Prof. Tzong-Lin Wu Department of Electrical …

1 Prof. T. L. WuMicrowave Filter DesignChp4. Transmission Lines and ComponentsProf. Tzong-Lin WuDepartment of Electrical EngineeringNational taiwan UniversityProf. T. L. WuMicrostrip LinesMicrostrip Structure Inhomogeneous structure: Due to the fields within two guided wave media, the microstrip does not support a pure TEM wave. When the longitudinal components of the fields for the dominant mode of a microstripline is much smaller than the transverse components, the quasi TEM approximation is applicable to facilitate T. L. WuMicrostrip Lines - Transmission Line ParametersEffective Dielectric Constant ( re) and Characteristic Impedance(ZC) For thin conductors ( , t 0), closed form expression (error 1 % ): W/h 1: re W/h 1: For thin conductors ( , t 0), more accurate expressions: Effective dielectric constant (error % ): Characteristic impedance (error % ):Prof.

2 T. L. WuMicrostrip Lines - Transmission Line Parameters Guided wavelength Propagation constant Phase velocity Electrical length0gre =300( )gremmf GHz =or2g =prec = = = oZ,Prof. T. L. WuMicrostrip Lines - Transmission Line Parameters Losses Conductor loss Dielectric loss Radiation loss Dispersion re(f) Zo(f) Surface Waves and higher order modes Coupling between the quasi TEM mode and surface wave mode become significant when the frequency is above fs Cutoff frequency fcof first higher order modes in a microstrip The operating frequency of a microstrip line < Min (fs, fc)1tan21 = rsrcfh ()2 +crcfW h Prof. T. L. WuMicrostrip Lines - Tx-Line Synthesis of transmission line Electrical or physical parameters Prof. T. L. WuCoupled LinesCoupled line Structure The coupled line structure supports two quasi TEM modes: odd mode and even wallOdd modeMagnetic WallElectric fieldMagnetic fieldEven modeProf.

3 T. L. WuCoupled Lines Odd- and Even- ModeEffective Dielectric Constant ( re) and Characteristic Impedance(ZC) Odd and Even Mode:The characteristic impedances (Zcoand Zce) and effective dielectric constants ( ore and ere) are obtained from the capacitances (Co and Ce): Odd Mode: Even Mode:Odd modeEven mode Caoand Caeare even and odd mode capacitances for the coupled microstripline configuration with air as T. L. WuCoupled Lines Odd- and Even- ModeEffective Dielectric Constant ( re) and Characteristic Impedance(ZC) Odd and Even Mode Capacitances: Odd Mode: Even Mode:Odd modeEven mode Cpdenotes the parallel plate capacitance between the strip and the ground plane: Cfis the fringe capacitance as if for an uncoupled single microtrip line: Cf accounts for the modification of fringe capacitance Cf: Cgdmay be found from the corresponding coupled stripline geometry: Cgacan be modified from the capacitance of the corresponding coplanar strips:,,,Prof.

4 T. L. WuDiscontinuities And Components Discontinuities Microstrip discontinuities commonly encountered in the layout of practical filters include steps, open ends, bends, gaps, and junctions. The effects of discontinuities can be accurately modeled by full wave EM simulator or closed form expressions and taken into account in the filter designs. Steps in width: Open ends: Gaps: Bends:Prof. T. L. WuDiscontinuities Steps in widthNote : Lwifor i = 1, 2 are the inductances per unit length of the appropriate micriostrips, having widths W1and W2, reidenote the characteristic impedance and effective dielectric constant corresponding to width Wi, and h is the substrate thickness in T. L. WuDiscontinuities Open ends The fields do not stop abruptly but extend slightly further due to the effect of the fringing field. Closed form expression:where The accuracy is better than % for the range of W/h 100 and r 128 Prof.

5 T. L. WuDiscontinuities Gapswhere The accuracy is within 7 % for W/h 2 and r 15 Prof. T. L. WuDiscontinuities Bends The accuracy on the capacitance is quoted as within 5% over the ranges of r 15 and W/h 5. The accuracy on the inductance is about 3 % for W/h T. L. WuComponents lumped inductors and capacitors Lumped inductors and capacitorsThe elements whose physical dimensions are much smaller than the free space wavelength 0of the highest operating frequency (smaller than 0). design of inductors High impedance line Meander line Circular spiral Square spiral Circuit representation Initial design formula for straight line inductorProf. T. L. WuComponents lumped inductors and capacitors design of capacitors Interdigital capacitorAssuming the finger width W equals to the space and empirical formula for capacitance is shown as follow Metal insulator metal (MIM) capacitorEstimation of capacitance and resistance is approximated by parallel plate Circuit representationProf.

6 T. L. WuComponents Quasilumped elements (1) Quasilumped elementsPhysical lengths are smaller than a quarter of guided wavelength g. High impedance short line elementgl <<<<8cossin1sincosccjZA BjC DZ = ()11122122cos1sinsin1cos1sinsinccccAD BCDjZjZY YBBY YAjZjZBB == 222221112cossincossin2sintancos1222222si n22sin cos2sin cos2222ccccBY YjjjZZjZjZ + + ===== Derivation 1211sincYjZjx == inductive element:capacitive element:Y11+Y12 Y12Y22+Y12 Prof. T. L. WuComponents Quasilumped elements (2) Quasilumped elements Low impedance short line elementgl <<<<8cossin1sincosccjZA BjC DZ = ()11122122cossinsincos1sinsinccccZZAD BCAZ ZjjC CZ ZZ ZDjjC C == 121sincZZjjB == Derivation 1112cos1tansin22ccZxZ ZjZjj === inductive element:capacitive element:tan22cxZ = sincBZ = Zc, Prof.

7 T. L. WuComponents Quasilumped elements (3) Quasilumped elements Open and short circuited stubs (assuming the length L is smaller than a quarter of guided wavelength g)8gl <8gl <CLProf. T. L. WuComponents ResonatorsProf. T. L. WuLoss Considerations for Microstrip Resonators Unloaded quality factor Qu is served as a justification for whether or not the required insertion loss of a bandpass filter can be met. The total unloaded quality factor of a resonator can be found by adding conductor, dielectric, and radiation loss together. Quality factors Qcand Qdfor a microstrip line EM simulatoror