
21
1 ++−−==− &)7'
= &)*' &)7'
!
==
−≈+
−==
− 0
221
is
orsur
I
C
Im
Cm
is
osus
U
Uk
R
R
Rg
Rg
U
Uk
&)8'
6
& ' CMRR &
' CMRR $
=
sur
ur
k
kCMRR
−
= &)9'
2 &)+'&)7'&)9'
*9
( )( ) 21
21
21
2121 2
2
4
mm
Imm
mm
Immmm
gg
Rgg
gg
RggggCMRR
−≈
−++= &):'
( & 21 mm gg = 'CMRR →∞
=
us
ur
k
kCMRR = &)'
( &)+'&)*'&)'
21
2141
mm
Imm
gg
RggCMRR
++= &)+'
( &)+'
Im RgCMRR 2= &))'
?! CMRR
= CMRR
!
=
, $
0=isU
00 ==
==isis Ub
ir
Ui
irir I
U
I
UR &)'
)7
IIrR T
C
Tbeir
ϕβϕβ 00 42
2 =≈= &)'
,
0021 2==
=+
=irir Ub
is
Uii
isis I
U
II
UR &)*'
2 &)7'
( ) IIbe
is RRr
R 00 12
ββ ≈++= &)7'
*:
,
CR
2 #$!$%&!$'"-"+%((3-$*$,',1"'$
3
5
6 !
)8
=
"4 ! 5
(
)+7
"4 EZ2
EZ !
a)
±8LU
8R
5&
J 8P E H
JE H
8E H
,E
b) ,E
8E H
JE H
8LV
J 8P E H
=(
5& 8
RV
,)8, - '
!'
1 IR CSC
!
EZ2 IR2
2/CSC
ICS
IE RCj
RZ
ω+=
1
22 &)8'
( )ICSI
C
E
Cus RCj
R
R
Z
Rjk ωω +−=−≈ 1
22)( &)9'
3 urk
usk
CMRR )9
*
[ log]
[log]
+20dB/dek
-20dB/dek
[log]
-20dB/dek
-40dB/dek
dB
dB
dBXV
XU
IJ
I(
,)93 -'
!'' &055
, &)9'
+@A
IIE CR
fπ2
1= &):'
( CMRR
!)9
4 #$!$('5$(!(#+,-"!-#
! !
$ ! !
. !
-
osU & '
7+
osI & '
CMRR
2 osU
! !
!
( )2121
12CCCC UUUUiros UUUU == −=−= &)'
( osI
& ' !
!
!
( )2121
21CCCC UUiiUUiros IIII == −== &)*+'
"
$
.
!
)µ!"#$
))
CR
T
CCCmur
RIRgk
ϕ−=−= &)*)'
= CC RI !
CR
, ! CR
!
, !
!5
BC 4
!
& '
= !
):
7)
T1 T 2
T 4T 3T 6
T 7 T5
T1 T 2
T 4T3
T5
E
a) b)+8&&
+8&&
,&
,&
,&
,&
88
,2
−8((
−8((
8
,
8&
8&
55()
,
8
82
8%%
,):!-'
55 !'
55
): RC
. . %
..5()
! & . '
..&!'
@
! .
. &):!' !
!):
! &
):' ! .
. 5 .
. ( irU
. I∆
. OI∆
IIIIII CCCCO ∆=∆−∆=∆−∆=∆ 22124 &)*'
.
. & . .
' ! =
! CMRR &
IR ∞→CMRR
7
E
E
a)
b)
c)
8LU
8LU
8LU
8LU
8EH
8EH
UFH
UEH
UEH
J 8P EH
J 8P EH
UEH
UFH
UEH
J8
P
LU
J8
P
LU
UFH
UFH
UEH
UFH
UFH
UEH
UEH
UEH
8EH 8
EH
8EH
=8
EH
J 8P EH
J 8P EH
UFH
UFH
UFH
UFH
8R
8RJ 8
P EH
JP
8R
UFHJ 8
P EH UFHJ
8P
LU
J8
P
LU
JP
UEH
UEH
8EH
,)6 ):!
- '
4!' 4
' !
2 )
):!
0' =bbr & ber ebr ' 'DE
( . . -
21 bebe rr = 21 mm gg = 21 bebe UU −=
!
. . 4
(
5cer
# 33 bem Ug
3mg
3beU
,)
+
++
+==42433
411
1
2
1
cecebebem
mmm
ir
our rrggg
ggg
U
Uk &)*'
. . . 43 mm gg = ,
7
433 , bebem ggg >> &)*'
PNAPTANTcece
m
ir
our UUgg
g
U
Uk
ηηϕϕ +=
+=
+== 11
42
1 &)**'
ANU APU 4F ANTN Uϕη =
APTP Uϕη = 4F
5 5 55
( 4102 −⋅=Nη 4105 −⋅=Pη !
