Transcript Outline - 正修科技大學

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):
Cf
5

 exp[2.2036 k (log )i 1 ] ; pF/m

h
i 1
Coefficients for k
Equivalent End-Effect Length

The microstrip line is longer than it actually is to account for the endeffect.
cZ0C f
leo 
;
 eff
accuracy over therange 2  f  20 GHz
and alumuna substrateless than1 mm thick.
 More general formula :
(by Hammerstad and Bekkadal)
w  0.262
 eff  0.3
leo  0.412h(
)( h
)
 eff  0.258 w  0.813
h
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):
(
leo
2
) max  ln 2
h

Cf : equivalent and fringing
capacitance
Leo : 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 :
leo 
cZ0C1  C2
 eff
;
C1 : field fringingcapacitor
C2 : gap couplingcapacitor

More general formula by Garg and Bahl:
Co ( r )  9.6C0 (
Ce ( r )  9.6Ce (
r
9.6
r
9.6
)0.8
)0.9
Co  C1  2C2
Ce  2C1
Relationshold over therange 2.5   r  15
and an accuracy of 7% is quoted.
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):
weff
weff 2
ln(
)(
) ;
d e
d e

d e  0.03  0.44d ( d : act ual holediamet er)
weff 
h0
Z 0  eff
(effect ivemicrost ripwidt h)
 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.
Lvia
C fringing
Grad  surf
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):
C (14 r  12.5) w h  (1.83 r  2.25)

pF/m; For w  1
h
w
wh
C
w
 (9.5 r  1.25)  5.2 r  7 pF/m; For w  1
h
w
h
L
w
 100[4
 4.21] nH/m
h
h
Accuracy is within5% over therange :
2.5   r  15 and 0.1  w  5.0
h
Example4: Calculate the parasitic effects for a bend on an w=0.75mm
and h=0.5mm alumina substrate (r=9.9).
Solution
For w  1.5  1
h
 C  0.135pF and L  0.031nH
At 10 GHz
L  2 ; 1/C  120
 The 2/120  reactances in
series/parallel connection with 50  line
will have a pronounced influence
on circuit response.
0.031nH 0.031nH
0.135pF
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:
b
1
 0.6 
2w

b  0.57w
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.
les  leo (1 
Curve-fitting formulas:
L1  L
Lm1 
Lm1
;
Lm1  Lm 2
Z o1  eff 1
c
For  r  10 ;
;
Lm 2
; L  L1  L2
Lm1  Lm 2
L2  L
Lm 2 
1.5 
w2
w1
) ;leo : extra end-effect length
w2
Z o 2  eff 2
c
w1
All inductances are in nH/m
 3.5 :
w2
C
 12.6log  r  3.17
 (10.1log  r  2.33)
w1
w1w2
For  r  9.6 ;
3.5 
w2
w1
w2
C
 130log( )  44
w1
w1w2
 10 :
pF/m
pF/m
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.
ΔL 0 a ' 2

( )
h
2 A
Z 0, w
a'
where
 1 '
A
Z 0, w  a
 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.
Frequency-Dependence of Discontinuity Effects
 Open-Circuit
Edward
Figure
7.27
Edward
Figure
7.25
7.26
 Open-Circuit
 Open-Circuit
Series Gap
 Cross-Junction
Bend