MCP608 [MICROCHIP]
2.5V TO 5.5V MICROPOWER CMOS OP AMPS; 2.5V至5.5V微功耗CMOS运算放大器型号: | MCP608 |
厂家: | MICROCHIP |
描述: | 2.5V TO 5.5V MICROPOWER CMOS OP AMPS |
文件: | 总37页 (文件大小:795K) |
中文: | 中文翻译 | 下载: | 下载PDF数据表文档文件 |
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢀ
)($785(6
ꢀꢁꢂ9ꢃWRꢃꢂꢁꢂ9ꢃ0LFURSRZHUꢃ&026ꢃ2Sꢃ$PSV
'(6&5,37,21
/RZꢀ3RZHUꢀ,''ꢀ ꢀꢁꢂ $ꢃꢀPD[ꢀ
7KHꢀ ꢉ&3ꢊꢅꢊꢃꢀꢉ&3ꢊꢅꢌꢃꢀꢉ&3ꢊꢅꢇꢀ DQGꢀ ꢉ&3ꢊꢅꢍꢀIURP
ꢉLFURFKLSꢀ 7HFKQRORJ\ꢃꢀ ,QFꢈꢀ DUHꢀ XQLW\ꢀ JDLQꢀ VWDEOHꢃꢀ ORZ
RIIVHWꢀYROWDJHꢀRSHUDWLRQDOꢀDPSOLILHUVꢀFDSDEOHꢀRIꢀSUHFLꢆ
VLRQꢀORZꢀSRZHUꢀVLQJOHꢀVXSSO\ꢀRSHUDWLRQꢈꢀ3HUIRUPDQFH
FKDUDFWHULVWLFVꢀLQFOXGHꢀXOWUDꢀORZꢀRIIVHWꢀYROWDJHꢀ0ꢁꢂꢅ 9
PD[ꢈ1ꢃꢀUDLOꢆWRꢆUDLOꢀRXWSXWꢀVZLQJꢀFDSDELOLW\ꢃꢀDQGꢀORZꢀLQSXW
ELDVꢀFXUUHQWꢀ0ꢇꢅ S$#ꢇꢂ&1ꢈꢀ7KHVHꢀIHDWXUHVꢀPDNHꢀWKLV
IDPLO\ꢀRIꢀDPSOLILHUVꢀZHOOꢀVXLWHGꢀIRUꢀVLQJOHꢀVXSSO\ꢀSUHFLꢆ
VLRQꢃꢀKLJKꢀLPSHGDQFHꢃꢀEDWWHU\ꢀSRZHUHGꢀDSSOLFDWLRQVꢈ
/RZꢀ2IIVHWꢀ9ROWDJHꢄꢀꢁꢂꢅ 9ꢃꢀPD[
5DLOꢆWRꢆ5DLOꢀ6ZLQJꢀDWꢀ2XWSXW
ꢇꢅ S$ꢃꢀ/RZꢀ,QSXWꢀ%LDVꢀ&XUUHQWꢀRYHUꢀ7HPSHUDWXUH
6SHFLILFDWLRQVꢀUDWHGꢀIRUꢀꢁꢈꢂ9ꢀWRꢀꢂꢈꢂ9ꢀ6XSSOLHV
8QLW\ꢀ*DLQꢀ6WDEOH
&KLSꢀ6HOHFWꢀ0&61&DSDELOLW\ꢀZLWKꢀꢉ&3ꢊꢅꢇ
,QGXVWULDOꢀ7HPSHUDWXUHꢀUDQJHꢀVXSSRUWHG
ꢋRꢀ3KDVHꢀ5HYHUVDO
7KHꢀ VLQJOHꢀ ꢉ&3ꢊꢅꢊꢀ LVꢀ DYDLODEOHꢀ LQꢀ VWDQGDUGꢀ ꢇꢆOHDG
3',3ꢃꢀ62,&ꢃꢀDQGꢀ76623ꢀSDFNDJHVꢈꢀ$QRWKHUꢀYHUVLRQꢀRI
WKHꢀ VLQJOHꢀ RSꢀ DPSꢃꢀ ꢉ&3ꢊꢅꢇꢀ LVꢀ RIIHUHGꢀ ZLWKꢀ Dꢀ &KLS
6HOHFWꢀ RSWLRQꢀ LQꢀ VWDQGDUGꢀ ꢇꢆOHDGꢀ 3',3ꢃꢀ 62,&ꢃꢀ DQG
76623ꢀSDFNDJHVꢈꢀ7KHꢀGXDOꢀꢉ&3ꢊꢅꢌꢀLVꢀRIIHUHGꢀLQꢀVWDQꢆ
GDUGꢀꢇꢆOHDGꢀ3',3ꢃꢀ62,&ꢃꢀDVꢀZHOOꢀDVꢀWKHꢀ76623ꢀSDFNꢆ
DJHꢈꢀ )LQDOO\ꢃꢀ WKHꢀ TXDGꢀ ꢉ&3ꢊꢅꢍꢀ LVꢀ RIIHUHGꢀ LQꢀ ꢎꢏꢆOHDG
3',3ꢃꢀ62,&ꢀDQGꢀ76623ꢀSDFNDJHVꢈꢀ$OOꢀGHYLFHVꢀDUHꢀIXOO\
VSHFLILHGꢀIURPꢀꢆꢏꢅ&ꢀWRꢀCꢇꢂ&ꢀZLWKꢀSRZHUꢀVXSSOLHVꢀIURP
ꢁꢈꢂ9ꢀWRꢀꢂꢈꢂ9ꢈ
$YDLODEOHꢀLQꢀ6LQJOHꢃꢀ'XDOꢃꢀDQGꢀ4XDG
$33/,&$7,216
%DWWHU\ꢀ3RZHUꢀ,QVWUXPHQWV
+LJKꢀ,PSHGDQFHꢀ$SSOLFDWLRQV
ꢆ 3KRWRGLRGHꢀ3UHꢆDPSV
ꢆ S+ꢀSUREHꢀ%XIIHUꢀ$PSOLILHU
ꢆ ,QIUDUHGꢀ'HWHFWRUV
ꢆ 3UHFLVLRQꢀ,QWHJUDWRUV
ꢆ &KDUJHꢀ$PSOLILHUꢀIRUꢀ3LH]RHOHFWULF
7UDQVGXFHUV
6WUDLQꢀ*DXJHV
ꢉHGLFDOꢀ,QVWUXPHQWV
7HVWꢀ(TXLSPHQW
$9$,/$%/(ꢀ722/6
6SLFHꢀꢉDFURPRGHOVꢀ0DWꢀZZZꢈPLFURFKLSꢈFRP1
70
)LOWHU/DE ꢀ6RIWZDUHꢀ0DWꢀZZZꢈPLFURFKLSꢈFRP1
3$&.$*(6
0&3ꢀꢁꢀ
3',3ꢂꢃ62,&ꢂ76623
0&3ꢀꢁꢄ
3',3ꢂꢃ62,&ꢂ76623
0&3ꢀꢁꢅ
3',3ꢂꢃ62,&ꢂ76623
0&3ꢀꢁꢆ
3',3ꢂꢃ62,&ꢂ76623
0&3ꢀꢁꢀ
627ꢇꢈꢉꢊ
1&
9ꢀꢀ
ꢂ
ꢃ
ꢄ
ꢅ
ꢆ
ꢇ
ꢈ
ꢉ
1&
ꢂ
ꢃ
ꢄ
ꢅ
ꢂ
ꢃ
ꢄ
ꢅ
1&
9ꢀꢀ
ꢆ
ꢇ
ꢈ
ꢉ
ꢆ
ꢇ
ꢈ
ꢉ
287$
&6
ꢉ
ꢅ
287
ꢂ
ꢂ
ꢃ
ꢄ
ꢅ
287'
287$
ꢂꢅ
ꢂꢄ
ꢂꢃ
ꢂꢂ
ꢂꢊ
ꢋ
$
ꢀ
$
ꢀ
ꢁ
ꢀ
'
ꢁ
ꢁ,1
ꢀ,1
9$$
ꢁ
287
ꢁ
9ꢀꢀ
287
1&
9$$
ꢁ,1
ꢀ,1
9$$
ꢃ
ꢄ
ꢁ,1
ꢀ,1$
9$$
9ꢀꢀ
287
1&
ꢁ
ꢁ,1'
ꢁ,1$
ꢀ,1$
9ꢀꢀ
ꢀ
ꢁ
%
ꢀ
ꢀ
ꢀ
ꢁ
ꢁ,1%
ꢁ,1
ꢀ,1'
ꢀ,1
ꢀ,1%
9$$
ꢀ,1&
ꢁ,1&
ꢀ,1%
ꢁ,1%
ꢉ
ꢈ
ꢇ
ꢁ
ꢀ ꢀ
&
ꢁ
%
287ꢂ
ꢆ
287&
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢁꢂꢃ
(/(&75,&$/ꢀ&+$5$&7(5,67,&6
0D[LPXPꢂ5DWLQJVꢃ
ꢀꢁꢀ
3,1ꢀ)81&7,21ꢀ7$%/(
9
ꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢌꢈꢅ9
''
1DPH
)XQFWLRQ
$OOꢀLQSXWVꢀDQGꢀRXWSXWVꢀZꢈUꢈWꢈꢀ ꢈꢈꢈꢈ 966ꢀ±ꢅꢈꢐ9ꢀWRꢀ9''ꢀCꢅꢈꢐ9
'LIIHUHQFHꢀ,QSXWꢀYROWDJHꢀ ꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈ _9''ꢀꢆꢀ9
ꢇ,1ꢈꢇ,1$ꢈꢇ,1%ꢈꢇ,1&ꢈꢇ,1'
1RQꢆLQYHUWLQJꢀ,QSXW
7HUPLQDOV
_
VV
ꢆ,1ꢈꢆ,1$ꢈꢆ,1%ꢈꢆ,1&ꢈꢆ,1'
,QYHUWLQJꢀ,QSXWꢀ7HUPLQDOV
3RVLWLYHꢀ3RZHUꢀ6XSSO\
1HJDWLYHꢀ3RZHUꢀ6XSSO\
2XWSXWꢀ6KRUWꢀ&LUFXLWꢀ&XUUHQWꢀꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈFRQWLQXRXV
&XUUHQWꢀDWꢀ,QSXWꢀ3LQꢀ ꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢀꢁ P$
&XUUHQWꢀDWꢀ2XWSXWꢀDQGꢀ6XSSO\ꢀ3LQVꢀꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢀꢐꢅ P$
6WRUDJHꢀWHPSHUDWXUH ꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢆꢊꢂ&ꢀWRꢀCꢎꢂꢅ&
$PELHQWꢀWHPSꢈꢀZLWKꢀSRZHUꢀDSSOLHG ꢈꢈꢈꢈꢈꢆꢂꢂ&ꢀWRꢀCꢎꢁꢂ&
6ROGHULQJꢀWHPSHUDWXUHꢀRIꢀOHDGVꢀ0ꢎꢅꢀVHFRQGV1 ꢈꢈ Cꢐꢅꢅ&
(6'ꢀSURWHFWLRQꢀRQꢀDOOꢀSLQV ..................................... ≥ ꢁ N9
9''
966
287ꢈ287$ꢈ287%ꢈ287&ꢈ287' 2XWSXWꢀ7HUPLQDOV
&6
1&
&KLSꢀ6HOHFW
1RꢀLQWHUQDOꢀFRQQHFWLRQꢀ
WRꢀ,&
ꢀ1RWLFHꢁꢀ6WUHVVHVꢀDERYHꢀWKRVHꢀOLVWHGꢀXQGHUꢀ³0D[LPXPꢀ5DWLQJV´ꢀPD\
FDXVHꢀSHUPDQHQWꢀGDPDJHꢀWRꢀWKHꢀGHYLFHꢁꢀ7KLVꢀLVꢀDꢀVWUHVVꢀUDWLQJꢀRQO\ꢀDQG
IXQFWLRQDOꢀ RSHUDWLRQꢀ RIꢀ WKHꢀ GHYLFHꢀ DWꢀ WKRVHꢀ RUꢀ DQ\ꢀ RWKHUꢀ FRQGLWLRQV
DERYHꢀWKRVHꢀLQGLFDWHGꢀLQꢀWKHꢀRSHUDWLRQDOꢀOLVWLQJVꢀRIꢀWKLVꢀVSHFLILFDWLRQꢀLV
QRWꢀLPSOLHGꢁꢀ([SRVXUHꢀWRꢀPD[LPXPꢀUDWLQJꢀFRQGLWLRQVꢀIRUꢀH[WHQGHGꢀSHULꢂ
RGVꢀPD\ꢀDIIHFWꢀGHYLFHꢀUHOLDELOLW\ꢁ
'&ꢀ&+$5$&7(5,67,&6
8QOHVVꢀRWKHUZLVHꢀVSHFLILHG+ꢀDOOꢀOLPLWVꢀDUHꢀVSHFLILHGꢀIRUꢀ9''ꢀ ꢀꢇꢁꢄꢉ9ꢀWRꢀꢇꢉꢄꢉ9+ꢀ966ꢀ ꢀ*1'+ꢀ7$ꢀ ꢀꢁꢉꢀ&+ꢀ9&0ꢀ ꢀ9''ꢈꢁ+ꢀ5/ꢀ ꢀꢃꢂꢂ NΩ WR
''ꢈꢁ+ꢀDQGꢀ9287ꢀaꢀ9''ꢈꢁ
3$5$0(7(56
9
6<0%2/
0,1ꢀ
7<3ꢀ
0$;ꢀ
81,76
&21',7,216
,1387ꢁ2))6(7
,QSXWꢀ2IIVHWꢀ9ROWDJHꢀ
926
ꢆꢁꢉꢂ
²
²
ꢃꢄꢊ
ꢌꢍ
ꢇꢁꢉꢂ
²
9
'ULIWꢀZLWKꢀ7HPSHUDWXUH
G926ꢈG7
3655
9ꢈ& 7$ ꢀꢆꢋꢂ&ꢀWRꢀꢇꢊꢉ&
3RZHUꢀ6XSSO\ꢀ5HMHFWLRQ
,1387ꢁ%,$6ꢁ&855(17ꢁ$1'ꢁ,03('$1&(
,QSXWꢀ%LDVꢀ&XUUHQW
ꢊꢂ
²
G%
IRUꢀ9''ꢀ ꢀꢁꢄꢉ9ꢀWRꢀꢉꢄꢉ9
,
²
²
²
²
²
ꢃ
²
²
ꢊꢂ
²
²
²
S$
S$
%
2YHUꢀ7HPSHUDWXUH
,
7$ ꢀꢆꢋꢂ&ꢀWRꢀꢇꢊꢉ&
%
,QSXWꢀ2IIVHWꢀ%LDVꢀ&XUUHQW
&RPPRQꢀ0RGHꢀ,QSXWꢀ,PSHGDQFH
'LIIHUHQWLDOꢀ,QSXWꢀ,PSHGDQFH
&20021ꢁ02'(
,
ꢃ
S$
26
=
ꢃꢂꢁꢂ__ꢎ
ꢃꢂꢁꢂ__ꢎ
Ω__S)
Ω__S)
&0
=
',))
&RPPRQꢆ0RGHꢀ,QSXWꢀ5DQJH
&RPPRQꢆ0RGHꢀ5HMHFWLRQꢀ5DWLR
9&0
9VV−ꢂꢄꢍ
ꢅꢉ
9''−ꢃꢄꢃ
²
9
&055ꢀ≥ꢀꢅꢉ G%
&055
ꢌꢃ
G%
9
''ꢀ ꢀꢉ9+
9&0ꢀ ꢀꢆꢂꢄꢍꢀWRꢀꢍꢄꢌ9ꢀ
23(1ꢁ/223ꢁ*$,1
'&ꢀ2SHQꢀ/RRSꢀ*DLQ
$
ꢃꢂꢉ
ꢃꢂꢂ
ꢃꢁꢃ
ꢃꢃꢊ
²
²
G%
G%
5/ꢀ ꢀꢁꢉ NΩ WRꢀ9''ꢈꢁ+
ꢉꢂ P9ꢀꢏꢀ9287ꢀꢏꢀ
A9''ꢀ−ꢀꢉꢂ P9B
5/ꢀ ꢀꢉ NΩꢀWRꢀ9''ꢈꢁ+
ꢃꢂꢂ P9ꢀꢏꢀ9287ꢀꢏ
A9''ꢀ−ꢀꢃꢂꢂ P9B
2/
'&ꢀ2SHQꢀ/RRSꢀ*DLQ
$
2/
287387
/RZꢀ/HYHOꢈꢐLJKꢀ/HYHOꢀ2XWSXWꢀ9ROWDJHꢀ6ZLQJ
9
2/+ꢀ92+
2/+ꢀ92+
9287
966ꢀꢇꢀꢂꢄꢂꢃꢉ
966ꢀꢇꢀꢂꢄꢂꢋꢉ
966ꢀꢇꢀꢂꢄꢂꢉꢂ
²
²
²
9''ꢀ−ꢀꢂꢄꢂꢁꢂ
9''ꢀ−ꢀꢂꢄꢂꢎꢂ
9''ꢀ−ꢀꢂꢄꢂꢉꢂ
9
9
9
5/ꢀ ꢀꢁꢉ NΩꢀWRꢀ9''ꢈꢁ
5/ꢀ ꢀꢉ NΩꢀWRꢀ9''ꢈꢁ
5/ꢀ ꢀꢁꢉ NΩꢀWRꢀ9''ꢈꢁ+
9
/LQHDUꢀ5HJLRQꢀ0D[LPXPꢀ2XWSXW
9ROWDJHꢀ6ZLQJꢀ
$
2/ꢀ≥ꢀꢃꢂꢉ G%
5/ꢀ ꢀꢉ NΩꢀWRꢀ9''ꢈꢁ+
≥ꢀꢃꢂꢂ G%
9287
966ꢀꢇꢀꢂꢄꢃꢂꢂ
²
ꢃꢅ
9''ꢀ−ꢀꢂꢄꢃꢂꢂ
9
$
2/
2XWSXWꢀ6KRUWꢀ&LUFXLWꢀ&XUUHQW
32:(5ꢁ6833/<
,
P$
9287ꢀ ꢀꢁꢄꢉ9+ꢀ9''ꢀ ꢀꢉ9
6&
6XSSO\ꢀ9ROWDJH
96
ꢁꢄꢉ
²
²
ꢉꢄꢉ
ꢁꢉ
9
4XLHVFHQWꢀ&XUUHQWꢀ3HUꢀ$PSOLILHU
,
ꢃꢊꢄꢅ
$
,2ꢀ ꢀꢂ
4
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
$&ꢀ&+$5$&7(5,67,&6
8QOHVVꢀRWKHUZLVHꢀVSHFLILHG+ꢀDOOꢀOLPLWVꢀDUHꢀVSHFLILHGꢀIRUꢀ9''ꢀ ꢀꢇꢁꢄꢉ9ꢀWRꢀꢇꢉꢄꢉ9+ꢀ966ꢀ ꢀ*1'+ꢀ7$ꢀ ꢀꢁꢉ&+ꢀ9&0ꢀ ꢀ9''ꢈꢁ+
5/ꢀ ꢀꢃꢂꢂ NΩ WRꢀ9''ꢈꢁ+ꢀDQGꢀ9287ꢀaꢀ9''ꢈꢁ
3$5$0(7(56
6<0%2/
0,1ꢀ
²
7<3ꢀ
ꢃꢉꢉ
ꢎꢁ
0$;ꢀ
²
81,76
&21',7,216
*DLQꢀ%DQGZLGWKꢀ3URGXFW
*%:3
Nꢐ]
9''ꢀ ꢀꢉ9+ꢀ&/ꢀ ꢀꢎꢂ S)
3KDVHꢀ0DUJLQꢀDWꢀ8QLW\ꢀ&URVVLQJ
6OHZꢀ5DWH
θ
65
HQ
HQ
LQ
²
²
GHJUHHV 9''ꢀ ꢀꢉ9+ꢀ&/ꢀ ꢀꢎꢂ S)
9ꢈV *ꢀ ꢀꢃ+ꢀ9''ꢀ ꢀꢉ9+ꢀ&µꢀ ꢀꢎꢂ S)
²
ꢂꢄꢂꢊ
ꢁꢄꢊ
ꢍꢊ
²
,QSXWꢀ9ROWDJHꢀ1RLVH
1RLVHꢀ'HQVLW\
²
²
9SꢆS Iꢀ ꢀꢂꢄꢃ ꢐ]ꢀWRꢀꢃꢂ ꢐ]
²
²
Q9ꢈ√ꢐ] Iꢀ ꢀꢃ Nꢐ]
,QSXWꢀ&XUUHQWꢀ1RLVHꢀ'HQVLW\
²
ꢍ
²
I$ꢈ√ꢐ] Iꢀ ꢀꢃ Nꢐ]
63(&,),&$7,216ꢀ)25ꢀ0&3ꢄꢃꢅꢀ&+,3ꢀ6(/(&7ꢀ)($785(
8QOHVVꢀRWKHUZLVHꢀVSHFLILHG+ꢀDOOꢀOLPLWVꢀDUHꢀVSHFLILHGꢀIRUꢀ9''ꢀ ꢀꢇꢁꢄꢉ9ꢀWRꢀꢇꢉꢄꢉ9+ꢀ966ꢀ ꢀ*1'+ꢀ7$ꢀ ꢀꢁꢉ&+ꢀ9&0ꢀ ꢀ9''ꢈꢁ+
5/ꢀ ꢀꢃꢂꢂ NΩ WRꢀ9''ꢈꢁ+ꢀDQGꢀ9287ꢀaꢀ9''ꢈꢁ
3$5$0(7(56
&6ꢁ/2:ꢁ63(&,),&$7,216
&6ꢀ/RJLFꢀ7KUHVKROG+ꢀ/RZ
&6ꢀ,QSXWꢀ&XUUHQW+ꢀ/RZ
6<0%2/
ꢁ0,1ꢀ
ꢁ7<3ꢀ
ꢁ0$;ꢀ
81,76
&21',7,216
9,/
966
²
ꢂꢄꢁꢀ9''
²
9
)RUꢀHQWLUHꢀ9''ꢀUDQJH
&6ꢀ ꢀꢂꢄꢁ9''
,
ꢆꢂꢄꢃ
ꢂꢄꢂꢃ
$
&6/
&6ꢁ+,*+ꢁ63(&,),&$7,216
&6ꢀ/RJLFꢀ7KUHVKROG+ꢀꢐLJK
&6ꢀ,QSXWꢀ&XUUHQW+ꢀꢐLJK
9
ꢂꢄꢊꢀ9''
²
²
ꢂꢄꢂꢃ
ꢂꢄꢂꢉ
ꢃꢂ
9''
ꢂꢄꢃ
ꢁ
9
)RUꢀHQWLUHꢀ9''ꢀUDQJH
&6ꢀ ꢀ9''
,+
,
$
$
Q$
&6+
&6ꢀ,QSXWꢀꢐLJK+ꢀ*1'ꢀ&XUUHQW
$PSOLILHUꢀ2XWSXWꢀ/HDNDJH+ꢀ&6ꢀꢐLJK
'<1$0,&ꢁ63(&,),&$7,216
,
²
&6ꢀ ꢀ9''
4
²
²
&6ꢀ ꢀꢂꢄꢊ9''
&6ꢀ/RZꢀWRꢀ$PSOLILHUꢀ2XWSXWꢀꢐLJK
7XUQꢆRQꢀ7LPH
W21
²
²
²
ꢌ
ꢃꢂꢂ
²
V
V
9
&6ꢀORZꢀ ꢀꢂꢄꢁ9''
287ꢀ ꢀꢂꢄꢌꢀꢑ9''ꢈꢁ+
*ꢀ ꢀꢇꢃ9ꢈ9
&6ꢀKLJKꢀ ꢀꢂꢄꢊ9''+ꢀ
287ꢀ ꢀꢂꢄꢃꢀꢑ9''ꢈꢁ+ꢀ
+
9
&6ꢀꢐLJKꢀWRꢀ$PSOLILHUꢀ2XWSXWꢀꢐLJKꢀ=
W2))
ꢂꢄꢃ
ꢂꢄꢎ
9
*ꢀ ꢀꢇꢃ9ꢈ9
ꢐ\VWHUHVLV
²
9''ꢀ ꢀꢉ9
7(03(5$785(ꢀ63(&,),&$7,216
8QOHVVꢀRWKHUZLVHꢀVSHFLILHG+ꢀDOOꢀOLPLWVꢀDUHꢀVSHFLILHGꢀIRUꢀ9''ꢀ ꢀꢇꢁꢄꢉ9ꢀWRꢀꢇꢉꢄꢉ9+ꢀ966ꢀ ꢀ*1'
3$5$0(7(56
7(03(5$785(ꢁ5$1*(6
6<0%2/
0,1ꢀ
7<3ꢀ
0$;ꢀ
81,76
&21',7,216
6SHFLILHGꢀ7HPSHUDWXUHꢀ5DQJH
2SHUDWLQJꢀ7HPSHUDWXUHꢀ5DQJH
6WRUDJHꢀ7HPSHUDWXUHꢀ5DQJH
7+(50$/ꢁ3$&.$*(ꢁ5(6,67$1&(
7KHUPDOꢀ5HVLVWDQFH+ꢀꢉ/ꢆ627ꢁꢍ
7KHUPDOꢀ5HVLVWDQFH+ꢀꢊ/ꢆ3',3
7KHUPDOꢀ5HVLVWDQFH+ꢀꢊ/ꢆ62,&
7KHUPDOꢀ5HVLVWDQFH+ꢀꢊ/ꢆ76623
7KHUPDOꢀ5HVLVWDQFH+ꢀꢃꢋ/ꢆ3',3
7KHUPDOꢀ5HVLVWDQFH+ꢀꢃꢋ/ꢆ62,&
7KHUPDOꢀ5HVLVWDQFH+ꢀꢃꢋ/ꢆ76623
