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quality of an existing transducer design, but also added two-frequency
operation.
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Material 1
Material 2
Z1
Z2
Incident Sound
Wave
Transmitted
Sound Wave (T)
Reflected
Sound
Wave (R)
Z = ρc
where Z = Acoustic Impedance
ρ = Density of the Material
c = Velocity of Sound through the Material
Transmission Equation:
T
2Z 2
Z2 Z1
Reflection Equation:
R
Z 2–Z 1
Z2 Z1
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Linear Phased Array
Table I
Characteristic Acoustic Impedances
of Several Biological and Nonbiological Materials
Material
Air at S.T.P.
Water at 20°C
Blood
Muscle
Fat
Soft Tissue
Kidney
Liver
Bone
Polyethylene, LowĆDensity
Vinyl (rigid)
Lucite
Valox, Black (glassĆfilled nylon)
Aluminum
Lead Zirconium Titanate
Stainless Steel
Element
Pulsing
Patterns
Acoustic Impedance
(106 Rayls)
0.0004
1.48
1.67
1.70
1.38
1.63
1.62
1.64
3.8 to 7.4
1.8
3.0
3.2
3.8
17.0
28 to 36
45.4
Phased Array
Coupling
Gel
Body
Body
Image
Shape
Fig. 3. Comparison of linear phasedĆarray and phasedĆarray ultraĆ
sound transducers.
receivers which are called elements. Typically, each transĆ
ducer element is connected to one system channel. Two
different types of transducers are commonly used: sector
phasedĆarray and linear phasedĆarray transducers. The main
difference is how these transducers are electrically excited.
Each element in a sector phasedĆarray transducer is activated
at a slightly different time delay, which allows the sound
wave to be shaped into a beam of sound and steered at difĆ
ferent angles, producing a picture shaped like a pie slice.
Linear phased arrays have the additional ability to activate
groups of elements in a type of sequential scanning of the
image, producing a rectangularĆshaped picture. Fig. 3 shows
a pictorial comparison of the element pulse patterns and the
respective image shapes produced by the linear and phasedĆ
array transducers.
There are three main modalities in ultrasonic imaging: 2D,
Doppler, and color flow. The 2D image is a realĆtime grayĆ
scale image display. A typical 2D linear image of a carotid
artery in the neck is shown in Fig. 4. Doppler is a way of
measuring the flow velocity and movement within an image
and is named for the principle it uses. The information is
presented either with an audible tone or a visual plot. Color
flow imaging detects the flow of blood and colorĆcodes it
depending on the direction and velocity of flow. An image
showing color flow in the carotid artery is shown in Fig. 5.
The references provide more detailed information on
phasedĆarray ultrasound imaging systems3 and on color flow
and Doppler processing.4
Fig. 2. HP Sonos 1000 ultrasound imaging system.
August 1994 HewlettĆPackard Journal
As mentioned above, a transducer consists of many small
elements. An element is a multilayer sandwich of piezoelecĆ
tric and other materials. The basic acoustic transducer eleĆ
ment is shown in Fig. 6. Lead zirconium titanate, PZT, is a
commonly used piezoelectric ceramic sensor material having
an acoustic impedance between 28 and 36×106 kg/m2s (Rayl).
