Microwave Filter

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  • 1.MicrowaveFilter Microwave Engineering CHO, Yong Heui

2. Microwave EngineeringCircuit Resonator2 EM Wave Lab 3. Microwave Engineering1. LC resonatorApplications Filter Oscillator Frequency meter Tuned amplifier 3EM Wave Lab 4. Microwave Engineering1. LC resonatorLC resonator: ideal resonator Input impedance j Z in = jL C Input power 1 * 1 2 1 2j Pin = VI = Z in I = I jL 222 C Resonant frequency: Wm = We1=LC 4 EM Wave Lab 5. Microwave Engineering1. LC resonatorSeries resonator R, L, C Input impedance j Z in = R + jL C Input power1 * 1 2 1 2j Pin = VI = Z in I = I R + jL 222 C Resonant frequency1=LC 5 EM Wave Lab 6. Microwave Engineering1. LC resonatorQuality factor DefinitionAverage energe stored Q = Energy loss/second 3 dB bandwidthf0Q= BW Q in terms of R, L, C 2Wm 0 L1Q = 0 = =Pl R 0 RC 6 EM Wave Lab 7. Microwave Engineering1. LC resonatorPerturbation Input impedance 2 0 2Z in = R + jL 2 R + j 2 L 7EM Wave Lab 8. Microwave Engineering1. LC resonatorParallel resonator R, L, C Input admittance1j Yin = + j CR L Input power 1 * 1 * 2 1 2 1 jPin = VI = Yin V = V + j C 22 2 R L Resonant frequency1=LC8EM Wave Lab 9. Microwave Engineering1. LC resonatorQuality factor Q in terms of R, L, C2WmR Q = 0 == 0 RC Pl 0 L 9 EM Wave Lab 10. Microwave Engineering1. LC resonatorPerturbation Input admittance1 2 0 12 Yin = + jC 2 R + j 2CR10EM Wave Lab 11. Microwave Engineering1. LC resonatorLoaded Q Unloaded Q: resonant circuit itself Loaded Q: External load resistor1 1 1=+QL Qe Q 11 EM Wave Lab 12. Microwave Engineering2. Tx line resonator Short-circuited half-wave line Transmission line Input impedance: lossy mediumZ in = Z 0 tanh ( + j ) ltanh(l ) + j tan( l )= Z0 1 + j tan( l ) tanh(l )12EM Wave Lab 13. Microwave Engineering2. Tx line resonator Approximation Low-loss transmission line tanh(l ) l Phase: = 0 + , l = / 2 tan( l ) = tan( + )00 13 EM Wave Lab 14. Microwave Engineering2. Tx line resonator Equivalence Input impedancel + j ( / 0 ) Z in Z 0 Z 0 l + j 1 + j ( / 0 )l 0 = R + 2 jL Quality factor0 L Q= == R2l 2 14EM Wave Lab 15. Microwave Engineering2. Tx line resonator Open-circuited half-wave line Transmission line Input impedance: lossy mediumZ in = Z 0 coth ( + j ) l 1 + j tan( l ) tanh(l )= Z0tanh(l ) + j tan( l )15EM Wave Lab 16. Microwave Engineering2. Tx line resonator Approximation Low-loss transmission line tanh(l ) l Phase: = 0 + , l = / 2 tan( l ) = tan( + )00 16 EM Wave Lab 17. Microwave Engineering2. Tx line resonator Equivalence Input impedance1 + j ( / 0 )lZ0 Z in Z 0l + j ( / 0 ) l + j ( / 0 ) 1 = 1 / R + 2 jC Quality factor Q = 0 RC == 2l 217 EM Wave Lab 18. Microwave Engineering3. Waveguide cavityRectangular waveguide Metallic wall Propagation constant22 m n mn = k 2 a b Resonant condition mn d = l18EM Wave Lab 19. Microwave Engineering3. Waveguide cavityResonant wavenumber Resonant wavenumber 22 2 m n l k mnl = + + a b d TE101 mode and TM110 mode Q of cavity2We Q = 0 Pl 19EM Wave Lab 20. Microwave Engineering3. Waveguide cavityCircular waveguide Metallic wall Propagation constant Resonant condition mn d = l TE111 mode and TM110 mode20EM Wave Lab 21. Microwave Engineering4. Dielectric cavity Dielectric material High QFringing field High permittivity: magnetic wall Mechanical tuning TE01 mode Notation = 2 L / g < 1 21 EM Wave Lab 22. Microwave Engineering5. Mirror Fabry-Perot resonator Two mirrorsHigh Q Laser Millimeter and optical applications 22EM Wave Lab 23. Microwave EngineeringMicrowave Filter23EM Wave Lab 24. Microwave Engineering1. Filter Characteristics 2 port network: S parametersPass band and stop bandReturn loss and insertion lossRipple and selectivity (skirt)Pole