ele241
TRANSCRIPT
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א ٢٤١ א
א
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אאאאאאאאאאא א א א א א א ،א
אאאאאא،אאאאאא
אאאK
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א ، אא א אא אא،אאאאאאאאאאאאאאאאא
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אאאא
א
١
א٢٤١ א א א
א א
- ١ -
אאWאאאאאW
• א• א • אאא • א • אאאא • אאאא
W
אאאWo אאDiode o אאאBJT o אאאאIGBT o אMOSFET o Thyristor o Triac o Diac o אאUJTK
אאאWאא،אאאאא
אאאאאאאK
אThyristorWאאאאsemiconductors
١٩٥٧General Electricsאאא
א٢٤١ א א א
א א
- ٢ -
אKאאWאאAnode (A) ،אא Cathode (K)אא Gate (G)אF١J١KE
אF١J١WEא
אSilicon Controlled Rectifier (SCR)K
אאאאאאאKאאאאאאא
אON stateK
אStates of a thyristorWWאאForward biased stateאא
אReverse biased stateKאאאKאאאאאFאKE
אאאStatic Characteristic of a thyristorWאאאאאא
אאK
• אאFאאEאאJ١J٣אאאJ٢אאKא
A
G
K
Anode األنود(A)
Gate البوابة(G)
Cathode الكاثود(K)
P N P N
J٣ J٢ J١
א٢٤١ א א א
א א
- ٣ -
אאאאאאKאאאאForward leakage current،
אאאForward Blocking (off) stateFאOAאF١J٢KEE
אאאאאא
אאForward Breakdown VoltageאJ٢א،אאאא
אאא On StateFאBCאF١J٢KEEאאאאאJ٢אא
אאאאאKאאאאאא
אאאאKאאאאאאאא‘IH’Holding
currentK
• אאFאאEאאJ٢אאאJ١J٣אאK
אאאאאאאאReverse leakage current
אאFאODאF١J٢KEE
• אאאאאאאאAvalanche
FאDEאF١J٢KEE
א٢٤١ א א א
א א
- ٤ -
אF١J٢WEאאא
אאאIdeal characteristic of a thyristorW
אאאאFאאאאEא
FאOAאF١J٣KEE
אאKאאאאKא
אאFאOCאF١J٣EEאאאFאOBאF١J٣KEE
+VAK
IG٠=٠
+IA
-VAK
-IA
VFB
IH
VRB
IG١>IG٠ IG٢>IG١
O
A
B
C
D
E
א٢٤١ א א א
א א
- ٥ -
אF١J٣WEאאא
אMethods of triggering a thyristorWא،אאאאאאאא
אאK
אאאThermal and light triggeringWאאא
אאאאKאאאKאאא
אאאLight Activated Silicon Controlled Rectifier
(LASCR)K
O
A
B C
IA
VAK
א٢٤١ א א א
א א
- ٦ -
אאHigh voltage triggeringWאאאא
אאאאאאKאאאא
אK
אאאtriggeringdtdvW
אאאאאאKאאאאאאאאאאK
،אאאאאdtdvא
א٢٠٢٠٠אאאK
אאGate triggeringWאאFאאאאE
אאאא١٠٥٠אאאK
אאFiring circuits of a thyristorWאאאW
• אאאא،א • ،א • אאאאאאK
אאאאאאW• אאא• אאא
א٢٤١ א א א
א א
- ٧ -
• אא
אאאDC firing circuitsWאF١J٤EאאאEg،
RgאDKאאSWאאאאאRgKאאאאKא
אאאאאאאאאKאאאאאאאא
אאאאאאאאאאאאKאאאK
אF١J٤WEאאא
אאאAC firing circuitsWאאאאאא
אאאKאF١J٥EאאאR١R٢אאאאאאD
אאR٢אאאKאאאאאR٢RgKאאא
אאאאאאאא٩٠אKאאאאאK
א٢٤١ א א א
א א
- ٨ -
אF١J٥WEאאא
Pulse triggering circuitsWאאאאאאאא
אKאא،אאאאPulse transformersKאF١J٦Eא
אאאאQ١R١CאאאKאאאR١א
אאVpאאאאR٢אQ٢אאאK
א٢٤١ א א א
א א
- ٩ -
אF١J٦WEאא
אThyristor protectionWאאאאאאאא
אאKאאאאאאאאאא
אאKאF١J٧EאאאאאאW
• אאאאFuseאאאKאאא،אאא
אאK • אאאאאאאא
Snubber circuitאאKאאאאK
• אאאאאאאאאא
א٢٤١ א א א
א א
- ١٠ -
אF١J٧WEאא
אTriacWאאאא
אאאאאאאאאF١J٨KE
אF١J٨WEאFEאFEאFEאאא
T١
G
T٢
Gate )أ( البوابة(G)
Terminal (T١)الطرف
P
N
P
N N
N
Terminal (T٢)الطرف
)ب(
A١
G١
K١
K٢
G٢
A٢
T١ T٢
G
)ج(
א٢٤١ א א א
א א
- ١١ -
אאאאאKאאאW
• אT١אT٢אT١T٢אאאGאT٢K
• אT٢אT١אT٢T١אאאGאT١K
אאKא
אאאאאאאאK
אאאאאאאא
אF١J٩KE
אF١J٩WEאא
V
IG٠=٠
I
VB
IH
IG١>IG٠
IG٢>IG١
O
-VB
א٢٤١ א א א
א א
- ١٢ -
אDiacWאאאאאW
• אT١אT٢אT١אT٢אא
• אT٢אT١אT٢אT١אאK
אF١J١٠EאאאאK
אF١J١٠WEאFEאFEא
אאאאF١J١١Eאא
אאIGאKאאאאאאאK
T١ T٢
)أ(
Terminal P N P (T١)الطرف
Terminal (T٢)الطرف
N
N
)ب(
א٢٤١ א א א
א א
- ١٣ -
אF١J١١WEאא
V
I
VB٠
IBR
O
א٢٤١ א א א
א א
- ١٤ -
W
١J؟ ١א ١J؟ ٢אאא ١J؟ ٣אאא ١J؟ ٤אאא ١J٥ ؟אאא ١J؟ ٦אא ١J٧ אאאאאא ١J؟ ٨א ١J٩ אאאT١אT؟٢ ١J١٠ אאאא ١J١١ ؟ ١J١٢ אאאT١אT؟٢ ١J؟ ١٣
אאאאאאאאאא
אא
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א
א
א
אא
٢
א٢٤١ א א א
אאאאא א
- ١٥ -
אאWאאאאאאאW
• אאאאאא
• אאאאאאא
•
Wאאאאאאאאא
אאKאאאא(R)(R-L)Kאא
אאאאVmVmאאאאאK
אאאFאאאWEאאא(Thyristor)אאא
(SCR)אFEאאW
١K אאאאאאאאאא
אK ٢K אאאא
٢אπאא
٢πאF٢J١Eאאאאא
אאK
א٢٤١ א א א
אאאאא א
- ١٦ -
FE
FE
אF٢J١WEאאאFWEאאאFEאאK
אאאא Single-Phase Half-Wave Controlled Rectifiers with a resistive load
אF٢J٢EאRKאאאאאFEא
אאאאאאאאאאאFtoE
אF٢J٣EאאאFREאאFtoEאFVoEאא
אאK
א'R'FπZtoEאאאאאאאאאאאאאא
אאאאאאא'R'אאKאאאאאא
אא٢πZtoאF٢J٣Eאא
α ٢π+α ωt
Ig
α ٢π+α ωt
Ig
א٢٤١ א א א
אאאאא א
- ١٧ -
אFאE'vo'א'io'אאא'vT'אאאאאW
⎪⎩
⎪⎨
⎧
<<<<
<<=
ωππωπω
/2/,0/,sin
0,0
0
0
0
twtttV
ttV m
אא٠toאאאאאאאאאאtoאאωtoאאαא
אωtoπאאγK
אF٢J٢WEא'R'K
א٢٤١ א א א
אאאאא א
- ١٨ -
אF٢J٣WEאאאאF٢J٢KE
אאאAverage load voltage and currentWאאאאאאאאF٢J٢EW
)cos1.(2)( απ
+=VV mavgo F٢J١E
Vm،אאאאאαאאKאאאאW
RVI avg
avgo)(0
)( = F٢J٢E
אF٢J٢EאF٢J١EאF٢J٢WE
)cos1.(2)( απ
+=R
VI mavgo F٢J٣E
אאאאאא'Im'W
)cos1.(2)( απ
+= II mavgo F٢J٤E
א٢٤١ א א א
אאאאא א
- ١٩ -
ImאאאVm/R K
אאאR.M.S. value of the load voltage and currentאאאאאאאאF٢J٢E
W
)2
2sin1(.2)( π
απα+−=VV m
rmso F٢J٥E
אאאאאאW
)2
2sin1(.2)( π
απα+−= II m
rmso F٢J٦E
אאאאאאאFαEאאFαEאאאFαEאK
אא(Vdo)אF٠ZαEאF٢J١EVdoW
πVV m
do = F٢J٧E
אאאVoאאאאאאא
אאאK
אא(Power Factor)אא'PF'אאא'P'אאא'S'אW
SPPF = F٢J٨E
אאאאאאא
RP I rms2= F٢J٩E
VI srmsS = F٢J١٠E
א٢٤١ א א א
אאאאא א
- ٢٠ -
אאאאאאF٢J٩EF٢J١٠EאF٢J٨EW
VI
s
rms RPF = F٢J١١E
אאאאא'R'אF٢J٦EאF٢J١١EW
)2
2sin1.(21
πα
πα+−=PF F٢J١٢E
٢J١W
אא١٢٠
VKאאא١٠ Ω،אאא'Vo'א'PL'אאאW
FE α = ٠oFEα = ٤٥oFEα = ٩٠o
FEα = ١٣٥oFEα = ١٨٠o
אWאאאא'Vm'W
7.16921202 ===VV sm V
אא'Vo(avg)'א'PL'אאF٢J١EF٢J٩EW
)cos1.(2)( απ
+=VV mavgo
RIP rmsL2=
FEאאα = ٠oאאW54)0cos1.(
27.169
)( =+= oavgoV π
V
485.80120
7.169)2
2sin1(.2)( =−=+−=
πα
πα
RVI m
rmso A
72010.485.8 22)( === RIP rmsoL W
א٢٤١ א א א
אאאאא א
- ٢١ -
FEאאα = ٤٥oW1.46)45cos1.(
27.169
)(=+= o
avgoV π V
09.8290sin1.