7$
7$
7$
ꢆꢋꢂ
ꢆꢋꢂ
ꢆꢎꢉ
²
²
²
ꢇꢊꢉ
ꢇꢊꢉ
&
&
&
ꢇꢃꢉꢂ
θ
²
²
²
²
²
²
²
ꢁꢉꢎ
ꢊꢉ
²
²
²
²
²
²
²
&ꢈ:
&ꢈ:
&ꢈ:
&ꢈ:
&ꢈ:
&ꢈ:
&ꢈ:
-$
θ
-$
θ
ꢃꢎꢍ
ꢃꢁꢋ
ꢅꢂ
-$
θ
-$
θ
-$
θ
ꢃꢁꢂ
ꢃꢂꢂ
-$
θ
-$
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢍ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢆꢂꢃ
7<3,&$/ꢀ3(5)250$1&(ꢀ&859(6
1RWHꢋꢀ8QOHVVꢀRWKHUZLVHꢀLQGLFDWHGꢃꢀ7$ꢀ ꢀꢁꢂS&ꢃꢀ9&0ꢀ ꢀ9''ꢀꢑꢀꢁꢀDQGꢀ9287ꢀaꢀ9''ꢑꢁꢃꢀ966ꢀ ꢀ*ꢋ'ꢈ
),*85(ꢀꢁꢂꢃꢄ 2IIVHWꢀ9ROWDJHꢀYVꢁꢀ1XPEHUꢀRIꢀ
2FFXUUHQFHVꢀZLWKꢀ9''ꢀ ꢀꢂꢁꢂ9ꢁ
),*85(ꢀꢁꢂꢆꢄ 2IIVHWꢀ9ROWDJHꢀ'ULIWꢀYVꢁꢀ1XPEHUꢀRIꢀ
2FFXUUHQFHVꢀZLWKꢀ9''ꢀ ꢀꢂꢁꢂ9ꢁ
),*85(ꢀꢁꢂꢁꢄ 2IIVHWꢀ9ROWDJHꢀYVꢁꢀ1XPEHUꢀRIꢀ
),*85(ꢀꢁꢂꢇꢄ 2IIVHWꢀ9ROWDJHꢀ'ULIWꢀYVꢁꢀ1XPEHUꢀRIꢀ
2FFXUUHQFHVꢀZLWKꢀ9''ꢀ ꢀꢃꢁꢂ9ꢁ
2FFXUUHQFHVꢀZLWKꢀ9''ꢀ ꢀꢃꢁꢂ9ꢁ
),*85(ꢀꢁꢂꢅꢄ 4XLHVFHQWꢀ&XUUHQWꢀYVꢁꢀ3RZHUꢀ6XSSO\ꢀ
),*85(ꢀꢁꢂꢈꢄ 4XLHVFHQWꢀ&XUUHQWꢀYVꢁꢀ7HPSHUDWXUHꢁ
9ROWDJHꢀYVꢁꢀ7HPSHUDWXUHꢁ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢋ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
1RWHꢋꢀ8QOHVVꢀRWKHUZLVHꢀLQGLFDWHGꢃꢀ7$ꢀ ꢀꢁꢂS&ꢃꢀ9&0ꢀ ꢀ9''ꢀꢑꢀꢁꢀDQGꢀ9287ꢀaꢀ9''ꢑꢁꢃꢀ966ꢀ ꢀ*ꢋ'ꢈ
),*85(ꢀꢁꢂꢉꢄ 1RUPDOL]HGꢀ2IIVHWꢀ9ROWDJHꢀYVꢁꢀ
7HPSHUDWXUHꢁ
),*85(ꢀꢁꢂꢃꢌꢄ ,QSXWꢀ2IIVHWꢀ9ROWDJHꢀYVꢁꢀ&RPPRQꢀ
0RGHꢀ9ROWDJHꢁ
),*85(ꢀꢁꢂꢊꢄ 2SHQꢀ/RRSꢀ*DLQꢀDQGꢀ3KDVHꢀYVꢁꢀ
),*85(ꢀꢁꢂꢃꢃꢄ 3KDVHꢀ0DUJLQꢄꢀ*DLQꢀ%DQGZLGWKꢀ
3URGXFWꢀYVꢁꢀ7HPSHUDWXUHꢍ
)UHTXHQF\ꢁ
),*85(ꢀꢁꢂꢋꢄ 3KDVHꢀ0DUJLQꢄꢀ*DLQꢀ%DQGZLGWKꢄꢀYVꢁꢀ
),*85(ꢀꢁꢂꢃꢁꢄ ,QSXWꢀ9ROWDJHꢀ1RLVHꢀ'HQVLW\ꢀYVꢁꢀ
/RDGꢀ5HVLVWDQFHꢁ
)UHTXHQF\ꢁ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢉ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
1RWHꢋꢀ8QOHVVꢀRWKHUZLVHꢀLQGLFDWHGꢃꢀ7$ꢀ ꢀꢁꢂS&ꢃꢀ9&0ꢀ ꢀ9''ꢀꢑꢀꢁꢀDQGꢀ9287ꢀaꢀ9''ꢑꢁꢃꢀ966ꢀ ꢀ*ꢋ'ꢈ
),*85(ꢀꢁꢂꢃꢅꢄ ,QSXWꢀ%LDVꢀ&XUUHQWꢄꢀ,QSXWꢀ2IIVHWꢀ
&XUUHQWꢀYVꢁꢀ7HPSHUDWXUHꢁ
),*85(ꢀꢁꢂꢃꢈꢄ ,QSXWꢀ%LDVꢀ&XUUHQWꢄꢀ,QSXWꢀ2IIVHWꢀ
&XUUHQWꢀYVꢁꢀ&RPPRQꢀPRGHꢀ,QSXWꢀ9ROWDJHꢁ
),*85(ꢀꢁꢂꢃꢆꢄ '&ꢀ2SHQꢀ/RRSꢀ*DLQꢀYVꢁꢀ2XWSXWꢀ/RDGꢀ
),*85(ꢀꢁꢂꢃꢉꢄ '&ꢀ2SHQꢀ/RRSꢀ*DLQꢀYVꢁꢀ3RZHUꢀ6XSSO\ꢀ
5HVLVWDQFHꢁ
9ROWDJHꢁ
),*85(ꢀꢁꢂꢃꢇꢄ &RPPRQꢅ0RGHꢀ5HMHFWLRQꢀ5DWLRꢄꢀ
),*85(ꢀꢁꢂꢃꢊꢄ &RPPRQꢅ0RGHꢀ5HMHFWLRQꢀ5DWLRꢄꢀ
3RZHUꢀ6XSSO\ꢀ5HMHFWLRQꢀ5DWLRꢀYVꢁꢀ)UHTXHQF\ꢁ
3RZHUꢀ6XSSO\ꢀ5HMHFWLRQꢀ5DWLRꢀYVꢁꢀ7HPSHUDWXUHꢁ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢎ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
1RWHꢋꢀ8QOHVVꢀRWKHUZLVHꢀLQGLFDWHGꢃꢀ7$ꢀ ꢀꢁꢂS&ꢃꢀ9&0ꢀ ꢀ9''ꢀꢑꢀꢁꢀDQGꢀ9287ꢀaꢀ9''ꢑꢁꢃꢀ966ꢀ ꢀ*ꢋ'ꢈ
),*85(ꢀꢁꢂꢃꢋꢄ /RZꢀ/HYHOꢀDQGꢀ+LJKꢀ/HYHOꢀ2XWSXWꢀ
6ZLQJꢀYVꢁꢀ/RDGꢀ5HVLVWDQFHꢁ
),*85(ꢀꢁꢂꢁꢁꢄ /RZꢀ/HYHOꢀDQGꢀ+LJKꢀ/HYHOꢀRXWSXWꢀ
6ZLQJꢀYVꢁꢀ7HPSHUDWXUHꢄꢀ5/ ꢂNΩ.
),*85(ꢀꢁꢂꢁꢌꢄ 0D[LPXPꢀ2XWSXWꢀ9ROWDJHꢀ6ZLQJꢀYVꢁꢀ
),*85(ꢀꢁꢂꢁꢅꢄ /RZꢀ/HYHOꢀDQGꢀ+LJKꢀOHYHOꢀ2XWSXWꢀ
6ZLQJꢀYVꢁꢀ7HPSHUDWXUHꢄꢀ5/ ꢃꢂNΩ
)UHTXHQF\
),*85(ꢀꢁꢂꢁꢃꢄ 6OHZꢀ5DWHꢀYVꢁꢀ7HPSHUDWXUHꢁ
),*85(ꢀꢁꢂꢁꢆꢄ 2XWSXWꢀ6KRUWꢀ&LUFXLWꢀ&XUUHQWꢀYVꢁꢀ
7HPSHUDWXUHꢁ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢅ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
1RWHꢋꢀ8QOHVVꢀRWKHUZLVHꢀLQGLFDWHGꢃꢀ7$ꢀ ꢀꢁꢂS&ꢃꢀ9&0ꢀ ꢀ9''ꢀꢑꢀꢁꢀDQGꢀ9287ꢀaꢀ9''ꢑꢁꢃꢀ966ꢀ ꢀ*ꢋ'ꢈ
),*85(ꢀꢁꢂꢁꢇꢄ /DUJHꢀ6LJQDOꢀ1RQꢅLQYHUWLQJꢀ6LJQDOꢀ
3XOVHꢀ5HVSRQVHꢁ
),*85(ꢀꢁꢂꢁꢊꢄ /DUJHꢀ6LJQDOꢀ,QYHUWLQJꢀ6LJQDOꢀ3XOVHꢀ
5HVSRQVHꢁ
),*85(ꢀꢁꢂꢁꢈꢄ 6PDOOꢀ6LJQDOꢀ1RQꢅLQYHUWLQJꢀ3XOVHꢀ
),*85(ꢀꢁꢂꢁꢋꢄ 6PDOOꢀ6LJQDOꢀ,QYHUWLQJꢀ6LJQDOꢀ3XOVHꢀ
5HVSRQVHꢁ
5HVSRQVHꢁ
),*85(ꢀꢁꢂꢁꢉꢄ &KDQQHOꢀWRꢀ&KDQQHOꢀ6HSDUDWLRQꢀ
),*85(ꢀꢁꢂꢅꢌꢄ &KLSꢀ6HOHFWꢀWRꢀ$PSOLILHUꢀ2XWSXWꢀ
ꢆ0&3ꢇꢈꢉꢀDQGꢀ0&3ꢇꢈꢊꢀRQO\8ꢁ
5HVSRQVHꢀ7LPHꢀꢆ0&3ꢇꢈꢋꢀRQO\8ꢁ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢊ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
1RWHꢋꢀ8QOHVVꢀRWKHUZLVHꢀLQGLFDWHGꢃꢀ7$ꢀ ꢀꢁꢂS&ꢃꢀ9&0ꢀ ꢀ9''ꢀꢑꢀꢁꢀDQGꢀ9287ꢀaꢀ9''ꢑꢁꢃꢀ966ꢀ ꢀ*ꢋ'ꢈ
),*85(ꢀꢁꢂꢅꢃꢄ &6ꢀ+\VWHUHVLVꢀꢆ0&3ꢇꢈꢋꢀRQO\8ꢁ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢌ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
7KHꢀ/LQHDUꢀ5HJLRQꢀꢉD[LPXPꢀ2XWSXWꢀ9ROWDJHꢀ6ZLQJꢀRI
WKHꢀ ꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑꢊꢅꢍꢀ IDPLO\ꢀ LVꢀ VSHFLILHGꢀ ZLWKLQ
ꢂꢅP9ꢀIURPꢀWKHꢀSRVLWLYHꢀDQGꢀQHJDWLYHꢀUDLOꢀZLWKꢀDꢀꢁꢂ NΩ
ORDGꢀDQGꢀꢎꢅꢅ P9ꢀIURPꢀWKHꢀUDLOVꢀZLWKꢀDꢀꢂ NΩꢀORDGꢈꢀ7KH
RYHUULGLQJꢀFRQGLWLRQꢀWKDWꢀGHILQHVꢀWKHꢀOLQHDUꢀUHJLRQꢀRIꢀWKH
DPSOLILHUꢀLVꢀWKHꢀRSHQꢀORRSꢀJDLQꢀWKDWꢀLVꢀVSHFLILHGꢀRYHUꢀWKDW
UHJLRQꢈꢀ ,Qꢀ WKHꢀ YROWDJHꢀ RXWSXWꢀ UHJLRQꢀ EHWZHHQꢀ 966ꢀ C
ꢂꢅ P9ꢀDQGꢀ9''ꢀꢆꢀꢂꢅ P9ꢃꢀWKHꢀRSHQꢀORRSꢀJDLQꢀLVꢀVSHFLILHG
WRꢀꢎꢅꢂ G%ꢀ0PLQ1ꢀZLWKꢀDꢀꢁꢂ NΩꢀORDGꢈꢀ
ꢇꢂꢃ
$33/,&$7,216ꢀ,1)250$7,21
7KHꢀꢀꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑꢊꢅꢍꢀIDPLO\ꢀRIꢀRSHUDWLRQDOꢀDPSOLꢆ
ILHUVꢀ DUHꢀ IDEULFDWHGꢀ RQꢀ ꢉLFURFKLS¶Vꢀ VWDWHꢆRIꢆWKHꢆDUW
&ꢉ26ꢀSURFHVVꢈꢀ7KH\ꢀDUHꢀXQLW\ꢀJDLQꢀVWDEOHꢀDQGꢀVXLWDEOH
IRUꢀDꢀZLGHꢀUDQJHꢀRIꢀJHQHUDOꢀSXUSRVHꢀDSSOLFDWLRQVꢈꢀ:LWK
WKLVꢀIDPLO\ꢀRIꢀRSHUDWLRQDOꢀDPSOLILHUVꢃꢀWKHꢀSRZHUꢀVXSSO\
SLQꢀVKRXOGꢀEHꢀE\SDVVHGꢀZLWKꢀDꢀꢅꢈꢎ µ)ꢀFDSDFLWRUꢈꢀ
ꢄꢁꢀ
5DLOꢅWRꢅ5DLOꢂ2XWSXWꢂ6ZLQJ
7KHꢀFODVVLFDOꢀGHILQLWLRQꢀRIꢀWKHꢀ'&ꢀRSHQꢀORRSꢀJDLQꢀRIꢀDQ
DPSOLILHUꢀLVꢄ
7KHUHꢀDUHꢀWZRꢀVSHFLILFDWLRQVꢀWKDWꢀGHVFULEHꢀWKHꢀRXWSXW
VZLQJꢀFDSDELOLW\ꢀRIꢀWKHꢀꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑꢊꢅꢍꢀIDPLO\ꢀRI
RSHUDWLRQDOꢀ DPSOLILHUVꢈꢀ 7KHꢀ ILUVWꢀ VSHFLILFDWLRQꢃꢀ /RZ
/HYHOꢀ DQGꢀ +LJKꢀ /HYHOꢀ 2XWSXWꢀ 9ROWDJHꢀ 6ZLQJꢃꢀ GHILQHV
WKHꢀ DEVROXWHꢀ PD[LPXPꢀ VZLQJꢀ WKDWꢀ FDQꢀ EHꢀ DFKLHYHG
XQGHUꢀ VSHFLILHGꢀ ORDGHGꢀ FRQGLWLRQVꢈꢀ )RUꢀ LQVWDQFHꢃꢀ WKH
/RZꢀ/HYHOꢀ2XWSXWꢀ9ROWDJHꢀ6ZLQJꢀRIꢀWKHꢀꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑ
ꢊꢅꢇꢑꢊꢅꢍꢀIDPLO\ꢀLVꢀVSHFLILHGꢀWRꢀEHꢀDEOHꢀWRꢀVZLQJꢀDWꢀOHDVW
WRꢀ ꢎꢂ P9ꢀIURPꢀ WKHꢀQHJDWLYHꢀUDLOꢀZLWKꢀDꢀꢁꢂ NΩꢀORDGꢀWR
∆9287
∆926
$
ꢀꢁ ORJꢀꢁ
ꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂ
2/
ZKHUHꢄ
$
ꢀLVꢀWKHꢀ'&ꢀRSHQꢀORRSꢀJDLQꢀRIꢀWKHꢀDPSOLILHUꢃ
2/
∆9
ꢀLVꢀHTXDOꢀWRꢀ09''ꢀꢆꢀꢂꢅ P91ꢀꢆꢀ0966Cꢀꢂꢅ P91
287
IRUꢀ5/ ꢀꢁꢂ NΩꢃꢀDQG
9
''ꢑꢁꢈꢀ
∆9 ꢀ LVꢀ WKHꢀ FKDQJHꢀ LQꢀ RIIVHWꢀ YROWDJHꢀ ZLWKꢀ WKH
26
7KLVꢀRXWSXWꢀVZLQJꢀSHUIRUPDQFHꢀLVꢀVKRZQꢀLQꢀ)LJXUHꢀꢐꢆꢎꢃ
ZKHUHꢀWKHꢀRXWSXWꢀRIꢀDQꢀꢉ&3ꢊꢅꢊꢀLVꢀFRQILJXUHGꢀLQꢀDꢀJDLQ
RIꢀCꢁ9ꢑ9ꢀDQGꢀRYHUGULYHQꢀZLWKꢀDꢀꢏ N+]ꢀWULDQJOHꢀZDYHꢈꢀ,Q
WKLVꢀILJXUHꢃꢀWKHꢀGHJUDGDWLRQꢀRIꢀWKHꢀRXWSXWꢀVZLQJꢀOLQHDULW\
LVꢀFOHDUO\ꢀLOOXVWUDWHGꢈꢀ7KLVꢀGHJUDGDWLRQꢀRFFXUVꢀDIWHUꢀWKH
SRLQWꢀ DWꢀ ZKLFKꢀ WKHꢀ RSHQꢀ ORRSꢀ JDLQꢀ RIꢀ WKHꢀ DPSOLILHUꢀ LV
VSHFLILHGꢀDQGꢀEHIRUHꢀWKHꢀDPSOLILHUꢀUHDFKHVꢀLWVꢀPD[LPXP
DQGꢀPLQLPXPꢀRXWSXWꢀVZLQJꢈ
FKDQJLQJꢀRXWSXWꢀYROWDJHꢀRIꢀWKHꢀDPSOLILHUꢈ
ꢄꢁꢆ
,QSXWꢂ9ROWDJHꢂDQGꢂ3KDVHꢂ5HYHUVDO
6LQFHꢀ WKHꢀ ꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑꢊꢅꢍꢀ DPSOLILHUꢀ IDPLO\ꢀ LV
GHVLJQHGꢀZLWKꢀ&ꢉ26ꢀGHYLFHVꢃꢀLWꢀGRHVꢀQRWꢀH[KLELWꢀSKDVH
LQYHUVLRQꢀZKHQꢀWKHꢀLQSXWꢀSLQVꢀH[FHHGꢀWKHꢀQHJDWLYHꢀVXSꢆ
SO\ꢀYROWDJHꢈꢀ)LJXUHꢀꢐꢆꢁꢀVKRZVꢀDQꢀLQSXWꢀYROWDJHꢀH[FHHGꢆ
LQJꢀERWKꢀVXSSOLHVꢀZLWKꢀQRꢀUHVXOWLQJꢀSKDVHꢀLQYHUVLRQꢈ
),*85(ꢀꢅꢂꢃꢄ /RZꢀ/HYHOꢀDQGꢀ+LJKꢀ/HYHOꢀ2XWSXWꢀ
6ZLQJꢁ
),*85(ꢀꢅꢂꢁꢄ 7KHꢀ0&3ꢇꢈꢇꢌꢇꢈꢉꢌꢇꢈꢋꢌꢇꢈꢊꢀIDPLO\ꢀRIꢀ
RSꢀDPSVꢀGRꢀQRWꢀKDYHꢀSKDVHꢀUHYHUVDOꢀLVVXHVꢁꢀ)RUꢀWKLVꢀ
JUDSKꢄꢀWKHꢀDPSOLILHUꢀLVꢀLQꢀDꢀJDLQꢀRIꢀ<ꢃ9ꢌ9ꢁ
7KHꢀ VHFRQGꢀ VSHFLILFDWLRQꢀ WKDWꢀ GHVFULEHVꢀ WKHꢀ RXWSXW
VZLQJꢀFDSDELOLW\ꢀRIꢀWKHVHꢀDPSOLILHUVꢀLVꢀWKHꢀ/LQHDUꢀ5HJLRQ
ꢉD[LPXPꢀ 2XWSXWꢀ 9ROWDJHꢀ 6ZLQJꢈꢀ 7KLVꢀ VSHFLILFDWLRQ
GHILQHVꢀ WKHꢀ PD[LPXPꢀ RXWSXWꢀ VZLQJꢀ WKDWꢀ FDQꢀ EH
DFKLHYHGꢀZKLOHꢀWKHꢀDPSOLILHUꢀLVꢀVWLOOꢀRSHUDWLQJꢀLQꢀLWVꢀOLQHDU
UHJLRQꢈ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢂ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
7KHꢀ PD[LPXPꢀ RSHUDWLQJꢀ FRPPRQꢀ PRGHꢀ YROWDJHꢀ WKDW
FDQꢀEHꢀDSSOLHGꢀWRꢀWKHꢀLQSXWVꢀLVꢀ966ꢀꢆꢀꢅꢈꢐ9ꢀWRꢀ9''ꢀꢆꢀꢎꢈꢎ9ꢈ
,Qꢀ FRQWUDVWꢃꢀ WKHꢀ DEVROXWHꢀ PD[LPXPꢀ LQSXWꢀ YROWDJHꢀ LV
9
66 ꢆ ꢅꢈꢐ9ꢀDQGꢀ9''ꢀCꢀꢅꢈꢐ9ꢈꢀ9ROWDJHVꢀRQꢀWKHꢀLQSXWꢀWKDW
H[FHHGꢀ WKLVꢀ DEVROXWHꢀ PD[LPXPꢀ UDWLQJꢀ FDQꢀ FDXVH
H[FHVVLYHꢀFXUUHQWꢀWRꢀIORZꢀLQꢀRUꢀRXWꢀRIꢀWKHꢀLQSXWꢀSLQVꢈꢀ&XUꢆ
UHQWꢀEH\RQGꢀꢁ P$ꢀFDQꢀFDXVHꢀSRVVLEOHꢀUHOLDELOLW\ꢀSUREꢆ
OHPVꢈꢀ $SSOLFDWLRQVꢀ WKDWꢀ H[FHHGꢀ WKLVꢀ UDWLQJꢀ PXVWꢀ EH
H[WHUQDOO\ꢀOLPLWHGꢀZLWKꢀDQꢀLQSXWꢀUHVLVWRUꢀDVꢀVKRZQꢀLQ
)LJXUHꢀꢐꢆꢐꢈ
),*85(ꢀꢅꢂꢆꢄ *DLQꢀ %DQGZLGWKꢄꢀ 3KDVHꢀ 0DUJLQꢀ YVꢁ
&DSDFLWLYHꢀ/RDG
ꢆ
5,1
9
0&3ꢀꢁ;
''
C
ꢆ
5
,62
9
0&3ꢀꢁ;
287
0D[LPXPꢃH[SHFWHGꢃYROWDJH ± 9