Recall that soft tissue has an impedance in the 1ĆtoĆ2ĆMRayl
region. Because of the impedance mismatch, there is a lot of
reflected energy at the transducer/tissue interface, and such
a transducer would not couple much energy to the human
body. To improve coupling, a front matching layerĊa couĆ
pling material with an intermediate acoustic impedanceĊis
Body
Backing
Piezoelectric
Ceramic
Lens
Matching
Layers
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Lateral
Aperture
Transducer
Elements
Lateral Plane
Elevation Plane
Elevation
Beam
Width
Focal
Length
Lateral
Beam
Width
Fig. 5. (%(* %(/ #&! ( *(,# *,*1
Fig. 7. (-+ & +"(/#'! %.,#(' ' %,*% )%'+
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R
0 dB
1
F
–10 dB
–20-dB Beam Width
Return Echo (dB)
–20 dB
R
–30 dB
2
F
–40 dB
–50 dB
Formula: 10
F+
–60 dB
–20
–10
0
10
20
Angle between Target and Transducer Face
(degrees)
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a1
X1
F1
a2
X2
F2
Formulas: 9
a2
F+
X +
a
F
X
1
10 mm
4.5 mm
2
7 mm
500
mm
250
mm
3.2 mm
( = 0.2 mm at 7.5 MHz)
0.89 Z 2a
Where:
F = Focal Length
X = Beam Width
= Wavelength
Z = Distance from Aperture
a = Aperture / 2
Fig. 9. ""!0 +" ,!.01.! /%6! +* !(!20%+* !) 3% 0$ * "+(
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R
F
1
25 mm
50 mm
2
15 mm
30 mm
R
VB
VL
*1
Where:
F = Focal Length
R = Radius of Lens
VB = Velocity of Sound in Body
VL = Velocity of Sound in Lens
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+.,:7* 4:9 -4< 94 .2574;* 9-* 3*&7 +.*1) "-4:1) 9-* +7*A
6:*3(> '* (-&3,*) #-* &5*79:7* 8.?* #-* +4(&1 54.39
9 9-.8 54.39 .3 9.2* <* 3**)*) & +7&2*<470 +47 47,&3.?.3,
9-* .3+472&9.43 <* -&) &8 <*11 &8 842* <&> 94 -.,-1.,-9
&7*&8 9-&9 7*6:.7*) 247* )&9& 3 47,&3.?&9.43&1 9441 (&11*)
6:&1.9> +:3(9.43 )*514>2*39 ! <&8 .)*39.+.*) &8 43*
<&> 94 -*15 :8 97&381&9* <-&9 9-* (:8942*7 <&39*) .394 &
574):(9 #-* ! 2*9-4) .8 '&8*) 43 9-* (43897:(9.43 4+ &
@-4:8* 4+ 6:&1.9>
#-* +.789 89*5 .3 ':.1).3, & -4:8* 4+ 6:&1.9> .8 94 9&':1&9*
(:8942*7 <&398 &3) &88.,3 9-*2 <*.,-.3, +&(9478 .;*3
*34:,- .3.9.&1 +**)'&(0 4:7 9*&2 <&8 &'1* 94 )*;*145 &3)
).897.':9* & 8:7;*> 9-&9 1.89*) 2&3> (:8942*7 @<&398 &3)
&80*) +47 7*1&9.;* <*.,-98 +47 *&(- #-* 3*=9 89*5 .3 ':.1).3,
9-* -4:8* 4+ 6:&1.9> .8 94 9&':1&9* 9-48* *3,.3**7.3, (-&7&(A
9*7.89.(8 9-&9 &++*(9 842* 47 &11 4+ 9-* (:8942*7 <&398 #-.8
1.89 (439&.38 &11 9-* 5&798 4+ 9-* )*8.,3 9-&9 *3,.3**7.3, (4:1)