180.451.
207.169 0
)( =+−=ππ
πI rmso A
55.65410.09.8 2 ==∴PL W
FEאאα = ٩٠oW27)90cos1.(
27.169
)( =+= oavgoV π
V
62180sin1.
180.901.
207.169 0
)( =+−=ππ
πI rmso A
36010.62 ==∴PL W
FEאא:α = ١٣٥o91.7)135cos1.(
27.169
)( =+= oavgoV π
V
56.22270sin1.
180.1351.
207.169 0
)( =+−=ππ
πI rmso A
4.6510.56.2 2 ==∴PL W
FEאאα = ١٨٠oW0)180cos1.(
27.169
)(=+= o
avgoV π V
02360sin1.
180.1801.
207.169 0
)( =+−=ππ
πI rmso A
0=∴PL W
אאאאאאאא'α'אאW
α ٤٥ ٠o ٩٠o ١٣٥o ١٨٠o Vo(avg) V ٥٤ ٠ ٩١٧ ٢٧ ١٤٦ PL W ٠ ٤٦٥ ٣٦٠ ٦٦٥٤ ٧٢٠
א٢٤١ א א א
אאאאא א
- ٢٢ -
٢J٢Wאא١٢٠
VKאאא١٠ Ωאאא‘α’٦٠o،WJ אאאאא'PL'KJ אאא'PF'K
אWJ אאא'Im'W
97.1610
2120===
RVI m
m A
J אאWRIP rmsL
2=
)2
2sin1(.2)( π
απα+−= II m
rmsoQ
5792120sin
180.601.(10.
497.16)
22sin1.(.
4
22
=+−=+−=∴π
πππ
απαRmI
PL W
J א' PF'אאF٢J١٢EW
)2
2sin1.(21
πα
πα+−=PFQ
634.)2120sin
180.601.(
21
=+−=∴π
ππ
PF Lag.
٢J٣W
אא١٥٠ V٦٠ Hz١٠ ΩKאאא'α'٣٠o،WJ אאא'Im'K J אאא'Vo(avg)'K J אאא'Io(avg)'K J אאא'Io(rms)'K J אאא'PL'K J אא'γ'K
א٢٤١ א א א
אאאאא א
- ٢٣ -
J א'fo'K J אא'PF'K
אWJ אאא'Vm'
21221502 ===VV sm V
J אאא‘Im’
2.2110212
===R
VI mm A
J אאא‘Vo(avg)’
63)30cos1.(2212)cos1.(
20
)( =+=+=π
απ
VV mavgo
V
J אאא‘Io(avg)’
3.61063)(
)( ===R
VI avgoavgo A
J אאא‘Io(rms)'
45.102
60sin180
.301.2
2.21)2
2sin1(.2)( =+−=+−=
ππ
ππα
πα o
mrmso
IIQ A
J אאא'PL'109210.45.10 22 === RIP rmsL W
J אא'γ''R'oooo 15030180180 =−=−= αγ
אFאEאאאאF٢J٣KEאא'fo'אאW
60== ff so Hz
J אא'PF'
)2
2sin1.(21
πα
πα+−=PFQ
7.0)2
60sin180
.301.(21
=+−=∴π
ππ
PF Lag.
א٢٤١ א א א
אאאאא א
- ٢٤ -
אאאאSingle-Phase Half-Wave Controlled Rectifiers with an Inductive Load 'R-L'
אF٢J٤Eא
‘R-L’אF٢J٥Eאא'vs'א'vo'א'io'אאאא'vT'K
אF٢J٤WEא'R-L'K
אאWאאF٢J٥EW
אאא'vs'FEא’α’אאאאא
אאאאאωt = αאא'α'אא⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛= −
RωLtanΦ 1
אאאאאאא'β'אאא(Extinction angle)K
אאאא١٨٠oאאאאאאאאאאאא
א٢٤١ א א א
אאאאא א
- ٢٥ -
אאאאאאאאאא'β'א١٨٠oאאא
אאאπ < ωt < βKאאאא'vT'אאα < ωt <β אF٢J٥Eאאא
א'R'אאK
אF٢J٥WEאאאאF٢J٤E
אאאWאאאאאאאא
F٢J٤EW
)cos.(cos2)( βαπ
−=VV mavgo F٢J١٣E
אאאאW
א٢٤١ א א א
אאאאא א
- ٢٦ -
)cos.(cos2
)()( βα
π−==
RRVVI mavgo
avgo F٢J١٤E
אא' β'אאWφβα
φααβ tan)
().sin()sin(
−
−=− e W
αאאΦאאאא⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛=Φ −
RLω1tanK
אא' β'אF٢J٦Eא
א'α'אא'Φ'Kβ Φ א αאא'γ'β(β = γ + α)KאF٢J
٦EאאאΦ = ٠oאא'R' אΦ = ٩٠oאאא(L)K
WאאW
• אא'α'WאאאאאאאאאאאאאK
• אא'β'Wאאאאאאאאאאאאא
אאK• אא'γ'Wאאאאא
אK
א٢٤١ א א א
אאאאא א
- ٢٧ -
אF٢J٦Eאא'α'א'β'אא'Φ'
אאאאאאSingle-Phase Half-Wave Controlled Rectifiers with an Inductive Load and a Free-Wheeling Diode אאאאאא
אאאאאאא
אאאא(Free-wheeling diode)K
אF٢J٧Eא‘R-L’אאאאאאאאא
אאאאאאאאאאא
א٢٤١ א א א
אאאאא א
- ٢٨ -
א(Short-circuit)אאאאאאאאאאF٢J٧KE
אF٢J٧Eא 'R-L'אאK
אאWאאאF٢J٧Eאאא
F٢J٨EKאאאאאאא
אא'α'אאאאאF٢J٨KEאאא
٠א < ωt < αאאאא'α'אאאωt = αא
אאאאאאאא'β'Kאאα < ωt < βα
<ωt < π،π < ωt < βאאאα < ωt < πאאאאאאאאאאא'vs'אא'R-L'א'vo'א'vs'vo = vs
אאאאאאאKאF٢J٨Eאאωt = π
א٢٤١ א א א
אאאאא א
- ٢٩ -
אאאאאאFאאאאEאאאπ < ωt < βא
אאאאאאאאאאאאאאאאאא
אאאאאאאאאאאאאאK
אF٢J٨WEאאאאF٢J٧E
א٢٤١ א א א
אאאאא א
- ٣٠ -
אאאאWאאאאאאאW
א'vo'אאאKאאאא
אאאאאאאאK
אאאאאאF٢J١E،F٢J٣EW
)cos1.(2)( απ
+=VV mavgo
)cos1.(2)( απ
+=R
VI mavgo
٢J٤Wאא ١٥٠ V
٦٠ HzאאKאא'R'א١٠ Ωאא'ωL'١٠ ΩKאאא٣٠oאא،
אK
אWאאאאאW
)cos1.(2)( απ
+=VV mavgo
)cos1.(2)( απ
+=R
VI mavgo
אא
63)30cos1.(2
2150)( =+= o
avgoV π V
3.61063
)( ==I avgo A
א٢٤١ א א א
אאאאא א
- ٣١ -
אאSingle Phase Full-Wave Controlled Rectifier
אאResistive Load אF٢J٩Eאא،אא
א’Vs’ ‘R’.אא٤אאF٢J٩KE
אF٢J٩WEאא 'R'K
אאאאאWאאאאא‘T١, T٢’
אאא‘T٣,T٤’אאאאאאאאאאא
אאאאאאKT١T٤א٠ ≤ ωt ≤ πT٢
T٣אπ ≤ ωt ≤ ٢πאאאא‘Pulse Transformer’אאא‘Opto-Coupler’K
א٢٤١ א א א
אאאאא א
- ٣٢ -
אאWאאאF٢J٩Eאאא
F٢J١٠KEאT١אT٤א‘α’אאאא‘٠ ≤ ωt ≤ π’אא
אאT١,T٤אאאא
אאאאאאאאvsאT١אא‘R’אT٤א‘Vo’אא
אא‘R’אFאאEאאK אאאאאאT٢,T٣
אאאאא+ παאאאאאאאאא T٢אא‘R’ אT٣
אאאאT٤,T١אאT٢,T٣ ١٨٠oאאאאאאא
אאT١אT٤ אT٢אT٣ אא‘vAK’
אאאאא‘is’אא
א‘io’אאאאאKאπ
אאאאK
א٢٤١ א א א
אאאאא א
- ٣٣ -
אF٢J١٠WEאאאא
'R'K
אאאWאאאאאאF٢J٩Eאא
אאאאאF٢J٢EאאאאאW
)cos1.()( απ
+=VV mavgoF٢J١٥E
אאאאאW
א٢٤١ א א א
אאאאא א
- ٣٤ -
)cos1.()()( α
π+==
RRVVI mavgo
avgo F٢J١٦EאF٢J١٦EW
)cos1.()( απ
+= II mavgoF٢J١٧E
WVmאאאאא
Vsאאאאא ImאאאאIm אאW
RRVVI sm
m
2==F٢J١٨E
אאאWאאאאאאאא
F٢J٩EW
)2
2sin1(.2)( π
απα+−=VV m
rmsoF٢J١٩E
אאאאאאW
)2
2sin1(.2)( π
απα+−= II m
rmsoF٢J٢٠E
٢J٥Wא
١٥٠אV٦٠ Hzאא‘R’١٠ Ω Kאא٣٠אo،W
J אאא‘Vo(avg)’K J אאא‘Io(avg)’K J אא‘Im’K J אאא'Io(rms)'K J אאא'PL'K J א'fo'K J אא'PF'K
א٢٤١ א א א
אאאאא א
- ٣٥ -
אWJ אאאאW
)cos1.()( απ
+=VV mavgo
126)30cos1.(2150)( =+=∴ o
avgoV π V
J אאאW
6.1210
126)()( ===
RVI avgo
avgo A
J אאאW
2.2110
2150===
RVI m
m A
J אאאW
77.14260sin
180.301.
