Design of planar filters

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

Low-Pass Prototype Filter

Butterworth Low-Pass Prototype LAR = 3.01 dB Requirement LAS = 40 dB, ΩS = 2 rad/s n = 6.644 → 7-pole Butterworth prototype filter

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

Elliptic Function Low-Pass Prototype Filter

Low-Pass Prototype Filter with inverters

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

Low-Pass Transformation

High-Pass Transformation

Band-Pass Transformation

Band-Stop Transformation

Planar filters stepped impedance

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

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 = 1.0316 g2 = 1.1474

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

Low-Pass Stepped Impedance design (3) Substrate parameters: Dielectric constant: 10.8 Substrate height: 1.27 mm Selection of characteristic impedances: Input / output: 50  Inductive segment: 93  Capacitive segment: 24 

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

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

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

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

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

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

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

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

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

Low-Pass … design (13)

References HONG, J.-S., LANCASTER, M. J. Microstrip Filters for RF / Microwave Applications. New York: John Wiley and Sons. 2001. ISBN 0-4713-8877-7.