24).+> 94 ,.;* (:8942*78 <-&9 9-*> <&39
#-* +.3&1 89*58 .3 9-* -4:8*':.1).3, 574(*88 9440 9-* 2489
9.2* #-* (425*9.9.438 574):(98 <*7* '*3(-2&70*) 7*1&9.;*
94 8 94 8** .3 <-&9 &7*&8 4+ (:8942*7 <&398 <* <*7*
<.33.3, 47 148.3, #-* *3,.3**7.3, (-&7&(9*7.89.(8 <*7* 7*A
1&9*) 94 (:8942*7 <&398 .3 2&97.= +472 84 9-&9 <* (4:1) 8**
<-&9 (-&7&(9*7.89.(8 &++*(9*) <-.(- (:8942*7 <&39 &3) '>
-4< 2:(- #-* +.3&1 -4:8* 4+ 6:&1.9> 574;.)*) & ,7&5-.(&1
2*&38 4+ ).851&>.3, &11 9-.8 )&9& .3 & 7*&)&'1* +472&9 82&11 5.*(* 4+ 4:7 -4:8* .8 8-4<3 .3 ., #-* &(9:&1
-4:8* -&) <&398 &3) (-&7&(9*7.89.(8 &3) 8*;*7&1
@74428 1.0* 9-* *=&251* .3 ., #-* -4:8* 4+ 6:&1.9> <&8 &3 *++*(9.;* 9441 94 8-4< <-&9 <*
-&) 94 )4 94 ,.;* (:8942*78 <-&9 9-*> <&39*) *=9 9-*
574/*(9 9*&2 3**)*) 94 (-&3,* 9-* )*8.,3 4+ 9-* 97&38):(*7 94 (7*&9* 9-* $8.3, (:8942*7 )&9& 49-*7 74428 .3 9-* -4:8* 4+ 6:&1.9>
8-4<*) 9-&9 9-* 97&38):(*7 <&8 &5574=.2&9*1>
*6:.;&1*39 94 .98 (425*9.9478 .3 9-* &7*&8 4+ (4147 +14< &3)
4551*7 5*7+472&3(* 4<*;*7 .9 <&8 .3+*7.47 94 .98 (42A
5*9.9478 .3 3*&7A+.*1) .2&,* 6:&1.9> #-* -4:8* 4+ 6:&1.9>
&184 8-4<*) 9-&9 *1*;&9.43 '*&2 <.)9- <&8 9-* *3,.3**7.3,
(-&7&(9*7.89.( 2489 89743,1> 7*1&9*) 94 .2&,* 6:&1.9> #-.8
'*(&2* 9-* +.789 &7*& 4+ 7*)*8.,3 43 9-* #-* -4:8* 4+ 6:&1.9> 574;.)*) .3+472&9.43 9-&9 4:7 (:8942*78
(438.)*7*) 9-* 3*&7 +.*1) 94 '* 4;*7 & ;*7> 85*(.+.( )*597&3,* .394 9-* '4)> *< )*8.,38 <*7* ':.19 &3)
*;&1:&9*) +47 *1*;&9.43 '*&2 <.)9-8 .3 9-.8 7&3,* #-* )*8.,38 .3(1:)*) (42'.3&9.438 4+ 82&11*7 *1*;&9.43
:,:89 *<1*99A &(0&7) 4:73&1
X
# = Strong Interaction
#
X = Medium Interaction
= Weak Interaction
Less Clutter
8
X
Good Color Flow
9
X
Good Detail Resolution
6
Importance j i Weightj
Relationship Matrix Values
=9
=3
X =1
15
3
Importance j
Pulse Length
Lateral Beam Width
Want i
Weight i
Elevation Beam Width
Characteristic j
71
54
Matrix Value ij
Fig. 12. 82'11 5479/43 4, 9.+ 6:'1/9> ,:3)9/43 *+514>2+39
@.4:8+ 4, 6:'1/9> ,47 9.+ ;'8):1'7 :197'84:3* 97'38*:)+7
'5+79:7+8 '3* 9/-.9+7 1+38 7'*// #.+ -7'5. /3 /- 8.4<8
9.+ +1+;'9/43 (+'2 </*9. 4, 9<4 8:). *+8/-38 )425'7+* 94
9.+ 9 1+'89 +/-.9 */,,+7+39 *+8/-38 ,47 9.+ <+7+ (:/19 '3*
9+89+* /3 9+728 4, 9.+ )7/9/)'1 ,+< +3-/3++7/3- ).'7')9+7/89/)8
8.4<3 94 (+ /25479'39 94 ):8942+7 8'9/8,')9/43 ,+< 4, 9.+
2489 5742/8/3- *+8/-38 <+7+ 9'0+3 94 57+,+7+3)+ 97/'18 '3*
9+89+* '-'/389 9.+ )425+9/9/43
–20-dB Elevation Beam Width
#.+ /3/9/'1 57+,+7+3)+ )1/3/)'1 97/'18 <+7+ .+1* /3A.4:8+ </9.