5,1 ꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂ'ꢂꢂꢂꢂ'ꢂꢂ
ꢀP$
9
ꢀ
&
/
C
,1
RU
),*85(ꢀꢅꢂꢇꢄ $PSOLILHUꢀ FLUFXLWVꢀ WKDWꢀ FDQꢀ EHꢀ XVHG
9
66 ± 0LQLPXPꢃH[SHFWHGꢃYROWDJH
5,1 ꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂ
ZKHQꢀGULYLQJꢀKHDY\ꢀFDSDFLWLYHꢀORDGVꢁ
ꢀP$
,Iꢀ WKHꢀ DPSOLILHUꢀ LVꢀ UHTXLUHGꢀ WRꢀ GULYHꢀ ODUJHUꢀ FDSDFLWLYH
ORDGVꢃꢀWKHꢀFLUFXLWꢀVKRZQꢀLQꢀ)LJXUHꢀꢐꢆꢂꢀFDQꢀEHꢀXVHGꢈꢀ$
VPDOOꢀVHULHVꢀUHVLVWRUꢀ05,621ꢀDWꢀWKHꢀRXWSXWꢀRIꢀWKHꢀDPSOLILHU
LPSURYHVꢀWKHꢀSKDVHꢀPDUJLQꢀZKHQꢀGULYLQJꢀODUJHꢀFDSDFLꢆ
WLYHꢀORDGVꢈꢀ7KLVꢀUHVLVWRUꢀGHFRXSOHVꢀWKHꢀFDSDFLWLYHꢀORDG
IURPꢀWKHꢀDPSOLILHUꢀE\ꢀLQWURGXFLQJꢀDꢀ]HURꢀLQꢀWKHꢀWUDQVIHU
IXQFWLRQꢈꢀ
),*85(ꢀꢅꢂꢅꢄ ,IꢀWKHꢀLQSXWVꢀRIꢀWKHꢀDPSOLILHUꢀH[FHHGꢀWKH
$EVROXWHꢀ 0D[LPXPꢀ 6SHFLILFDWLRQVꢄꢀ DQꢀ LQSXWꢀ UHVLVWRUꢄ
5,1 ꢄꢀVKRXOGꢀEHꢀXVHGꢀWRꢀOLPLWꢀWKHꢀFXUUHQWꢀIORZꢀLQWRꢀWKDW
SLQꢁꢀ
ꢄꢁꢄ
&DSDFLWLYHꢂ/RDGꢂDQGꢂ6WDELOLW\
7KLVꢀ]HURꢀDGMXVWVꢀWKHꢀSKDVHꢀPDUJLQꢀE\ꢀDSSUR[LPDWHO\ꢄ
'ULYLQJꢀFDSDFLWLYHꢀORDGVꢀFDQꢀFDXVHꢀVWDELOLW\ꢀSUREOHPV
ZLWKꢀPDQ\ꢀRIꢀWKHꢀKLJKHUꢀVSHHGꢀDPSOLILHUVꢈ
∆θ WDQ±ꢀ(ꢀπ*%:3 × 5,62 × &/)
P
)RUꢀ DQ\ꢀ FORVHGꢀ ORRSꢀ DPSOLILHUꢀ FLUFXLWꢃꢀ Dꢀ JRRGꢀ UXOHꢀ RI
WKXPEꢀLVꢀWRꢀGHVLJQꢀIRUꢀDꢀSKDVHꢀPDUJLQꢀWKDWꢀLVꢀQRꢀOHVV
WKDQꢀꢏꢂSꢈꢀ7KLVꢀLVꢀDꢀFRQVHUYDWLYHꢀWKHRUHWLFDOꢀYDOXHꢃꢀKRZꢆ
HYHUꢃꢀLIꢀWKHꢀSKDVHꢀPDUJLQꢀLVꢀORZHUꢃꢀOD\RXWꢀSDUDVLWLFVꢀFDQ
GHJUDGHꢀ WKHꢀ SKDVHꢀ PDUJLQꢀ IXUWKHUꢀ FDXVLQJꢀ Dꢀ WUXO\
XQVWDEOHꢀFLUFXLWꢈꢀ$ꢀV\VWHPꢀSKDVHꢀVKLIWꢀRIꢀꢏꢂSꢀZLOOꢀKDYH
DQꢀ RYHUVKRRWꢀ LQꢀ LWVꢀ VWHSꢀ UHVSRQVHꢀ RIꢀ DSSUR[LPDWHO\
ꢁꢂꢒꢈꢀ
ZKHUHꢄ
∆θ ꢀLVꢀWKHꢀLPSURYHPHQWꢀLQꢀSKDVHꢀPDUJLQꢃ
P
*%:3ꢀLVꢀWKHꢀJDLQꢀEDQGZLGWKꢀSURGXFWꢀRIꢀWKH
DPSOLILHUꢃ
5
ꢀLVꢀWKHꢀFDSDFLWLYHꢀGHFRXSOLQJꢀUHVLVWRUꢃꢀDQG
,62
& ꢀLVꢀWKHꢀORDGꢀFDSDFLWDQFH
/
$ꢀEXIIHUꢀFRQILJXUDWLRQꢀZLWKꢀDꢀFDSDFLWLYHꢀORDGꢀLVꢀWKHꢀPRVW
GLIILFXOWꢀFRQILJXUDWLRQꢀIRUꢀDQꢀDPSOLILHUꢀWRꢀPDLQWDLQꢀVWDELOꢆ
LW\ꢈꢀ7KHꢀ3KDVHꢀYHUVXVꢀ&DSDFLWLYHꢀ/RDGꢀRIꢀWKHꢀꢉ&3ꢊꢅ;
DPSOLILHUꢀLVꢀVKRZQꢀLQꢀ)LJXUHꢀꢐꢆꢏꢈꢀ,QꢀWKLVꢀILJXUHꢃꢀLWꢀFDQꢀEH
VHHQꢀWKDWꢀWKHꢀDPSOLILHUꢀKDVꢀDꢀSKDVHꢀPDUJLQꢀDERYHꢀꢏꢅSꢁ
ZKLOHꢀGULYLQJꢀFDSDFLWDQFHꢀORDGVꢀXSꢀWRꢀꢁꢁꢅ S)ꢈꢀ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢃ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
&6
9
W
,+
9
,/
W
21
2))
+Lꢆ=
+Lꢆ=
2XWSXW
ꢎꢇꢈꢌ P$ꢀ0W\S1
ꢎꢇꢈꢌ P$ꢀ0W\S1
ꢂꢅ Q$ꢀ0W\S1
ꢂꢅ Q$ꢀ0W\S1
9
ꢀ6XSSO\
''
&XUUHQW
),*85(ꢀꢅꢂꢈꢄ 7LPLQJꢀ'LDJUDPꢀIRUꢀWKHꢀ&6ꢀIXQFWLRQꢀRIꢀWKHꢀ0&3ꢇꢈꢋꢀDPSOLILHUꢁ
ꢄꢁꢇ
7KHꢂ&KLSꢂ6HOHFWꢂ2SWLRQꢂRIꢂWKHꢂ0&3ꢈꢉꢊ
7KHꢀꢉ&3ꢊꢅꢇꢀLVꢀDꢀVLQJOHꢀDPSOLILHUꢀZLWKꢀDꢀ &KLSꢀ6HOHFW
RSWLRQꢈꢀ :KHQꢀ &6ꢀ LVꢀ SXOOHGꢀ KLJKꢃꢀ WKHꢀ VXSSO\ꢀ FXUUHQW
GURSVꢀWRꢀꢂꢅ Q$ꢀ0W\S1ꢈꢀ,QꢀWKLVꢀVWDWHꢃꢀWKHꢀDPSOLILHUꢀLVꢀSXW
LQWRꢀ Dꢀ KLJKꢀ LPSHGDQFHꢀ VWDWHꢈꢀ %\ꢀ SXOOLQJꢀ &6ꢀ ORZꢃꢀ WKH
DPSOLILHUꢀLVꢀHQDEOHGꢈꢀ,IꢀWKHꢀ &6ꢀSLQꢀLVꢀ OHIWꢀIORDWLQJꢃꢀWKH
DPSOLILHUꢀZLOOꢀQRWꢀRSHUDWHꢀSURSHUO\ꢈꢀ)LJXUHꢀꢐꢆꢊꢀVKRZVꢀWKH
RXWSXWꢀ YROWDJHꢀ DQGꢀ VXSSO\ꢀ FXUUHQWꢀ UHVSRQVHꢀ WRꢀ Dꢀ &6
SXOVHꢈ
ꢆ,Q
C,Q
9ꢆ
ꢄꢁꢋ
/D\RXWꢂ&RQVLGHUDWLRQV
*XDUGꢀ5LQJ
,QꢀDSSOLFDWLRQVꢀZKHUHꢀORZꢀLQSXWꢀELDVꢀFXUUHQWꢀLVꢀFULWLFDOꢃ
3&ꢀERDUGꢀVXUIDFHꢀOHDNDJHꢀHIIHFWVꢀDQGꢀVLJQDOꢀFRXSOLQJ
IURPꢀWUDFHꢆWRꢆWUDFHꢀQHHGꢀWRꢀEHꢀWDNHQꢀLQWRꢀFRQVLGHUDWLRQꢈꢀ
),*85(ꢀꢅꢂꢉꢄ ([DPSOHꢀ RIꢀ *XDUGꢀ 5LQJꢀ IRUꢀ WKH
0&3ꢇꢈꢇꢄꢀ WKHꢀ $ꢅDPSOLILHUꢀ RIꢀ WKHꢀ 0&3ꢇꢈꢉꢀ RUꢀ WKH
0&3ꢇꢈꢋꢀLQꢀDꢀ3&ꢀ%RDUGꢀ/D\RXWꢁ
ꢐꢈꢂꢈꢎ
685)$&(ꢀ/($.$*(
&LUFXLWꢀH[DPSOHVꢀRIꢀULQJꢀLPSOHPHQWDWLRQVꢀDUHꢀVKRZQꢀLQ
)LJXUHꢀꢐꢆꢇꢈꢀ,Qꢀ)LJXUHꢀꢐꢆꢇ$ꢃꢀ%ꢀDQGꢀ&ꢃꢀWKHꢀJXDUGꢀULQJꢀLV
ELDVHGꢀWRꢀWKHꢀFRPPRQꢀPRGHꢀYROWDJHꢀRIꢀWKHꢀDPSOLILHUꢈ
7KLVꢀW\SHꢀRIꢀJXDUGꢀULQJꢀLVꢀPRVWꢀHIIHFWLYHꢀIRUꢀDSSOLFDWLRQV
ZKHUHꢀ WKHꢀ FRPPRQꢀ PRGHꢀ YROWDJHꢀ RIꢀ WKHꢀ LQSXWꢀ VWDJH
FKDQJHVꢃꢀVXFKꢀDVꢀEXIIHUVꢃꢀQRQꢆLQYHUWLQJꢀJDLQꢀDPSOLILHUV
RUꢀLQVWUXPHQWDWLRQꢀDPSOLILHUVꢈ
6XUIDFHꢀOHDNDJHꢀDFURVVꢀDꢀ3&ꢀERDUGꢀLVꢀDꢀFRQVHTXHQFH
RIꢀGLIIHULQJꢀ'&ꢀYROWDJHVꢀEHWZHHQꢀWZRꢀWUDFHVꢀFRPELQHG
ZLWKꢀKLJKꢀKXPLGLW\ꢃꢀGXVWꢀRUꢀFRQWDPLQDWLRQꢀRQꢀWKHꢀERDUGꢈ
)RUꢀ LQVWDQFHꢃꢀ WKHꢀ W\SLFDOꢀ UHVLVWDQFHꢀ IURPꢀ 3&ꢀ ERDUG
ꢀꢁ
WUDFHꢆWRꢆSDGꢀLVꢀDSSUR[LPDWHO\ꢀꢎꢅ ΩꢀXQGHUꢀORZꢀKXPLGꢆ
LW\ꢀFRQGLWLRQVꢈꢀ,IꢀDQꢀDGMDFHQWꢀWUDFHꢀLVꢀELDVHGꢀWRꢀꢂ9ꢀDQG
WKHꢀLQSXWꢀSLQꢀRIꢀWKHꢀDPSOLILHUꢀLVꢀELDVHGꢀDWꢀRUꢀQHDUꢀ]HUR
YROWVꢃꢀDꢀꢂ S$ꢀOHDNDJHꢀFXUUHQWꢀZLOOꢀDSSHDUꢀRQꢀWKHꢀDPSOLꢆ
ILHU¶VꢀLQSXWꢀQRGHꢈꢀ7KLVꢀW\SHꢀRIꢀ3&%ꢀOHDNDJHꢀLVꢀILYHꢀWLPHV
WKHꢀURRPꢀWHPSHUDWXUHꢀLQSXWꢀELDVꢀFXUUHQWꢀ0ꢎ S$ꢃꢀW\S1ꢀRI
WKHꢀꢀꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑꢊꢅꢍꢀIDPLO\ꢀRIꢀDPSOLILHUVꢈ
7KHꢀVWUDWHJ\ꢀVKRZQꢀLQꢀ)LJXUHꢀꢐꢆꢇ'ꢃꢀELDVHVꢀWKHꢀFRPPRQ
PRGHꢀYROWDJHꢀDQGꢀJXDUGꢀULQJꢀWRꢀJURXQGꢈꢀ7KLVꢀW\SHꢀRI
JXDUGꢀULQJꢀLVꢀW\SLFDOO\ꢀXVHGꢀLQꢀSUHFLVLRQꢀSKRWRꢀVHQVLQJ
FLUFXLWVꢈ
7KHꢀVLPSOHVWꢀWHFKQLTXHꢀWKDWꢀFDQꢀEHꢀXVHGꢀWRꢀUHGXFHꢀWKH
HIIHFWVꢀRIꢀ3&ꢀERDUGꢀOHDNDJHꢀLVꢀWRꢀGHVLJQꢀDꢀULQJꢀDURXQG
VHQVLWLYHꢀSLQVꢀDQGꢀWUDFHVꢈꢀ$QꢀH[DPSOHꢀRIꢀWKLVꢀW\SHꢀRI
OD\RXWꢀLVꢀVKRZQꢀLQꢀ)LJXUHꢀꢐꢆꢌꢈꢀ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢁ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢐꢈꢂꢈꢁ
6,*ꢋ$/ꢀ&283/,ꢋ*
)LJXUHꢃꢈꢉꢅ$
7KHꢀLQSXWꢀSLQVꢀRIꢀWKHꢀꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑꢊꢅꢍꢀDPSOLILHUV
KDYHꢀ Dꢀ KLJKꢀ LPSHGDQFHꢀ SURYLGLQJꢀ DQꢀ RSSRUWXQLW\ꢀ IRU
QRLVHꢀ LQMHFWLRQꢀ LIꢀ OD\RXWꢀ LVVXHVꢀ DUHꢀ QRWꢀ FRQVLGHUHGꢈ
7KHVHꢀKLJKꢀLPSHGDQFHꢀLQSXWꢀWHUPLQDOVꢀDUHꢀVHQVLWLYHꢀWR
LQMHFWHGꢀFXUUHQWVꢈꢀ7KLVꢀFDQꢀRFFXUꢀLIꢀWKHꢀWUDFHꢀIURPꢀDꢀKLJK
LPSHGDQFHꢀLQSXWꢀLVꢀQH[WꢀWRꢀDꢀWUDFHꢀWKDWꢀKDVꢀIDVWꢀFKDQJꢆ
LQJꢀYROWDJHVꢃꢀVXFKꢀDVꢀDꢀGLJLWDOꢀRUꢀFORFNꢀVLJQDOꢈꢀ:KHQꢀD
KLJKꢀLPSHGDQFHꢀWUDFHꢀLVꢀLQꢀFORVHꢀSUR[LPLW\ꢀWRꢀDꢀWUDFH
ZLWKꢀWKHVHꢀW\SHVꢀRIꢀYROWDJHꢀFKDQJHVꢃꢀFKDUJHꢀLVꢀFDSDFLꢆ
WLYHO\ꢀFRXSOHGꢀLQWRꢀWKHꢀKLJKꢀLPSHGDQFHꢀWUDFHꢈꢀ
ꢆ
0&3ꢂꢃ;
C
)LJXUHꢃꢈꢉꢅ%
3&%ꢀ7UDFH
Z/ε ε
ꢁ
U
& ꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂ
5ꢀ
G
ꢆ
/
0&3ꢂꢃ;
/
C
Z
AW\SꢀꢂꢄꢂꢂꢍPPB
)LJXUHꢃꢈꢉꢅ&
3&%
&URVVꢆ6HFWLRQ
Zꢀ ꢀWKLFNQHVVꢀRIꢀ3&%ꢀWUDFH
/ꢀ ꢀOHQJWKꢀRIꢀ3&%ꢀWUDFH
Gꢀ ꢀGLVWDQFHꢀEHWZHHQꢀWKHꢀWZRꢀ3&%ꢀWUDFHV
ꢆ
),*85(ꢀꢅꢂꢋꢄ &DSDFLWRUVꢀ FDQꢀ EHꢀ EXLOWꢀ ZLWKꢀ 3&%
WUDFHVꢀDOORZLQJꢀIRUꢀFRXSOLQJꢀRIꢀVLJQDOVꢀIURPꢀRQHꢀWUDFH
WRꢀDQRWKHUꢁ
0&3ꢂꢃ;
9ROWDJH
5HIHUHQFH
AFRXOGꢀEHꢀJURXQGB
C
$VꢀVKRZQꢀLQꢀ)LJXUHꢀꢐꢆꢍꢃꢀWKHꢀYDOXHꢀRIꢀWKHꢀFDSDFLWDQFH
EHWZHHQꢀWZRꢀWUDFHVꢀLVꢀSULPDULO\ꢀGHSHQGHQWꢀRQꢀWKHꢀGLVꢆ
WDQFHꢀ0G1ꢀEHWZHHQꢀWKHꢀWUDFHVꢀDQGꢀWKHꢀGLVWDQFHꢀWKDWꢀWKH
WZRꢀ WUDFHVꢀ DUHꢀ LQꢀ SDUDOOHOꢀ 0/1ꢈꢀ )URPꢀ WKLVꢀ PRGHOꢃꢀ WKH
DPRXQWꢀRIꢀFXUUHQWꢀJHQHUDWHGꢀLQWRꢀWKHꢀKLJKꢀLPSHGDQFH
WUDFHꢀLVꢀHTXDOꢀWRꢄ
)LJXUHꢃꢈꢉꢅ'
9''
ꢆ
∂9
∂W
, &
ꢂꢂꢂꢂꢂꢂ
0&3ꢂꢃ;
C
ZKHUHꢄꢀ
,ꢀ HTXDOVꢀ WKHꢀ FXUUHQWꢀ WKDWꢀ DSSHDUVꢀ RQꢀ WKHꢀ KLJK
LPSHGDQFHꢀWUDFHꢈ
),*85(ꢀꢅꢂꢊꢄ ([DPSOHVꢀRIꢀKRZꢀWRꢀGHVLJQꢀ3&ꢀ%RDUG
WUDFHVꢀ WRꢀ PLQLPL]Hꢀ OHDNDJHꢀ SDWKVꢀ WRꢀ WKHꢀ KLJK
LPSHGDQFHꢀ LQSXWꢀ SLQVꢀ RIꢀ WKHꢀ 0&3ꢇꢈꢇꢌꢇꢈꢉꢌꢇꢈꢋꢌꢇꢈꢊ
DPSOLILHUVꢁ
&ꢀHTXDOVꢀWKHꢀYDOXHꢀRIꢀFDSDFLWDQFHꢀEHWZHHQꢀWKHꢀWZR
3&%ꢀWUDFHVꢈ
∂9ꢀHTXDOVꢀWKHꢀFKDQJHꢀLQꢀYROWDJHꢀRIꢀWKHꢀWUDFHꢀWKDWꢀLV
VZLWFKLQJꢈ
∂Wꢀ HTXDOVꢀ WKHꢀ DPRXQWꢀ RIꢀ WLPHꢀ WKDWꢀ WKHꢀ YROWDJH
FKDQJHꢀWRRNꢀWRꢀJHWꢀIURPꢀRQHꢀOHYHOꢀWRꢀWKHꢀQH[Wꢈ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢍ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
VSHHGꢀ VHQVLQJꢈꢀ 7KLVꢀ LVꢀ GRQHꢀ E\ꢀ UHYHUVHꢀ ELDVLQJꢀ WKH
SKRWRGHWHFWRUꢃꢀZKLFKꢀUHGXFHVꢀWKHꢀSDUDVLWLFꢀFDSDFLWDQFH
RIꢀWKHꢀGLRGHꢈꢀ
ꢄꢁꢈ
7\SLFDOꢂ$SSOLFDWLRQV
ꢐꢈꢊꢈꢎ
/2:ꢀ6,'(ꢀ%$77(5<ꢀ&855(ꢋ7ꢀ6(ꢋ6,ꢋ*
7KHꢀNH\ꢀ VSHFLILFDWLRQVꢀ WKDWꢀLQIOXHQFHꢀ WKHꢀDFFXUDF\ꢀRI
WKHVHꢀFLUFXLWVꢀDUHꢀORZꢀRIIVHWꢀYROWDJHꢃꢀORZꢀLQSXWꢀELDVꢀFXUꢆ
UHQWꢃꢀKLJKꢀLQSXWꢀLPSHGDQFHꢀDQGꢀDQꢀLQSXWꢀFRPPRQꢀPRGH
UDQJHꢀEHORZꢀJURXQGꢈꢀ7KHꢀORZꢀLQSXWꢀRIIVHWꢀYROWDJHꢀDQG
ORZꢀLQSXWꢀELDVꢀFXUUHQWꢀSURYLGHꢀDQꢀHQYLURQPHQWꢀZKHUH
WKHUHꢀLVꢀPLQLPDOꢀYROWDJHꢀSODFHGꢀDFURVVꢀWKHꢀSKRWRGHWHFꢆ
WRUꢃꢀ FRQVHTXHQWO\ꢀ WKHꢀOLQHDULW\ꢀRIꢀ WKHꢀSKRWRGHWHFWRUꢀLV
QRWꢀ FRPSURPLVHGꢈꢀ *LYHQꢀ WKDWꢀ WKHꢀ ꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑ
ꢊꢅꢍꢀDPSOLILHUVꢀDUHꢀVSHFLILHGꢀIRUꢀDꢀꢁꢂꢅ µ9ꢀ0PD[1ꢀRIIVHW
YROWDJHꢀ DQGꢀ LQSXWꢀ ELDVꢀ FXUUHQWVꢀ LQꢀ WKHꢀ SLFRꢀ DPSHUH
UHJLRQꢃꢀ WKH\ꢀ DUHꢀ LGHDOꢀ IRUꢀ WKHVHꢀ FLUFXLWVꢈꢀ $GGLWLRQDOO\ꢃ
WKHVHꢀWZRꢀFLUFXLWVꢀZLOOꢀRQO\ꢀZRUNꢀLIꢀWKHꢀFRPPRQꢀPRGH
UDQJHꢀRIꢀWKHꢀDPSOLILHUꢀLQFOXGHVꢀ]HURꢃꢀZKLFKꢀLVꢀWKHꢀFDVH
ZLWKꢀWKHꢀꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑꢊꢅꢍꢀDPSOLILHUVꢈ
