Discontinuities of Microstrip Line. The Main Discontinuities All practical distributed circuits must inherently contain discontinuities. Such discontinuities
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Discontinuities of Microstrip Line
The Main DiscontinuitiesAll practical distributed circuits must inherently contain discontinuities. Such discontinuities give rise to small capacitances and inductances ( often < 0.1pF and < 0.1nH) and these reactances become significant at high frequencies.Several form of discontinuities :Open-end circuit (Stub)Series coupling gapsShort-circuit through to the ground plane (Via)Right-angled corner (Bend) Step width changeTransverse slitT-junctionCross-junction
A HMIC microwave amplifier using a GaAs MESFET, showing several discontinuities in the microstrip lines.
Open-EndThree phenomena associated with the open-end :Fringing fields. CfSurface waves.Radiation. Terms 2 and 3 equivalent to a shunt conductance (G), but minimization can be carried out to suppress the effects.Curve-fitting formula (by Silvester and Benedek):
Coefficients for k
Equivalent End-Effect LengthThe microstrip line is longer than it actually is to account for the end-effect.More general formula : (by Hammerstad and Bekkadal)Over a wide range of materials and w/h, the expression gives error of 5%. Where such error is accepted.Upper limit to end-effect length (by Cohn):Cf : equivalent and fringing capacitanceLeo : equivalent extra TL of length
Normalized end-effect length (Leo /h ) as a function of shape ratio w /h.
The Series GapThe gap end-effect line extension may be written :More general formula by Garg and Bahl:
Via-GroundThe via hole provides a fairly good short-circuit to ground at lower frequency range, but the parasitic effects increase at high frequencies.Optimum via-hole dimension for minimum reactance ( by Owens):For a 50 line on alumina substrate(r =10.1, h=0.635mm), the hole diameterneeds 0.26mm for a good broadbandshort-circuit. To accurately and repeatablylocate these holes or shunt posts, Computer-controlled laser drilling can providePrecision realization.
Right-Angle Bend or CornerThe bend usually pass through an angle of 90 and the line does not change width.The capacitance arises through additional charge accumulation at the corners particularly around the outer part of bend where electric fields concentrate.The inductance arise because of current flow interruption.Reactance formula ( by Gupta):
Example4: Calculate the parasitic effects for a bend on an w=0.75mm and h=0.5mm alumina substrate (er=9.9). SolutionThe 2/120 reactances in series/parallel connection with 50 linewill have a pronounced influence on circuit response.
Mitred or Matched BendA mitred bend can greatly reduce the effects of reactance and hence improving circuit performance.An equivalent line-length lc occurs and increase with enhanced mitred.The champing function should be restricted to around:
A bend acts like a reflector.
Magnitude of the current densities on (a) a right-angled bend, and (b) an optimally mitred bend.
The Symmetrical StepLike the bend, the shunt capacitance is the dominant factor.Curve-fitting formulas:les
The Asymmetrical StepThe values of reactances are about half of the values obtained for the symmetrical step. The Narrow Transverse SlitA narrow slit yields a series inductance effect, and it may be used to compensate for excess capacitance at discontinuities or to fine-tune lengths of microstrip such as stubs. A narrow slit width causes parasitic capacitance to parallel connection with L. While wide slit forms the asymmetrical steps. Therefore b < h.
T-JunctionThe junction necessarily occurs in a wide variety of microstrip circuits such as matching elements, stub filters, branch-line couplers, and antenna element feeds.Garg et. al. and Hammerstad et. al. have provided formulas for extracting the elements of equivalent circuit. However, some limitations to the accuracy of formulas should be noticed.
Parameter trends for the T-junction.
Compensated T-JunctionDydyk have modified the microstrip in the vicinity of junction in order to compensate for reference plane shifts, at least over a specified range of frequencies.The treatment of the junction can exclude radiation loss with little error in circuit performance results, at least up to a frequency of 17 GHz.
Cross-JunctionA cross-junction may be symmetrical or asymmetrical, where the lines forming the cross do not all have the same widths.Theoretical and experimental agreement is not good, especially for some inductance parameter.The coupling effects that occur with cross-junctions illustrates the origin of cross-talk in complicated interconnection networks.One kind of applications is that used two stubs placed on each side of microstrip to instead of single one. The method can prevent wider stub from sustaining transverse resonance modes at higher operating frequency.
Edward Figure 7.257.26
Frequency-Dependence of Discontinuity Effects Open-CircuitEdward Figure 7.27