22.21)
22sin1(.
2)( =+−=+−=π
πππ
απα o
mrmso
II A
J אאאW 218210.77.14 22 === RIP ormsL W
J אאאא120)60.(22 ===∴ ff o
Hz
J אאאאא ‘Io(rms)’ אאא‘Is’
VI
IVI
s
orms
ormss
orms RRPF ==
2
98.0150
)10.(77.14==∴PF Lag.
אא‘R-L’אF٢J١١Eאאאא
(R-L) K
א٢٤١ א א א
אאאאא א
- ٣٦ -
אF٢J١١WEאא 'R-L'K
אאWאאאT١,T٤
אאאא ωt = αאאT٢,T٣אאאאא ωt = α + πאF٢J١٢Eאאאאאא
KאאαאT١,T٤אאאאאא ‘vs’
ωt = π אאאאאT٤אאא T١אאא אאאאא
Rאאאvoאvsאאאאא
אא‘β’אT١, T٤אאא‘vo’אא π < ωt <βא
אאאאא‘L’אאKאF٢J١٢EאT٢, T٣
אאωt = π + αאאאאאאאאא ‘vs’ אT٢ אאא
א٢٤١ א א א
אאאאא א
- ٣٧ -
T٣אאאאאωt = π + βאאא
אאא‘ωL’אאאאאאאאאאאאאאא
F٢J١٢E،F٢J١٣EאאאאKאF٢J١٢Eאא
١٨٠oאאא‘is’٣٦٠oאF٢J١٣Eאא‘β’π +
αאאאאאאאאא
K
אF٢J١٢WEאאאא
'R-L'K
א٢٤١ א א א
אאאאא א
- ٣٨ -
אF٢J١٣WEאאאא
אK
אאאWאאאאאאאא
F٢J١١EאאאFאאאEW
)cos.(cos)(
βαπ
−=VV mavgo
F٢J٢١Eאאאאאאאא
F٢J١١EאאאאFאאאEאאאW
απ
cos.2)( VV mavgo=F٢J٢٢E
אאאI avgo )(Vo(avg)/R
א٢٤١ א א א
אאאאא א
- ٣٩ -
אאאאאאאאF٢J١١EאאאFאאאEW
)cos.(cos)( βαπ
−=R
VI mavgoF٢J٢٣E
אאאאאאאאF٢J١١EאאאFאאאEW
απ
cos.2)( VI mavgo R=F٢J٢٤E
אF٢J٢٢Eאאאא٠ א ٩٠oאא
(rectifier)אא ٩٠o ١٨٠oאאאא(inverter)א
אאאאאאאאאאא(٢-Quadrant)אא
אאאאאאאאאאאאאK
אאאVAKW
אT١אT٢FEאאאT٢
אאאT١אאאאאאאvsאT١אT٢
אאאאאW
VVV TsT 12+=F٢J٢٥E
אאT١אאאT٢אאvsVV sT
=2K
א٢٤١ א א א
אאאאא א
- ٤٠ -
٢J٦Wאא
٢٣٠V٦٠ Hzאאאא ‘ωL >> R’א.٥٠ Ω אאא
א٢٠٠א VK
אWאאאאא ωL >> Rא
F٢J٢٢EWα
πcos.2
)( VV mavgo=
απ
cos).2230.(2200 =∴ o15966.0cos =∴=∴ αα
٢J٧Wא א
١٢٠V ٦٠ HzאאאאωL >> R’’א.١٠ Ω אאא٣٠o،W
J אאא’Vo(avg)’K J אאא'Io(avg)’K J אאא‘Im’K J אאא'Io(rms)'K J אאא‘IoTh’K J אאא'PL'K J אא‘PF’K
אWJ אאאאא‘Vm’
17021202 ===VV sm V
J אאאFאE
א٢٤١ א א א
אאאאא א
- ٤١ -
9430cos.170.2cos.2)(
=== omavgo VV π
απ
V
J אאא
6.91094)(
)( ===R
VI avgoavgo A
J אאאאאאאW
4.9)( == II avgom A
J אאאאאאW 4.9)( == II avgoorms A
J ‘١٨٠o’אאאאא
7.424.9
21
)( === II avgooTh A
J אאא3.88310.4.9 22 === RIP ormsL W
J אאאאאאאאאW
78.012094
2
====V
IIV
Is
orms
ormss
orms RRPF Lag.
אאאאW
אאאאאF٢J١١EאאאאאאFאEא
אאאKאאאאאאאאאאאאאאאא
אF٢J١٤EאאאאאK
א٢٤١ א א א
אאאאא א
- ٤٢ -
אF٢J١٤WEאאא
אK
אאאאאF٢J١٤Eאאא
F٢J١٥Eאאאא‘ωL >> R’אאאאW
אאT١,T٤אאאא ωt = αאאאאאאא ‘vs
אT١ אאאT٤אאאאωt = π אא(α ≤ ωt ≤ π)אאאאא
Kאאאאאאאωt = πאאאא
אאאאאאאאאאא(π ≤ ωt ≤ π +α)אאאא א
אאאאאאאאאאאאאאאא‘is’אא
אאאאאא‘ωt+π’אאאT٢ ,T٣אאאאא
א٢٤١ א א א
אאאאא א
- ٤٣ -
אאאT٢אאאT٣אאאא‘vo = - vs’
אאאωt = ٢πאאאאאאωt = ٢ π + α אאאאאאאאאאא
אאאאאאאאא
אT١,T٤KאF٢J١٥Eאאאאאאאאאא
אאאאK
אF٢J١٥WEאאאא
אאאK
א٢٤١ א א א
אאאאא א
- ٤٤ -
אאאWאF٢J١٠E،F٢J١٥E
אאאאאאאאאFF١٥٢EEW
)cos1.()( απ
+=VV mavgoF٢J٢٦E
אאא
)cos1.()()( α
π+==
RRVVI mavgo
avgoF٢J٢٧E
אאאאאאאאאאאF٢J١٥Eא
אאאאאאא٢π
אאאאאאאαאאאאאW
)cos1.(. 2)()( απα
πα
+==R
VII mavgoavgDF٢J٢٨E
٢J٨Wא א
١٢٠V ٦٠ Hzאאאא‘ωL >> R’א١٠ ΩאאKאאא
٣٠o،WJ אאא'Vo'K J אאא'Io(avg)' J אאא‘Im’K J אאא'Iorms'K J אאאאאא‘ID(avg)’K J אאא‘IoTh’K
א٢٤١ א א א
אאאאא א
- ٤٥ -
J אאא'PL'K J אא‘PF’K
אWJ אאאאא‘Vm’
17021202 ===VV sm V
J אאאFאE
101)30cos1.(170)cos1.( 0)(
=+=+=π
απ
VV mavgo
V
J אא
1.1010101)(
)( ===R
VI avgoavgo A
J אאאאא
1.10)( == II avgom A
J אאאאא1.10)( == II avgoorms A
J אאאאא683.1)
18030(1.10.)()( ===
παII avgoavgD A
J١٨٠oאא٣٠oאא
21.4)1.10.(360150.
2)(
)( ==−
= II avgooTh παπ A
J אאא102010.)1.10( 22 === RIP ormsL W
J אאW
IIVP
srmssrmss
LPF120
1020== (I)
Is(rms)אאאאW
AII avgosrms 22.91801501.10)( ==
−=
παπ (II)
(II)א(I)W
א٢٤١ א א א
אאאאא א
- ٤٦ -
92.0)22.9.(120
0201==PF Lag.
