1. Design of planar filters

2. Planar Filters design
Selection of a proper low-pass prototype (filter order, passband ripple, ...)
Computing corresponding planar implementation (widths and lengths of microstrip segments)

3. Low-Pass Prototype Filter

4. Butterworth Low-Pass Prototype LAR = 3.01 dB
Requirement LAS = 40 dB, ΩS = 2 rad/s
n = → 7-pole Butterworth prototype filter

5. Chebyshev Low-Pass Prototype
Requirement LAS = 40 dB, ΩS = 2 rad/s
n = 5.45 → 6-pole Chebyshev prototype filter

6. Elliptic Function Low-Pass Prototype Filter

7. Low-Pass Prototype Filter with inverters

8. Frequency and Element Transformations
0.90
0.95
1.00
1.05
1.10
0.85
1.15
-40
-30
-20
-10
-50
freq, GHz

9. Low-Pass Transformation

10. High-Pass Transformation

11. Band-Pass Transformation

12. Band-Stop Transformation

13. Planar filters stepped impedance

14. Microstrip segments inductance, capacity
High impedance:
Low impedance:
Characteristic impedance:

15. Low-Pass Stepped Impedance design (1)
Requirements:
Cutoff frequency: 1 GHz
Passband ripple: 0.1 dB
Impedance: 50 
Order: 3
Chebyshev low-pass prototype (c = 1 rad/s):
g0 = g4 = 1
g1 = g3 =
g2 =

16. Low-Pass Stepped Impedance design (2)
Inductance:
Capacity:

17. Low-Pass Stepped Impedance design (3)
Substrate parameters:
Dielectric constant: 10.8
Substrate height: mm
Selection of characteristic impedances:
Input / output: 50 
Inductive segment: 93 
Capacitive segment: 24 

18. Low-Pass Stepped Impedance design (4)
Width of microstrip segments: see the 4th lecture

19. Low-Pass Stepped Impedance design (5)
Width of microstrip segments: see the 4th lecture

20. Low-Pass Stepped Impedance design (6)
Width of microstrip segments:
Input / output: 1.1 mm
Inductive segment: 0.2 mm
Capacitive segment: 4.0 mm

21. Low-Pass Stepped Impedance design (7)
Effective permitivity of segments: see the 4th lecture
Newly:

22. Low-Pass Stepped Impedance design (8)
Wavelength of segments: see the 4th lecture
Input / output: 112 mm
Inductive segment: 118 mm
Capacitive segment: 105 mm

23. Low-Pass Stepped Impedance design (9)
High-impedance segment:

24. Low-Pass Stepped Impedance design (10)
Low-impedance segment:

25. Low-Pass Stepped Impedance design (11)
Length of segments:  

26. Low-Pass Stepped Impedance design (12)
Correcting reactance and susceptance:

27. Low-Pass … design (13)

28. References
HONG, J.-S., LANCASTER, M. J. Microstrip Filters for RF / Microwave Applications. New York: John Wiley and Sons ISBN