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5-23<br />
Quarter-Wave Transformer 四分之一波長(傳輸線)阻抗轉換匹配<br />
( only useful for pure-resistance matching )<br />
transmission<br />
line 1<br />
V1 ( z)<br />
<br />
<br />
V1 ( z)<br />
0 X<br />
( Z 0)<br />
( Z 0)<br />
Z<br />
in<br />
quarter-wavelength<br />
transmission line 2<br />
l / 4<br />
ZL<br />
jZ0<br />
tanl<br />
( Z0<br />
) Z0<br />
Z<br />
jZ tanl<br />
l<br />
<br />
<br />
&<br />
2<br />
tan<br />
2011-12 H.-R. Chuang EE NCKU<br />
Z<br />
in<br />
Z<br />
0<br />
Z<br />
Z<br />
2<br />
0<br />
0<br />
0<br />
l <br />
<br />
4<br />
ZL<br />
jZ0<br />
( )<br />
Z0<br />
Z0<br />
Z0<br />
Z<br />
jZ ( )<br />
Z<br />
Ex: A microstrip quarter-wave trasformer that matches a 50 miscrostrip line to<br />
a 20 load at f = 4 GHz (substrate: r=2.5, thickness h = 0.75 mm)<br />
2.13[mm] 4.03[mm]<br />
50[ ]<br />
31. 62[<br />
]<br />
<br />
12.73[mm]<br />
L<br />
20[ ]<br />
* Double Quarter-Wave Transformer for wider (matching b<strong>and</strong>width)<br />
ZL<br />
L<br />
L<br />
L
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