אאאאאאאאאאאאאא
אאאK
אאאא'R-L' Single-Phase Full-Wave Half-Controlled Rectifiers with an Inductive Load
אא
אאאאאאאאאאאאאאאאאא
אאאאאאאאאאאא
אאאאאאאאאאאאאא
(١-Quadrant)אF٢J١٦EאאאאאאF٢J١٦EאאאF٢J١٠EאאT٣, T٤אD٣, D٤F٢J١٦KE
אאאאאאאF٢J١٧E
אאאא‘ωL >> R’אאאאW
א٢٤١ א א א
אאאאא א
- ٤٧ -
F٢J١٦WEאא 'R-L'K
אאT١אαאא
אאאאאאאאאא‘vs’אT١אאאאD٤אאאאωt = π
אאאאאα ≤ ωt≤ πא‘io’אאא‘is’אא א
אאאאאאωt = πאאאא‘io’אאאאאאא
א‘T١’אאאאD٣אאאאאωt =
π + αאאאאאאאאאאא
אאאאאאאF٢J١٤KEאאאאאאאאאאאא
אא‘vs’אT٢אאאאD٣א אאאωt = ٢πאאאאאπ + α ≤ ωt≤ ٢π
א٢٤١ א א א
אאאאא א
- ٤٨ -
אאאאאאאאאאא
אאא٢π ≤ ωt≤ ٢π + α אאאאאאאאT٢אאאאD٤
אאאאאT٢אאD٤אאאאאאאF٢J١٤KE
אאאא
אאאאאאF٢J١٤EאאK
אאאאאF٢J١٦E
אאאF٢J١٤EאאאאF٢J٢٦E،F٢J٢٧EאאF٢J١٤EW
)cos1.()(
απ
+=VV mavgo
F٢J٢٩Eאאא
)cos1.()( απ
+=R
VI mavgoF٢J٣٠E
א٢٤١ א א א
אאאאא א
- ٤٩ -
אF٢J١٧WEאאאא
אK
٢J٩Wאא‘vo’אאא
F٢J١٦Eאא١٢٠אV٦٠
Hzאאאא ‘ωL >> R’א١٠ ΩאאW
FEα = ٠KFEα = ٤٥oK FEα = ٩٠oK
FEα = ١٣٥oK
א٢٤١ א א א
אאאאא א
- ٥٠ -
אWאא
אאאאאאאאאαK
FE אאאאאT١אאD٤אאאα = ٠
אאאאאאאאT٢אאD٣א
אאF٢J١٨FEEאא‘vs’א‘vo’K
FE אאאאT١אאD٤
אאאאω = ٤٥oא ω = πאא٠ ≤ ωt≤ ٤٥oא
אאT١א‘vo’אאπ ≤ ωt≤ ٢٢٥oאאT٢א
אT٢אאD٣אאאאF٢J١٨FEE
אא‘vs’א‘vo’K
FE אFEFEאאW
אא٠ ≤ ωt ≤ ٩٠° אאאאא٩٠o ≤ ωt≤ ١٨٠oאאא
אT١אאD٤אאאא١٨٠o ≤ ωt≤ ٢٧٠o
אאאא٢٧٠אo ≤ ωt≤ ٣٦٠oF٢J١٨FEEאא‘vs’א‘vo’K
א٢٤١ א א א
אאאאא א
- ٥١ -
FE אFE،FEFEאאא
F٢J١٨FEEאא‘vs’א‘vo’K
FE
FE
FE
F٢J١٨WEאאאKאא
א٢٤١ א א א
אאאאא א
- ٥٢ -
W٢J١ אאא'vs'א'vo'א'io'
אאא'vAK': J אא'R'
J אאאאאאK
٢J٢ אאאא'Vo(avg)'אא'α'
אאאאא٢٢٠אVK
٢J٣ hאFאE'io'אא
אאאאKW J אא 'α' J אא'γ' J אא'β'K
٢J٤ אאאאאאאאאd؟א
אאאאאאא؟אאאא K؟
٢J٥ אא'L'אאאאא
א؟א'io'K
א٢٤١ א א א
אאאאא א
- ٥٣ -
٢J٦ אאאאאאא(ωL>>R):
J אאK J אאK
٢J٧ אא'vo'א'io'א'is'אא:
J אא'٦٠ 'K J אא'٦٠ 'K
٢J٨ אאא٢٢٠V٦٠Hz٥٠ ΩKאא'٦٠ ':
J אאא J אאא J אאא J אאK
٢J٩ אאאאא
אKאא٢٢٠V٦٠Hz٥٠ ΩKאאא'٦٠ 'K
J אאא J אאא J אאא J אאא J אאאאFאE J אאאאאK
א٢٤١ א א א
אאאאא א
- ٥٤ -
٢J١٠ אאאא٢٢٠V٦٠HzKא
אא٢٠ Ωאא'٦٠ 'KWJ אא J J אאא
אאאא
אא
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א
א
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אא א
- ٥٥ -
אאWאאאאאאאW
• א• אאא • אאאאא • אאאאK
W
אאאאאאאאאאאאאאאאאאא
אאאאאאאאאאאא
אאאאאאאאאאאאאאK
אאאאאאאאאאאאאאא
אאאאא(duty cycle)אאאאאאKאא
WJ step-down (buck) choppersאאאאא
אאאKJ א step-up (boost) chopperאאא
אאאK
אא ٢٤١ א א
אא א
- ٥٦ -
אאאA Basic DC ChopperWאF٣J١Eאאאא
אSאא‘Vs’RKאא‘Thyristor’אא‘Power
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א‘turn-on’KJ אאאאא
‘turn-off’K J אאאK
אאאאא‘power loss’א
אאאא‘Input dc power’אא‘output dc
power’W
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: VsאאK: Voאאא?אK?
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אא ٢٤١ א א
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- ٥٧ -
אF٣J١WERK
אDuty CycleWאאאאאא‘TOFF’
א‘TON’אאאאאאאאאF٣J٢Eאא
אאאא‘Pulse-Width Modulation’א‘TON’אאאאאאא‘T’אאאאא‘TOFF + TON’אK
א‘D’אאאאאאאW
TD T
TTT ON
OFFON
ON =+
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:TONאאK:TOFFאאK
io
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אא ٢٤١ א א
אא א
- ٥٨ -
אF٣J٢WEאK
אF٣J٢Eאאאאא(٠ ≤ D ≤ ١)
אאאאאאאאאאאאא
אKאאאאא‘Base current’אאא١אא
אאאאאאאאאאא
אאאאאאאאא(Auxiliary Circuit)FEאאא‘Commutation circuit’K
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אאאאאאאאאאK
VPULSE
TON ٠ T T+TON
t
TOFF
אא ٢٤١ א א
אא א
- ٥٩ -
אאאאR The Principle of Operation of a Basic DC Chopper Connected with a Resistive Load:
אא‘vo’אאאF٣J١E
אאא‘Vs’(٠ ≤ vo ≤ Vs)אאאא‘S’אאא
אKא‘vo’אאאא‘vo’א
א‘Vs’אאאF٣J٣Eא‘vo’K
אאאאW
אאאא‘Vo’W
VTVTTTV s
ONs
OFFON
ONo T
.. =+
=F٣J٣E
K
אF٣J٣WE‘vo’אאK
אF٣J٢EאF٣J٣Eאאאאא
VV soD=F٣J٤E
TON ٠ T T+TON
t
TOFF Vs
vo
אא ٢٤١ א א
אא א
- ٦٠ -
אF٣J٤Eאאאא‘Vo’א‘D’אF٣J٤EאאVoא
א‘Vs’٠ ≤ V٠ ≤ VsK אאאאא‘Io’אאאאF٣J٣E
אאא‘Io’אאאאאאאאW
VVI so
o RD
R.==F٣J٥E
אF٣J٤WEאאאא‘Vo’א‘D’K
אאאאW
אאאא‘Vo(rms)’אא‘Io(rms)’W
DVV srmso=
)(F٣J٦E
DDR IVI s
srmso ==)(F٣J٧E
WאIsאאאא‘R’
٠ ١ D
Vo
Vs
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אא א
- ٦١ -
אאWאאאאאאא
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RD VP s
i
2
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J אPulse-Width Modulation (PWM)KJ אPulse-Frequency Modulation (PFM)K
א‘TON’א‘PWM’אאא‘T’אF٣J٥Eא
אא‘PFM’אא‘TON’אא‘T’אאאא
F٣J٦EאאאאאאאאKאאאא
אאאאאאאאאא
אאאYPWM’א‘PFM’Kאאאאא
‘PFM’אא‘S’אאאאאאא
‘high current ripples’אאאאאאאאאK
אא ٢٤١ א א
אא א
- ٦٢ -
אYPWM’אאאאאאא‘filters’א
אK
FE
FE
FE
אF٣J٥WEא‘vo’אאK
vo
vo
٠ T
t ٢T ٣T
Vo
vo
VS
vo
٠ T t
٢T ٣T
Vo
VS
٠ T t
٢T ٣T
Vo
vo
VS
אא ٢٤١ א א
אא א
- ٦٣ -
FE
FE
FE
אF٣J٦WEא‘vo’אאא
٠ T t
vo
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vo
٠ T t
Vo
Vs
٠ T t
vo
Vo
Vs
אא ٢٤١ א א
אא א
- ٦٤ -
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אאאF٣J١E٢٢٠ Vאא١٠ ΩKאאאא
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אWJ אאאאאאF٣J٤EW
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J אאאאאאF٣J٦EW 6.1555.0220)( === DVV srmso V
J אאאאאאF٣J٨EW
242010
2205.022
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D VP si W
אאאStep-Down (Buck) DC ChoppersW
אאCase of An Inductive LoadWאאאאאא
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אאאאאאאאאKאF٣J٧Eא
