Discontinuities of Microstrip Line

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 :

1. Open-end circuit (Stub)

2. Series coupling gaps

3. Short-circuit through to the ground plane (Via)

4. Right-angled corner (Bend)

5. Step width change

6. Transverse slit

7. T-junction

8. Cross-junction

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

Open-End Three phenomena associated with the open-end :

1. Fringing fields. Cf

2. Surface waves.

3. 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):

pF/m ; ])(log2036.2exp[ 15

1

i

i

f

hk

C

Coefficients for k

Equivalent End-Effect Length

The microstrip line is longer than it actually is to account for the end-effect.

thick.mm 1 thanless substratealumuna and

GHz 202 range over theaccuracy

; 0

f

CcZl

eff

feo

More general formula :

(by Hammerstad and Bekkadal)

hw

hw

h.leff

effeo )

813.0

262.0()

258.0

3.0(4120

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):

2ln2

)( max

h

leo

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 Gap The gap end-effect line extension may be written :

capacitor coupling gap:C

capacitor fringing field:

;

2

1

210

C

CCcZl

effeo

More general formula by Garg and Bahl:

quoted. is 7% ofaccuracy an and

152.5 range over the hold Relations

2

2

)6.9

(6.9)(

)6.9

(6.9)(

1

21

9.0

8.00

r

e

o

rere

rro

CC

CCC

CC

CC

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):

width)microstrip (effective

diameter) hole actual:( 44.003.0

; )()ln(

0

0eff

2

eff

e

e

eff

e

eff

Z

hw

ddd

d

w

d

w

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.

fringingC rad surfG viaL

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):

0.51.0 and 155.2

:range over the 5% withinisAccuracy

nH/m ]21.44[100

1 For ;pF/m 72.5)25.15.9(

1 For ;pF/m )25.283.1()5.1214(

hw

h

w

h

L

hw

h

w

w

C

hw

hw

hw

w

C

r

rr

rr

Example4: Calculate the parasitic effects for a bend on an w=0.75mm and h=0.5mm alumina substrate (r=9.9).

1201/ ; 2

GHz 10At

nH031.0 and pF135.0

15.1For

CL

LCh

w

Solution

The 2/120 reactances in

series/parallel connection with 50 line

will have a pronounced influence

on circuit response.

0.135pF

0.031nH0.031nH

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:

wbw

b57.0 6.0

21

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 Step Like the bend, the shunt capacitance is the dominant factor.

Curve-fitting formulas:

1 21 2 1 2

1 2 1 2

1 1 2 2

1 2

2

1

2

11 2

; ;

; All inductances are in nH/m

For 10 ; 1.5 3.5 :

(10.1log 2.33) 12.6log 3.17 pF/m

For 9.6

m m

m m m m

o eff o eff

m m

r

r r

r

L LL L L L L L L

L L L L

Z ZL L

c cw

w

C w

ww w

2

1

2

11 2

; 3.5 10 :

130log( ) 44 pF/m

ww

C w

ww w

1

2

(1 ) ; : extra end-effect lengthes eo eo

wl l l

w

les

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.

',0

,0

20

1'

here

)'

(2

aw

w

Z

Z

A

aw

A

a

h

ΔL

A narrow slit width causes parasitic capacitance to parallel connection with L. While wide slit forms the asymmetrical steps. Therefore b < h.

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.

Parameter trends for the T-junction.

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.

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.

Edward Figure 7.25

7.26

Frequency-Dependence of Discontinuity Effects Open-Circuit

Edward Figure 7.27

Open-Circuit

Open-Circuit

Series Gap

Cross-Junction

Bend