Transcript Outline - 正修科技大學
Effects of Finite Strip Thickness
At larger value of t / w the significance of the thickness increase.
w e h
w h w h
1.25t
h
1.25t
h
(1 (1 ln ln 4
πw t
2
h t
); );
w h w h
2 2
Z
0
eff
60 120
eff
eff (
t
) (
r
ln( ln( 8
h w e w e h
1 ) 4 .
6
t h w h
w e
4
h
),
w h
1 .
393 0 .
667 ;
eff
(
t
)
w e h eff
1 .
444 ),
w h
eff
(
t
) 1 1
w e
w
,where w e is effective width of strip
t
w e
;
Z
0 ;
eff
Increasing thickness t E-fields
Effects of Metallic Enclosure (Housing)
The purpose of metallic enclosure provide hermetic sealing, mechanical strength, EM shielding, connector mounting, and module handling.
The conducting top and side walls lower both increase proportion of electric flux in air.
eff and Z 0 , which is due to
eff
Z
0
r
2 1 (
r
2 1
R
) tanh[ 0 .
18 0 .
237
h h
' ( 0
h
' .
415
h
) 2
R
( shielded [ 1 [ 1 ) 12 12 ( (
h w h
)] 0 .
5 )] 0 .
5 0 ,
w
Z Z
0 0 ( ( unshielded unshielded .
04 ) ) ( 1
Z Z w h
0
s
1 0
s
2 ) , 2 , ,
w h w h w h w h
1 .
3 1 1 1 .
3 ] h’
Z
0
s
1 270 [ 1 tanh( 0 .
28 1 .
2
h
'
h
)]
Z
0
s
2
Z
0
s
1 ( 1 tanh{ 1 0 .
48 [( [ 1
w e
(
h
'
h
)
h
)] 2 1 ] 0 .
5 }) h
Effects of Propagation Delay
One of the most significant properties of microstrip for applications in high speed digital or time-domain applications ( e.g. computer logic, digit communication, sampler for oscilloscope, counter) to carry signal pulses is propagation delay.
Crosstalk between adjacent circuits is a serious problem in pulse systems.
d
c eff
; s/m For example, a 50
d
1 ;
v p
1
v p LC
microstrip line on high-purity alumina: eff =6.7
d
6 .
7 3 10 8 8.6
ns/m 8 .
6 ps/mm High-speed gates typically have around 50 ps delay per gate, it means that 5-10 mm of microstrip is needed to realize such a gate. For instance, such length of line is not feasible to implement in chips.
Equivalence
L
or
C
d
length of line
Recommendations to The Static-TEM Approaches
The Static-TEM formulas will exhibit significant errors once operation frequency beyond a few GHz.
Always start with a slightly lower impedance than the actually desired, i.e. larger w / h , if trimming (etch or laser-trim) is contemplated.
The physical lengths of line should slightly longer than required for adjusting operation frequency. In general, 1% reduction in length can be expected approximately a 1% increase in frequency.
The length of a top-cover shield might be adjusted to trim the performance of MICs.
High Frequency Characters of Microstrip Line
Dispersion in Microstrip (Frequency Dependence)
r
Microstrip Line
High loss Low dispersion air
eff
0 0 0
eff
Planar Waveguide Model Microstrip Line Medium loss High dispersion Low loss substrate Low dispersion Good for Applications
As frequency goes higher, EM fields tend to distribute in the substrate region in a higher ratio.
Frequency-Dependent Effective Dielectric Constant (
f
) for Microstrip Line
The reason of dispersion generated : eff 1) Higher TE and TM modes (hybrid mode) generated 2) Surface wave couples with dominate mode
eff
(
f
,
h
,
r
) Getsinger Formula :
eff
r
(
f
)
r
1 0 0
eff
1
G
(
f
( ( /
f
) 2
f
p
) 2 0 ) where
f p
Z
0 /( 2 0
h
),
eff
eff
eff
(
f
(
f
(
f
) always increase with frequency 0 ) )
eff
r
; ;
G
is empirical formula and sensitive to
Z
0
For alumina (
eff
9 .
9 ) with
h
0 .
635
mm G
0 .