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FEאאאא
אא ٢٤١ א א
אא א
- ٦٥ -
אאאאאאK
אאWאאאאSאא
אאאF٣J٢Eא'S'KאSא
אF٣J٧FEEאאאאDאאאאאאאא
א‘Vs’אSאא‘R-L’אאאאאאאאאאאאאאא
א٠‘א ≤ t ≤ TON’א‘vo’אאאאF٣J٧FEEאאאאK
אאSאאt = TONאאאאאF٣J٧FEEאא
אאאאאאאאF٣J٧FEEאא٠‘ א ≤ t ≤ TOFF’אאאאא
אאאאאאאאאKאאאאF٣J٧FEEא
אאאאאאF٣J٧FEEאאאאאא
٠‘א ≤ t ≤ TOFF’אאאאאאKאאאאאאאא
אאא‘dv/dt’K
אא ٢٤١ א א
אא א
- ٦٦ -
FE
FE
FE
אF٣J٧WEאאאאK
אאאאאאאאאאאאאאאאא
אאאאאאאאא
אאאאK
io
vo VD +
-
io
vo
ID=io
Is=٠
io
vo VD=Vs
ID=٠
+
-
Is=io
אא ٢٤١ א א
אא א
- ٦٧ -
אאContinuous Current ModeW
אאאF٣J٧FEEאאאא
WJ אאאKJ אK J א‘S’K
אאאאאאאKאאאאא‘filter’
‘L’אאאאאאאאאא
אאאאאKאאאאאאאא
אאאאאאא‘τ’אאτ>> L/R
אאאminImaxIאא
אTKאF٣J٨EאאאF٣J٧EאאאאF٣J٨FEEא
אVsאאS ‘٠ ≤ t ≤ TON’אא‘TON ≤ t ≤ T’אאאא٣J٨FEאא
אא٣J٨FEא‘is’אS٣J٨FEאא٣J٨FE،٣J٨FE،٣J٨FE
אאאאאאא‘TON ≤ t ≤ T’אא‘is’אאא‘٠ ≤ t ≤ TON’א
אאאW
אא ٢٤١ א א
אא א
- ٦٨ -
2minmax IIII Lo
+==F٣J٩E
FE
FE
FE
FETON ٠ T T+TON
t
io
Imin
٢T
Imax
TON ٠ T T+TON
t
Is
Imin
٢T
Imax
TON ٠ T T+TON
t
ID
Imin
٢T
Imax
TON ٠ T T+TON
t
TOFF
Vo
TON
٢T
Vs
אא ٢٤١ א א
אא א
- ٦٩ -
אF٣J٨WEאאKאאאאW
RVI o
o =F٣J١٠EאF٣J٩E،F٣J١٠EאאאW
RVII o2minmax =+F٣J١١E
minImaxIאKאאאאא
אW
VV oo
L dtdi
L ==F٣J١٢E أو
ti
LV
dtdi oOo
∆∆
==
tL
Vi OO ∆=∆∴ F٣J١٣E
Oi∆אאא W
minmax IIiO −=∆F٣J١٤Eאאאt∆W
OFFTt =∆F٣J١٥EאF٣١٤E،F٣J١٥EאF٣J١٣EאאאW
OFFo T
LVII =− minmaxF٣J١٦E
א F٣J١٦EF٣J١١EminI،maxI
OFFoo TL
VRVI
2max +=F٣J١٧E
OFFOO TL
VR
VI2min −=F٣J١٨E
אאאOPP iI ∆=−Wminmax III PP −=−F٣J١٩E
LTI V
OFFPP0=−F٣J٢٠E
אא ٢٤١ א א
אא א
- ٧٠ -
אאאSאא‘Is’אאאא‘ID’
א‘D’W
ITII oON
os TD ==F٣J٢١E
ITII oOFF
oD TD =−= )1(F٣J٢٢E
IoאאאIDאאאאאאKאאisא
Tאאאאא VsאאאאאאK
אאDiscontinuous Current ModeW
אאאא‘D’אאא
אא‘S’Kא‘S’אאאאאאאאאאאאKאSאא
אאאאאאאא
אאKאאאאאTON ≤ t ≤ TK
אF٣J٩EאאאF٣J٧EאאאF٣J٩Eאאאאאאאא
אאא‘τ’אSאTONKאF٣J٩Eאאאאא
אSאאTON ≤ t ≤ TאאאאSאא٠ ≤ t ≤ TONK
אאאא
אא ٢٤١ א א
אא א
- ٧١ -
אא‘L’KאאאאאאאKא
אאאא‘Imin’F٣J١٨EW
OFFOO TL
VR
VI2
0min −==
LRVTV o
OFFo
2=∴
2T OFFRL= F٢J٢٣E
אאאאאK
אא ٢٤١ א א
אא א
- ٧٢ -
FE
FE
FE
FEאF٣J٩WEאאK
TON ٠ T T+TON t
io
٢T
Imax
TON ٠ T T+TON t
ID
٢T
Imax
TON ٠ T T+TON
t
Is
٢T
Imax
TON ٠ T T+TON
t
Vo
٢T
Vs
אא ٢٤١ א א
אא א
- ٧٣ -
٣J٢WאF٣J٧E
١٠٠ Vאאא١٠ Ωאא٥٠ mHKאאאS ١ KHzא
FאE٥٠ VWJ א‘D’KJ א‘TON’K J אא‘Vo(rms)’K J אאא‘Io’K J אאא‘Imin’אא‘Imax’K J אאאאא‘Ip-p’K J אאאאא‘Ip-p’
אא٥ KHzK J אאאאא‘Ip-p’
אא٢٥٠ mHK אW
J אאאF٣J٤EWVV so D=Q
5.010050
===∴VV
s
oD
J אאאא'TON'אאF٣J٢EW
fDTD
TD TT
ONON ==∴=
5.01000
5.0==∴T ON ms
J אאאא'TOFF'W5.05.01 =−=−= TT ONOFF T ms
J אאאאאF٣J٦EW 7.705.0100
)(=== DVV srmso V
אא ٢٤١ א א
אא א
- ٧٤ -
J אאאW
5.010050
===R
VI oo A
J אאאאאאF٣J١٧EF٣J١٨EW
25.55.050*2
501050
2max =+=+= OFFoo TL
VRVI A
75.45.050*2
501050
2min =−=−= OFFOO TL
VR
VI A
J IP-PW 5.075.425.5minmax =−=−=
− III PP A
J IP-Pאאא٥ KHz٥٠אW
fDTDT OFF
)1()1( −=−=
1.010*5
)5.01(3 =
−=∴T OFF ms
05.51.050*2
501050
2max =+=+=∴ OFFoo TL
VRVI A
95.41.050*2
501050
2min =−=−= OFFOO TL
VR
VI A
1.095.405.5minmax =−=−=∴− III PP A
אאIP-PאאאאK
J IP-Pא٢٥٠ mHא١ KHz٥٠אW
fDTDT OFF
)1()1( −=−=
1.010*5
)5.01(3 =
−=∴T OFF ms
05.55.0250*2
501050
2max =+=+=∴ OFFoo TL
VRVI A
95.45.0250*2
501050
2min =−=−= OFFOO TL
VR
VI A
1.095.405.5minmax =−=−=∴− III PP A
אא ٢٤١ א א
אא א
- ٧٥ -
אאIP-PאאאאאKאאא
IP-PאאאאאK
٣J٣W
אF٣J٧E١٠٠ Vאאא١٠ Ωא١٠٠ mHKא
אאS ١ KHzאא‘TON’٥٠ msW
J א‘D’KJ א‘TOFF’K J אאא‘Vo’K J אאא‘Io’K J אאא‘Vo(rms)’K J אאאאK
אW J אW
110*111
3 ===f
T ms
5.015.0===
TD T ON ms
J אW 5.05.01 =−=−= ONOFF TTT ms
J אאאW 50100*5.0 === VV so D V
J אאאW
51050
===R
VI oo A
אא ٢٤١ א א
אא א
- ٧٦ -
J אאאW 7.705.0100
)(=== DVV srmso V
J אאאא W
5.210*25.0
2=== RL T OFF ms
٣J٤WאF٣J٧E
٢٠٠ Vאאא٤ Ωא٥٠٠ mHKאאאא٢٠ Aאאאא
א‘Ip-p’٤ Aאאא١٠٠ Hzאא‘TON’٤ msW
J א‘D’K J א‘TOFF’K J אאאא‘Is’K J אאאאאא‘ID’K J אאא‘Imin’אא‘Imax’K
אW
J אW
10100
11===
fT ms
4.0104===
TD T ON ms
J אW 6410 =−=−= ONOFF TTT ms
J אאאאW 820*4.0 === II os D A
J אאאאW
1220*)6.01()1( 0 =−=−= II DD A
אא ٢٤١ א א
אא א
- ٧٧ -
J אאא‘Imin’אא‘Imax’W
222420
2max =+=+= −III ppo A
182420
2max =−=−= −III ppo A
אאאאאאא‘τ’אאאא‘T’
1254
500===
RLτ ms and T = ١٠ ms
٣J٥WאF٣J٧E
٢٥Vאא٥ ΩKאאאS ٤ KHzאא١٥ VWJ א‘D’K J אאא‘Io’K J אאאאK J אאא‘Imin’אא‘Imax’K
אW
J אW
6.02515
===VV
s
oD
J אאאW
35
15===
RVI o
o A
J אאאא W
1.04
)6.01()1()1( =−
=−
=−=fDTDT OFF ms
25.05*21.0
2=== RL T OFF mH
אא ٢٤١ א א
אא א
- ٧٨ -
J אאאאW
6331.0*25.0*2
155
152max =+=+=+= OFF
oo TL
VRVI A
0332min =−=−= OFF
OO TL
VR
VI
אאאאאאאאאK
W
٣J١ אא'D' ٣J؟ ٢אאאאא ٣J٣ אאאאK ٣J٤ אאאאאאK ٣J٥ אאאאאאאK ٣Jא ٦אאא:
J א J אFKE
٣J٧ אאאאאK
٣J٨ ١١٠V
٢٠ΩKאאא١KHz٤٠W J אאאK J אאאK J אאאK J אאאK J אאאK
אא ٢٤١ א א
אא א
- ٧٩ -
٣J٩ ١٠٠V٥Ω٥٠VKW
J אKJ אאאאFאKE
٣J١٠ ١KHzאא ١١٠ Vאא٧٥ VKא
אFTON,TOFFKE ٣J١١ ١١٠V
א٨Ωא٤mHKאאא١KHz٤٠،אאW
J אאאK J אאאK J אאאאK J אאאאK J אאאא٥אKHzK J אאK
אאאא
אא
אאאã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
אאאא
אא
٤
אאא ٢٤١ א א
אא א
- ٨٠ -
אאWאאאאאאאW
• א • אא • אאא • אאא • אאאאאא• אאא• א • אא
W
אאאאאאאאאאאאאאאאאאא
אאאKאאאאאאאאא
אאאאאאאאאאאKא
אא'Inverters' אאאאאאאאאא
אאאאאאאאאאIGBTKKKKאאאא
אאאאאאאאKא
אאאאאW• אאא• אאא
אאא ٢٤١ א א
