1. Discontinuities of Microstrip Line

2. The Main Discontinuities
All 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 gaps
Short-circuit through to the ground plane (Via)
Right-angled corner (Bend)
Step width change
Transverse slit
T-junction
Cross-junction

3. A HMIC microwave amplifier using a GaAs MESFET, showing several discontinuities in the microstrip lines.

4. Open-End Three phenomena associated with the open-end :
Fringing fields. Cf
Surface 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

5. Equivalent End-Effect Length
The 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.
Cf : equivalent and fringing capacitance
Leo : equivalent extra TL of length
Upper limit to end-effect length (by Cohn):

6. Normalized end-effect length (Leo /h ) as a function of shape ratio w /h.

7. The Series Gap The gap end-effect line extension may be written :
More general formula by Garg and Bahl:

8. Via-Ground
The 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 diameter
needs 0.26mm for a good broadband
short-circuit. To accurately and repeatably
locate these holes or ‘shunt posts’,
Computer-controlled laser drilling can provide
Precision realization.

9. Right-Angle Bend or Corner
The 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):

10. Example4: Calculate the parasitic effects for a bend on an w=0
Example4: Calculate the parasitic effects for a bend on an w=0.75mm and h=0.5mm alumina substrate (er=9.9).
Solution
The 2/120  reactances in
series/parallel connection with 50  line
will have a pronounced influence
on circuit response.

11. Mitred or Matched Bend
A 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.

12. Magnitude of the current densities on
(a) a right-angled bend, and (b) an optimally mitred bend.

13. The Symmetrical Step
Like the bend, the shunt capacitance is the dominant factor.
Curve-fitting formulas:
les

14. The Narrow Transverse Slit
The Asymmetrical Step
The values of reactances are about half of the values obtained for the symmetrical step.
The Narrow Transverse Slit
A 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.

15. T-Junction
The 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.

16. Parameter trends for the T-junction.

17. Compensated T-Junction
Dydyk 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.

18. Cross-Junction
A 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.

19. Frequency-Dependence of Discontinuity Effects
Open-Circuit
Edward Figure 7.27
Edward Figure 7.25
7.26

20. Open-Circuit

21. Open-Circuit

22. Series Gap

23. Cross-Junction

24. Bend