7KHꢀ ꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑꢊꢅꢇꢑꢊꢅꢍꢀ DPSOLILHUVꢀ FDQꢀ EHꢀ XVHGꢀ WR
VHQVHꢀWKHꢀRXWSXWꢀFXUUHQWꢀRQꢀWKHꢀORZꢀVLGHꢀRIꢀDꢀEDWWHU\
XVLQJꢀWKHꢀFLUFXLWꢀLQꢀ)LJXUH ꢐꢆꢎꢅꢈꢀ,QꢀWKLVꢀFLUFXLWꢃꢀWKHꢀFXUꢆ
UHQWꢀIURPꢀWKHꢀSRZHUꢀVXSSO\ꢀ0PLQXVꢀWKHꢀFXUUHQWꢀUHTXLUHG
WRꢀSRZHUꢀWKHꢀꢉ&3ꢊꢅꢊ1ꢀIORZVꢀWKURXJKꢀDꢀWHQꢀRKPꢀUHVLVWRU
IURPꢀWKHꢀUHVWꢀRIꢀWKHꢀFLUFXLWꢀLQꢀWKHꢀV\VWHPꢈꢀ7KLVꢀFXUUHQWꢀLV
FRQYHUWHGꢀWRꢀDꢀYROWDJHꢀWKURXJKꢀWKHꢀVHQVHꢀUHVLVWRUꢀDQG
JDLQHGꢀE\ꢀWKHꢀUHVLVWRUVꢀDURXQGꢀWKHꢀDPSOLILHUꢈꢀ6LQFHꢀWKH
LQSXWꢀELDVꢀFXUUHQWꢀDQGꢀRIIVHWꢀYROWDJHꢀRIꢀWKHꢀꢉ&3ꢊꢅꢊꢀLV
ORZꢃꢀWKHUHꢀLVꢀYHU\ꢀOLWWOHꢀHUURUꢀJHQHUDWHGꢀE\ꢀWKHꢀDPSOLILHUꢈ
$GGLWLRQDOO\ꢃꢀWKHꢀDPSOLILHUꢀLVꢀFDSDEOHꢀRIꢀVZLQJLQJꢀEHORZ
JURXQGꢀ DQGꢀ WKHꢀ TXLHVFHQWꢀ FXUUHQWꢀ LVꢀ YHU\ꢀ ORZꢈꢀ7KHVH
IRXUꢀVSHFLILFDWLRQVꢀPDNHꢀWKLVꢀDPSOLILHUꢀDSSURSULDWHꢀIRU
WKLVꢀW\SHꢀRIꢀFLUFXLWꢈ
&
ꢃ
,
5
/2$'
ꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆ
6(16(
5ꢃ
5
)
ꢃ ꢇ ꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆ
5
9''
'
ꢁ
,1
ꢀꢁ NΩ
,
'ꢁ
ꢆ
ꢑ
9''
5)
9287
0&3ꢂꢃꢂ
/LJKW
9''
ꢇ
ꢃꢄꢅꢀꢂWR
ꢀꢅꢀ9
ꢀ NΩ
ꢆ
5,1
0&3ꢂꢃꢂ
&
ꢃ
ꢇ
966
9%,$6
'
5ꢃ
966
ꢁ
ꢃꢂ
Ω
9''
7RꢂO RDG
,
'ꢁ
/LJKW
),*85(ꢀꢅꢂꢃꢌꢄ /RZꢀ6LGHꢀ%DWWHU\ꢀ&XUUHQWꢀ6HQVLQJ
ꢆ
ꢑ
9287
0&3ꢂꢃꢂ
ꢐꢈꢊꢈꢁ
35($ꢉ3/,),(5ꢀ)25ꢀ3+272ꢀ'(7(&7,2ꢋꢀ
&,5&8,7
ꢇ
$Q\ꢀDPSOLILHUꢀIURPꢀWKLVꢀIDPLO\ꢀRIꢀRSHUDWLRQDOꢀDPSOLILHUV
FDQꢀEHꢀXVHGꢀWRꢀFRQYHUWꢀDQꢀRXWSXWꢀFXUUHQWꢀVLJQDOꢀIURPꢀD
VHQVRUꢀLQWRꢀDꢀYROWDJHꢈꢀ$ꢀVHQVRUꢀWKDWꢀILWVꢀWKLVꢀGHVFULSWLRQ
LVꢀDꢀSKRWRGHWHFWRUꢀDVꢀVKRZQꢀLQꢀ)LJXUH ꢐꢆꢎꢎꢈꢀ7KLVꢀW\SHꢀRI
FLUFXLWꢀ LVꢀ LPSOHPHQWHGꢀ ZLWKꢀ Dꢀ VLQJOHꢀ UHVLVWRUꢀ DQGꢀ DQ
RSWLRQDOꢀFDSDFLWRUꢀLQꢀWKHꢀIHHGEDFNꢀORRSꢀRIꢀWKHꢀDPSOLILHUꢈ
$VꢀOLJKWꢀLPSLQJHVꢀRQꢀWKHꢀSKRWRꢀGLRGHꢃꢀFKDUJHꢀLVꢀJHQHUꢆ
DWHGꢃꢀFDXVLQJꢀDꢀFXUUHQWꢀWRꢀIORZꢀLQꢀWKHꢀUHYHUVHꢀELDVꢀGLUHFꢆ
WLRQꢀRIꢀWKHꢀSKRWRGHWHFWRUꢈ
9
&%ꢀ ꢀ5ꢀꢀ,ꢁꢂ
ꢑ%\SDVVꢀ&DSDFLWRU+ꢀꢃ)
),*85(ꢀꢅꢂꢃꢃꢄ 3UHꢅ$PSOLILHUꢀ IRUꢀ 3KRWRꢀ 'HWHFWLRQ
&LUFXLWꢁ
7ZRꢀFLUFXLWVꢀDUHꢀVKRZQꢀLQꢀ)LJXUH ꢐꢆꢎꢎꢈꢀ7KHꢀWRSꢀFLUFXLWꢀLV
GHVLJQHGꢀWRꢀSURYLGHꢀSUHFLVLRQꢀVHQVLQJꢀIURPꢀWKHꢀSKRWRꢆ
GHWHFWRUꢈꢀ,QꢀWKLVꢀFLUFXLWꢃꢀWKHꢀYROWDJHꢀDFURVVꢀWKHꢀGHWHFWRU
LVꢀ QHDUO\ꢀ ]HURꢀ DQGꢀ HTXDOꢀ WRꢀ WKHꢀ RIIVHWꢀ YROWDJHꢀ RIꢀ WKH
DPSOLILHUꢈꢀ:LWKꢀWKLVꢀFRQILJXUDWLRQꢃꢀFXUUHQWꢀWKDWꢀDSSHDUV
DFURVVꢀWKHꢀUHVLVWRUꢃꢀ5 ꢃꢀLVꢀSULPDULO\ꢀDꢀUHVXOWꢀRIꢀWKHꢀOLJKW
ꢁ
H[FLWDWLRQꢀRQꢀWKHꢀSKRWRGHWHFWRUꢈꢀ7KHꢀSKRWRVHQVLQJꢀFLUꢆ
FXLWꢀRQꢀWKHꢀERWWRPꢀRIꢀ)LJXUH ꢐꢆꢎꢎꢀLVꢀGHVLJQHGꢀIRUꢀKLJKHU
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢋ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢐꢈꢊꢈꢐ
7:2ꢀ23ꢀ$ꢉ3ꢀ,ꢋ6758ꢉ(ꢋ7$7,2ꢋꢀ
$ꢉ3/,),(5
9''
9ꢃ
5ꢄ
9''
5ꢂ
ꢑ
ꢇ
0&3ꢂꢃꢄ
ꢆ
7KHꢀ WZRꢀ RSꢀ DPSꢀ LQVWUXPHQWDWLRQꢀ DPSOLILHUꢀ VKRZQꢀ LQ
)LJXUH ꢐꢆꢎꢁꢀVHUYHVꢀWKHꢀIXQFWLRQꢀRIꢀWDNLQJꢀWKHꢀGLIIHUHQFH
RIꢀWZRꢀLQSXWꢀYROWDJHVꢃꢀOHYHOꢀVKLIWLQJꢀWKHQꢀDQGꢀSURYLGLQJ
Dꢀ VLQJOHꢀ RXWSXWꢈꢀ 7KLVꢀ FRQILJXUDWLRQꢀ LVꢀ EHVWꢀ VXLWHGꢀ IRU
KLJKHUꢀJDLQVꢈꢀ³0JDLQꢀ!ꢀꢐꢀ9ꢑ91´ꢀLVꢀVKRZQꢀLQꢀ)LJXUH ꢐꢆꢎꢁꢈ
7KHꢀ NH\ꢀ VSHFLILFDWLRQVꢀ WKDWꢀ PDNHꢀ WKHꢀ ꢉ&3ꢊꢅꢊꢑꢊꢅꢌꢑ
ꢊꢅꢇꢑꢊꢅꢍꢀ IDPLO\ꢀ DSSURSULDWHꢀ IRUꢀ WKLVꢀ DSSOLFDWLRQꢀ FLUFXLW
DUHꢀORZꢀLQSXWꢀELDVꢀFXUUHQWꢃꢀORZꢀRIIVHWꢀYROWDJHꢀDQGꢀKLJK
FRPPRQꢆPRGHꢀUHMHFWLRQꢈꢀ7KHꢀUHIHUHQFHꢀYROWDJHꢀRIꢀWKLV
FLUFXLWꢀLVꢀVXSSOLHGꢀWRꢀWKHꢀILUVWꢀRSꢀDPSꢀLQꢀWKHꢀVLJQDOꢀFKDLQꢈ
7\SLFDOO\ꢃꢀWKLVꢀYROWDJHꢀLVꢀKDOIꢀRIꢀWKHꢀVXSSO\ꢀYROWDJHꢀLQꢀD
VLQJOHꢀVXSSO\ꢀHQYLURQPHQWꢈ
ò
ꢆ
5ꢃ
5ꢃ
ꢑ
ò
5*
0&3ꢂꢃꢄ
5ꢂ
9287
ꢇ
5ꢄ
95()
ꢆ
0&3ꢂꢃꢄ
ò
9ꢁ
ꢇ
ꢂ5
(9 ±9 ) ꢁ ꢄ ꢃꢃꢃꢃꢃꢃꢃꢃꢃꢃꢃ
5
ꢂ
ꢅ
9
ꢄ 9
ꢃꢃꢃꢃꢃꢃꢃ
ꢆ
287
ꢁ
ꢂ
5()
5
5
*
5*
ꢑ%\SDVVꢀ&DSDFLWRU+ꢀꢃ)
5ꢃ
5ꢁ
),*85(ꢀꢅꢂꢃꢅꢄ 7KUHHꢀ2Sꢀ$PSꢀ,QVWUXPHQWDWLRQꢀ
$PSOLILHUꢁ
9''
95()
ꢐꢈꢊꢈꢂ
35(&,6,2ꢋꢀ*$,ꢋꢀ:,7+ꢀ*22'ꢀ/2$'ꢀ
,62/$7,2ꢋ
ꢆ
5ꢁ
ò
0&3ꢂꢃꢄ
ꢑ
5ꢃ
ꢇ
,Qꢀ )LJXUH ꢐꢆꢎꢏꢃꢀ WKHꢀ ORZꢀ LQSXWꢀ RIIVHWꢀ YROWDJHꢀ RIꢀ WKH
ꢉ&3ꢊꢅꢊꢀLVꢀXVHGꢀWRꢀLPSOHPHQWꢀDꢀFLUFXLWꢀZLWKꢀDꢀKLJKꢀJDLQꢈ
7KLVꢀSUHFLVLRQꢀPHDVXUHPHQWꢀFDQꢀHDVLO\ꢀEHꢀGLVUXSWHGꢀE\
FKDQJLQJꢀWKHꢀRXWSXWꢀFXUUHQWꢀGULYHꢀRIꢀWKHꢀGHYLFHꢀWKDWꢀLV
GRLQJꢀWKHꢀDPSOLILFDWLRQꢀZRUNꢈꢀ&RQVHTXHQWO\ꢃꢀWKHꢀSUHFLꢆ
VLRQꢀDPSOLILHUꢀFRQILJXUDWLRQꢀLVꢀIROORZHGꢀE\ꢀDꢀꢉ&3ꢊꢅꢎ
DPSOLILHUꢀ ZKLFKꢀ LVꢀ FDSDEOHꢀ RIꢀ GULYLQJꢀ KLJKHUꢀ FXUUHQWVꢈ
6LQFHꢀWKHꢀWZRꢀDPSOLILHUVꢀDUHꢀKRXVHGꢀLQꢀVHSDUDWHꢀSDFNꢆ
DJHVꢃꢀWKHUHꢀLVꢀPLQLPDOꢀFKDQJHꢀLQꢀRIIVHWꢀYROWDJHꢀRIꢀWKH
ꢉ&3ꢊꢅꢊꢀGXHꢀWRꢀORDGLQJꢀHIIHFWVꢈ
9ꢃ
ꢆ
ò
0&3ꢂꢃꢄ
9ꢁ
9287
ꢇ
5
ꢁ
ꢂ5
ꢁ
9
(9 ± 9 ) ꢁ ꢄ ꢃꢃꢃꢃꢃꢃꢃ ꢄ ꢃꢃꢃꢃꢃꢃꢃꢃꢃꢃꢃ ꢄ 9
287
ꢑ%\SDVVꢀ&DSDFLWRU+ꢀꢂꢄꢃP)
),*85(ꢀꢅꢂꢃꢁꢄ 7ZRꢀ2Sꢀ$PSꢀ,QVWUXPHQWDWLRQꢀ$PSOLILHU
ꢁ
ꢂ
5()
5
5
ꢂ
*
ꢐꢈꢊꢈꢏ
7+5((ꢀ23ꢀ$ꢉ3ꢀ,ꢋ6758ꢉ(ꢋ7$7,2ꢋꢀ
$ꢉ3/,),(5
5ꢁ
5ꢃ
9''
9''
$ꢀ FODVVLFꢃꢀ WKUHHꢀ RSꢀ DPSꢀ LQVWUXPHQWDWLRQꢀ DPSOLILHUꢀ LV
LOOXVWUDWHGꢀLQꢀ)LJXUHꢀꢐꢆꢎꢂꢈꢀ7KHꢀLQSXWꢀRSHUDWLRQDOꢀDPSOLILꢆ
HUVꢀLQꢀWKLVꢀFLUFXLWꢀSURYLGHꢀVLJQDOꢀJDLQꢈꢀ7KHꢀRXWSXWꢀRSHUDꢆ
WLRQDOꢀDPSOLILHUꢀFRQYHUWVꢀWKHꢀVLJQDOꢀIURPꢀWZRꢀLQSXWVꢀWRꢀD
VLQJOHꢀ HQGHGꢀ RXWSXWꢀ ZLWKꢀ Dꢀ GLIIHUHQFHꢀ DPSOLILHUꢈꢀ 7KH
JDLQꢀRIꢀWKLVꢀFLUFXLWꢀLVꢀVLPSO\ꢀDGMXVWHGꢀZLWKꢀRQHꢀUHVLVWRUꢃ
ꢆ
ꢑ
ꢆ
0&3ꢂꢃꢅ
ꢑ
9287
0&3ꢂꢃꢂ
ꢇ
9,1
ꢇ
%XIIHU
5 ꢈꢀ 7KHꢀ UHIHUHQFHꢀ YROWDJHꢀRIꢀWKHꢀ GLIIHUHQFHꢀ VWDJHꢀ RI
*
3UHFLVLRQꢀ$PSOLILHU
ꢑ%\SDVVꢀ&DSDFLWRU+ꢀꢃ)
WKLVꢀLQVWUXPHQWDWLRQꢀDPSOLILHUꢀLVꢀFDSDEOHꢀRIꢀVSDQQLQJꢀD
ZLGHꢀUDQJHꢈꢀꢉRVWꢀW\SLFDOO\ꢃꢀWKLVꢀQRGHꢀLVꢀUHIHUHQFHGꢀWR
KDOIꢀRIꢀWKHꢀVXSSO\ꢀYROWDJHꢀLQꢀDꢀVLJQDOꢀVXSSO\ꢀDSSOLFDWLRQꢈ
),*85(ꢀꢅꢂꢃꢆꢄ 3UHFLVLRQꢀ*DLQꢀZLWKꢀ*RRGꢀ/RDGꢀ
,VRODWLRQꢁ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢉ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢈꢂꢃ 63,&(ꢀ0$&5202'(/
7KHꢀ 6SLFHꢀ PDFURPRGHOꢀ IRUꢀ WKHꢀ ꢉ&3ꢊꢅꢊꢃꢀ ꢉ&3ꢊꢅꢌꢃ
ꢉ&3ꢊꢅꢇꢀDQGꢀꢉ&3ꢊꢅꢍꢀVLPXODWHVꢀWKHꢀW\SLFDOꢀDPSOLILHU
SHUIRUPDQFHꢀRIꢀRIIVHWꢀYROWDJHꢃꢀ'&ꢀSRZHUꢀVXSSO\ꢀUHMHFꢆ
WLRQꢃꢀ LQSXWꢀ FDSDFLWDQFHꢃꢀ '&ꢀ FRPPRQꢀ PRGHꢀ UHMHFWLRQ
UDWLRꢃꢀRSHQꢀORRSꢀJDLQꢀRYHUꢀIUHTXHQF\ꢃꢀSKDVHꢀPDUJLQꢀZLWK
QRꢀFDSDFLWLYHꢀORDGꢃꢀRXWSXWꢀVZLQJꢃꢀ'&ꢀSRZHUꢀVXSSO\ꢀFXUꢆ
UHQWꢃꢀSRZHUꢀVXSSO\ꢀFXUUHQWꢀFKDQJHꢀZLWKꢀVXSSO\ꢀYROWDJHꢃ
LQSXWꢀFRPPRQꢀPRGHꢀUDQJHꢀDQGꢀLQSXWꢀYROWDJHꢀQRLVHꢈ
7KHꢀ FKDUDFWHULVWLFVꢀ RIꢀ WKHꢀ ꢉ&3ꢊꢅꢊꢃꢀ ꢉ&3ꢊꢅꢌꢃ
ꢉ&3ꢊꢅꢇꢃꢀDQGꢀꢉ&3ꢊꢅꢍꢀDPSOLILHUVꢀDUHꢀVLPLODUꢀLQꢀWHUPV
RIꢀSHUIRUPDQFHꢀDQGꢀEHKDYLRUꢈꢀ7KLVꢀVLQJOHꢀRSꢀDPSꢀPDFꢆ
URPRGHOꢀVXSSRUWVꢀDOOꢀIRXUꢀGHYLFHVꢀZLWKꢀWKHꢀH[FHSWLRQꢀRI
WKHꢀFKLSꢀ VHOHFWꢀ IXQFWLRQꢀRIꢀWKHꢀꢉ&3ꢊꢅꢇꢃꢀ ZKLFKꢀLVꢀ QRW
PRGHOHGꢈ
7KHꢀOLVWLQJꢀIRUꢀWKLVꢀPDFURPRGHOꢀLVꢀVKRZQꢀRQꢀWKHꢀQH[W
SDJHꢈꢀ 7KHꢀ PRVWꢀ UHFHQWꢀUHYLVLRQꢀ RIꢀ WKHꢀ PRGHOꢀ FDQꢀ EH
GRZQORDGHGꢀIURPꢀꢉLFURFKLS¶VꢀZHEꢀVLWHꢀDWꢀ ZZZꢈPLFURꢆ
FKLSꢈFRPꢈ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢎ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
6RIWZDUHꢃ/LFHQVHꢃ$JUHHPHQW
7KHꢀVRIWZDUHꢀVXSSOLHGꢀKHUHZLWKꢀE\ꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFRUSRUDWHGꢀAWKHꢀ³&RPSDQ\´BꢀLVꢀLQWHQGHGꢀDQGꢀVXSSOLHGꢀWRꢀ\RX+ꢀWKHꢀ&RPꢆ
SDQ\¶VꢀFXVWRPHU+ꢀIRUꢀXVHꢀVROHO\ꢀDQGꢀH[FOXVLYHO\ꢀRQꢀ0LFURFKLSꢀSURGXFWVꢄ
7KHꢀVRIWZDUHꢀLVꢀRZQHGꢀE\ꢀWKHꢀ&RPSDQ\ꢀDQGꢈRUꢀLWVꢀVXSSOLHU+ꢀDQGꢀLVꢀSURWHFWHGꢀXQGHUꢀDSSOLFDEOHꢀFRS\ULJKWꢀODZVꢄꢀ$OOꢀULJKWVꢀDUHꢀUHVHUYHGꢄ
$Q\ꢀXVHꢀLQꢀYLRODWLRQꢀRIꢀWKHꢀIRUHJRLQJꢀUHVWULFWLRQVꢀPD\ꢀVXEMHFWꢀWKHꢀXVHUꢀWRꢀFULPLQDOꢀVDQFWLRQVꢀXQGHUꢀDSSOLFDEOHꢀODZV+ꢀDVꢀZHOOꢀDVꢀWRꢀFLYLO
OLDELOLW\ꢀIRUꢀWKHꢀEUHDFKꢀRIꢀWKHꢀWHUPVꢀDQGꢀFRQGLWLRQVꢀRIꢀWKLVꢀOLFHQVHꢄ
7ꢐ,6ꢀ62)7:$5(ꢀ,6ꢀ3529,'('ꢀ,1ꢀ$1ꢀ³$6ꢀ,6´ꢀ&21',7,21ꢄꢀ12ꢀ:$55$17,(6+ꢀ:ꢐ(7ꢐ(5ꢀ(;35(66+ꢀ,03/,('ꢀ25ꢀ67$78ꢆ
725<+ꢀ,1&/8',1*+ꢀ%87ꢀ127ꢀ/,0,7('ꢀ72+ꢀ,03/,('ꢀ:$55$17,(6ꢀ2)ꢀ0(5&ꢐ$17$%,/,7<ꢀ$1'ꢀ),71(66ꢀ)25ꢀ$ꢀ3$57,&8ꢆ
/$5ꢀ 385326(ꢀ $33/<ꢀ 72ꢀ 7ꢐ,6ꢀ 62)7:$5(ꢄꢀ 7ꢐ(ꢀ &203$1<ꢀ 6ꢐ$//ꢀ 127+ꢀ ,1ꢀ $1<ꢀ &,5&8067$1&(6+ꢀ %(ꢀ /,$%/(ꢀ )25
63(&,$/+ꢀ,1&,'(17$/ꢀ25ꢀ&216(48(17,$/ꢀ'$0$*(6+ꢀ)25ꢀ$1<ꢀ5($621ꢀ:ꢐ$762(9(5ꢄ
.subckt mcp606 1 2 3 4 5
*
*
*
*
*
*
*
| | | | |
| | | | Output
| | | Negative supply
| | Positive Supply
| Inverting input
Non-inverting input
* Macromodel for MCP606 (single), MCP607 (dual), MCP608 (single w/CS), and MCP609 (quad)
*
* The characteristics of the MCP606, MCP607, MCP608, and MCP609 have the same fundamental
* performance and behavior. Consequently, this single op amp macromodel supports all four
* devices. However, the chip select function of the MCP608 is not modeled.