אא א
- ٨١ -
• אא • אאא
אאאW
١K אא(VSI)''Voltage Source InverterאאK
٢K אא(CSI)''Current Source InverterאאK
אאאאאאאאK
אאא
אאאאאאWo אאא (induction motors)אאא
(synchronous motors)K o אאFinduction heatingKE o אאאFaircraft power suppliesKE o אאFuninterruptible power supplies UPSKE o אאאאאF high-voltage DC transmissionKE o אאFstandby power suppliesKE
אFbatteryEFsolar cellEאאאא٢٢٠
٦٠٢٢٠٤٠٠אאאאאאאאא٢٢٠L٣٨٠٥٠١٢٠L٢٠٨٦٠
١١٥L٢٠٠٤٠٠K
אאא ٢٤١ א א
אא א
- ٨٢ -
אאThe Basic Inverter
אאRWאF٤J١Eאאאאא
אאאאאאKאא٢א
אאאאאאKאאS١אS٢אאא
אS١،S٢אאF٤J٢EאאS١אאS٢
אאאאאאאVsאS١،S٢KאS١אS٢
אאאאאאאS٢אS١אאאאא
אאאא'T'אF٤J٢Eא
א'fo'אאW
HzTf o
1=F٤J١E
אאא ٢٤١ א א
אא א
- ٨٣ -
אF٤J١WEאאאאRK
i٢
Vs
Vs
Vo
R + -
S١
S٢
i١
אאא ٢٤١ א א
אא א
- ٨٤ -
אF٤J٢WEאS٢, S١אאא
א א א א
אS١،S٢ K אאא אאאאאK
S١ S١
S٢
-Vs
Vs
2T T
23T
Vo
t ٠
Vs
S٢
2T
T
Vs٢
t ٠
Vs
S١ S١
2T
T 2
3T
Vs١
t ٠
אאא ٢٤١ א א
אא א
- ٨٥ -
א א אא'filter'אאא אא אאא א
א א א אאKאאא
א'PWM'K
אאאאאאאאאאאאא
אK
אאVoltage Source Inverter (VSI) אא א א א אא א א
אאאאאאאאא א א א א א א
אאאאאאאאאK
אאאא ١-Phase Half-Bridge (VSI) Inverter א א א אא א אא
אF٤J٣Eאאאאא אא٢S٢ ,S١א'Vs'٢א
אאאאKאא א א א א א א א אKKK
Kא
אאא ٢٤١ א א
אא א
- ٨٦ -
אא Case of a Resistive Load Rאא S٢ ,S١אאF٤J٣E
RאS١אS٢אא٠ ≤ t ≤
T/٢אא'Vs'אאאאא א א א א א א S١ א
אi١אS٢אS١אאT/٢ ≤ t
≤ TאS١אאt = T/٢אא'-Vs'אאאi٢אאאאא
א א א אאS٢ א אi٢ א i١ אF٤J٤EאRאf
א אאאאT/١אאK
אאאאאאאא'Vs'K
אF٤J٣WEאאאאא
Vs
Vs
S١
S٢
D١
D٢
- + الحمل
Vo
is١ iD١
is٢ iD٢
אאא ٢٤١ א א
אא א
- ٨٧ -
אF٤J٤WEאאאא
אאCase of an Inductive load
אאאאioא א א א Vo א
אאאאאאאאאאאK אF٤J٥ Eא א א K
אאאWאא٠ ≤ t ≤ T/٢אVoאא
אאS١אאאאD١Kאioאאאאאא٠ ≤ t ≤ t١
אאאאאאאאא D١אאאאאVSאא t١ ≤ t ≤ T/٢אא
אא א א אאS١אא אא א אאאS١אא٠ ≤ t ≤ T/٢א
אאא t١ ≤ t ≤ T/٢אK
Vo
S١ S١
S٢
-Vs
Vs
2T T
23T
t ٠
אאא ٢٤١ א א
אא א
- ٨٨ -
אF٤J٥WEאא
אאt = T/٢א S١אאאאאאא S١אאא VSאא
-Vs
Vs
2T T
23T
Vo
t
io
t١ ٠
Vo
-Vs
Vs
S١ S١
S٢ 2T T
23T
t ٠
2T
T 2
3T
i١
t ٠ t١
i٢
2T T
t ٠
אאא ٢٤١ א א
אא א
- ٨٩ -
אאאאאאאאאאD٢אאt=t٢אאאאא D٢אא
א S٢אאt٢ ≤ t ≤TאאאאאאאאאאאS٢אS٢א
אT/٢ ≤ t ≤ Tאא א א א T K אF٤J٥ E א אאא א א א
א ioא אאאאאאאF٤J٥E
אאאi٢ ,i١אאאioאאאאאאא
אא ٠א ≤ t ≤ T/٢א א אא א אאאאאT/٢ ≤ t ≤ TK
אאאאאאW
אאאאאWVV so =F٤J٢E
אאאאV١(rms)W
א א א א א F٤J٣ EאW
tnnn
srms
VV ωπ
sin4
,...5,3,1)(1 ∑
∞
=
=F٤J٣E
nאאωאאאאrad/sאאאאאאאn = ١W
VVV ss
rms 9.02
4)(1 ==
πF٤J٤E
אאא ٢٤١ א א
אא א
- ٩٠ -
٤J١WאאאF٤J٣E'R'٤٢ Ω
'Vs'٢٤ VKWFE אאא'Vo(rms)'KFE אאא'Io(rms)'K FE אאאאא'V١(rms)'K FE א'Po'K
אWFE אאאאא
אF٤J٢EW 24
)(==VV srmso V
FE אאאW
104.2
24)()( ===
RVI rmso
rmso A
FE א א אא א אא אF٤J٣EW
6.2124*9.09.0)(1
=== VV srms V
FE אW
2404.2
2422
)( ===R
VP rmsoo W
אאאא١-Phase Voltage Source Bridge Inverter
אאRאאאאאא
א א F٤J٦ Eא א אא אא אא٤א ٤אא
א KאאאאאאKאאאא
אאא ٢٤١ א א
אא א
- ٩١ -
אS٤, S١אS٣, S٢אS٣, S٢אS٤, S١אאS٤, S١
אS٣, S٢אא'T/٢'אא W אS٤, S١ א א ٠ ≤ t ≤ T/٢
א א א א א אS٣,S٢א א א א א אא א
א א אS٤, S١ א 'Vo'א אא'Vs'אS٤, S١אS٣, S٢אא
T/٢ ≤ t ≤ TאאאאאאאאאאאאאS٣, S٢אאאא
א א א א א'-Vo'אאF٤J٧E
א Vs K א א אאא'fo'א
א'T'fo = ١/TK
אF٤J٦WEאאאאאאאא
Vs
S١
S٢
S٣
S٤
D١
D٢
D٣
D٤
is١ iD١
is٢ iD٢
+ - Vo R
is٣ iD٣
is٤ iD٤
is
אאא ٢٤١ א א
אא א
- ٩٢ -
אF٤J٧WEאאאא
אאאאאאVo(rms)W
אאאאאF٤J٢EאאאאאK
אאאאאV١(rms)W
א א א א אאאאאאאאאn = ١F٤J٣EF٤J٤E
אK
٤J٢WאאאF٤J٣E'R'٤٢ Ω
'Vs'٤٨ VKWFE אאא'Vo(rms)'KFE אאא'Io(rms)'K FE אאאאא'V١(rms)'KFE א'Po'K
-Vs
Vo
S١, S٤ S١, S٤
S٢, S٣
Vs
2T T
23T
t ٠
אאא ٢٤١ א א
אא א
- ٩٣ -
אWאאאאאאאאא?
F٤J١?Eאאאאאאאאאאאאאאאא
אאאאאאאאW
FE א א א א א א F٤J٢EW
48
)(==VV srmso V
FE אאאאW
204.2
48)()( ===
RVI rmso
rmso A
FE אאאאא אאאF٤J٣EW
2.4348*9.09.0)(1
=== VV srms V
FE א
9604.2
4822
)( ===R
VP rmsoo W
אאאאאא
א א א א ٤ אאאאאK
אא'R-L' אF٤J٨ Eאא אאאא'R-L'
אאאאאאF٤J٦Eאאאא'R''R-L' אF٤J٩ E א'Vo' א io
אאא ٢٤١ א א
אא א
- ٩٤ -
אאאS٤, S٣, S٢, S١אאאאאאD٤, D٣, D٢, D١ א א א 'is'א א אא
W
אF٤J٨WEאאאאאאK
א'io'אF٤J٩Eאא'vo'אא
S٤, S١אא٠ ≤ t ≤ t١t١אא א אא א
אאאאאאא א א אא א א t = t١א
אt = T/٢ א א٠ ≤ t ≤ tא١ א אאא אא אא א אD٤, D١ א א א 'Vs'אא א
אאאאאS٤, S١אאאאאt١
≤ t ≤ T/٢אאאא'Vo' אאא'Vs' א א٠ ≤ t ≤ T/٢א
א א'io' א א t = t١ אאt = T/٢א
Vs
S١
S٢
S٣
S٤
D١
D٢
D٣
D٤
الحمل
is١
is
iD١
is٢ iD٢
+ -
Vo
is٣ iD٣
is٤ iD٤
אאא ٢٤١ א א
אא א
- ٩٥ -
אאt = T/٢אאאאאאא א אאS٤, S١אאאאא
'Vs'אאאD٢ ,D٣אאאאאאאאאאT/٢≤ t ≤ t٢ אאאא
Vo = - Vsאא א א 'io' א א t = t٢
אS٢, S٣ אאאT/٢ ≤ t ≤ t٢אאאאא
אאא'io'אאאt٢ ≤ t ≤ TאS٢, S٣ אאאאאא
אאאאS٢, S٣אאא'Vs'אאאאVo = - Vs
א'Imin'אאt=T, t=٠א'Imax'אאt=٣⋅T/٢, t=T/٢אIminא
אאאאאאא
אאא ٢٤١ א א
אא א
- ٩٦ -
K
אF٤J٩WEאאאאאאאאאאאאאK
is
2T T
t ٠
vo
-Vs
Vs
2T T
23T
t
io
t١ ٠
2T
T 2
3T
is١, is٤
t ٠ t١
2T
T 2
3T
is٢, is٣
٠ t١
t
2T
23T
t T
iD١, iD٤
٠ t١
2T
23T
t T
iD٢, iD٣
٠ t١
אאא ٢٤١ א א
אא א
- ٩٧ -
אאאאWאאאא
א א אא א א אF٤J١KE
אאאW
אאאאאאW
⎪⎩
⎪⎨⎧
=≤≤−+
≤≤++−
−
−+−
cTtRR
TtTRR
oeVIV
eVIV
tss
Ttssi 2
0)(
2)(
/min
/)2
(max
τ
ττF٤J٤E
Wτ WאאאL/RK
IminWאאאKImaxWאאאK
א א א א א א א
W
II maxmin −=F٤J٥EאאאאאW
⎥⎦
⎤⎢⎣
⎡
+−
=−=−
−
τ
τ
2/
2/
minmax 11
T
Ts
ee
RVIIF٤J٦E
٤J٣W
אאאF٤J٨E'R'א١٠ ΩאL = ٢٥ mH'Vs'١٠٠ VKא
אא٦٠ Hzאא،W
אאא ٢٤١ א א
אא א
- ٩٨ -
אWאאאאאאW
0167.06011===
f o
T s
0025.010025.0
===RLτ s
67.60025.0*2
0167.02
==∴τ
T
אאאאאאF٤J٥EW
31.911.