- 3104,1 ⋅=urk
6
)
( )APAN
APANcece
ceceUo
oo UUI
UUrr
ggI
UR
ir+
==+
===
2||
142
420
&)*7'
0
0 *%+,(%-,-+.%(/$'""#$!$
6"#
! #
6"#!
))+
M 1 M 2
M5
REFL*HQLH
DNW\ZQH
+8''
−866
−866
8'
8'
25
U2
U2
U2
,'
,'
8*6
8*6
8*
8*
8**
,
−66
,))+#
6"#
?
6 6 !
! $
7*
6 6
TTT UUU == 21 ))+
21
2
2
21
1
12121
22
−
=−=−=
ββDD
GSGSGGIR
IIUUUUU &)*8'
const21 =+= DD III &)*9'
=
=
L
WC
L
WK in
2'
µβ
iC 5 !5
nµ 5
W 5
L 5
'K 5
, &)*8' &)*9' & &)*8'
' 1DI 2DI (
βββ == 21
−+=
2
42
1 422 I
U
I
UIII IRIR
D
ββ&)*:'
−−=
2
42
2 422 I
U
I
UIII IRIR
D
ββ&)*'
(
212
βI
U IR ≤ &)7+'
66 !
&)*:'&)*' $)))
.
ORI $
)(21 IRDDOR UfIII =−= &)7)'
0=IRU &
'
77
-12 1
0,2
1
2-
0,4
0,6
0,8
0,0
0
,'
,'
,
,
'
β,8
,5
,))) 3
6"#
&)*:)*)7)'
( ) 1
21
1
11
21
1
1211
'2'm
D
IR
ORmr g
L
WIK
L
IWKI
U
Ig =
=
=== β
∂∂
&)7'
.
2/I
0 #$!$(%&!$'"('5$(!(#+,-"!-#!1# '-)! '"
. 6"#
! ))DE
))!
6 6 BC ;
33 gsm Ug !
44 gsm Ug !
31 mg ! 41 mg gsU
dsU
mg1
urk
))!!
6 6
3dsr 4dsr
6
))
78
M1 M 2
M 4
M 5
M 3
M 1 M 2
M 4
M 5
M 3
S
M 1 M 2
M 4
M 5
M 3
S
a) b)
c)
+8''
+8''
−866
8**
,
8*6
8*6
8*6
8*6
8**
−866
,
,'
,'
,'
,'
,'
,' ,
','
8**
8*
8*
+8''
8' 8
'
8' 8
'
8* 8
*
8* 8
*
,
−866
8**
82
,)) ( 6"# !
- ' 6"# BC !'
6"# '
6"#
( 21 mm gg =
221 irgg UUU =−= !
))! !
6 6 #
21 irgs UU = 22 irgs UU −=
))!
( )31
111 2 dsds
m
ir
dur gg
g
U
Uk
+−== &)7'
( )42
222 2 dsds
m
ir
dur gg
g
U
Uk
+== &)7*'
79
S
a)
b)
S
GV
JV
JV
J
J
P JV
P JV
GV
GV
GV
GV
G
G
G
G
RU
R
R
GV
GV
GV
GV
JV
JV
P
LU
P
LU
J8
P
LU
J8
P
LU
GV
LU
LU
,)) 6
! ))! &'
&!'
42
2
31
1
dsds
m
dsds
m
ir
orur gg
g
gg
g
U
Uk
+−=
+−== &)77'
311
1
dsdso gg
R+
= &)78'
422
1
dsdso gg
R+
= &)79'
(
isgg UUU == 21 gsgsgs UUU == 21
))
( ) 512 dsgsmgsis rUgUU +=
5121 dsm
isgs rg
UU
+= &)7:'
7:
gsU
1dsr 2dsr
))
51
31121 21 dsm
dsm
is
dususus rg
rg
U
Ukkk
+−≈=== &)7'
; &)77' &)7'
CMRR
( )42
513 21
dsds
dsmds
us
ur
gg
rgg
k
kCMRR
++
== &)8+'
)) !
6 6 %
!
% ))
))* (
))!
J8
P
LU
J8
P
LU
UGV
JP
UGV 8
JVUGV J 8
P JV UGV
8R
,))* 6
))
+
++
+==42331
411
1
2
1
dsdsdsmds
mmm
ir
our ggggg
ggg
U
Uk &)8)'
( 6 6 & 43 mm gg = '
313 , dsdsm ggg >> &)8)' !
42
1
dsds
mur gg
gk
+≈ &)8'
7
( &)77' &)8'
!
&)8'
( )( )
21
1
1'1
4242
21
11'1 22
+
=+
=IL
WK
I
LWIKkur λλλλ
&)8'
21, λλ
66
( 11 LW >)+ I >)++µ?