/39+73'1 +=5+798 '3* 842+ /3;/9+* 4:98/*+ ;'8):1'7 :197'A
84:3* :8+78 2'-+8 <+7+ ')6:/7+* :8/3- 9.+ ;'7/4:8 97'38A
*:)+7 *+8/-38 '3* ):8942+78 <+7+ '80+* 94 -7'*+ 9.+ /2'-+8
7+1'9/;+ 94 +'). 49.+7 "42+ 57+,+7+3)+ 97/'18 <+7+ )43A
*:)9+* '9 ):8942+7 8/9+8 #.+ /3/9/'1 )422+398 43 9.+ 3+<
*+8/-38 <+7+ ;+7> 548/9/;+ ,742 :8+78 4, 9.+ ))47*/3- 94 9.+8+ :8+78 9.+ /3/9/'1 <'8 *+,/A
3/9+1> '3 /2574;+2+39 4;+7 9.+ +85+)/'11> /3 9.+
3+'7 ,/+1* $3,479:3'9+1> 9.+ *+8/-38 */* 349 ,'7+
<+11 /3 9.+ +>+8 4, 9.48+ :8+78 9.'9 .'* +=5+7/+3)+ </9. 4:7
)425+9/9/43 3+ 9+).3414-/89 8:22+* :5 9.+ (+89 4, 4:7
3+< *+8/-38 '8 @(+99+7 9.'3 9.+ 41* 43+ … '(4:9 '8
-44* '8 2> (7'3* %
HP 21258A
3 9+728 4, 97'38*:)+7 /2574;+2+398 2'3> 4, 9.+ 8+)43*'7>
+3-/3++7/3- ).'7')9+7/89/)8 8:). '8 5:18+ 1+3-9. <+7+ 8.4<3
94 (+ 24*+7'9+1> /25479'39 94 ):8942+7 <'398 49 43+ (:9
2'3> ).'7')9+7/89/)8 <4:1* .';+ 94 (+ ).'3-+* 94 2'0+
1'7-+ /2574;+2+398 /3 97'38*:)+7 5+7,472'3)+ "/3)+ <+
.'* '17+'*> (++3 9.74:-. 57+,+7+3)+ 97/'18 <+ <+7+ 57+99>
,'7 '143- 9.+ 574*:)9 *+;+1452+39 )>)1+ '3* ' 7+*+8/-3
<4:1* .';+ 9'0+3 944 2:). 9/2+ 9 9./8 54/39 842+ 9+).A
3/6:+ 94 ).'3-+ 9.+ 97'38*:)+7 *+8/-3 8/-3/,/)'391> /3 ' 8.479
5+7/4* 4, 9/2+ <'8 3++*+*
9 <'8 )1+'7 9.'9 '3 /2574;+2+39 /3 9.+ '=/'1 7+841:9/43 <'8
7+6:/7+* *+)7+'8+ /3 9.+ 5:18+ 1+3-9. <4:1* .+15 ,9+7
/3;+89/-'9/3- */,,+7+39 <'>8 94 /2574;+ 9.+ 5:18+ 7+85438+ 4,
9.+ 97'38*:)+7 43+ /*+' <'8 94 '** ' 8+)43* 2'9)./3- 1'>+7
94 9.+ 8+3847 89')0 *+8/-3
'9)./3- 1'>+78 '7+ ;+7> /25479'39 94 9.+ 97'38*:)+7 )43A
897:)9/43 #.+ 2'9)./3- 1'>+7 /8 '99').+* 94 9.+ ,7439 ,')+ 4,
9.+ 8+3847 2'9+7/'1 '3* /98 2'/3 ,:3)9/43 /8 94 .+15 +,,/)/+391>
)4:51+ 9.+ +3+7-> 94 '3* ,742 9.+ (4*> 2'9)./3- 1'>+7 /8
43+ 6:'79+7 4, ' <';+1+3-9. 9./)0 94 574;/*+ ,47 )43897:)9/;+
/39+7,+7+3)+ '8 9.+ 84:3* <';+8 97';+1 9.74:-. /9 > '**/3247+ 9.'3 43+ 2'9)./3- 1'>+7 9.+ +3+7-> /8 +;+3 247+ +,,/A
)/+391> )4:51+* 7+8:19/3- /3 7+*:)+* 5:18+ 1+3-9. #./8 <4:1*
)477+8543* 94 '3 /2574;+2+39 /3 9.+ '=/'1 7+841:9/43
#.+ /3;+89/-'9/43 4, '**/3- ' 8+)43* 2'9)./3- 1'>+7 (+-'3
(> :8/3- )425:9+7 24*+18 9.'9 8.4<+* ' 7+*:)9/43 /3 9.+
5:18+ 1+3-9. <.+3 ' 8+)43* 2'9)./3- 1'>+7 <'8 '**+* 94 '
8+3847 )425'7/843 4, 9.+ 9<4 24*+1+* A? *+8/-38
/8 8.4<3 /3 /- #.+ 3+=9 89+58 /3 9.+ 574)+88 <+7+ 94
*+,/3+ 9.+ *+8/7'(1+ 2'9+7/'1 5745+79/+8 ,47 9.+ 8+)43*
2'9)./3- 1'>+7 2'9+7/'1 '3* 9.+3 8+1+)9 '3* 9+89 '3 '557457/A
'9+ 2'9+7/'1