10100
67.6
67.6
minmax =⎥⎦
⎤⎢⎣
⎡+−
=−=−
−
eeII A
אאאאF٤J٤EW
601
120131.1910
)10
10031.9(10100)(
1201031.1910
)10
10031.9(10100)(
0025.0/)00835.0(
0025.0/)2
0167.0(
0025.0/
0025.0/
≤≤+=
++−
=
≤≤−=
−−+−
=
−−
−−
−
−
te
et
te
et
t
t
o
t
to
i
i
אאInverter Voltage Control Techniques אאאאא
אאאאאW١K אאאK٢K אאאK ٣K אאאK
אאאאאא
אאאאאאאאאא
אאאאא
אאא ٢٤١ א א
אא א
- ٩٩ -
אאאאאאאא
אאK
אאאאאאאאאא‘PWM’אאא
אאאאאאאא
אאK
אPulse-Width Modulation PWMאאאאאאא
אW١K אSingle Pulse-Width ModulationK٢K אMultiple Pulse-Width ModulationK ٣K אSinusoidal Pulse-Width ModulationK
אאאאאא
KאF٤J١٠EאאאאS٢, S١אאאא
אאF٤J٦EאArAcKאאאאאFאאEאArAcאδא
אא١٨٠oArAcא‘Modulation Index’אאW
אאא ٢٤١ א א
אא א
- ١٠٠ -
AA
c
rM =F٤J٦E
אאא‘Vo’אW
πδVV so
=F٤J٧EW
MWאKVsWאאאKArWאאאKAcWאאאKδ :א.
אF٤J١٠WEאאאאS٢, S١
א
g٢
٠ ωt
Vo
٠
Ar
Ac
ωt
٠
g١
ωt
vo
٠ ωt
2δ
2π−
2δ
2π+ 2
π π ٢π ٣π/٢
אאא ٢٤١ א א
אא א
- ١٠١ -
אאאאאאאאא
אאfoאאאאאאאאא
אאfcKאF٤J١١EאאאאאאאאאאאW
ff
mmff
o
cf
fcP === ,22 0
F٤J٨E
WPWאאKfcWאאאK foWאאאK
mfWאK
אא‘M’M١אVsא
π/PאאאאאאW
πδPVV so
=F٤J٩E
אאא ٢٤١ א א
אא א
- ١٠٢ -
אF٤J١١WEאאאאאאא
אאאאא
אאאאאKאאאאאאא
אאאKאF٤J١٢EאS٢, S١אאfofc
אאאאאאאאאאא‘M’אאא
א‘Vo’אF٤J١٢EאאאKאאאאW
∑=
=P
m
mso VV
1 πδ
W
٠
vo
Ar
٠
Ac
ωt ٢π
π ١/fc
e
ωt ٢π
π
δ
αm
π+αm
Vs
-Vs
אאא ٢٤١ א א
אא א
- ١٠٣ -
PWאאK: δmאאmK
VsWאאאK
אF٤J١٢WEאS٢, S١אא
אK
אאCurrent Source Inverter CSIאאאאאא
אאKאאאאאא
אאאאאאK
Vs
-Vs
vo
ωt
δm
αm
٠
g٤
٠ ωt
٠ ωt
g١
٠
Ac
Ar
١/fc
אאא ٢٤١ א א
אא א
- ١٠٤ -
אאאא١-Phase Current Source Bridge InverterאF٤J١٣Eאאאאא
אא אא א א אאWאS١, S٤ אא٠ ≤ t ≤ T/٢
אאאאאאאאאאאאאאא אאא
אLאS١, S٤ א F EאS١, S٤ א אאאTאאS٢, S٣
אא אאאאאS٢, S٣ אאאאאאא
I אא٠ ≤ t ≤ T/٢-IאאT/٢ ≤ t ≤ TאאTאא
אא TאאKאF٤J١٤EאאK
אאא ٢٤١ א א
אא א
- ١٠٥ -
אF٤J١٣WEאאאאא
אF٤J١٤WEאא
is
I
t
io
S١, S٤ S١, S٤
S٢, S٣
-I
I
2T T
23T
t ٠
Vs الحمل
L
S١
S٢
S٣ S٤
+ -
vo
is
io
אאא ٢٤١ א א
אא א
- ١٠٦ -
WJ ؟א J אאא؟א J ؟אאאא J ؟א J ؟אאאאא J ؟אאא J ؟אאאאא J ؟אאאאאא J אא؟אאא
J ؟אאאא אא؟
J ؟אאאאא J א٢٢٠V
٢٠ΩKW 'Vo'אאא -أ 'V١'אאאאא -ب Kאאא -ج
٤J١٣ אאאFא٤J١٢EאK
אאאאאא
אא
אאאã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
אאאא
א
א
א
٥
א٢٤١ א א א
אאא א
- ١٠٧ -
אאWאאאאאW
• אאאאאאאא
• אאאא • אאאאא
א • אאאא
W
אאאאאאאאאאאאאאאאאאK
אאאאאאא
אאאאאאאאאK
אאאאאאאאאאאאאאאאאאאאKאאא
אאאאאאאאאאאא
אאאאVaאאאאא
אאאאאאאאאאאאאאאאאאאא
אאאאאαK
א٢٤١ א א א
אאא א
- ١٠٨ -
אאאאאאאאאאאאאאK
אאאאאאאאא Speed Control of a DC Motor Using single-Phase Controlled Rectifiers
אF٥J١Eאאאא
אאאKF٥J٢EאVaאאאאiaאLaא
אאאאאאαH πZ βאאאאW
)(cos
22)( α
πα VV sa
=F٥J١EאאF٢J٢٢Eאא
אאאאαא= ٠αα = ١٨٠oאאVa(α)אאא٩٠א
אאאא)(α>٩٠אאאאאאα = ٩٠oא
אאאאKאאאK
א٢٤١ א א א
אאא א
- ١٠٩ -
אF٥J١WEאאאא
א
אF٥J٢WEאאא
אאאאאאW
א٢٤١ א א א
אאא א
- ١١٠ -
Va = Ea +Ia RaF٥J٢E
Ea = K Φ ω = Kb ωF٥J٣E
Ta = K Φ Ia = KT IaF٥J٤E
אאאאΦאאאאEaאωאאאאא
NW
602 Nπ
ω =F٥J٥EאאKb, KTאPאאΦ
אZאאאaW
aPZKK Tb π
φ2
==F٥J٦Eאא ωאTaאאVa(α)
אF٥J٢EF٥J٣E،F٥J٤EאאW
TKKR
KV
aTb
a
b
a −=)(α
ωF٥J٧E
אאאא אF٥J١EאF٥J٧EאW
TKKR
KV
aTb
a
b
s −= )(cos22
αωπ
F٥J٨E
א(N.m) Taאאאω(Rad/Sec)אאא
אאאאאאאאאאאאאאאoω
W
א٢٤١ א א א
אאא א
- ١١١ -
)(cos22
αωK
Vb
s=F٥J٩E
אF٥J٣Eאאoωאאאα=٠ α = ١٨٠oאא α > ٩٠
אKאF٥J٤EאאωאTaאאאF٥J٨KE
אF٥J٤EאאאאαKאאאאאאאא
אאאאאאאאFאאאEאאFאאאEF٥J٥KE
אF٥J٣WEאאωoאאאאα
א٢٤١ א א א
אאא א
- ١١٢ -
אF٥J٤WEאאωאא
FEFE
אF٥J٥WEאאאא
א٢٤١ א א א
אאא א
- ١١٣ -
F٥J١WE١٢٠٠ rpm,١٠ HP, ٢٣٠ Vא
אאF٥J١KEאאIa= ٣٨ A א Ra = ٣٠ ΩאVs=٢٦٠ VKאאKb = KT
= ٧٤١אאאאα =٣٠oWJ אאא J אאא J אK
אW
J אאאF٥J٤EW
mNTIKT
a
aTa
.121.6638*74.1 ==∴
=Q
J אאאאאF٥J٨EW
TKKR
KV
aTb
a
b
s −= )(cos22
αωπ
sec/11055.656.116
121.6674.1
3.0)(cos74.1
260222
rad=−=
−=∴ απ
ω
אאאF٥J٥EW
602 Nπ
ω =Q
rpmN 10512
110*602
60===∴
ππω
J אאאW
IVIV
ss
aaPF =
אאאאאאאW
א٢٤١ א א א
אאא א
- ١١٤ -
82.202)30(cos260*22
)(cos22
=== osa
VV πα
πV
78.0260
82.202===∴
VV
s
aPF
אאאאSpeed Control of A DC Motor Using DC Choppers
אאאא
F٥J٦Eאאאאאאאאא
אKאאאאF٥J٢EאF٥J٩EאF٥J١EאאאW
VV sa
D=F٥J٩EDאK
אאK
אF٥J٦WEאאאא
א٢٤١ א א א
אאא א
- ١١٥ -
F٥J٢WEVs = ١٥٠ VK
אאאWRa = ٥٠ Ω, La = ١٠ mH, Kb = ٠٥٠ V/rpm
אא(TON)٦١ msאאN = ٢٠٠٠ rpmא٤٠ AK
אW
אאאF٥J٢E,F٥J٣EWIRKV aaba
N += 1202010040*5.02000*05.0 =+=+=V a
V
אאאF٥J١٠EW
8.0150120
===VV
s
aD
אW
TTON
ON fT
D ==Q
50010*6.18.0
3 ===∴−T ON
Df Hz
א٢٤١ א א א
אאא א
- ١١٦ -
W٥J١ אאאאאאאא
אא
٥J٢ אאאאאאאא
٥J٣ אאאאאאא
٥J٤ ١٠٠٠ rpm,١٠ kW, ٢٤٠ Vא
אאF٥J١KEאאIa= ٤٣٥١ A א Ra = ٤٥٠ ΩאVs=٢٤٠ VKאא
Kb = KT = ٢אאאאα =٢٠oW
J אאא J אאא J אK
٥J٥ Vs = ٢٢٠ VK
אאאWRa = ٣٠ Ω, La = ١٥ mH, Kb = ٠٤٠ V/rpm
אא(TON)١ msאאN = ٢٠٠٠ rpmא٢٥ AK
٢٤١ א א א
א
- ١١٧ -
א ٣-٢ α=٥٥°, γ=١٦٠°, β=٢١٥° ٨-٢ Vo=١٤٨٫٦ V, Io=٣٫٩٥ A, Po=٧٧٨٫٨ W, PF=٠٫٩ lag ٩-٢ Vo=١٤٨٫٦ V, Io=٢٫٩٧٢ A, Io(rms)=٢٫٩٧٢ A, Po=٤٤١٫٦ W, ISCR(avg)=٠٫٩٩
A, IFWD(avg)=٠٫٩٩ A ١٠-٢ ITh(avg)=٢٫٤٧ A, ITh(max)=٧٫٤٣ A, VTh(max)=٣١١ V, Po=١١٠٤ W ٤٤ ٨-٣ V, ٢٫٢ A, ٦٩٫٦ V, ٥٫٥ A, ٢٤٢ W ٩-٣ D=٠٫٥, Is(avg)=١٠ A, Is(rms)=١٤٫١٤ A ١٠-٣ Ton=٠٫٦٨ ms, Toff=٠٫٣٢ ms ٤٤ ١١-٣ V, ٥٫٥ A, ٦٩٫٦ V, ٥٫٥ A, ٢٫٢ A, ٣٫٣ A, ٦٫١٦ A, ٢٫٤ ,٤٫٨٤ mH ١١٠ ١٢-٤ V, ٩٩ V, ٦٠٥ W ٢٢٠ ١٣-٤ V, ١٩٨ V, ٢٤٢٠ W ١٠٢٫٨٦ ٤-٥ N.m, ٨٦٠ rpm, ٠٫٨٥ ٤٠٠ ٥-٥ Hz
א٢٤١ א א א
א
- ١١٨ -
אא (١) Ashfaq Ahmed : “Power Electronics for Technology”, Prentice-Hall,
١٩٩٩. (٢) M. H. Rashid: “Power Electronics: Circuits, Devices, and
Applications”, Second Edition, Prentice-Hall, ١٩٩٣. (٣) David A. Bradley: “Power Electronics”, Second Edition, Nelson
Thornes, ١٩٩٥. (٤) Ned Mohan, Tore M. Undeland, and William P. Robbins: “Power
Electronics: Converters, Applications, and Design”, Second Edition, John Wiley & Sons, ١٩٩٥.