103≈urk 1 36"#
& '
!
& )7'
,
))*
( ) IIggR
dsdso λλλ
121
4242
≈+
=+
= &)8*'
2 6
2 ',"'"(" $"'$"#$!$-'.(%$-/!-$*
!
! 1
))
!
& &)))7''
2 ))7 !
ou
1inu
&G' 2inu &5'
( ) dudininudo ukuuku =−= 21 &)87'
8+
udk 5
du 5
ograniczenie
ch-ka idealna
ograniczenie
+
-0
XR
N XXG G
NXG
→ ∞
XLQ
XG
XLQ
XRPD[
XRPLQ
R
NXG
X X XG LQ LQ
= −
,))7 - ' ! !'
u f uo d= ( )
/
!
& ∞→udk ' !
!
& ∞→CMRR '
# ! ! du &
' & '
( ) 221 ininc uuu += ))8
$ !
% $
!
( ) 221 BBIN III += 1BI 2BI !
+
-
a)
+
-
b)
XR
X
X X
F
LQ LQ=+
XG
XG
XG
XR
XG
XLQ
XLQ
,))8# -'
!' ! ud
uc
8)
. - ≈INI )+5
)++? ! ≈INI +)5)+ ?
6"#H4.
% 2121 BBININN IIIII −=−=
1 7+? !
+7 ?
% NU
.
)57< ! 5)+<
% udk
- doud uuk = 0=cu . udk
)++@ ! 9+ @
% & couc uuk = 0=du
uck
uc
ud
k
kCMRR log20= CMRR
! )++@
8+@
indR
+56Ω !
indR ! $
oR !
)++Ω
'
&! '
&
'&' .!
3
&
' )5+6I
! 5+6I
8
( $
'( 5 SR& ' $
t
u
dt
tduSR oo
∆∆
≈=)(
&)88'
SR !"µ
)5)++!"µ !
! SR
))9
(+)
(-)
5R
N 8XF F
N 8XG 1
( )N X XXG LQ LQ
−
,, ,
,1
,1 ,1=+
,,1
,,1
,,
,1
1−
,,
,1
1+
&
&
5LQF
5LQF
5LQG &
XLQ
XLQ
81
XR
,))9J
2 3'""#$!$-'.(%$-/!-$*
#
#
$
CMRR =
!
#
8
!
"
!
&; !
! !
'
/ .
!
!
T1
T12 T9 T3
T2
T3T4
T7
T5 T6 T17
T16
T23
T 22 T 24
T18
T19 T15
T14
T13A
T13B
T21T20
wy
22
27
50k
T10
50k 1k
kompensac jaQLH]UyZQRZD*HQLD
1k5k
39k
+ -
T11
50k 100
40kAB
T1
T3
T5 T6
T4T3
T2
17
T
T16
T13AT13B
T23
T20
T8
T9
T14
b)
a)
5
5
5
5
5
+8&&
+8&&
5
5
5&
.
5
5
+8&&
−8((
5
5
,UHI
8UHI
8UHI
,R
XLQ X
LQ
XR
,)): # µ?9*)- '
!'
8*
2)):
µ?9*) )):!
%-
)' &. 5.'
! & . 5 .'
&.5.'K
' & . 5 .' !
&.5.'K
' &....'
....
"35"@ !
..
. . ! 2
!..
. $ "3
. .
#
! ! .
# ..
!
( 36"#
))
M 4M 3
M1 M 2
M 5
M 8
M 7M 6
W Y
55()
LG
LG
LG
&N
XLQ
XLQ
R
−866
+''
−866
,))( 36"#
66
66
62 GGU ! 6 6
87
REFR
6 BC
"!
6 6 2
6 $
"#!6
!
kC " !
!
2 )+
@36"#
6 > .
% ! !
))
6 6
. 5 5&5 5
@36"#'
, 6 6
!
zR ,
! 6 $ ! zR kC
&
' 2
DDU+ ! SSU−
M 10
M 11
M 12
M 9M 8
M13=T1
M 7
M 3 M 4
M 1 M 2
M 5M 6
XLQ
−866
+8''
XR
XLQ
5UHI
,)+= @36"#
88
20 7'#.(!$/($*%+,(%-,-+$,',1"'$'"(/"#$!$'.(%$-/!()'
.
)):!
# !
"4&!"# '!
& kC '
%
))
8LQ
8LQ
8G
J 8P, G
5
&N
& 8
J 8P,,
&
8
5
8R
8
,))#
? ))
& $ 6
'
1 ! kC
DE
( )( ) ( )( )''
''0
''
''21
)(
)(
III
IIIu
III
IIImIImI
d
o
ss
k
ss
RgRg
sU
sU
ωωωω
ωωωω
++=
++−= &)89'
22
''
11
''
1
1
CRp
CRp
IIII
II
=−=
=−=
ω
ω &)8:'
, ! 'Ip '
IIp $
) )
@
= 'IIω
5*+@A ) &+@'
2
89
!?
