1. A Microstrip Half-Wave Filter

2. Cg -q Yc
Admittance inverter used in the
Microstrip half-wave filter

4. Microstrip Parallel Coupled Filter1 a b 2
-I2 I1 I1 -V I2 V V V
(a)
(b)
Even Mode
Odd mode q
Equivalent circuit Y1 Y2 Y3 1 2
(c)

7. Parallel Coupled Filter
S.C Yc 1
Yea, Yoa 2 3 Yc
Yeb, Yob
Yec, Yoc
Yea
Yec
(Yoa-Yea)/2
(Yoc-Yec)/2
(Yob-Yeb)/2
Yeb
Parallel Coupled Filter

8. Reduced equivalent circuit for Parallel Coupled Filter
(Yoc-Yec)/2
(Yoa-Yea)/2
(Yob-Yeb)/2
Yea
Yea
Yec
Yec
Reduced equivalent circuit for Parallel Coupled Filter

9. q a b c d
Zoa+ Zob
Zob+ Zoc
Zoc+ Zod
Zoa
Zod
(Zea- Zoa)/2
(Zeb- Zob)/2
(Zec- Zoc)/2
(Zed - Zod)/2 Z2 Z3 a q Z1 b q
Parallel coupled filter using open-circuited coupled line sections
And its equivalent circuit.

11. Example: Chebyshev bandpass filter
Design a two-section Chebyshev Filter with 30% bandwidth,
passband tolerance K2 =0.5, center freq.=6 GHz.
Input/output impedance =50 Ohms. Z1 Z3 Z3 Z1 Zc Zc Z2 Z4 Z2
Two section parallel coupled line and its equivalent circuit

13. Design of a three section half wave bandpass filter
Design a filter with f0 =10GHz, a bandwidth of 1 GHz, passband
Tolerance k2 =0.1 , max VSWR=1.863

17. L2
R=1 C3 C1
R=1
Low-pass prototype circuit