*
* Revision History:
*
*
REV A : 6-30-99 created BCB
* This macromodel models typical amplifier offset voltage, DC power supply rejection, input
* capacitance, open loop gain over frequency, phase margin with 60pF load, output swing,
* power supply current, input voltage noise, slew rate.
*
* NOTICE: THE INFORMATION PROVIDED HEREIN IS BELIEVED TO BE RELIABLE,
* HOWEVER, MICROCHIP ASSUMES NO RESPONSIBILITY FOR INACCURACIES OR
* OMISSIONS. MICROCHIP ASSUMES NO RESPONSIBILITY FOR THE USE OF THIS
* INFORMATION, AND ALL USE OF SUCH INFORMATION SHALL BE ENTIRELY AT
* THE USER'S OWN RISK. NO INTELLECTURAL PROPERTY RIGHTS OR LICENSES
* TO ANY OF THE TECNOLOGY DESCRIBED HEREIN ARE IMPLIED OR GRANTED TO
* ANY THIRD PARTY. MICROCHIP RESERVES THE RIGHT TO CHANGE THIS MODEL
* AT ANY TIME WITHOUT NOTICE.
*
*
*Input Stage, pole at 300kHz
M1
M2
9
8
1
1
2
3
8
9
8
3
64
2
2
4
4
7
6
6
9
7
7
3
3
Ptype
Ptype
CDIFF
CCM1
CCM2
IDD
RA
RB
CA
ICOMP
3E-12
6E-12
6E-12
13.33e-6
1.839e3
1.839e3
125e-12
-194.63e-6
4
*Input Stage Common-Mode Clampling
VCMM
ECM
4
55
6
4
0.35
3 64 1
RCM
DCMP
VCMP
57
56
57
56
55
4
1E3
DY
1.2
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢅ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
RST
DST
VST
58
59
58
59
55
4
1E3
DX
1.6
GCMP2 23 4 POLY(2) 57 56 58 59 0 0 0;0 -0.5E-3 0.5E-3
*Input errors (vos, en, psr)
ERR 64
1
poly(2) (67,4) (3, 4) -229.9e-6 1 23e-6
*Second Stage, pole at 0.183Hz
GS
R1
C2
23
23
23
4
4
4
8
9
543.78e-6
8.2144e9
110e-12
VSOM
VSOP
DSOM
DSOP
3
24
4
24
23
4.784
-3.98
DY
25
23
25
DY
*HCM
23
3
VCMP
FS 3 4 POLY(11) VO3 VO5 VO4 VO6 VO1 VO2 VO9 VO10 VMID1 VSOP VSOM
+ 200E-6 -1 -1 -1 1 -1 -1 1 1 -1 -1 -1
*mid-supply reference
RMID1
VMID1
RMID2
3
35
4
35
34
34
4
61.62E3
0
61.62E3
23
ELEVEL 34
4
-1
*output stage
DO3
DO4
DO5
DO6
DO7
DO8
VO3
VO4
34
44
3
3
4
4
43
5
43
34
45
46
45
46
5
DY
DY
DY
DY
DY
DY
0.1
0.03
44
GO5
VO5
GO6
VO6
GO1
VO1
3
47
4
48
49
49
47
5
48
5
4
45
3
0
34
0
5
34
4
10E-3
10E-3
10E-3
34
0
GO2
VO2
RO9
VO9
RO10
VO10
50
50
3
51
52
52
4
34
0
100
0
100
0
5
10E-3
46
51
5
4
5
* input voltage noise
VN1
DN1
RN1
65
65
67
4
67
4
0.6
DX
10E3
.model Ptype PMOS L=2 W=105
.model DY D (IS=1e-15 BV =50)
.model DX D (IS=1e-18 AF=0.6 KF=10e-17)
.ENDS
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢊ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢉꢂꢃ
3$&.$*,1*ꢀ,1)250$7,21
ꢋꢁꢀ
3DFNDJHꢂ0DUNLQJꢂ,QIRUPDWLRQ
ꢉꢁ/HDGꢂ627ꢁꢊꢄꢁꢉ
([DPSOHꢇ
;;11
6%11
ꢀꢁ/HDGꢂ3',3ꢂꢃꢄꢅꢅꢂPLOꢆ
([DPSOHꢇ
XXXXXXXX
XXXXXNNN
MCP606
I/PNNN
YYWW
YYWW
ꢀꢁ/HDGꢂ62,&ꢂꢃꢈꢉꢅꢂPLOꢆ
([DPSOHꢇ
XXXXXXXX
XXXXYYWW
MCP606
I/SNYYWW
NNN
NNN
([DPSOHꢇ
ꢀꢁ/HDGꢂ76623
XXXX
YYWW
606
IYWW
NNN
NNN
/HJHQGꢋꢀꢀꢀꢀ;;ꢈꢈꢈ; &XVWRPHUꢀVSHFLILFꢀLQIRUPDWLRQꢓ
<<
<HDUꢀFRGHꢀ0ODVWꢀꢁꢀGLJLWVꢀRIꢀFDOHQGDUꢀ\HDU1
::
ꢋꢋꢋ
:HHNꢀFRGHꢀ0ZHHNꢀRIꢀ-DQXDU\ꢀꢎꢀLVꢀZHHNꢀµꢅꢎ¶1
$OSKDQXPHULFꢀWUDFHDELOLW\ꢀFRGH
1RWHꢄ ,QꢀWKHꢀHYHQWꢀWKHꢀIXOOꢀꢉLFURFKLSꢀSDUWꢀQXPEHUꢀFDQQRWꢀEHꢀPDUNHGꢀRQꢀRQHꢀOLQHꢃꢀLWꢀZLOO
EHꢀFDUULHGꢀRYHUꢀWRꢀWKHꢀQH[WꢀOLQHꢀWKXVꢀOLPLWLQJꢀWKHꢀQXPEHUꢀRIꢀDYDLODEOHꢀFKDUDFWHUV
IRUꢀFXVWRPHUꢀVSHFLILFꢀLQIRUPDWLRQꢈ
*
6WDQGDUGꢀPDUNLQJꢀFRQVLVWVꢀRIꢀꢉLFURFKLSꢀSDUWꢀQXPEHUꢃꢀ\HDUꢀFRGHꢃꢀZHHNꢀFRGHꢃꢀWUDFHDELOLW\ꢀFRGHꢀ0IDFLOLW\
FRGHꢃꢀ PDVNꢀ UHYꢔꢃꢀ DQGꢀ DVVHPEO\ꢀ FRGH1ꢈꢀ )RUꢀ PDUNLQJꢀ EH\RQGꢀ WKLVꢃꢀ FHUWDLQꢀ SULFHꢀ DGGHUVꢀ DSSO\ꢈꢀ 3OHDVH
FKHFNꢀZLWKꢀ\RXUꢀꢉLFURFKLSꢀ6DOHVꢀ2IILFHꢈ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢃꢌ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
3DFNDJHꢂ0DUNLQJꢂ,QIRUPDWLRQꢂꢌ&RQWLQXHGꢍ
ꢈꢋꢁ/HDGꢂ3',3ꢂꢃꢄꢅꢅꢂPLOꢆꢂꢃ0&3ꢌꢅꢍꢆ
([DPSOHꢇ
XXXXXXXXXXXXXX
XXXXXXXXXXXXXX
MCP609-I/P
XXXXXXXXXXXXXX
YYWWNNN
YYWWNNN
ꢈꢋꢁ/HDGꢂ62,&ꢂꢃꢈꢉꢅꢂPLOꢆꢂꢃ0&3ꢌꢅꢍꢆ
([DPSOHꢇ
XXXXXXXXXX
XXXXXXXXXX
YYWWNNN
MCP6091SL
XXXXXXXXXXX
YYWWNNN
([DPSOHꢇ
ꢈꢋꢁ/HDGꢂ76623ꢂꢃ0&3ꢌꢅꢍꢆ
XXXXXXXX
YYWW
609IST
YYWW
NNN
NNN
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢂ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢋꢅ/HDGꢂ3ODVWLFꢂ6PDOOꢂ2XWOLQHꢂ7UDQVLVWRUꢂꢌ27ꢍꢂꢌ627ꢆꢄꢍ
(
(ꢃ
S
%
Sꢃ
'
Q
ꢃ
α
F
$
$ꢈ
φ
$ꢃ
/
β
8QLWV
,1&+(6<
120
0,//,0(7(56
'LPHQVLRQꢀ/LPLWV
0,1
0$;
0,1
120
ꢅ
0$;
Q
S
1XPEHUꢀRIꢀ3LQV
ꢅ
3LWFK
ꢁꢄꢇꢋ
ꢁꢄꢉꢅ
ꢁꢄꢆꢌ
ꢁꢄꢆꢇ
ꢁꢄꢄꢇ
ꢁꢃꢃꢄ
ꢁꢄꢌꢆ
ꢁꢃꢃꢌ
ꢁꢄꢃꢋ
ꢅ
ꢄꢁꢊꢅ
ꢃꢁꢊꢄ
Sꢃ
2XWVLGHꢀOHDGꢀSLWFKꢀꢍEDVLFꢎ
2YHUDOOꢀ+HLJKW
$
$ꢈ
$ꢃ
(
ꢁꢄꢇꢅ
ꢁꢄꢇꢅ
ꢁꢄꢄꢄ
ꢁꢃꢄꢈ
ꢁꢄꢅꢊ
ꢁꢃꢃꢄ
ꢁꢄꢃꢆ
ꢄ
ꢁꢄꢅꢉ
ꢄꢁꢊꢄ
ꢄꢁꢊꢄ
ꢃꢁꢃꢋ
ꢃꢁꢃꢄ
ꢄꢁꢄꢋ
ꢈꢁꢋꢄ
ꢃꢁꢌꢇ
ꢈꢁꢊꢅ
ꢄꢁꢆꢅ
ꢅ
ꢃꢁꢆꢅ
ꢃꢁꢇꢄ
ꢄꢁꢃꢅ
ꢇꢁꢄꢄ
ꢃꢁꢉꢅ
ꢇꢁꢃꢄ
ꢄꢁꢅꢅ
ꢃꢄ
0ROGHGꢀ3DFNDJHꢀ7KLFNQHVV
ꢁꢄꢅꢃ
ꢁꢄꢄꢌ
ꢁꢃꢃꢋ
ꢁꢄꢌꢊ
ꢁꢃꢈꢈ
ꢁꢄꢈꢈ
ꢃꢄ
6WDQGRII
ꢄꢁꢄꢄ
ꢈꢁꢌꢄ
ꢃꢁꢅꢄ
ꢈꢁꢋꢄ
ꢄꢁꢇꢅ
ꢄ
2YHUDOOꢀ:LGWK
0ROGHGꢀ3DFNDJHꢀ:LGWK
2YHUDOOꢀ/HQJWK
(ꢃ
'
)RRWꢀ/HQJWK
/
φ
)RRWꢀ$QJOH
F
/HDGꢀ7KLFNQHVV
/HDGꢀ:LGWK
ꢁꢄꢄꢆ
ꢁꢄꢃꢆ
ꢄ
ꢁꢄꢄꢌ
ꢁꢄꢃꢉ
ꢅ
ꢁꢄꢄꢋ
ꢁꢄꢈꢄ
ꢃꢄ
ꢄꢁꢄꢊ
ꢄꢁꢇꢅ
ꢄ
ꢄꢁꢃꢅ
ꢄꢁꢆꢇ
ꢅ
ꢄꢁꢈꢄ
ꢄꢁꢅꢄ
ꢃꢄ
%
α
β
0ROGꢀ'UDIWꢀ$QJOHꢀ7RS
0ROGꢀ'UDIWꢀ$QJOHꢀ%RWWRP
ꢄ
ꢅ
ꢃꢄ
ꢄ
ꢅ
ꢃꢄ
<ꢀ&RQWUROOLQJꢀ3DUDPHWHU
ꢀ6LJQLILFDQWꢀ&KDUDFWHULVWLF
1RWHVꢏ
'LPHQVLRQVꢀ'ꢀDQGꢀ(ꢃꢀGRꢀQRWꢀLQFOXGHꢀPROGꢀIODVKꢀRUꢀSURWUXVLRQVꢁꢀ0ROGꢀIODVKꢀRUꢀSURWUXVLRQVꢀVKDOOꢀQRWꢀH[FHHGꢀ
ꢁꢄꢃꢄ´ꢀꢍꢄꢁꢈꢅꢆPPꢎꢀSHUꢀVLGHꢁ
-('(&ꢀ(TXLYDOHQWꢏꢀꢀ02ꢂꢃꢉꢋ
'UDZLQJꢀ1Rꢁꢀ&ꢄꢆꢂꢄꢊꢃ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢃ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢊꢅ/HDGꢂ3ODVWLFꢂ'XDOꢂ,QꢅOLQHꢂꢌ3ꢍꢂ±ꢂꢄꢉꢉꢂPLOꢂꢌ3',3ꢍ
(ꢃ
'
ꢈ
Q
ꢃ
α
(
$ꢈ
$
/
F
$ꢃ
β
%ꢃ
%
S
H%
8QLWV
,1&+(6<
120
0,//,0(7(56
'LPHQVLRQꢀ/LPLWV
0,1
0$;
0,1
120
ꢋ
0$;
Q
S
1XPEHUꢀRIꢀ3LQV
3LWFK
ꢋ
ꢁꢃꢄꢄ
ꢁꢃꢅꢅ
ꢁꢃꢇꢄ
ꢈꢁꢅꢆ
7RSꢀWRꢀ6HDWLQJꢀ3ODQH
$
ꢁꢃꢆꢄ
ꢁꢃꢉꢄ
ꢇꢁꢅꢌ
ꢈꢁꢊꢈ
ꢇꢁꢊꢆ
ꢇꢁꢇꢄ
ꢆꢁꢇꢈ
0ROGHGꢀ3DFNDJHꢀ7KLFNQHVV
%DVHꢀWRꢀ6HDWLQJꢀ3ODQH
6KRXOGHUꢀWRꢀ6KRXOGHUꢀ:LGWK
0ROGHGꢀ3DFNDJHꢀ:LGWK
2YHUDOOꢀ/HQJWK
$ꢈ
$ꢃ
(
ꢁꢃꢃꢅ
ꢁꢄꢃꢅ
ꢁꢇꢄꢄ
ꢁꢈꢆꢄ
ꢁꢇꢌꢄ
ꢁꢃꢈꢅ
ꢁꢄꢄꢋ
ꢁꢄꢆꢅ
ꢁꢄꢃꢆ
ꢁꢇꢃꢄ
ꢅ
ꢁꢃꢆꢅ
ꢇꢁꢌꢋ
ꢄꢁꢇꢋ
ꢉꢁꢌꢈ
ꢌꢁꢃꢄ
ꢊꢁꢃꢆ
ꢇꢁꢃꢋ
ꢄꢁꢈꢄ
ꢃꢁꢃꢆ
ꢄꢁꢇꢌ
ꢉꢁꢋꢉ
ꢅ
ꢁꢇꢃꢇ
ꢁꢈꢅꢄ
ꢁꢇꢉꢇ
ꢁꢃꢇꢄ
ꢁꢄꢃꢈ
ꢁꢄꢅꢋ
ꢁꢄꢃꢋ
ꢁꢇꢉꢄ
ꢃꢄ
ꢁꢇꢈꢅ
ꢁꢈꢌꢄ
ꢁꢇꢋꢅ
ꢁꢃꢇꢅ
ꢁꢄꢃꢅ
ꢁꢄꢉꢄ
ꢁꢄꢈꢈ
ꢁꢆꢇꢄ
ꢃꢅ
ꢉꢁꢊꢆ
ꢌꢁꢇꢅ
ꢊꢁꢆꢌ
ꢇꢁꢇꢄ
ꢄꢁꢈꢊ
ꢃꢁꢆꢌ
ꢄꢁꢆꢌ
ꢊꢁꢆꢄ
ꢃꢄ
ꢋꢁꢈꢌ
ꢌꢁꢌꢄ
ꢊꢁꢉꢋ
ꢇꢁꢆꢇ
ꢄꢁꢇꢋ
ꢃꢁꢉꢋ
ꢄꢁꢅꢌ
ꢃꢄꢁꢊꢈ
ꢃꢅ
(ꢃ
'
7LSꢀWRꢀ6HDWLQJꢀ3ODQH
/HDGꢀ7KLFNQHVV
/
F
8SSHUꢀ/HDGꢀ:LGWK
%ꢃ
%
/RZHUꢀ/HDGꢀ:LGWK
2YHUDOOꢀ5RZꢀ6SDFLQJ
0ROGꢀ'UDIWꢀ$QJOHꢀ7RS
0ROGꢀ'UDIWꢀ$QJOHꢀ%RWWRP
H%
α
β
ꢅ
ꢃꢄ
ꢃꢅ
ꢅ
ꢃꢄ
ꢃꢅ
<ꢀ&RQWUROOLQJꢀ3DUDPHWHU
ꢀ6LJQLILFDQWꢀ&KDUDFWHULVWLF
1RWHVꢏ
'LPHQVLRQVꢀ'ꢀDQGꢀ(ꢃꢀGRꢀQRWꢀLQFOXGHꢀPROGꢀIODVKꢀRUꢀSURWUXVLRQVꢁꢀ0ROGꢀIODVKꢀRUꢀSURWUXVLRQVꢀVKDOOꢀQRWꢀH[FHHGꢀ
ꢁꢄꢃꢄ´ꢀꢍꢄꢁꢈꢅꢆPPꢎꢀSHUꢀVLGHꢁ
-('(&ꢀ(TXLYDOHQWꢏꢀꢀ06ꢂꢄꢄꢃ
'UDZLQJꢀ1Rꢁꢀ&ꢄꢆꢂꢄꢃꢋ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢁ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢊꢅ/HDGꢂ3ODVWLFꢂ6PDOOꢂ2XWOLQHꢂꢌ61ꢍꢂ± 1DUURZ4ꢂꢀꢋꢉꢂPLOꢂꢌ62,&ꢍ
(
(ꢃ
S
'
ꢈ
ꢃ
%
Q
K
α
ꢆꢅ°
F
$ꢈ
$
φ
β
/
$ꢃ
8QLWV
,1&+(6<
120
0,//,0(7(56
'LPHQVLRQꢀ/LPLWV
0,1
0$;
0,1
120
ꢋ
0$;
Q
S
1XPEHUꢀRIꢀ3LQV
3LWFK
ꢋ
ꢁꢄꢅꢄ
ꢁꢄꢌꢃ
ꢁꢄꢅꢌ
ꢁꢄꢄꢉ
ꢁꢈꢇꢉ
ꢁꢃꢅꢆ
ꢁꢃꢊꢇ
ꢁꢄꢃꢅ
ꢁꢄꢈꢅ
ꢆ
ꢃꢁꢈꢉ
2YHUDOOꢀ+HLJKW
$
ꢁꢄꢅꢇ
ꢁꢄꢌꢊ
ꢃꢁꢇꢅ
ꢃꢁꢇꢈ
ꢃꢁꢅꢅ
ꢃꢁꢆꢈ
ꢄꢁꢃꢋ
ꢌꢁꢄꢈ
ꢇꢁꢊꢃ
ꢆꢁꢊꢄ
ꢄꢁꢇꢋ
ꢄꢁꢌꢈ
ꢆ
ꢃꢁꢉꢅ
0ROGHGꢀ3DFNDJHꢀ7KLFNQHVV
6WDQGRII
$ꢈ
$ꢃ
(
ꢁꢄꢅꢈ
ꢁꢄꢄꢆ
ꢁꢈꢈꢋ
ꢁꢃꢆꢌ
ꢁꢃꢋꢊ
ꢁꢄꢃꢄ
ꢁꢄꢃꢊ
ꢄ
ꢁꢄꢌꢃ
ꢁꢄꢃꢄ
ꢁꢈꢆꢆ
ꢁꢃꢅꢉ
ꢁꢃꢊꢉ
ꢁꢄꢈꢄ
ꢁꢄꢇꢄ
ꢋ
ꢃꢁꢅꢅ
ꢄꢁꢈꢅ
ꢌꢁꢈꢄ
ꢇꢁꢊꢊ
ꢅꢁꢄꢄ
ꢄꢁꢅꢃ
ꢄꢁꢉꢌ
ꢋ
ꢄꢁꢃꢄ
ꢅꢁꢉꢊ
ꢇꢁꢉꢃ
ꢆꢁꢋꢄ
ꢄꢁꢈꢅ
ꢄꢁꢆꢋ
ꢄ
2YHUDOOꢀ:LGWK
0ROGHGꢀ3DFNDJHꢀ:LGWK
2YHUDOOꢀ/HQJWK
(ꢃ
'
&KDPIHUꢀ'LVWDQFH
)RRWꢀ/HQJWK
K
/
φ
)RRWꢀ$QJOH
F
/HDGꢀ7KLFNQHVV
/HDGꢀ:LGWK
ꢁꢄꢄꢋ
ꢁꢄꢃꢇ
ꢄ
ꢁꢄꢄꢊ
ꢁꢄꢃꢉ
ꢃꢈ
ꢁꢄꢃꢄ
ꢁꢄꢈꢄ