3 9+728 4, 97'38*:)+7 *+8/-3 9.+7+ '7+ 9<4 /25479'39 2'9+A
7/'1 5745+79/+8 4, ' 2'9)./3- 1'>+7 9.+ ')4:89/) /25+*'3)+
'3* 9.+ '99+3:'9/43 #>5/)'11> 9.+ 57+,+77+* ')4:89/) /25+*A
'3)+ 4, 9.+ 2'9)./3- 1'>+7 /8 9.+ -+42+97/) 2+'3 4, 9.+ /2A
5+*'3)+8 4, 9.+ 9<4 2'9+7/'18 /9 /8 8'3*</).+* (+9<++3 47
+='251+ /, 9.+ ,/789 2'9)./3- 1'>+7 .'8 '3 /25+*'3)+ 4, !'>18 '3* 9.+ (4*> /8 !'>18 9.+ *+8/7'(1+ /25+*'3)+
4, 9.+ 8+)43* 2'9)./3- 1'>+7 <4:1* (+ !'>18
& &&
!'>18 × !'>18
Design 2
0
Design 1
& !'>18
*+'11> 9.+ '99+3:'9/43 8.4:1* (+ 14< 94 2/3/2/?+ 9.+
'24:39 4, +3+7-> 1489 <.+3 9.+ <';+ 97';+18 9.74:-. 9.+
2'9)./3- 1'>+7
Depth into Body
Fig. 13. 1+;'9/43 (+'2 </*9.8 4, 9.+ 97'38*:)+7 '3*
9<4 /2574;+* *+8/-38
#.+ */8'554/39/3- 5+7,472'3)+ 4, 9.+ /3/9/'1 *+8/-38 7+6:/7+* 7++='2/3'9/43 4, 9.+ +3-/3++7/3- *+8/-3 94
/*+39/,> ,:79.+7 455479:3/9/+8 ,47 /2574;+2+39 #.+ 3+=9
2489 /25479'39 +3-/3++7/3- ).'7')9+7/89/)8 '8 *+,/3+* (> 9.+
.4:8+ 4, 6:'1/9> <+7+ 349 97'38*:)+7 *+8/-3 ).'3-+8 (:9
:197'84:3* 8>89+2 ).'3-+8 /3;41;/3- 1'9+7'1 (+'2 </*9.
#.+7+ <+7+ 842+ 43-4/3- /3;+89/-'9/438 /394 8>89+2 /2A
574;+2+398 (:9 </9. 9.+ 57+,+7+3)+ 97/'1 7+8:198 9.+8+ +,A
,4798 7+)+/;+* 247+ '99+39/43
:-:89 +<1+99A')0'7* 4:73'1
3 '**/9/43 94 9.+ ')4:89/) 7+6:/7+2+398 49.+7 2'9+7/'1
5745+79/+8 4, 9.+ 8+)43* 2'9)./3- 1'>+7 <+7+ /25479'39 #.+
2'9+7/'1 3++*+* 94 (+ (43*'(1+ 8/3)+ /9 <'8 -4/3- 94 (+
Pulse-Echo (two-way) Impulse Response
–25
Pulse Length
Spectrum (dB)
Linear Amplitde
Amplitude Relative to Maximum: –40 dB
–30 dB
–20 dB
0.000
0.000
Time (s)
Frequency (MHz)
(a)
Pulse-Echo (two-way) Impulse Response
–25
HP 21258A
No Second
Matching
Layer
Transducer
HP 21258B
Second
Matching
Layer
Spectrum (dB)
Linear Amplitde
Fig. 15. 0.1#3+40/ 0( 16-4' -'/)5*4 #5 7#3+064 53#/4.+55'& $'#.
#.1-+56&'4 $'-08 5*' .#9+.6. (03 <; 53#/4&6%'34 8+5*
#/& 8+5*065 4'%0/& .#5%*+/) -#:'34
0.000
0.000
(b)
–75
5.000
20.00
0
Time (s)
Frequency (MHz)
–75
5.000
20.00
0
Fig. 14. # 6-4' #/& 41'%536. 0( 5*' .0&'-'& <;
53#/4&6%'3 $ 6-4' #/& 41'%536. 0( 5*' .0&'-'& <; 53#/4&6%'3
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Fig. 16. /3'-+9 5, :.+ 8'*/'2
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:8'49*;)+8 8/-.: !
:8'49*;)+8
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:.+ /4)8+'9+ /4 :.+/8 ('4*=/*:. &/:. 953+ 9?9:+3 ).'4-+9
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(+)'3+ ' A@ :8'49*;)+8 $./9 *;'2A,8+7;+4)?