&N
≠
&N
=
Mω
σS,
S,
S,,
S,,
,) , !
dB
-20dB/dek
-40dB/dek
-40dB/dek
-20dB/dek
1
NX
ORJ NX
ω,
ω,
ω,,
ω,,
ω7
ω]
,) 3
. DE
( )[ ] ( ) ( )[ +++++−−= kmIIkud
o CCRCCRsgsCksU
sU222110 11
)(
)(
] ( )[ ]2121212
21 CCCCCRRsCRRg kkmII ++++ &)8'
? !
kmIIII CRRg
p21
1−≈−=ω &)9+'
kk
kmIIIIII CCCCCC
Cgp
1221 ++−=−=ω &)9)'
k
mII
C
gz = &)9'
1 ) ! 'Ip
Ip ! 'IIp
IIp J )
1! kC !
8:
IIT ωω ≤ &)9'
! $
*7° (
!
k
mIT C
gGB ==ω &)9*'
" !
'
22 -5+'8!%,!!.$"-/$'"()'
( !
( !
6
SR & '
du I− I+&)*'
kC =
kC
I
2
∫= IdtC
tuk
o
1)( &)97'
( ! &)97'
k
o
C
I
dt
tduSR == )(
&)98'
(µ?9*) =I +µ?
=kC + H SR >+89<Aµ 1 SR
=
8
SR
<Aµ
1 kC &)9*'
&)98'
m
T
mI
T
gI
gISR
ωω == &)99'
( &)99' mg
$ -
± !
TTTT
IISR ωϕϕω
22
== &)9:'
±
SR IK W
LI
ITT= =
ωβ
ω2
2'
&)9'
4 6
'
2 )*
5 ".? &
'/".?
gR LR ∞→inR ∞→oR
T4T3
T1 T2
T6 T5 T10T9
T7 T8
−8((
+8&&
L J XR P LQ
=
5/
LQ
,5()
85(*
,)*#
9+
inmo UgI = &):+'
T
REFm
Ig
ϕ2= &):)'
1 &):+ ):)'
REGU ! R
".? !
$
!'
@
& '
'
#
! & '
' ! !
)+
! $
36"#
b)
11
+
-
a)Y
X
+
-
Y
X
X ] ,R 7 Q
=] ,7 Q
,Q
X X[ LQ
≈
XLQ
XLQ ,
Q
7
XR
5
5
5R
5R
,)7 ' !'
2 )7
)7!
$
!
1R 2R
inu
L M=
9)
2
nTo Izu = nI
M )( ωjzT
)=
)7!
inyx UUU ==
221 || R
U
RR
UI oin
n −= &):'
nTo IjzU )( ω=
, &):'
( ) ( )
( )
k jU
U
R
R R z j
R
R T j
fo
in T
ωω
ω
= = +
+
=
= +
+
))
)
))
) )
/
/
&):'
2)()( RjzjT T ωω = &):*'
1
TR !
g
TT j
Rjz
ωωω
+=
1)( &):7'
TTg CR
1=ω &):8'
!
( &):7' &):' &):8'
gf
ff jkjk
ωωω
+=
1
1)( 0 &):9'
9
1
2
2
1
2
0 11
1
R
R
R
RR
R
k
T
f +≈+
+= & 2RRT >> ' &)::'
22
1R
R
R
R Tg
Tggf ωωω ≈
+= &):'
&)::):'
GB k
R
RRR
R
R
R
R
R
R
R
R
f gf
T
Tg
g Tg
Tgf
)
)
)
)
= =+
++
≈
≈ +
≈ ≈
ω ω
ωω ω
&)+'
&)::'&):'
! 1R 2R
gfω 2R
/
! 2R
! ! 1R
6 GBgf ≈ω
0fk
2 )8
R
R
(
'oR ''
oR
& )7!
!
9
1
10
100
1k 10k 100k 1 M 1 0 M 1 0 0 M
5
= Ω
5
= NΩ
5
= NΩ
5 FRQVW
= =NΩ
ωJI
FRQVW=I
NI
,)8 ( 5
'oR
''oR
1R
& 1R 2R >'
T10 T12
T7
T8
T11
T15
T16T14T13
T9
T5
T6
T1
T2
T3
T4
ZXY
b)
ZX
Y
LP
LPa)
x1x1
−8((
XLQ
XR
,
,
&7
&7
+8&&
+8&&
&7
7
R
X X; LQ
=
X X; LQ
=
,Q
,Q
UHI
UHI
XLQ
−((
,)9 - '
!!'