ꢃꢅ
ꢄꢁꢈꢄ
ꢄꢁꢇꢇ
ꢄ
ꢄꢁꢈꢇ
ꢄꢁꢆꢈ
ꢃꢈ
ꢄꢁꢈꢅ
ꢄꢁꢅꢃ
ꢃꢅ
%
α
β
0ROGꢀ'UDIWꢀ$QJOHꢀ7RS
0ROGꢀ'UDIWꢀ$QJOHꢀ%RWWRP
ꢄ
ꢃꢈ
ꢃꢅ
ꢄ
ꢃꢈ
ꢃꢅ
<ꢀ&RQWUROOLQJꢀ3DUDPHWHU
ꢀ6LJQLILFDQWꢀ&KDUDFWHULVWLF
1RWHVꢏ
'LPHQVLRQVꢀ'ꢀDQGꢀ(ꢃꢀGRꢀQRWꢀLQFOXGHꢀPROGꢀIODVKꢀRUꢀSURWUXVLRQVꢁꢀ0ROGꢀIODVKꢀRUꢀSURWUXVLRQVꢀVKDOOꢀQRWꢀH[FHHGꢀ
ꢁꢄꢃꢄ´ꢀꢍꢄꢁꢈꢅꢆPPꢎꢀSHUꢀVLGHꢁ
-('(&ꢀ(TXLYDOHQWꢏꢀꢀ06ꢂꢄꢃꢈ
'UDZLQJꢀ1Rꢁꢀ&ꢄꢆꢂꢄꢅꢉ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢍ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢊꢅ/HDGꢂ3ODVWLFꢂ7KLQꢂ6KULQNꢂ6PDOOꢂ2XWOLQHꢂꢌ67ꢍꢂ±ꢂꢇꢁꢇꢂPPꢂꢌ76623ꢍ
(
(ꢃ
S
'
ꢈ
ꢃ
Q
%
α
$
F
$ꢃ
$ꢈ
φ
β
/
8QLWV
,1&+(6
120
0,//,0(7(56<
'LPHQVLRQꢀ/LPLWV
0,1
0$;
0,1
120
ꢋ
0$;
Q
S
1XPEHUꢀRIꢀ3LQV
3LWFK
ꢋ
ꢁꢄꢈꢌ
ꢄꢁꢌꢅ
2YHUDOOꢀ+HLJKW
$
ꢁꢄꢆꢇ
ꢃꢁꢃꢄ
ꢄꢁꢊꢅ
ꢄꢁꢃꢅ
ꢌꢁꢅꢄ
ꢆꢁꢅꢄ
ꢇꢁꢃꢄ
ꢄꢁꢉꢄ
ꢋ
0ROGHGꢀ3DFNDJHꢀ7KLFNQHVV
6WDQGRII
$ꢈ
$ꢃ
(
ꢁꢄꢇꢇ
ꢁꢄꢇꢅ
ꢁꢄꢄꢆ
ꢁꢈꢅꢃ
ꢁꢃꢉꢇ
ꢁꢃꢃꢋ
ꢁꢄꢈꢆ
ꢆ
ꢁꢄꢇꢉ
ꢁꢄꢄꢌ
ꢁꢈꢅꢌ
ꢁꢃꢉꢉ
ꢁꢃꢈꢈ
ꢁꢄꢈꢋ
ꢋ
ꢄꢁꢋꢅ
ꢄꢁꢄꢅ
ꢄꢁꢊꢄ
ꢄꢁꢃꢄ
ꢌꢁꢇꢋ
ꢆꢁꢆꢄ
ꢇꢁꢄꢄ
ꢄꢁꢌꢄ
ꢆ
ꢁꢄꢄꢈ
ꢁꢈꢆꢌ
ꢁꢃꢌꢊ
ꢁꢃꢃꢆ
ꢁꢄꢈꢄ
ꢄ
2YHUDOOꢀ:LGWK
ꢌꢁꢈꢅ
ꢆꢁꢇꢄ
ꢈꢁꢊꢄ
ꢄꢁꢅꢄ
ꢄ
0ROGHGꢀ3DFNDJHꢀ:LGWK
0ROGHGꢀ3DFNDJHꢀ/HQJWK
)RRWꢀ/HQJWK
(ꢃ
'
/
φ
)RRWꢀ$QJOH
F
/HDGꢀ7KLFNQHVV
ꢁꢄꢄꢆ
ꢁꢄꢄꢉ
ꢄ
ꢁꢄꢄꢌ
ꢁꢄꢃꢄ
ꢅ
ꢁꢄꢄꢋ
ꢁꢄꢃꢈ
ꢃꢄ
ꢄꢁꢄꢊ
ꢄꢁꢃꢊ
ꢄ
ꢄꢁꢃꢅ
ꢄꢁꢈꢅ
ꢅ
ꢄꢁꢈꢄ
ꢄꢁꢇꢄ
ꢃꢄ
/HDGꢀ:LGWK
%
α
β
0ROGꢀ'UDIWꢀ$QJOHꢀ7RS
0ROGꢀ'UDIWꢀ$QJOHꢀ%RWWRP
ꢄ
ꢅ
ꢃꢄ
ꢄ
ꢅ
ꢃꢄ
<ꢀ&RQWUROOLQJꢀ3DUDPHWHU
ꢀ6LJQLILFDQWꢀ&KDUDFWHULVWLF
1RWHVꢏ
'LPHQVLRQVꢀ'ꢀDQGꢀ(ꢃꢀGRꢀQRWꢀLQFOXGHꢀPROGꢀIODVKꢀRUꢀSURWUXVLRQVꢁꢀ0ROGꢀIODVKꢀRUꢀSURWUXVLRQVꢀVKDOOꢀQRWꢀH[FHHGꢀ
ꢁꢄꢄꢅ´ꢀꢍꢄꢁꢃꢈꢉPPꢎꢀSHUꢀVLGHꢁ
-('(&ꢀ(TXLYDOHQWꢏꢀꢀ02ꢂꢃꢅꢇ
'UDZLQJꢀ1Rꢁꢀ&ꢄꢆꢂꢄꢋꢌ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢋ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢀꢇꢅ/HDGꢂ3ODVWLFꢂ'XDOꢂ,QꢅOLQHꢂꢌ3ꢍꢂ± ꢄꢉꢉꢂPLOꢂꢌ3',3ꢍ
(ꢃ
'
ꢈ
Q
ꢃ
α
(
$ꢈ
$
/
F
$ꢃ
%ꢃ
β
H%
S
%
8QLWV
,1&+(6<
120
0,//,0(7(56
'LPHQVLRQꢀ/LPLWV
0,1
0$;
0,1
120
ꢃꢆ
0$;
Q
S
1XPEHUꢀRIꢀ3LQV
3LWFK
ꢃꢆ
ꢁꢃꢄꢄ
ꢁꢃꢅꢅ
ꢁꢃꢇꢄ
ꢈꢁꢅꢆ
7RSꢀWRꢀ6HDWLQJꢀ3ODQH
$
ꢁꢃꢆꢄ
ꢁꢃꢉꢄ
ꢇꢁꢅꢌ
ꢈꢁꢊꢈ
ꢄꢁꢇꢋ
ꢉꢁꢌꢈ
ꢌꢁꢃꢄ
ꢃꢋꢁꢋꢄ
ꢇꢁꢃꢋ
ꢄꢁꢈꢄ
ꢃꢁꢃꢆ
ꢄꢁꢇꢌ
ꢉꢁꢋꢉ
ꢅ
ꢇꢁꢊꢆ
ꢇꢁꢇꢄ
ꢆꢁꢇꢈ
0ROGHGꢀ3DFNDJHꢀ7KLFNQHVV
%DVHꢀWRꢀ6HDWLQJꢀ3ODQH
6KRXOGHUꢀWRꢀ6KRXOGHUꢀ:LGWK
0ROGHGꢀ3DFNDJHꢀ:LGWK
2YHUDOOꢀ/HQJWK
$ꢈ
$ꢃ
(
ꢁꢃꢃꢅ
ꢁꢄꢃꢅ
ꢁꢇꢄꢄ
ꢁꢈꢆꢄ
ꢁꢉꢆꢄ
ꢁꢃꢈꢅ
ꢁꢄꢄꢋ
ꢁꢄꢆꢅ
ꢁꢄꢃꢆ
ꢁꢇꢃꢄ
ꢅ
ꢁꢃꢆꢅ
ꢇꢁꢌꢋ
ꢁꢇꢃꢇ
ꢁꢈꢅꢄ
ꢁꢉꢅꢄ
ꢁꢃꢇꢄ
ꢁꢄꢃꢈ
ꢁꢄꢅꢋ
ꢁꢄꢃꢋ
ꢁꢇꢉꢄ
ꢃꢄ
ꢁꢇꢈꢅ
ꢁꢈꢌꢄ
ꢁꢉꢌꢄ
ꢁꢃꢇꢅ
ꢁꢄꢃꢅ
ꢁꢄꢉꢄ
ꢁꢄꢈꢈ
ꢁꢆꢇꢄ
ꢃꢅ
ꢉꢁꢊꢆ
ꢌꢁꢇꢅ
ꢃꢊꢁꢄꢅ
ꢇꢁꢇꢄ
ꢄꢁꢈꢊ
ꢃꢁꢆꢌ
ꢄꢁꢆꢌ
ꢊꢁꢆꢄ
ꢃꢄ
ꢋꢁꢈꢌ
ꢌꢁꢌꢄ
ꢃꢊꢁꢇꢄ
ꢇꢁꢆꢇ
ꢄꢁꢇꢋ
ꢃꢁꢉꢋ
ꢄꢁꢅꢌ
ꢃꢄꢁꢊꢈ
ꢃꢅ
(ꢃ
'
7LSꢀWRꢀ6HDWLQJꢀ3ODQH
/HDGꢀ7KLFNQHVV
/
F
8SSHUꢀ/HDGꢀ:LGWK
%ꢃ
%
/RZHUꢀ/HDGꢀ:LGWK
2YHUDOOꢀ5RZꢀ6SDFLQJ
0ROGꢀ'UDIWꢀ$QJOHꢀ7RS
0ROGꢀ'UDIWꢀ$QJOHꢀ%RWWRP
H%
α
β
ꢅ
ꢃꢄ
ꢃꢅ
ꢅ
ꢃꢄ
ꢃꢅ
<ꢀ&RQWUROOLQJꢀ3DUDPHWHU
ꢀ6LJQLILFDQWꢀ&KDUDFWHULVWLF
1RWHVꢏ
'LPHQVLRQVꢀ'ꢀDQGꢀ(ꢃꢀGRꢀQRWꢀLQFOXGHꢀPROGꢀIODVKꢀRUꢀSURWUXVLRQVꢁꢀ0ROGꢀIODVKꢀRUꢀSURWUXVLRQVꢀVKDOOꢀQRWꢀH[FHHGꢀ
ꢁꢄꢃꢄ´ꢀꢍꢄꢁꢈꢅꢆPPꢎꢀSHUꢀVLGHꢁ
-('(&ꢀ(TXLYDOHQWꢏꢀꢀ06ꢂꢄꢄꢃ
'UDZLQJꢀ1Rꢁꢀ&ꢄꢆꢂꢄꢄꢅ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢉ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢀꢇꢅ/HDGꢂ3ODVWLFꢂ6PDOOꢂ2XWOLQHꢂꢌ6/ꢍꢂ± 1DUURZ4ꢂꢀꢋꢉꢂPLOꢂꢌ62,&ꢍ
(
(ꢃ
S
'
ꢈ
%
Q
ꢃ
α
K
ꢆꢅ°
F
$ꢈ
$
φ
$ꢃ
/
β
8QLWV
,1&+(6<
120
0,//,0(7(56
'LPHQVLRQꢀ/LPLWV
0,1
0$;
0,1
120
ꢃꢆ
0$;
Q
S
1XPEHUꢀRIꢀ3LQV
3LWFK
ꢃꢆ
ꢁꢄꢅꢄ
ꢁꢄꢌꢃ
ꢁꢄꢅꢌ
ꢁꢄꢄꢉ
ꢁꢈꢇꢌ
ꢁꢃꢅꢆ
ꢁꢇꢆꢈ
ꢁꢄꢃꢅ
ꢁꢄꢇꢇ
ꢆ
ꢃꢁꢈꢉ
2YHUDOOꢀ+HLJKW
$
ꢁꢄꢅꢇ
ꢁꢄꢌꢊ
ꢃꢁꢇꢅ
ꢃꢁꢇꢈ
ꢃꢁꢅꢅ
ꢃꢁꢆꢈ
ꢄꢁꢃꢋ
ꢅꢁꢊꢊ
ꢇꢁꢊꢄ
ꢋꢁꢌꢊ
ꢄꢁꢇꢋ
ꢄꢁꢋꢆ
ꢆ
ꢃꢁꢉꢅ
0ROGHGꢀ3DFNDJHꢀ7KLFNQHVV
6WDQGRII
$ꢈ
$ꢃ
(
ꢁꢄꢅꢈ
ꢁꢄꢄꢆ
ꢁꢈꢈꢋ
ꢁꢃꢅꢄ
ꢁꢇꢇꢉ
ꢁꢄꢃꢄ
ꢁꢄꢃꢌ
ꢄ
ꢁꢄꢌꢃ
ꢁꢄꢃꢄ
ꢁꢈꢆꢆ
ꢁꢃꢅꢉ
ꢁꢇꢆꢉ
ꢁꢄꢈꢄ
ꢁꢄꢅꢄ
ꢋ
ꢃꢁꢅꢅ
ꢄꢁꢈꢅ
ꢌꢁꢈꢄ
ꢇꢁꢊꢊ
ꢋꢁꢋꢃ
ꢄꢁꢅꢃ
ꢃꢁꢈꢉ
ꢋ
ꢄꢁꢃꢄ
ꢅꢁꢉꢊ
ꢇꢁꢋꢃ
ꢋꢁꢅꢌ
ꢄꢁꢈꢅ
ꢄꢁꢆꢃ
ꢄ
2YHUDOOꢀ:LGWK
0ROGHGꢀ3DFNDJHꢀ:LGWK
2YHUDOOꢀ/HQJWK
(ꢃ
'
&KDPIHUꢀ'LVWDQFH
)RRWꢀ/HQJWK
K
/
φ
)RRWꢀ$QJOH
F
/HDGꢀ7KLFNQHVV
/HDGꢀ:LGWK
ꢁꢄꢄꢋ
ꢁꢄꢃꢆ
ꢄ
ꢁꢄꢄꢊ
ꢁꢄꢃꢉ
ꢃꢈ
ꢁꢄꢃꢄ
ꢁꢄꢈꢄ
ꢃꢅ
ꢄꢁꢈꢄ
ꢄꢁꢇꢌ
ꢄ
ꢄꢁꢈꢇ
ꢄꢁꢆꢈ
ꢃꢈ
ꢄꢁꢈꢅ
ꢄꢁꢅꢃ
ꢃꢅ
%
α
β
0ROGꢀ'UDIWꢀ$QJOHꢀ7RS
0ROGꢀ'UDIWꢀ$QJOHꢀ%RWWRP
ꢄ
ꢃꢈ
ꢃꢅ
ꢄ
ꢃꢈ
ꢃꢅ
<ꢀ&RQWUROOLQJꢀ3DUDPHWHU
ꢀ6LJQLILFDQWꢀ&KDUDFWHULVWLF
1RWHVꢏ
'LPHQVLRQVꢀ'ꢀDQGꢀ(ꢃꢀGRꢀQRWꢀLQFOXGHꢀPROGꢀIODVKꢀRUꢀSURWUXVLRQVꢁꢀ0ROGꢀIODVKꢀRUꢀSURWUXVLRQVꢀVKDOOꢀQRWꢀH[FHHGꢀ
ꢁꢄꢃꢄ´ꢀꢍꢄꢁꢈꢅꢆPPꢎꢀSHUꢀVLGHꢁ
-('(&ꢀ(TXLYDOHQWꢏꢀꢀ06ꢂꢄꢃꢈ
'UDZLQJꢀ1Rꢁꢀ&ꢄꢆꢂꢄꢌꢅ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢎ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
ꢀꢇꢅ/HDGꢂ3ODVWLFꢂ7KLQꢂ6KULQNꢂ6PDOOꢂ2XWOLQHꢂꢌ67ꢍꢂ±ꢂꢇꢁꢇꢂPPꢂꢌ76623ꢍ
(
(ꢃ
S
'
ꢈ
ꢃ
Q
%
α
$
F
φ
$ꢃ
$ꢈ
β
/
8QLWV
,1&+(6
120
0,//,0(7(56<
'LPHQVLRQꢀ/LPLWV
0,1
0$;
0,1
120
ꢃꢆ
0$;
Q
S
1XPEHUꢀRIꢀ3LQV
3LWFK
ꢃꢆ
ꢁꢄꢈꢌ
ꢄꢁꢌꢅ
2YHUDOOꢀ+HLJKW
$
ꢁꢄꢆꢇ
ꢃꢁꢃꢄ
ꢄꢁꢊꢅ
ꢄꢁꢃꢅ
ꢌꢁꢅꢄ
ꢆꢁꢅꢄ
ꢅꢁꢃꢄ
ꢄꢁꢉꢄ
ꢋ
0ROGHGꢀ3DFNDJHꢀ7KLFNQHVV
6WDQGRII
$ꢈ
$ꢃ
(
ꢁꢄꢇꢇ
ꢁꢄꢄꢈ
ꢁꢈꢆꢌ
ꢁꢃꢌꢊ
ꢁꢃꢊꢇ
ꢁꢄꢈꢄ
ꢄ
ꢁꢄꢇꢅ
ꢁꢄꢄꢆ
ꢁꢈꢅꢃ
ꢁꢃꢉꢇ
ꢁꢃꢊꢉ
ꢁꢄꢈꢆ
ꢆ
ꢁꢄꢇꢉ
ꢁꢄꢄꢌ
ꢁꢈꢅꢌ
ꢁꢃꢉꢉ
ꢁꢈꢄꢃ
ꢁꢄꢈꢋ
ꢋ
ꢄꢁꢋꢅ
ꢄꢁꢄꢅ
ꢄꢁꢊꢄ
ꢄꢁꢃꢄ
ꢌꢁꢇꢋ
ꢆꢁꢆꢄ
ꢅꢁꢄꢄ
ꢄꢁꢌꢄ
ꢆ
2YHUDOOꢀ:LGWK
ꢌꢁꢈꢅ
ꢆꢁꢇꢄ
ꢆꢁꢊꢄ
ꢄꢁꢅꢄ
ꢄ
0ROGHGꢀ3DFNDJHꢀ:LGWK
0ROGHGꢀ3DFNDJHꢀ/HQJWK
)RRWꢀ/HQJWK
(ꢃ
'
/
φ
)RRWꢀ$QJOH
F
/HDGꢀ7KLFNQHVV
ꢁꢄꢄꢆ
ꢁꢄꢄꢉ
ꢄ
ꢁꢄꢄꢌ
ꢁꢄꢃꢄ
ꢅ
ꢁꢄꢄꢋ
ꢁꢄꢃꢈ
ꢃꢄ
ꢄꢁꢄꢊ
ꢄꢁꢃꢊ
ꢄ
ꢄꢁꢃꢅ
ꢄꢁꢈꢅ
ꢅ
ꢄꢁꢈꢄ
ꢄꢁꢇꢄ
ꢃꢄ
/HDGꢀ:LGWK
%ꢃ
α
β
0ROGꢀ'UDIWꢀ$QJOHꢀ7RS
0ROGꢀ'UDIWꢀ$QJOHꢀ%RWWRP
ꢄ
ꢅ
ꢃꢄ
ꢄ
ꢅ
ꢃꢄ
<ꢀ&RQWUROOLQJꢀ3DUDPHWHU
ꢀ6LJQLILFDQWꢀ&KDUDFWHULVWLF
1RWHVꢏ
'LPHQVLRQVꢀ'ꢀDQGꢀ(ꢃꢀGRꢀQRWꢀLQFOXGHꢀPROGꢀIODVKꢀRUꢀSURWUXVLRQVꢁꢀ0ROGꢀIODVKꢀRUꢀSURWUXVLRQVꢀVKDOOꢀQRWꢀH[FHHGꢀ
ꢁꢄꢄꢅ´ꢀꢍꢄꢁꢃꢈꢉPPꢎꢀSHUꢀVLGHꢁ
-('(&ꢀ(TXLYDOHQWꢏꢀꢀ02ꢂꢃꢅꢇ
'UDZLQJꢀ1Rꢁꢀ&ꢄꢆꢂꢄꢋꢉ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢅ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
127(6ꢊ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢊ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
6\VWHPVꢂ,QIRUPDWLRQꢂDQGꢂ8SJUDGHꢂ+RWꢂ/LQHꢂ
21ꢋ/,1(ꢀ6833257
7KHꢀ6\VWHPVꢀ,QIRUPDWLRQꢀDQGꢀ8SJUDGHꢀ/LQHꢀSURYLGHV
V\VWHPꢀ XVHUVꢀ Dꢀ OLVWLQJꢀ RIꢀ WKHꢀ ODWHVWꢀ YHUVLRQVꢀ RIꢀ DOOꢀ RI
ꢉLFURFKLSꢕVꢀ GHYHORSPHQWꢀ V\VWHPVꢀ VRIWZDUHꢀ SURGXFWVꢈ
3OXVꢃꢀWKLVꢀOLQHꢀSURYLGHVꢀLQIRUPDWLRQꢀRQꢀKRZꢀFXVWRPHUV
FDQꢀ UHFHLYHꢀ DQ\ꢀ FXUUHQWO\ꢀ DYDLODEOHꢀ XSJUDGHꢀ NLWVꢈ7KH
+RWꢀ/LQHꢀꢋXPEHUVꢀDUHꢄꢀ
ꢉLFURFKLSꢀ SURYLGHVꢀ RQꢆOLQHꢀ VXSSRUWꢀ RQꢀ WKHꢀ ꢉLFURFKLS
:RUOGꢀ:LGHꢀ:HEꢀ0:::1ꢀVLWHꢈ
7KHꢀZHEꢀVLWHꢀLVꢀXVHGꢀE\ꢀꢉLFURFKLSꢀDVꢀDꢀPHDQVꢀWRꢀPDNH
ILOHVꢀDQGꢀLQIRUPDWLRQꢀHDVLO\ꢀDYDLODEOHꢀWRꢀFXVWRPHUVꢈꢀ7R
YLHZꢀWKHꢀVLWHꢃꢀWKHꢀXVHUꢀPXVWꢀKDYHꢀDFFHVVꢀWRꢀWKHꢀ,QWHUQHW
DQGꢀ Dꢀ ZHEꢀ EURZVHUꢃꢀ VXFKꢀ DVꢀ ꢋHWVFDSHꢀ RUꢀ ꢉLFURVRIW
([SORUHUꢈꢀ )LOHVꢀ DUHꢀ DOVRꢀ DYDLODEOHꢀ IRUꢀ )73ꢀ GRZQORDG
IURPꢀRXUꢀ)73ꢀVLWHꢈ
ꢎꢆꢇꢅꢅꢆꢌꢂꢂꢆꢁꢐꢏꢂꢀIRUꢀ8ꢈ6ꢈꢀDQGꢀPRVWꢀRIꢀ&DQDGDꢃꢀDQGꢀ
ꢎꢆꢏꢇꢅꢆꢌꢍꢁꢆꢌꢐꢅꢁꢀIRUꢀWKHꢀUHVWꢀRIꢀWKHꢀZRUOGꢈ
ꢄꢃꢇꢄꢄꢃ
& RQ QH F W LQJ ꢂW RꢂW KH ꢂ0 LF URF K LSꢂ, QW H UQH W ꢂ: H Eꢂ6 LW H ꢂꢂꢂꢂꢂꢂ
7KHꢀ ꢉLFURFKLSꢀ ZHEꢀ VLWHꢀ LVꢀ DYDLODEOHꢀ E\ꢀ XVLQJꢀ \RXU
IDYRULWHꢀ,QWHUQHWꢀEURZVHUꢀWRꢀDWWDFKꢀWRꢄꢀ
ZZZꢌPLFURFKLSꢌFRP
7KHꢀILOHꢀWUDQVIHUꢀVLWHꢀLVꢀDYDLODEOHꢀE\ꢀXVLQJꢀDQꢀ)73ꢀVHUꢆ
YLFHꢀWRꢀFRQQHFWꢀWRꢄꢀ
IWSꢋꢍꢍIWSꢌPLFURFKLSꢌFRP
7KHꢀZHEꢀVLWHꢀDQGꢀILOHꢀWUDQVIHUꢀVLWHꢀSURYLGHꢀDꢀYDULHW\ꢀRI
VHUYLFHVꢈꢀ 8VHUVꢀ PD\ꢀ GRZQORDGꢀ ILOHVꢀ IRUꢀ WKHꢀ ODWHVW
'HYHORSPHQWꢀ 7RROVꢃꢀ 'DWDꢀ 6KHHWVꢃꢀ $SSOLFDWLRQꢀ ꢋRWHVꢃ
8VHUꢕVꢀ*XLGHVꢃꢀ$UWLFOHVꢀDQGꢀ6DPSOHꢀ3URJUDPVꢈꢀ$ꢀYDULꢆ
HW\ꢀRIꢀꢉLFURFKLSꢀVSHFLILFꢀEXVLQHVVꢀLQIRUPDWLRQꢀLVꢀDOVR
DYDLODEOHꢃꢀLQFOXGLQJꢀOLVWLQJVꢀRIꢀꢉLFURFKLSꢀVDOHVꢀRIILFHVꢃ
GLVWULEXWRUVꢀ DQGꢀ IDFWRU\ꢀ UHSUHVHQWDWLYHVꢈꢀ 2WKHUꢀ GDWD
DYDLODEOHꢀIRUꢀFRQVLGHUDWLRQꢀLVꢄ
/DWHVWꢀꢉLFURFKLSꢀ3UHVVꢀ5HOHDVHV
7HFKQLFDOꢀ6XSSRUWꢀ6HFWLRQꢀZLWKꢀ)UHTXHQWO\ꢀ$VNHGꢀ
4XHVWLRQVꢀ
'HVLJQꢀ7LSV
'HYLFHꢀ(UUDWD
-REꢀ3RVWLQJV