6 0 .
009
Z
0 ; For sapphire (
eff
10 .
7 ~ 11 .
6 ) with
h
0 .
5
mm G
[(
Z
0 5 ) wel l with / 60 ] 2 range 0 .
004
Z
0 ; 10
Z
0 For alumina (
eff
100 , 2 10 .
15 ) with
h
f 0 .
65
mm
18GHz
G
(
Z
0 3 ) 2 0 .
001
Z
0 ; well with range 30
Z
0 70 , 2 f 18GH 60
Example3:
Design a 50 substrate ( microstrip line on a 0.635 mm thick ceramic
r
=9.9). Calculate the wavelength of the line at 1 and 10 GHz. Assume that G = 0.6 + 0.009 Z 0 in Getsinger’s expression.
Solution
A
50 60 9 .
9 2 1 9 .
9 9 .
9 1 1 ( 0 .
23 0 .
11 ) 9 .
9 2 .
142
w
h
8
e
2 .
142
e
2 2 .
142 2 0 .
966
w
0 .
966 0 .
635 0 .
613 (mm)
eff
(
f
1 GHz ) 9 .
9 1 2 2 9 .
9 1 1 12 ( 0 .
635 / 0 .
613 ) 6 .
664 at 1 GHz 3 10 9 10 8 6 .
664 0 .
1162 (m) 116.2
(mm)
f p
2 4 10 7 50 0 .
635 10 3 31 .
33 10 9 (Hz) 31.33
(GHz)
G
0
.
6 0
.
009 50 1
.
05
eff
(
f
10 GHz ) 9 .
9 9 .
9 6 .
664 1 1 .
05 ( 10 / 31 .
33 ) 2 6 .
977 at 10 GHz 3 10 10 10 8 6 .
977 0 .
01136 (m) 11.36
(mm)
Other accurate formulas of
eff
(
f
)
Edwards and Owens’ expression : applicable for alumina and sapphire substrate under the range 10 r 12 (alumina type) and f 18 GHz.
eff
r
1 (
h
r
eff Z
0 ) 1 .
33 ( 0 .
43
f
2 0 .
009
f
3 ) ; where
h
is in mm and
f
is in GHz Yamashita expression : suitable for millimetre-wave design (up to 100GHz) but not accuracy for frequency below 18 GHZ.
eff
(
f
) (
r
1
eff
4
F
1 .
5
eff
) 2 ,
F
4
hf c
r
1 [ 0 .
5 { 1 2 log( 1
w
)} 2
h
] Advantage of these formulas are calculated-based design and inexpensively integrated into CAD tools. However, these approximate approaches based on some limited applications are their drawback.
Frequency-Dependent of Microstrip Characteristic Impedance (
Z 0
)
The problem of characteristic impedance as a function of frequency is difficult to settle. Because there are several definitions of Z 0 used different assumptions to derive results.
Planar waveguide model
Z
0 (
f
)
w eff
(
f
)
h
eff
(
f
)
w eff
(
f
)
w
1
w eff
(
f
w f p
) 2
Z
0 ,
a
V I Z
0 ,
b
P II
*
Z
0 ,
c
VV
*
P f p w eff
c
2
w eff
eff Z
0
h
eff
; 0 0
f w eff
;
Z
0 For a 50 line the increase is about 10% over 0-16GHz range
Dispersion of lossy gold microstrip on a 635 m thick alumina substrate ( w = 635 m, Z 0 r =9.8, =50 ) Dispersion of lossy copper microstrip on a 650 high resistivity silicon substrate ( =11.9, m thick w = 70 m, r Z 0 =83 )
Variation of effective permittivity and characteristic impedance for a lossy gold microstrip on a 635 m thick alumina substrate ( r =9.8)
Operation frequency Limitation
Two possible spurious effects restrict the desirable operating frequency: 1) The lowest-mode TM mode: the most significant modal limitation in microstrip are associated with strong coupling between the dominant quasi-TEM mode and the lowest-order TM mode.