,+':;8+ +4.'4)+* :.+ 6+8,583'4)+ 5, :.+9+ :8'49*;)+89 /4
'**/:/54 :5 3'1/4- :.+3 ;4/7;+ ': :.': :/3+ /4 :.+ <'9);2'8
/3'-/4- 3'81+:
'4;,'):;8/4- 3+:.5*9 =+8+ '295 /3685<+* ,58 :.+ <+89/54
2/4+'8 6.'9+* '88'?9 $'1/4- '*<'4:'-+ 5, 9:':+A5,A:.+A'8:
'99+3(2? :+).4/7;+9 /4 54+ 3'4;,'):;8/4- 9:+6 8+9;2:+* /4 '
:.8++,52* *+)8+'9+ /4 )?)2+ :/3+ =./2+ 3'1/4- :.+ 685)+99
+'9/+8 ,58 :.+ 56+8':589
45:.+8 ,+':;8+ :.': ='9 '**+* ='9 :.+ '(/2/:? 5, :.+ :8'49A
*;)+89 :5 /3'-+ '4 +>6'4*+* </+= $./9 4+= /3'-/4- ,58A
3': /9 )'22+* :8'6+@5/*'2 /3'-/4- '4* 9.5=9 ' 3;). 2'8-+8
'8+' $8'6+@5/*'2 /3'-/4- ='9 *+<+256+* 5;:9/*+ :.+ :8'49A
*;)+8 /3'-+ 7;'2/:? /3685<+3+4: 6850+): '4* /9 45: )5<+8+*
/4 *+:'/2 /4 :./9 '8:/)2+ )536'8/954 5, ' :?6/)'2 2/4+'8 '88'?
/3'-+ '4* ' :8'6+@5/*'2 /3'-+ /9 9.5=4 /4 /- $.+ +>A
6'4*+* </+= '225=9 9545-8'6.+89 :5 9++ 358+ 5, :.+ 2'8-+8
9:8;):;8+9 9;). '9 :.+ 1/*4+? '22 /4 54+ /3'-+ ++*(')1 54
:./9 4+= ,+':;8+ .'9 (++4 +>:8+3+2? 659/:/<+ ;9:53+89
Preference
2
1
0
HP 21258A
Competitor 1
HP 21258B
Competitor 2
Fig. 17. 2/4/)'2 :8/'2 8+9;2:9 9.5=/4- 3+'9;8+* ;9+8 68+,+8+4)+ ,58
/3'-+ 7;'2/:? 5, <'9);2'8 6+8,583'4)+ 5, '6685>/3':+2? A@
:8'49*;)+89 !8+,+8+4)+ /9 3+'9;8+* 8+2':/<+ :5 :.+ ! ;-;9: +=2+::A!')1'8* 5;84'2
.'<+ 8+658:+* (+::+8 '4* ,'9:+8 */'-459+9 =/:. :8'6+@5/*'2
/3'-/4- $.+ :8'6+@5/*'2 /3'-/4- ,583': /9 '45:.+8 */9:/4):
,+':;8+ 5, :.+9+ 4+= 2/4+'8A'88'? :8'49*;)+89
$.+ +8-5453/) 658:/54 5, :./9 6850+): ='9 '295 <+8? 9;))+99A
,;2 $.+ 9/@+ 5, :.+ <+89/54 :8'49*;)+8 ='9 8+*;)+* (?
358+ :.'4 )536'8+* :5 <+89/54 += )'(2+ :+).4525-?
'225=+* 93'22+8 '4* 2/-.:+8 )'(2+9 8+9;2:/4- /4 ' <+89/54 '99+3(2? :.': /9 :=5A:./8*9 :.+ =+/-.: 5, <+89/54 $.+ <+89/54 <'9);2'8 2/4+'8 '88'? :8'49*;)+89 '8+ 9.5=4 /4
/- 4 ;4+ 5, :.+ :=5 <+89/54 2/4+'8 6.'9+*A'88'? :8'49A
*;)+89 =+8+ /4:85*;)+* ': :.+ #5)/+:? 5, %'9);2'8 $+).4525-?