and zeroGroup delay 24EM Wave Lab 25. Microwave Engineering1. Filter Characteristics Phase response Signal distortion25EM Wave Lab 26. Microwave Engineering1. Filter Classification LPF (Low Pass Filter)HPF (High Pass Filter) BPF (Band Pass Filter) BSF (Band Stop Filter): notch filter26EM Wave Lab 27. Microwave Engineering1. Filter Filter response Maximally flat (Butterworth) filterChebyshev filter Elliptic function filter Bessel function filter27 EM Wave Lab 28. Microwave Engineering2. Filter design Design process Filter specificationsDesign of low pass filter Scaling and conversion Design of transmission line Implementation28 EM Wave Lab 29. Microwave Engineering2. Filter design Insertion loss method Precise design method Power loss ratio: transducer gainPower available from source1PLR = = 2Power delivered to load 1 ( ) Reflection coefficient2M ( 2 ) ( ) =M ( 2 ) + N ( 2 ) Results:M ( 2 )PLR = 1 +N ( 2 )29EM Wave Lab 30. Microwave Engineering2. Filter design Filter responses: LPF Maximally flat response 2N PLR = 1 + k 2 c Equal ripple response PLR = 1 + k T 2 2 N c Chebyshev polynomial TN (cos ) = cos(n )30 EM Wave Lab 31. Microwave Engineering2. Filter design Example Design 2-poles low pass filter in terms of theinsertion loss method where c = 1, Z S = 1PLR = 1 + 4Z L (1 jZ L C ) Z in = jL + 1 + (Z L C ) 231EM Wave Lab 32. Microwave Engineering2. Filter design Impedance scaling Z L (1 jZ L C ) L = Z 0 LZ in = jL +1 + (Z L C ) 2 CC = Example Z00 LQ= Zs = Z0 RZ L = Z0Z L1 0 = LC Series RLC resonator32 EM Wave Lab 33. Microwave Engineering2. Filter design Frequency scaling for LPF Basic equation PLR ( ) = PLR c LjX = jL = j L L = c c CjB = j C = jC C = c c33EM Wave Lab 34. Microwave Engineering2. Filter design Frequency scaling for HPF Basic equation c PLR ( ) = PLR c 1 1 jX = jL= L = j C cCc11 jB = j C =C = j L c L34EM Wave Lab 35. Microwave Engineering2. Filter design Frequency scaling for BPF Basic equation: 0 = 1 2 0 QPLR ( ) = PLR , Q = 0 0 2 1 0 1 jX = jQ L = jL1 jC 0 1 0 1 jB = jQ C = jC2 0 jL235EM Wave Lab 36. Microwave Engineering2. Filter design Frequency scaling for BSF Basic equation: 0 = 1 2 1 1 PLR ( ) = PLR 0 , Q = 0 Q 0 2 111j 0 1 jX = L = L C1 jQ 0 111j 0 1jB = C=j C L2 Q 0 2 36EM Wave Lab 37. Microwave Engineering2. Filter design Example Design 5-poles low pass filter with a cutofffrequency of 2 [GHz], impedance = 50 [Ohms],insertion loss = 15 dB at 3 [GHz]g1 = 0.618g 2 = 1.618g3 = 2g 4 = 1.618g 5 = 0.618 Maximally flat response 37EM Wave Lab 38. Microwave Engineering2. Filter design Richards transformation Transformation l = tan( l ) = tan v p Input impedance: stubjX = jL = jL tan( l )jB = jC = jC tan( l ) 38EM Wave Lab 39. Microwave Engineering2. Filter design LC to stubsjX = jL = jL tan( l )jB = jC = jC tan( l )39EM Wave Lab 40. Microwave Engineering2. Filter design Stub characteristics Resonance: wavelength/8 related to the cutofffrequency = 1 = tan( l ) Attenuation pole: wavelength/4 Period: wavelength/2 40 EM Wave Lab 41. Microwave Engineering2. Filter design Kurodas identity Stub transformation: shunt and series stub Series to shunt stub transform: microstrip line Z2N = 1+ Z1 Implementation41 EM Wave Lab 42. Microwave Engineering2. Filter design Kurodas identityStub transformation 42EM Wave Lab 43. Microwave Engineering2. Filter design Equivalent transmission line Series to shunt stub transform: microstrip line Implementation: realization43 EM Wave Lab 44. Microwave Engineering3. ImplementationMaterials Microstrip line Dielectric resonator Waveguide Semiconductor MEMS (Micro ElectroMechanical System) LTCC (Low Temperature Cofired Ceramic) SAW (Surface Acoustic Wave) FBAR (Film Bulk Acoustic Resonator) Superconductor44EM Wave Lab