End-Coupled, Half-Wavelength Resonator Filters - Design theory
End-Coupled, Half-Wavelength Resonator Filters - Design theory
End-Coupled, Half-Wavelength Resonator Filters - Design theory
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Combline <strong>Filters</strong><br />
- <strong>Design</strong> Concept<br />
Combline <strong>Filters</strong><br />
- Formulation<br />
<strong>Design</strong> formula for coupled-line:<br />
2<br />
⎛ N −1<br />
⎞ a b<br />
a1 = A − + +<br />
2 oe oe 12<br />
Y Y ⎜ ⎟ Y Y Y<br />
⎝ N ⎠<br />
2<br />
⎡ ⎛υC ⎞ ⎤<br />
01<br />
A ⎢1 ⎜ ⎟ ⎥<br />
YA<br />
( )<br />
= Y − + υ − C + C + C<br />
⎢⎣ ⎝ ⎠ ⎥⎦<br />
0 1 12<br />
( )<br />
Yaj = Y j + Y j− 1, j + Y j, j+ 1 = υ C j + C j− 1, j + Prof. C j, j+<br />
T. 1 L. Wu<br />
j= 2 to n−<br />
1<br />
A design procedure starts with choosing the resonator susceptance slope parameters bi<br />
a<br />
Y = υC<br />
oe a<br />
b<br />
Y = υC<br />
oe b<br />
( 2 )<br />
a<br />
Yoo = υ Ca + Cab<br />
N =<br />
υ C<br />
2YA<br />
+ 2C<br />
− C<br />
YA<br />
=<br />
υC<br />
( )<br />
ab<br />
B ( ω) = ωC −Y<br />
cotθ<br />
i Li ai<br />
0 0 Li ai 0<br />
0<br />
a<br />
b<br />
a ab a<br />
(Parallel LC)<br />
Q<br />
B( ω ) = ω C −Y cotθ ≡ 0<br />
∴ C = Y<br />
Li ai<br />
cotθ<br />
0<br />
ω<br />
Prof. T. L. Wu
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