'4* :.+ 3+8/)'4 #5)/+:? 5, ).5)'8*/525-? )54,+8+4)+9
$.+ :8'49*;)+89 =+8+ =+22A'))+6:+* (? 6.?9/)/'49 '4*
9545-8'6.+89 '4* :.+ 58*+8 8':+ ,58 :.+ <+89/54 2/4+'8
6.'9+*A'88'? :8'49*;)+89 /9 9+<+8'2 :/3+9 :.': ,58 :.+ <+89/54
2/4+'8 6.'9+*A'88'? :8'49*;)+89 $5*'? :.+9+ 4+= <'9);2'8
:8'49*;)+89 '8+ .+26/4- )2/4/)/'49 685</*+ 358+ '));8':+
*/'-459+9 =/:. /3685<+* /3'-+ 7;'2/:? /3685<+* +8-5453A
/)9 '4* :8'6+@5/*'2 /3'-/4- ,583':
'4? 6+562+ )54:8/(;:+* :5 :.+ 9;))+99 5, :.+ :8'49*;)+8
658:/54 5, :.+ <+89/54 2/4+'8 '88'? 6850+): "/)1 #4?*+8
).'36/54+* 9:++8'(2+ 2/4+'8 '88'?9 ': :.+ ! 3'-/4- #?9A
:+39 /</9/54 /4 :.+ +'82? 9:'-+9 "'? 544+22 ='9 :.+
" 3'4'-+8 ,58 :./9 6850+): #53+ 5, :.+ 58/-/4'2 /3'-+
7;'2/:? :+'3 3+3(+89 =+8+ '8:.' +22+8 '8? #+'<+? '4*
* !'84'-/'4 $.+ +8-5453/)9 :+'3 3+3(+89 /4)2;*+* *
!'84'-/'4 "+--/+ $;)1+8 '8:.' 58/54*5 '4* 8+!+':,/+2* $.+ :+'39 .'* -8+': :+).4/)/'4 .+26 ,853 /4.
!.'3 /;2/'4' /'82' #'4*? +)1+8 $54? ;-45 '4* 3'4?
5:.+8 3'4;,'):;8/4- 56+8':589 $.+ +4-/4++8/4- :+'39 =+8+
2':+8 +>6'4*+* :5 /4)2;*+ 8+- %5-+2 '9./ .'18'<'8:?
$85? /+29+4 #+'4 8'49:54 !';2 '8:/+8 54 "5;81+ '4*
'4 #:+36+2 25: 5, .+26 )'3+ ,853 3'81+:/4- =./). ='9
8+68+9+4:+* (? !': %+4:+89 '4* #:5)1:54 /22+8A54+9 '4
(a)
(b)
Fig. 18. 14)/-: :06>15/ ;0- *-5-.1;: 6. ;0- ;9)7-A61,)3 .694); ) 15-)9C)99)@ .694); * $9)7-A61,)3 .694);
6;- >): 8<1;- 0-37.<3 >1;0 ;0- ! )5, +<:;64-9 :<9=-@:
15)33@ )13 (>-9315/ )<3 )/515 ")@ 655-33 65
96.156 )5, "1+2 #5@,-9 >-9- )33 0-37.<3 15 -,1;15/ )5,
796=1,15/ ),=1+- 15 >91;15/ ;01: )9;1+3-
<+2 $ ! "
+),-41+ 9-:: #-3.91,/- B7796?14);- );-91)3 967-9;1-: 15 :6;9671+
);-91)3: &63 #%C
)@ 77 C
# % ! +;6*-9 -5;19- 1::<-
# % ! <5- 77 C
)9:65 B5 +6<:;1+ $9)5:,<+-9 99)@ .69 -,1+)3 4)/15/D
)9; # % ! &63 56 +;6*-9 77
C
133-9 B5 +6<:;1+ $9)5:,<+-9 99)@ .69 -,1+)3 4)/15/D
)9; # % ! &63 56 +;6*-9 77
C
$ #A)*6 )5, #-)=-@ B"),1);-, 6>-9 0)9)+;-91:;1+: 6. 1)/C
56:;1+ %3;9):6<5, $9)5:,<+-9: # % ! &63 56 +;6*-9 77 C
)<:-9 )5, 3)<:15/ B$0- 6<:- 6. !<)31;@ "
! "# &63 56 )@C<5- 77 C
156 ! " 9-5;1+-C)33 5+ )331,)@ )5, " "-:51+2 ! $ 605 '13-@ #65: Fig. 19. )5, 315-)9 70):-,C)99)@ =):+<3)9
<3;9):6<5, ;9)5:,<+-9:
</<:; ->3-;;C )+2)9, 6<95)3