End-Coupled, Half-Wavelength Resonator Filters - Design theory

Interdigital Filter
- Design Equations
Transform the lowpass prototype filter to the highpass prototype filter
Highpass
Transformation
J
0,1
=
Y0
L g g
p1
0 1
J
i, i+
1
=
1
LpiL ( 1)
gig p i+
i+
1
i= 1 to n=
1
J
n, n+
1
=
Yn+
1
L g g
pn n n+
1
BPF Response
Richard’s Transformation to decide the inductor value at edge frequency
of passband
θ
ω1 ω2 1
Y =
Lpi
pLpi
p = jω
1 Y1
Y = =
jω1L pi j tanθ
Y1
Y =
t Y1
t = j tanθ
1 Y1
=
L pi tanθ
FBW ω1 ω0
⎛ FBW ⎞
ω1= ω0 − ω0 => θ = l = l⎜1
− ⎟
2 up up
⎝ 2 ⎠
π ⎛ FBW ⎞
= ⎜1 −
2 Prof. 2 T. ⎟
⎝ ⎠L.
Wu
Interdigital Filter
- Design Equations
J-inverter value for the BPF
J
1
Y Y
1
i, i+
1 = = =
LpiL ( 1) gig i 1 tanθ
gig p i i 1 g
1 1 ig + + + i 1
i 1 to n 1
i to n +
= =
= = i= 1 to n=
1
From Richard’s transformation and previous derivations on interdigital filter
Input part:
Internal part:
Output part:
Y = Y + Y
1 a1
12
Y = Y + Y + Y
1 ai i− 1, i i, i+
1
Y = Y + Y −
1 an n 1, n
Y = Y -Y
a1
1 12
Y = Y -Y -Y
ai 1 i− 1, i i, i+
1
Y = Y -Y
−
an 1 n 1, n
Y 1 denotes the characteristic
impedance of the short-circuited stubs.
Y ai denotes the characteristic
impedance you have to find
from the interdigital filter .
Prof. T. L. Wu