2) The lowest-order transverse microstrip resonance. TM mode: it is identified when the associated two phase velocities are close.
f TEM
1
c
tan 2 (
r
1 ( 1 )
r
)
h
air Effective mode
The maximum restriction on usable substrate thickness: f TEM 1 TM 0
substrate
h M
0 .
345 0
r
1 Quasi-TEM h M f TEM 1 f TEM 1 can be regarded as the upper limitation of operating frequency.
f TEM 1 as a function of substrate thickness permittivity r .
h and relative
Lowest-Order Transverse Microstrip Resonance
Transverse microstrip resonance: For a sufficiently wide microstrip the resonant mode can also couple strongly to quasi TEM mode.
To suppress transverse resonance, slot can introduce into metal strip but sometimes it might excite resonance. A practice method is a change in circuit configuration to avoid wide microstip lines close adjacent.
At the cutoff frequency of transverse resonant mode, line has a length equivalent to capacitance: w d +2 d 0.2
, where h .
d accounts for the microstrip side-fringing The cutoff frequency:
f CT
c
r
( 2
w
0 .
8
h
)
Parameters governing the choice of substrate for any microstrip application.
Power Losses and Parasitic Coupling
Four separate mechanisms can be identified for power losses and parasitic coupling: 1) conductor losses Dissipative effects 2) dissipation in the dielectric of substrate 3) radiation loss 4) surface-wave propagation Parasitic phenomena The dissipative losses may be interpreted in terms of Q factor or can be lumped together as the attenuation coefficent .
Conductor Loss
c
g
0.072
f wZ
0 0
eff
g (dB/microstrip wavelength) ; where is in GHz and
Z
0
f -1/2
,
In practice the loss is approximately 60 % increased when surface roughness is taken into account.
h -1
Dielectric Loss
d
27.3
r eff eff
1) tan
r
1) (dB/microstrip wavelength)
Independent
f
,
h
In general conductor loss greatly exceed dielectric loss for most microstrip lines on alumina or sapphire substrates, but opposite condition to have larger dielectric loss for Si or GaAs substrates.
Q
c d
Q
g
(Np/m) 2
g
; 2
g
f Q However Q factor will be limited by parasitic effects at high frequencies.
Radiation
f 2
,
h 2
Microstrip is an asymmetric T.L. structure and is often used in unshielded or poorly shielded circuits where any radiations is either free to propagate away or to induce currents in the shielding. Further power loss is the net result.
Discontinuities of microstrip form essential features of a MIC and are the major sources of radiations unavoidably. Various techniques may be adopted to reduce radiation: 1) Metallic shielding or ‘screening’.
2)A lossy (absorbent) material near any radiation discontinuity.
3) Possibly shape the discontinuity in some way to reduce the radiation efficiency.
Surface-Wave Propagation
f 3~4
,
h 3~4
Surface wave trapped just beneath the surface of substrate dielectric, will be propagated away from microstrip discontinuities in the form of a range of TE or TM modes.
This effect can be reduced by above methods 1 and 2 , or by cutting slots into the substrate surface just in front of an open-circuit.
Power losses versus frequency for open-end discontinuity ( =10.2, w = 24 mil, h r =25 mil)
Parasitic Coupling
If shielding cannot be adopted due to space limitation as to use the absorbent material, the method will reduces the Q -factor .
High degree of isolation can suppress the parasitic coupling.
Various methods for increasing isolation: 1) Use relatively high permittivity substrate. 2) Use fairly thin substrate.
3) Employ high impedance stubs, wherever this is feasible. Conclusion : 1. Attenuation is mainly due to conductor and dielectric losses. 2. Radiation and surface-wave losses are negligible. The facts can be observed from the relative degree that these losses dependent to frequency.
Recommendations for Higher frequency Considerations
Select the substrate such that the TM mode effect is avoided. f TEM 1 , h M Check that the first-order transverse resonance cannot be exited at the highest frequency. If a resonance is occur, above mentioned solutions can be adopted to suppress. f CT Calculate the total losses and requirement. A reappraisal of design philosophy may be necessary when Q -factor is too low.
Q -factor to check if they satisfy the design Evaluate the frequency-dependent effective microstrip parameters to account for high-frequency effects. e.g. eff ( f ), Z 0 ( f )