ꢉLFURFKLSꢀ&RQVXOWDQWꢀ3URJUDPꢀꢉHPEHUꢀ/LVWLQJ
/LQNVꢀWRꢀRWKHUꢀXVHIXOꢀZHEꢀVLWHVꢀUHODWHGꢀWRꢀ
ꢉLFURFKLSꢀ3URGXFWV
&RQIHUHQFHVꢀIRUꢀSURGXFWVꢃꢀ'HYHORSPHQWꢀ6\VWHPVꢃꢀ
WHFKQLFDOꢀLQIRUPDWLRQꢀDQGꢀPRUH
/LVWLQJꢀRIꢀVHPLQDUVꢀDQGꢀHYHQWV
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢁꢌ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
5($'(5ꢀ5(63216(
,WꢀLVꢀRXUꢀLQWHQWLRQꢀWRꢀSURYLGHꢀ\RXꢀZLWKꢀWKHꢀEHVWꢀGRFXPHQWDWLRQꢀSRVVLEOHꢀWRꢀHQVXUHꢀVXFFHVVIXOꢀXVHꢀRIꢀ\RXUꢀꢉLFURFKLSꢀSURGꢆ
XFWꢈꢀꢀ,Iꢀ\RXꢀZLVKꢀWRꢀSURYLGHꢀ\RXUꢀFRPPHQWVꢀRQꢀRUJDQL]DWLRQꢃꢀFODULW\ꢃꢀVXEMHFWꢀPDWWHUꢃꢀDQGꢀZD\VꢀLQꢀZKLFKꢀRXUꢀGRFXPHQWDWLRQ
FDQꢀEHWWHUꢀVHUYHꢀ\RXꢃꢀSOHDVHꢀ)$;ꢀ\RXUꢀFRPPHQWVꢀWRꢀWKHꢀ7HFKQLFDOꢀ3XEOLFDWLRQVꢀꢉDQDJHUꢀDWꢀ0ꢏꢇꢅ1ꢀꢌꢍꢁꢆꢏꢎꢂꢅꢈ
3OHDVHꢀOLVWꢀWKHꢀIROORZLQJꢀLQIRUPDWLRQꢃꢀDQGꢀXVHꢀWKLVꢀRXWOLQHꢀWRꢀSURYLGHꢀXVꢀZLWKꢀ\RXUꢀFRPPHQWVꢀDERXWꢀWKLVꢀ'DWDꢀ6KHHWꢈ
7Rꢄ
7HFKQLFDOꢀ3XEOLFDWLRQVꢀꢉDQDJHU
5HDGHUꢀ5HVSRQVH
7RWDOꢀ3DJHVꢀ6HQW
5(ꢄ
)URPꢄ
ꢋDPH
&RPSDQ\
$GGUHVV
&LW\ꢀꢑꢀ6WDWHꢀꢑꢀ=,3ꢀꢑꢀ&RXQWU\
7HOHSKRQHꢄꢀ0BBBBBBB1ꢀBBBBBBBBBꢀꢆꢀBBBBBBBBB
)$;ꢄꢀ0BBBBBB1ꢀBBBBBBBBBꢀꢆꢀBBBBBBBBB
$SSOLFDWLRQꢀ0RSWLRQDO1ꢄ
:RXOGꢀ\RXꢀOLNHꢀDꢀUHSO\"ꢀꢀꢀꢀꢀꢀꢀ<ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢋ
/LWHUDWXUHꢀꢋXPEHUꢄꢀ
'6ꢎꢎꢎꢄꢄ&
'HYLFHꢄꢀ
0&3ꢀꢁꢀꢍꢀꢁꢄꢍꢀꢁꢅꢍꢀꢁꢆ
4XHVWLRQVꢄ
ꢎꢈ :KDWꢀDUHꢀWKHꢀEHVWꢀIHDWXUHVꢀRIꢀWKLVꢀGRFXPHQW"
ꢁꢈ +RZꢀGRHVꢀWKLVꢀGRFXPHQWꢀPHHWꢀ\RXUꢀKDUGZDUHꢀDQGꢀVRIWZDUHꢀGHYHORSPHQWꢀQHHGV"
ꢐꢈ 'Rꢀ\RXꢀILQGꢀWKHꢀRUJDQL]DWLRQꢀRIꢀWKLVꢀGDWDꢀVKHHWꢀHDV\ꢀWRꢀIROORZ"ꢀ,IꢀQRWꢃꢀZK\"
ꢏꢈ :KDWꢀDGGLWLRQVꢀWRꢀWKHꢀGDWDꢀVKHHWꢀGRꢀ\RXꢀWKLQNꢀZRXOGꢀHQKDQFHꢀWKHꢀVWUXFWXUHꢀDQGꢀVXEMHFW"
ꢂꢈ :KDWꢀGHOHWLRQVꢀIURPꢀWKHꢀGDWDꢀVKHHWꢀFRXOGꢀEHꢀPDGHꢀZLWKRXWꢀDIIHFWLQJꢀWKHꢀRYHUDOOꢀXVHIXOQHVV"
ꢊꢈ ,VꢀWKHUHꢀDQ\ꢀLQFRUUHFWꢀRUꢀPLVOHDGLQJꢀLQIRUPDWLRQꢀ0ZKDWꢀDQGꢀZKHUH1"
ꢌꢈ +RZꢀZRXOGꢀ\RXꢀLPSURYHꢀWKLVꢀGRFXPHQW"
ꢇꢈ +RZꢀZRXOGꢀ\RXꢀLPSURYHꢀRXUꢀVRIWZDUHꢃꢀV\VWHPVꢃꢀDQGꢀVLOLFRQꢀSURGXFWV"
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢍꢂ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
127(6ꢎ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢍꢃ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
127(6ꢎ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢍꢁ
ꢀ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
127(6ꢎ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢍꢍ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
352'8&7ꢀ,'(17,),&$7,21ꢀ6<67(0
7RꢀRUGHUꢀRUꢀREWDLQꢀLQIRUPDWLRQ+ꢀHꢄJꢄ+ꢀRQꢀSULFLQJꢀRUꢀGHOLYHU\+ꢀUHIHUꢀWRꢀWKHꢀIDFWRU\ꢀRUꢀWKHꢀOLVWHGꢀVDOHVꢀRIILFHꢄ
3$57ꢁ12ꢀ
'HYLFH
;
ꢆ;;
([DPSOHVꢇ
7HPSHUDWXUH 3DFNDJH
5DQJH
Dꢀ
Eꢀ
0&3ꢌꢄꢌꢂ,ꢐ3ꢀ,QGXVWULDOꢁ7HPSꢂꢃꢁ3',3ꢁSDFNDJH
0&3ꢌꢄꢌ7ꢂ,ꢐ3ꢀ7DSHꢀDQGꢀ5HHOꢒꢀ,QGXVWULDOꢁ7HPSꢂꢃꢁ
3',3ꢁSDFNDJH
ꢀꢀꢀ
'HYLFH
Fꢀ
Gꢀ
Hꢀ
0&3ꢄꢅꢄꢆ,ꢇ61ꢁ,QGXVWULDOꢁ7HPSꢂꢃꢁ62,&ꢁSDFNꢆ
DJH
0&3ꢌꢄꢌ
6LQJOHꢀ2SHUDWLRQDOꢀ$PSOLILHU
0&3ꢌꢄꢌ7 6LQJOHꢀ2SHUDWLRQDOꢀ$PSOLILHU
ꢍ7DSHꢀDQGꢀ5HHOꢂ62,&ꢐ76623ꢎ
0&3ꢌꢄꢉ
0&3ꢌꢄꢉ7 'XDOꢀ2SHUDWLRQDOꢀ$PSOLILHU
ꢍ7DSHꢀDQGꢀ5HHOꢂ62,&ꢐ76623ꢎ
0&3ꢄꢅꢄ7ꢂ,ꢐ61ꢀ7DSHꢀDQGꢀ5HHOꢒꢀ,QGXVWULDOꢀ7HPSꢁꢒꢀ
62,&ꢀSDFNDJH
'XDOꢀ2SHUDWLRQDOꢀ$PSOLILHU
0&3ꢄꢅꢄꢆ,ꢇ67ꢁ,QGXVWULDOꢁ7HPSꢂꢃꢁ76623ꢁSDFNꢆ
DJH
0&3ꢌꢄꢋ
6LQJOHꢀ2SHUDWLRQDOꢀ$PSOLILHUꢀZꢐ&6ꢀ)XQFWLRQ
Iꢀ
0&3ꢄꢅꢄ7ꢆ,ꢇ67ꢁ 7DSHꢁ DQGꢁ 5HHOꢃꢁ ,QGXVWULDO
7HPSꢂꢃꢁ76623ꢁSDFNDJH
0&3ꢌꢄꢋ7 6LQJOHꢀ2SHUDWLRQDOꢀ$PSOLILHUꢀZꢐ&6ꢀ)XQFWLRQ
ꢍ7DSHꢀDQGꢀ5HHOꢂ62,&ꢐ76623ꢎ
Jꢀ
Kꢀ
Lꢀ
0&3ꢄꢅꢄꢆ,ꢇ27ꢁ,QGXVWULDOꢀ7HPSꢁꢒꢀ627ꢂꢈꢇꢀSDFNꢂ
0&3ꢌꢄꢊ
4XDGꢀ2SHUDWLRQDOꢀ$PSOLILHU
0&3ꢌꢄꢊ7 4XDGꢀ2SHUDWLRQDOꢀ$PSOLILHU
ꢍ7DSHꢀDQGꢀ5HHOꢂ62,&ꢐ76623ꢎ
DJH
0&3ꢄꢅꢄ7ꢆ,ꢇ27ꢁ 7DSHꢀ DQGꢀ 5HHOꢒꢀ ,QGXVWULDO
7HPSꢁꢒꢀ627ꢂꢈꢇꢀSDFNDJH
7HPSHUDWXUHꢀ5DQJH
3DFNDJH
,
ꢀꢂꢆꢄ°&ꢀWRꢀꢑꢋꢅ°&
0&3ꢄꢅꢈꢂ,ꢐ3ꢀ ,QGXVWULDOꢁ 7HPSꢂꢃꢁ 3',3ꢁ SDFNꢆ
DJH
Mꢀ
0&3ꢄꢅꢈ7ꢂ,ꢐ3ꢀ,QGXVWULDOꢁ7HPSꢂꢃꢁ3',3ꢁSDFNꢆ
3
3ODVWLFꢀ',3ꢀꢍꢇꢄꢄꢀPLOꢀ%RG\ꢎꢒꢀꢋꢂOHDGꢀꢓꢀꢃꢆꢂOHDG
3ODVWLFꢀ62,&ꢀꢍꢃꢅꢄꢀPLOꢀ%RG\ꢎꢒꢀꢋꢂOHDG
3ODVWLFꢀ62,&ꢀꢍꢃꢅꢄꢀPLOꢀ%RG\ꢎꢒꢀꢃꢆꢂOHDG
3ODVWLFꢀ76623ꢒꢀꢋꢂOHDGꢀꢓꢀꢃꢆꢂOHDG
3ODVWLFꢀ627ꢂꢈꢇꢒꢀꢅꢂOHDG
DJH
61
6/
67
27
Nꢀ
Oꢀ
0&3ꢄꢅꢉꢂ,ꢐ61ꢀ,QGXVWULDOꢀ7HPSꢁꢒꢀ62,&ꢀSDFNDJH
0&3ꢄꢅꢉ7ꢂ,ꢐ61ꢀ 7DSHꢀ DQGꢀ 5HHOꢒꢀ ,QGXVWULDO
7HPSꢁꢒꢀ62,&ꢀSDFNDJH
Pꢀ 0&3ꢄꢅꢊꢂ,ꢐ3ꢀ ,QGXVWULDOꢁ 7HPSꢂꢃꢁ 3',3ꢁ SDFNꢆ
DJH
Qꢀ
0&3ꢄꢅꢊ7ꢂ,ꢐ3ꢀ,QGXVWULDOꢁ7HPSꢂꢃꢁ3',3ꢁSDFNꢆ
DJH
6DOHVꢂDQGꢂ6XSSRUW
'DWDꢁ6KHHWV
3URGXFWVꢀVXSSRUWHGꢀE\ꢀDꢀSUHOLPLQDU\ꢀ'DWDꢀ6KHHWꢀPD\ꢀKDYHꢀDQꢀHUUDWDꢀVKHHWꢀGHVFULELQJꢀPLQRUꢀRSHUDWLRQDOꢀGLIIHUHQFHVꢀDQGꢀUHFRPꢆ
PHQGHGꢀZRUNDURXQGVꢄꢀ7RꢀGHWHUPLQHꢀLIꢀDQꢀHUUDWDꢀVKHHWꢀH[LVWVꢀIRUꢀDꢀSDUWLFXODUꢀGHYLFH+ꢀSOHDVHꢀFRQWDFWꢀRQHꢀRIꢀWKHꢀIROORZLQJꢒ
ꢃꢄ <RXUꢀORFDOꢀ0LFURFKLSꢀVDOHVꢀRIILFH
ꢁꢄ 7KHꢀ0LFURFKLSꢀ&RUSRUDWHꢀ/LWHUDWXUHꢀ&HQWHUꢀ8ꢄ6ꢄꢀ)$;ꢒꢀAꢋꢊꢂBꢀꢅꢌꢁꢆꢅꢁꢅꢅ
ꢍꢄ 7KHꢀ0LFURFKLSꢀ:RUOGZLGHꢀ6LWHꢀAZZZꢄPLFURFKLSꢄFRPB
3OHDVHꢀVSHFLI\ꢀZKLFKꢀGHYLFH+ꢀUHYLVLRQꢀRIꢀVLOLFRQꢀDQGꢀ'DWDꢀ6KHHWꢀALQFOXGHꢀ/LWHUDWXUHꢀꢓBꢀ\RXꢀDUHꢀXVLQJꢄ
1HZꢁ&XVWRPHUꢁ1RWLILFDWLRQꢁ6\VWHP
5HJLVWHUꢀRQꢀRXUꢀZHEꢀVLWHꢀAZZZꢄPLFURFKLSꢄFRPꢈFQBꢀWRꢀUHFHLYHꢀWKHꢀPRVWꢀFXUUHQWꢀLQIRUPDWLRQꢀRQꢀRXUꢀSURGXFWVꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢍꢋ
ꢀ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
0&3ꢀꢁꢀꢂꢀꢁꢃꢂꢀꢁꢄꢂꢀꢁꢅ
,QIRUPDWLRQꢀ FRQWDLQHGꢀ LQꢀ WKLVꢀ SXEOLFDWLRQꢀ UHJDUGLQJꢀ GHYLFH
DSSOLFDWLRQVꢀDQGꢀWKHꢀOLNHꢀLVꢀLQWHQGHGꢀWKURXJKꢀVXJJHVWLRQꢀRQO\
DQGꢀPD\ꢀEHꢀVXSHUVHGHGꢀE\ꢀXSGDWHVꢄꢀ,WꢀLVꢀ\RXUꢀUHVSRQVLELOLW\ꢀWR
HQVXUHꢀ WKDWꢀ \RXUꢀDSSOLFDWLRQꢀ PHHWVꢀZLWKꢀ \RXUꢀVSHFLILFDWLRQVꢄ
1Rꢀ UHSUHVHQWDWLRQꢀ RUꢀ ZDUUDQW\ꢀ LVꢀ JLYHQꢀ DQGꢀ QRꢀ OLDELOLW\ꢀ LV
DVVXPHGꢀE\ꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFRUSRUDWHGꢀZLWKꢀUHVSHFW
WRꢀWKHꢀDFFXUDF\ꢀRUꢀXVHꢀRIꢀVXFKꢀLQIRUPDWLRQ+ꢀRUꢀLQIULQJHPHQWꢀRI
SDWHQWVꢀRUꢀRWKHUꢀLQWHOOHFWXDOꢀSURSHUW\ꢀULJKWVꢀDULVLQJꢀIURPꢀVXFK
XVHꢀRUꢀRWKHUZLVHꢄꢀ8VHꢀRIꢀ0LFURFKLS¶VꢀSURGXFWVꢀDVꢀFULWLFDOꢀFRPꢆ
SRQHQWVꢀLQꢀOLIHꢀVXSSRUWꢀV\VWHPVꢀLVꢀQRWꢀDXWKRUL]HGꢀH[FHSWꢀZLWK
H[SUHVVꢀZULWWHQꢀDSSURYDOꢀE\ꢀ0LFURFKLSꢄꢀ1RꢀOLFHQVHVꢀDUHꢀFRQꢆ
YH\HG+ꢀLPSOLFLWO\ꢀRUꢀRWKHUZLVH+ꢀXQGHUꢀDQ\ꢀLQWHOOHFWXDOꢀSURSHUW\
ULJKWVꢄ
7UDGHPDUNV
7KHꢀ0LFURFKLSꢀQDPHꢀDQGꢀORJR+ꢀWKHꢀ0LFURFKLSꢀORJR+ꢀ3,&+ꢀ3,&PLFUR+
3,&0$67(5+ꢀ 3,&67$57+ꢀ 352ꢀ 0$7(+ꢀ .((/24+ꢀ 6((9$/+
03/$%ꢀDQGꢀ7KHꢀ(PEHGGHGꢀ&RQWUROꢀ6ROXWLRQVꢀ&RPSDQ\ꢀDUHꢀUHJꢆ
LVWHUHGꢀWUDGHPDUNVꢀRIꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFRUSRUDWHGꢀLQꢀWKH
8ꢄ6ꢄ$ꢄꢀDQGꢀRWKHUꢀFRXQWULHVꢄ
7RWDOꢀ(QGXUDQFH+ꢀ,&63+ꢀ,Qꢆ&LUFXLWꢀ6HULDOꢀ3URJUDPPLQJ+ꢀ)LOWHUꢆ
/DE+ꢀ 0;'(9+ꢀ PLFUR,'+ꢀ )OH[520+ꢀ IX]]\/$%+ꢀ 03$60+
03/,1.+ꢀ 03/,%+ꢀ 3,&&+ꢀ 3,&'(0+ꢀ 3,&'(0ꢄQHW+ꢀ ,&(3,&+
0LJUDWDEOHꢀ 0HPRU\+ꢀ )DQ6HQVH+ꢀ (&212021,725+ꢀ 6HOHFW
0RGHꢀDQGꢀPLFUR3RUWꢀDUHꢀWUDGHPDUNVꢀRIꢀ0LFURFKLSꢀ7HFKQRORJ\
,QFRUSRUDWHGꢀLQꢀWKHꢀ8ꢄ6ꢄ$ꢄ
6HULDOL]HGꢀ4XLFNꢀ7HUPꢀ3URJUDPPLQJꢀA6473BꢀLVꢀDꢀVHUYLFHꢀPDUN
RIꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFRUSRUDWHGꢀLQꢀWKHꢀ8ꢄ6ꢄ$ꢄ
$OOꢀRWKHUꢀWUDGHPDUNVꢀPHQWLRQHGꢀKHUHLQꢀDUHꢀSURSHUW\ꢀRIꢀWKHLU
UHVSHFWLYHꢀFRPSDQLHVꢄ
ꢀ ꢁꢂꢂꢃ+ꢀ 0LFURFKLSꢀ 7HFKQRORJ\ꢀ ,QFRUSRUDWHG+ꢀ 3ULQWHGꢀ LQꢀ WKH
8ꢄ6ꢄ$ꢄ+ꢀ$OOꢀ5LJKWVꢀ5HVHUYHGꢄ
ꢀ3ULQWHGꢀRQꢀUHF\FOHGꢀSDSHUꢁ
0LFURFKLSꢀUHFHLYHGꢀ46ꢁꢂꢃꢃꢃꢀTXDOLW\ꢀV\VWHPꢀ
FHUWLILFDWLRQꢀIRUꢀLWVꢀZRUOGZLGHꢀKHDGTXDUWHUVꢄꢀ
GHVLJQꢀDQGꢀZDIHUꢀIDEULFDWLRQꢀIDFLOLWLHVꢀLQꢀ
&KDQGOHUꢀDQGꢀ7HPSHꢄꢀ$UL]RQDꢀLQꢀ-XO\ꢀꢅꢂꢂꢂꢆꢀ7KHꢀ
&RPSDQ\¶VꢀTXDOLW\ꢀV\VWHPꢀSURFHVVHVꢀDQGꢀ
SURFHGXUHVꢀDUHꢀ46ꢁꢂꢃꢃꢃꢀFRPSOLDQWꢀIRUꢀLWVꢀ
ꢀ
ꢀ
3,&PLFUR ꢇꢁELWꢀ0&8Vꢄꢀ.ꢁꢁ/ " FRGHꢀKRSSLQJꢀ
GHYLFHVꢄꢀ6HULDOꢀ((3520VꢀDQGꢀPLFURSHULSKHUDOꢀ