٢٤١ א א א
א
א
K K K K K K K K K K K K K K K K K K K K K K K K K K K KאאWאK K K K K K K K K K K K K K K K K K١
אאK K K K K K K K K K K K K K K K K K K K K K K K K K١K K K K K K K K K K K K K K K K K K K K K K K K K K K١١J١אK K K K K K K K K K K K K K K K K K K K K K K١١J١J١ אK K K K K K K K K K K K K K K K K K٢
١J١J٢אאK K K K K K K K K K K K K K K K K K K٢
٣J١J١אאאK K K K K K K K K K K K K K K K٤
١J١J٤אK K K K K K K K K K K K K K K K K K٥
١J١J٤J١אאאK K K K K K K K K K K٥
١J١J٤J٢ אאK K K K K K K K K K K K٦
١J١J٤J٣אאאK K K K K K K K K K٦
١J١J٤J٤אאK K K K K K K K K K K K K K٦
١J١J٥אאK K K K K K K K K K K K K K K K K٦
١J١J٥J١אאאK K K K K K K K K K٧
١J١J٥J٢אאאK K K K K K K K K K٧
١J١J٥J٣ אאK K K K K K K K K K K٨
١J١J٦אK K K K K K K K K K K K K K K K K K K٩
١J٢ אK K K K K K K K K K K K K K K K K K K K K K K K١٠
١J٣אK K K K K K K K K K K K K K K K K K K K K K K K K١٢
K K K K K K K K K K K K K K K K K K K K K K K K K K K١٤
٢٤١ א א א
א
אאWאאאאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK١٥אאK K K K K K K K K K K K K K K K K K K K K K K K K K١٥K K K K K K K K K K K K K K K K K K K K K K K K K K K١٥٢J١אאאFאאאEK K K K K K١٥٢J٢אאאאK K K K K K K١٦
٢J٢J١אאאK K K K K K K K K K K K K K١٨٢J٢J٢אאאK K K K K K K K K K K K K K K١٩٢J٢J٣אאK K K K K K K K K K K K K K K K K١٩٢J٣אאאאK K K K K K K٢٤
٢J٣J١אאK K K K K K K K K K K K K K K K K K K٢٤٢J٣J٢אאאK K K K K K K K K K K K K K٢٥٢J٣J٣K K K K K K K K K K K K K K K K K K K K K K٢٦٢J٤אאאאאאK K K٢٧
٢J٤J١אאK K K K K K K K K K K K K K K K K K K٢٨٢J٤J٢אאאאK K K K K K K K K K K K K K K K K K٣٠٢J٥אאK K K K K K K K K K٣١
٢J٥J١אאK K K K K K K K K K K K K K K K K K K K K٣٣٢J٥J١J١אאאאאK K K K K K K٣٣٢J٥J١J٢אאK K K K K K K K K K K K K٣٤٢J٥J١J٣אאאK K K K K K K K٣٥٢J٥J١J٤אאאK K K K K K K K K٣٦٢J٥J١J٥אא‘R-L’K K K K K K K K K K K٣٧٢J٥J١J٦ אאK K K K K K K K K K K٣٨٢J٥J١J٧אאאK K K K K K K K٤٠٢J٥J١J٨אאאVAKK K K K K K٤١
٢J٥J٢אאאאK K K K K K K K K K K K٤١٢J٥J٢J١ אאK K K K K K K K K K K٤٢
٢٤١ א א א
א
٢J٥J٢J٢אאאK K K K K K K K٤٤٢J٥J٢J٣אאאאאאK K K K K K K٤٤
٢J٦אאאא'R-L'K K K٤٦٢J٦J١אאK K K K K٤٦٢J٦J٢אאאK K K K K K K K K K K K K K٤٨K K K K K K K K K K K K K K K K K K K K K K K K٥٢
אאWאאK K K K K K K K K K K K K K K K K K K٥٥אאK K K K K K K K K K K K K K K K K K K K K K K K K K٥٥K K K K K K K K K K K K K K K K K K K K K K K K K K K٥٥٣J١אאאK K K K K K K K K K K K K K K K K K٥٦٣J٢אK K K K K K K K K K K K K K K K K K K K K K K٥٧٣J٣אאאאRK K K K K K K٥٩
٣J٣J١אאאאK K K K K K K K٥٩٣J٣J٢אאאאK K K K K K K K K٦٠٣J٣J٣אאK K K K K K K K K K K K K K K K K٦١٣J٣J٤אאאאאאK K K٦١٣J٤אאאK K K K K K K K K K K K K K K K K٦٤
٣J٤J١אאK K K K K K K K K K K K K K K K K K K٦٤٣J٤J٢אאK K K K K K K K K K K K K K K٦٥٣J٤J٣אאK K K K K K K K K K K K K K K K K K K٦٧٣J٤J٤אאK K K K K K K K K K K K K K K K K٧٠K K K K K K K K K K K K K K K K K K K K K K K K٧٨
٢٤١ א א א
א
אאאWאאK K K K K K K K K K K K K K K K K K K K K K٨٠אאK K K K K K K K K K K K K K K K K K K K K K K K K K٨٠K K K K K K K K K K K K K K K K K K K K K K K K K K K٨٠
٤J١אאאK K K K K K K K K K K K K K K K K٨١٤J٢אאK K K K K K K K K K K K K K K K K K K K K٨٢
٤J٢J١אאRK K K K K K K K K K K K K K K K K K٨٢٤J٣אאK K K K K K K K K K K K K K K K K K K K٨٥
٤J٣J١אאאאK K K K K K K K K٨٥٤J٣J١J١אאK K K K K K K K K K K K K٨٦٤J٣J١J٢אאK K K K K K K K K K K K K٨٧
٤J٣J٢אאאאK K K K K K K K K K K٩٠٤J٣J٢J١אאRK K K K K K K K K K K K K٩٠٤J٣J٢J٢אא'R-L'K K K K K K K K K K K٩٣
٤J٤אאK K K K K K K K K K K K K K K٩٨٤J٤J١אK K K K K K K K K K K K K K K K K K K٩٩
٤J٤J١J١אK K K K K K K K K K K٩٩٤J٤J١J٢אK K K K K K K K١٠١٤J٤J١J٣אK K K K K K K K K K١٠٢
٤J٥אאK K K K K K K K K K K K K K K K K K K١٠٣٤J٥J١אאאאK K K K K K K K K K١٠٤K K K K K K K K K K K K K K K K K K K K K K K١٠٦
אאWאK K K K K K K K K K K K K K K K١٠٧
אאK K K K K K K K K K K K K K K K K K K K K K K K K١٠٧K K K K K K K K K K K K K K K K K K K K K K K K K K١٠٧٥J١אאאאאאאאאK K K K K K K K K K K K K K K K K K K K١٠٨٥J٢אאאאK K K K١١٤
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K K K K K K K K K K K K K K K K K K K K K K K١١٦
אK K K K K K K K K K K K K K K K K K K K K K K K K K١١٧אאK K K K K K K K K K K K K K K K K K K K K K K K K K١١٨
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GOTEVOT appreciates the financial support provided by BAE SYSTEMS