SURGXFWVꢆꢀ,QꢀDGGLWLRQꢄꢀ0LFURFKLS¶VꢀTXDOLW\ꢀ
V\VWHPꢀIRUꢀWKHꢀGHVLJQꢀDQGꢀPDQXIDFWXUHꢀRIꢀ
GHYHORSPHQWꢀV\VWHPVꢀLVꢀ,62ꢀꢂꢃꢃꢅꢀFHUWLILHGꢆ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢍꢉ
ꢀ
$0(5,&$6
&RUSRUDWHꢁ2IILFH
ꢈꢇꢅꢅꢀ:HVWꢀ&KDQGOHUꢀ%OYGꢁ
&KDQGOHUꢒꢀ$=ꢀꢀꢋꢅꢈꢈꢆꢂꢌꢃꢊꢊ
7HOꢏꢀꢀꢆꢋꢄꢂꢉꢊꢈꢂꢉꢈꢄꢄꢀꢀ)D[ꢏꢀꢀꢆꢋꢄꢂꢉꢊꢈꢂꢉꢈꢉꢉ
7HFKQLFDOꢀ6XSSRUWꢏꢀꢆꢋꢄꢂꢉꢊꢈꢂꢉꢌꢈꢉ
:HEꢀ$GGUHVVꢏꢀKWWSꢏꢐꢐZZZꢁPLFURFKLSꢁFRP
:25/':,'(ꢃ6$/(6ꢃ$1'ꢃ6(59,&(
-DSDQ
0LFURFKLSꢀ7HFKQRORJ\ꢀ-DSDQꢀ.ꢁ.ꢁ
%HQH[ꢀ6ꢂꢃꢀꢌ)
ꢇꢂꢃꢋꢂꢈꢄꢒꢀ6KLQ\RNRKDPD
.RKRNXꢂ.XꢒꢀꢔRNRKDPDꢂVKL
.DQDJDZDꢒꢀꢈꢈꢈꢂꢄꢄꢇꢇꢒꢀ-DSDQ
7HOꢏꢀꢋꢃꢂꢆꢅꢂꢆꢉꢃꢂꢀꢌꢃꢌꢌꢀꢀ)D[ꢏꢀꢋꢃꢂꢆꢅꢂꢆꢉꢃꢂꢌꢃꢈꢈ
$6,$ꢍ3$&,),&
$XVWUDOLD
0LFURFKLSꢀ7HFKQRORJ\ꢀ$XVWUDOLDꢀ3W\ꢀ/WG
6XLWHꢀꢈꢈꢒꢀꢆꢃꢀ5DZVRQꢀ6WUHHW
(SSLQJꢀꢈꢃꢈꢃꢒꢀ16:
$XVWUDOLD
7HOꢏꢀꢌꢃꢂꢈꢂꢊꢋꢌꢋꢂꢌꢉꢇꢇꢀ)D[ꢏꢀꢌꢃꢂꢈꢂꢊꢋꢌꢋꢂꢌꢉꢅꢅ
.RUHD
5RFN\ꢁ0RXQWDLQ
&KLQDꢁꢈꢁ%HLMLQJ
0LFURFKLSꢀ7HFKQRORJ\ꢀ.RUHD
ꢃꢌꢋꢂꢃꢒꢀꢔRXQJERꢀ%OGJꢁꢀꢇꢀ)ORRU
6DPVXQJꢂ'RQJꢒꢀ.DQJQDPꢂ.X
6HRXOꢒꢀ.RUHDꢀꢃꢇꢅꢂꢋꢋꢈ
ꢈꢇꢅꢅꢀ:HVWꢀ&KDQGOHUꢀ%OYGꢁ
&KDQGOHUꢒꢀ$=ꢀꢀꢋꢅꢈꢈꢆꢂꢌꢃꢊꢊ
7HOꢏꢀꢀꢆꢋꢄꢂꢉꢊꢈꢂꢉꢊꢌꢌꢀꢀ)D[ꢏꢀꢀꢆꢋꢄꢂꢉꢊꢈꢂꢉꢆꢅꢌ
0LFURFKLSꢀ 7HFKQRORJ\ꢀ &RQVXOWLQJꢀ ꢍ6KDQJKDLꢎ
&Rꢁꢒꢀ/WGꢁꢒꢀ%HLMLQJꢀ/LDLVRQꢀ2IILFH
8QLWꢀꢊꢃꢅ
1HZꢀ&KLQDꢀ+RQJꢀ.RQJꢀ0DQKDWWDQꢀ%OGJꢁ
1Rꢁꢀꢌꢀ&KDR\DQJPHQꢀ%HLGDMLHꢀ
%HLMLQJꢒꢀꢃꢄꢄꢄꢈꢉꢒꢀ1Rꢁꢀ&KLQD
$WODQWD
ꢅꢄꢄꢀ6XJDUꢀ0LOOꢀ5RDGꢒꢀ6XLWHꢀꢈꢄꢄ%
$WODQWDꢒꢀ*$ꢀꢀꢇꢄꢇꢅꢄ
7HOꢏꢀꢉꢉꢄꢂꢌꢆꢄꢂꢄꢄꢇꢆꢀꢀ)D[ꢏꢀꢉꢉꢄꢂꢌꢆꢄꢂꢄꢇꢄꢉ
7HOꢏꢀꢋꢈꢂꢈꢂꢅꢅꢆꢂꢉꢈꢄꢄꢀꢀ)D[ꢏꢀꢋꢈꢂꢈꢂꢅꢅꢋꢂꢅꢊꢇꢆ
6LQJDSRUH
0LFURFKLSꢀ7HFKQRORJ\ꢀ6LQJDSRUHꢀ3WHꢀ/WGꢁ
ꢈꢄꢄꢀ0LGGOHꢀ5RDG
ꢕꢄꢉꢂꢄꢈꢀ3ULPHꢀ&HQWUH
6LQJDSRUHꢒꢀꢃꢋꢋꢊꢋꢄ
7HOꢏꢀꢀꢌꢅꢂꢇꢇꢆꢂꢋꢋꢉꢄꢀꢀ)D[ꢏꢀꢌꢅꢂꢇꢇꢆꢂꢋꢋꢅꢄ
7HOꢏꢀꢋꢌꢂꢃꢄꢂꢋꢅꢈꢋꢈꢃꢄꢄꢀ)D[ꢏꢀꢋꢌꢂꢃꢄꢂꢋꢅꢈꢋꢈꢃꢄꢆ
&KLQDꢁꢈꢁ&KHQJGX
$XVWLQꢁꢈꢁ$QDORJ
0LFURFKLSꢀ 7HFKQRORJ\ꢀ &RQVXOWLQJꢀ ꢍ6KDQJKDLꢎ
&Rꢁꢒꢀ/WGꢁꢒꢀ&KHQJGXꢀ/LDLVRQꢀ2IILFH
5Pꢁꢀꢈꢆꢄꢃꢒꢀ0LQJꢀ;LQJꢀ)LQDQFLDOꢀ7RZHU
1Rꢁꢀꢋꢋꢀ7,'8ꢀ6WUHHW
&KHQJGXꢀꢌꢃꢄꢄꢃꢌꢒꢀ&KLQD
7HOꢏꢀꢋꢌꢂꢈꢋꢂꢌꢉꢌꢌꢈꢄꢄꢀꢀ)D[ꢏꢀꢋꢌꢂꢈꢋꢂꢌꢉꢌꢌꢅꢊꢊ
ꢋꢇꢄꢇꢀ0R3DFꢀ([SUHVVZD\ꢀ1RUWK
6XLWHꢀ$ꢂꢈꢄꢃ
$XVWLQꢒꢀ7;ꢀꢀꢉꢋꢉꢅꢊ
7DLZDQ
0LFURFKLSꢀ7HFKQRORJ\ꢀ7DLZDQ
ꢃꢃ)ꢂꢇꢒꢀ1Rꢁꢀꢈꢄꢉ
7HOꢏꢀꢅꢃꢈꢂꢇꢆꢅꢂꢈꢄꢇꢄꢀꢀ)D[ꢏꢀꢅꢃꢈꢂꢇꢆꢅꢂꢌꢄꢋꢅ
%RVWRQ
ꢈꢀ/DQꢀ'ULYHꢒꢀ6XLWHꢀꢃꢈꢄ
:HVWIRUGꢒꢀ0$ꢀꢀꢄꢃꢋꢋꢌ
7HOꢏꢀꢊꢉꢋꢂꢌꢊꢈꢂꢇꢋꢆꢋꢀꢀ)D[ꢏꢀꢊꢉꢋꢂꢌꢊꢈꢂꢇꢋꢈꢃ
7XQJꢀ+XDꢀ1RUWKꢀ5RDG
7DLSHLꢒꢀꢃꢄꢅꢒꢀ7DLZDQ
7HOꢏꢀꢋꢋꢌꢂꢈꢂꢈꢉꢃꢉꢂꢉꢃꢉꢅꢀꢀ)D[ꢏꢀꢋꢋꢌꢂꢈꢂꢈꢅꢆꢅꢂꢄꢃꢇꢊ
&KLQDꢁꢈꢁ)X]KRX
0LFURFKLSꢀ 7HFKQRORJ\ꢀ &RQVXOWLQJꢀ ꢍ6KDQJKDLꢎ
&Rꢁꢒꢀ/WGꢁꢒꢀ)X]KRXꢀ/LDLVRQꢀ2IILFH
5Pꢁꢀꢅꢇꢃꢒꢀ1RUWKꢀ%XLOGLQJ
)XMLDQꢀ)RUHLJQꢀ7UDGHꢀ&HQWHUꢀ+RWHO
ꢉꢇꢀ:XVLꢀ5RDG
)X]KRXꢀꢇꢅꢄꢄꢄꢃꢒꢀ&KLQD
%RVWRQꢁꢈꢁ$QDORJ
8QLWꢀ$ꢂꢋꢂꢃꢀ0LOOEURRNꢀ7DUU\ꢀ&RQGRPLQLXP
ꢊꢉꢀ/RZHOOꢀ5RDG
&RQFRUGꢒꢀ0$ꢀꢀꢄꢃꢉꢆꢈ
(8523(
'HQPDUN
7HOꢏꢀꢊꢉꢋꢂꢇꢉꢃꢂꢌꢆꢄꢄꢀꢀ)D[ꢏꢀꢊꢉꢋꢂꢇꢉꢃꢂꢄꢄꢅꢄ
0LFURFKLSꢀ7HFKQRORJ\ꢀ'HQPDUNꢀ$S6
5HJXVꢀ%XVLQHVVꢀ&HQWUH
/DXWUXSꢀKRMꢀꢃꢂꢇ
%DOOHUXSꢀ'.ꢂꢈꢉꢅꢄꢀ'HQPDUN
7HOꢏꢀꢆꢅꢀꢆꢆꢈꢄꢀꢊꢋꢊꢅꢀ)D[ꢏꢀꢆꢅꢀꢆꢆꢈꢄꢀꢊꢊꢃꢄ
7HOꢏꢀꢋꢌꢂꢅꢊꢃꢂꢉꢅꢅꢉꢅꢌꢇꢀꢀ)D[ꢏꢀꢋꢌꢂꢅꢊꢃꢂꢉꢅꢅꢉꢅꢉꢈ
&KLFDJR
&KLQDꢁꢈꢁ6KDQJKDL
0LFURFKLSꢀ 7HFKQRORJ\ꢀ &RQVXOWLQJꢀ ꢍ6KDQJKDLꢎ
&Rꢁꢒꢀ/WGꢁ
5RRPꢀꢉꢄꢃꢒꢀ%OGJꢁꢀ%
ꢇꢇꢇꢀ3LHUFHꢀ5RDGꢒꢀ6XLWHꢀꢃꢋꢄ
,WDVFDꢒꢀ,/ꢀꢀꢌꢄꢃꢆꢇ
7HOꢏꢀꢌꢇꢄꢂꢈꢋꢅꢂꢄꢄꢉꢃꢀ)D[ꢏꢀꢌꢇꢄꢂꢈꢋꢅꢂꢄꢄꢉꢅ
'DOODV
ꢆꢅꢉꢄꢀ:HVWJURYHꢀ'ULYHꢒꢀ6XLWHꢀꢃꢌꢄ
$GGLVRQꢒꢀ7;ꢀꢉꢅꢄꢄꢃ
7HOꢏꢀꢊꢉꢈꢂꢋꢃꢋꢂꢉꢆꢈꢇꢀꢀ)D[ꢏꢀꢊꢉꢈꢂꢋꢃꢋꢂꢈꢊꢈꢆ
)UDQFH
)DUꢀ(DVWꢀ,QWHUQDWLRQDOꢀ3OD]D
1Rꢁꢀꢇꢃꢉꢀ;LDQꢀ;LDꢀ5RDG
6KDQJKDLꢒꢀꢈꢄꢄꢄꢅꢃ
$UL]RQDꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ6$5/
3DUFꢀG¶$FWLYLWHꢀGXꢀ0RXOLQꢀGHꢀ0DVV\
ꢆꢇꢀ5XHꢀGXꢀ6DXOHꢀ7UDSX
7HOꢏꢀꢋꢌꢂꢈꢃꢂꢌꢈꢉꢅꢂꢅꢉꢄꢄꢀꢀ)D[ꢏꢀꢋꢌꢂꢈꢃꢂꢌꢈꢉꢅꢂꢅꢄꢌꢄ
%DWLPHQWꢀ$ꢀꢂꢀOHUꢀ(WDJH
ꢊꢃꢇꢄꢄꢀ0DVV\ꢒꢀ)UDQFH
7HOꢏꢀꢇꢇꢂꢃꢂꢌꢊꢂꢅꢇꢂꢌꢇꢂꢈꢄꢀꢀ)D[ꢏꢀꢇꢇꢂꢃꢂꢌꢊꢂꢇꢄꢂꢊꢄꢂꢉꢊ
'D\WRQ
&KLQDꢁꢈꢁ6KHQ]KHQ
7ZRꢀ3UHVWLJHꢀ3ODFHꢒꢀ6XLWHꢀꢃꢇꢄ
0LDPLVEXUJꢒꢀ2+ꢀꢆꢅꢇꢆꢈ
7HOꢏꢀꢊꢇꢉꢂꢈꢊꢃꢂꢃꢌꢅꢆꢀꢀ)D[ꢏꢀꢊꢇꢉꢂꢈꢊꢃꢂꢊꢃꢉꢅ
0LFURFKLSꢀ 7HFKQRORJ\ꢀ &RQVXOWLQJꢀ ꢍ6KDQJKDLꢎ
&Rꢁꢒꢀ/WGꢁꢒꢀ6KHQ]KHQꢀ/LDLVRQꢀ2IILFH
5Pꢁꢀꢃꢇꢃꢅꢒꢀꢃꢇꢐ)ꢒꢀ6KHQ]KHQꢀ.HUU\ꢀ&HQWUHꢒ
5HQPLQQDQꢀ/X
6KHQ]KHQꢀꢅꢃꢋꢄꢄꢃꢒꢀ&KLQD
7HOꢏꢀꢋꢌꢂꢉꢅꢅꢂꢈꢇꢅꢄꢇꢌꢃꢀꢀ)D[ꢏꢀꢋꢌꢂꢉꢅꢅꢂꢈꢇꢌꢌꢄꢋꢌ
*HUPDQ\
$UL]RQDꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ*PE+
*XVWDYꢂ+HLQHPDQQꢀ5LQJꢀꢃꢈꢅ
'ꢂꢋꢃꢉꢇꢊꢀ0XQLFKꢒꢀ*HUPDQ\
'HWURLW
7ULꢂ$WULDꢀ2IILFHꢀ%XLOGLQJꢀ
ꢇꢈꢈꢅꢅꢀ1RUWKZHVWHUQꢀ+LJKZD\ꢒꢀ6XLWHꢀꢃꢊꢄ
)DUPLQJWRQꢀ+LOOVꢒꢀ0,ꢀꢀꢆꢋꢇꢇꢆ
7HOꢏꢀꢈꢆꢋꢂꢅꢇꢋꢂꢈꢈꢅꢄꢀ)D[ꢏꢀꢈꢆꢋꢂꢅꢇꢋꢂꢈꢈꢌꢄ
7HOꢏꢀꢆꢊꢂꢋꢊꢂꢌꢈꢉꢂꢃꢆꢆꢀꢄꢀꢀ)D[ꢏꢀꢆꢊꢂꢋꢊꢂꢌꢈꢉꢂꢃꢆꢆꢂꢆꢆ
+RQJꢂ.RQJ
*HUPDQ\ꢁꢈꢁ$QDORJ
/RFKKDPHUꢀ6WUDVVHꢀꢃꢇ
'ꢂꢋꢈꢃꢅꢈꢀ0DUWLQVULHGꢒꢀ*HUPDQ\
7HOꢏꢀꢆꢊꢂꢋꢊꢂꢋꢊꢅꢌꢅꢄꢂꢄꢀꢀ)D[ꢏꢀꢆꢊꢂꢋꢊꢂꢋꢊꢅꢌꢅꢄꢂꢈꢈ
0LFURFKLSꢀ7HFKQRORJ\ꢀ+RQJNRQJꢀ/WGꢁ
8QLWꢀꢊꢄꢃꢒꢀ7RZHUꢀꢈꢒꢀ0HWURSOD]D
ꢈꢈꢇꢀ+LQJꢀ)RQJꢀ5RDG
.ZDLꢀ)RQJꢒꢀ1ꢁ7ꢁꢒꢀ+RQJꢀ.RQJ
7HOꢏꢀꢋꢅꢈꢂꢈꢆꢄꢃꢂꢃꢈꢄꢄꢀꢀ)D[ꢏꢀꢋꢅꢈꢂꢈꢆꢄꢃꢂꢇꢆꢇꢃ
/RVꢁ$QJHOHV
ꢃꢋꢈꢄꢃꢀ9RQꢀ.DUPDQꢒꢀ6XLWHꢀꢃꢄꢊꢄ
,UYLQHꢒꢀ&$ꢀꢀꢊꢈꢌꢃꢈ
7HOꢏꢀꢊꢆꢊꢂꢈꢌꢇꢂꢃꢋꢋꢋꢀꢀ)D[ꢏꢀꢊꢆꢊꢂꢈꢌꢇꢂꢃꢇꢇꢋ
,WDO\
$UL]RQDꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ65/
&HQWURꢀ'LUH]LRQDOHꢀ&ROOHRQLꢀ
3DOD]]Rꢀ7DXUXVꢀꢃꢀ9ꢁꢀ/Hꢀ&ROOHRQLꢀꢃ
ꢈꢄꢄꢆꢃꢀ$JUDWHꢀ%ULDQ]D
,QGLD
0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢁ
,QGLDꢀ/LDLVRQꢀ2IILFH
'LY\DVUHHꢀ&KDPEHUV
1HZꢁ<RUN
ꢃꢅꢄꢀ0RWRUꢀ3DUNZD\ꢒꢀ6XLWHꢀꢈꢄꢈ
+DXSSDXJHꢒꢀ1ꢔꢀꢀꢃꢃꢉꢋꢋ
7HOꢏꢀꢌꢇꢃꢂꢈꢉꢇꢂꢅꢇꢄꢅꢀꢀ)D[ꢏꢀꢌꢇꢃꢂꢈꢉꢇꢂꢅꢇꢇꢅ
0LODQꢒꢀ,WDO\ꢀ
7HOꢏꢀꢇꢊꢂꢄꢇꢊꢂꢌꢅꢉꢊꢃꢂꢃꢀꢀ)D[ꢏꢀꢇꢊꢂꢄꢇꢊꢂꢌꢋꢊꢊꢋꢋꢇ
ꢃꢀ)ORRUꢒꢀ:LQJꢀ$ꢀꢍ$ꢇꢐ$ꢆꢎ
1Rꢁꢀꢃꢃꢒꢀ2¶6KDXJQHVVH\ꢀ5RDG
%DQJDORUHꢒꢀꢅꢌꢄꢀꢄꢈꢅꢒꢀ,QGLD
7HOꢏꢀꢊꢃꢂꢋꢄꢂꢈꢈꢊꢄꢄꢌꢃꢀ)D[ꢏꢀꢊꢃꢂꢋꢄꢂꢈꢈꢊꢄꢄꢌꢈ
6DQꢁ-RVH
0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢁ
ꢈꢃꢄꢉꢀ1RUWKꢀ)LUVWꢀ6WUHHWꢒꢀ6XLWHꢀꢅꢊꢄ
6DQꢀ-RVHꢒꢀ&$ꢀꢀꢊꢅꢃꢇꢃ
8QLWHGꢁ.LQJGRP
$UL]RQDꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ/WGꢁ
ꢅꢄꢅꢀ(VNGDOHꢀ5RDG
:LQQHUVKꢀ7ULDQJOH
:RNLQJKDPꢀ
%HUNVKLUHꢒꢀ(QJODQGꢀ5*ꢆꢃꢀꢅ78
7HOꢏꢀꢆꢆꢀꢃꢃꢋꢀꢊꢈꢃꢀꢅꢋꢌꢊ )D[ꢏꢀꢆꢆꢂꢃꢃꢋꢀꢊꢈꢃꢂꢅꢋꢈꢄ
7HOꢏꢀꢆꢄꢋꢂꢆꢇꢌꢂꢉꢊꢅꢄꢀꢀ)D[ꢏꢀꢆꢄꢋꢂꢆꢇꢌꢂꢉꢊꢅꢅ
7RURQWR
ꢌꢈꢋꢅꢀ1RUWKDPꢀ'ULYHꢒꢀ6XLWHꢀꢃꢄꢋ
0LVVLVVDXJDꢒꢀ2QWDULRꢀ/ꢆ9ꢀꢃ;ꢅꢒꢀ&DQDGD
7HOꢏꢀꢊꢄꢅꢂꢌꢉꢇꢂꢄꢌꢊꢊꢀꢀ)D[ꢏꢀꢀꢊꢄꢅꢂꢌꢉꢇꢂꢌꢅꢄꢊ
ꢊꢈꢌꢊꢂꢌꢊꢂ
'6ꢃꢃꢃꢅꢅ&ꢆSDJHꢀꢍꢎ
ꢀꢁꢂꢂꢃꢀ0LFURFKLSꢀ7HFKQRORJ\ꢀ,QFꢄ
This datasheet has been download from:
www.datasheetcatalog.com
Datasheets for electronics components.
相关型号:
SI9130DB
5- and 3.3-V Step-Down Synchronous ConvertersWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9135LG-T1
SMBus Multi-Output Power-Supply ControllerWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9135LG-T1-E3
SMBus Multi-Output Power-Supply ControllerWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9135_11
SMBus Multi-Output Power-Supply ControllerWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9136_11
Multi-Output Power-Supply ControllerWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9130CG-T1-E3
Pin-Programmable Dual Controller - Portable PCsWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9130LG-T1-E3
Pin-Programmable Dual Controller - Portable PCsWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9130_11
Pin-Programmable Dual Controller - Portable PCsWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9137
Multi-Output, Sequence Selectable Power-Supply Controller for Mobile ApplicationsWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9137DB
Multi-Output, Sequence Selectable Power-Supply Controller for Mobile ApplicationsWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9137LG
Multi-Output, Sequence Selectable Power-Supply Controller for Mobile ApplicationsWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
SI9122E
500-kHz Half-Bridge DC/DC Controller with Integrated Secondary Synchronous Rectification DriversWarning: Undefined variable $rtag in /www/wwwroot/website_ic37/www.icpdf.com/pdf/pdf/index.php on line 217
-
VISHAY
©2020 ICPDF网 联系我们和版权申明