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Microstrip Techniques
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MICROWAVES & RF ■ MARCH 2000
79
A number of different transmis-sion lines are generally used formicrowave ICs (MICs) as shown inFig. 1. Each type has its advantages
with respect to the others. In Fig. 1,it should be noted that the substratematerials are denoted by the dottedareas and the conductors are indicat-ed by the bold lines.
The microstrip line is a transmis-sion-line geometry with a single con-ductor trace on one side of a dielectricsubstrate and a single ground planeon the opposite side. Since it is anopen structure, microstrip line has amajor fabrication advantage overstripline. It also features ease ofinterconnections and adjustments.
In a microstrip line, the wave-length, L, is given by:
where:eeff = the effective dielectric con-
stant, which depends on the dielec-tric constant of the substrate materi-al and the physical dimensions of themicrostrip line, and
l = the free-space wavelength.In a microstrip line, the electro-
magnetic (EM) fields exist partly inthe air above the dielectric substrateand partly within the substrate itself.Intuitively, the effective dielectricconstant of the line is expected to begreater than the dielectric constant
Λ = λ ε/ ( ) (1)eff0.5
Leo G. Maloratsky Principal Engineer Rockwell Collins, 2100 West HibiscusBlvd., Melbourne, FL 32901; (407)953-1729, e-mail: [email protected].
Reviewing TheBasics Of MicrostripLines An understanding of the fundamentals of
microstrip transmission lines can guide high-frequency designers in the proper application of thisvenerable circuit technology.
DESIGN FEATURE
Microstrip Lines
PRINTED transmission lines are widely used, and for good reason.They are broadband in frequency. They provide circuits that arecompact and light in weight. They are generally economical to pro-duce since they are readily adaptable to hybrid and monolithic inte-
grated-circuit (IC) fabrication technologies at RF and microwave fre-quencies. To better appreciate printed transmission lines, and microstripin particular, some of the basic principles of microstrip lines will bereviewed here.
Basic lines Modifications
Finline
Suspendedmicrostrip line
Shielded suspended stripline
Invertedmicrostrip line Shielded microstrip line
Double-conductor stripline
W1
W2
a
a
a
a a a
a a a
a
a a a a
h h hh
h
h h h
h
h h h h
H
H
b
b
b
b b
b
b b
bd
b
Mic
rost
riplin
e
Microstrip line
Strip
line
Shielded high-Qsuspended stripline
Slotline
Symmetricalcoplanar line
Finl
ine
Copl
anar
wav
egui
deSl
otlin
eSu
spen
ded
strip
line
Stripline
t
t
t
t
t
t
t t
W
W
W W
W W
WSS
S
W
W W W W
W
W
W W
Shielded suspendeddouble-substrate stripline
Antipodal slotline
Bilateral slotline
Shielded coplanar waveguide
Bilateral finline
Antipodal finline Antipodal overlappingfinline
1. These are commonly used types of printed transmission lines for MICs.
MICROWAVES & RF ■ MARCH 2000
80
of air (1) and lessthan that of thedielectric sub-strate.1 Variouscurves for effec-tive dielectric con-stant are shown inFig. 2 as a func-tion of physicaldimensions andrelative dielectricconstant.
Referring againto Fig. 1, it shouldbe apparent that abasic (unshielded)microstrip line isnot really a practi-cal structure. It is
open to the air and, in reality, it isdesirable to have circuits that arecovered to protect them from theenvironment as well as to preventradiation and EM interference(EMI). Also, the microstrip configu-rations that have been so far dis-cussed are transversally infinite inextent, which deviates from reality.Covering the basic microstrip config-uration with metal top plates on thetop and on the sides leads to a morerealistic circuit configuration, ashielded microstrip line with a hous-ing (Fig. 1).
The main purposes of the housingor package are to provide mechanicalstrength, EM shielding, germetiza-tion, and heat sinking in the case ofhigh-power applications. Packagingmust protect the circuitry from mois-ture, humidity, dust, salt spray, andother environmental contaminants.In order to protect the circuit, certainmethods of sealing can be used: con-ductive epoxy, solder, gasket materi-als, and metallization tape.
An MIC mounted into a housingmay be looked on as a dielectricallyloaded cavity resonator (Fig. 3, left)with the following inner dimensions:a is the width, l is the length, and H isthe height of the enclosure. Thesedimensions should be selected in away so that the waveguide modes arebelow cutoff.
The parasitic modes appear in thisresonator if:
where:
R ( 2) [(M ) (N / a) ] (2a)02 2 2= +λ / / l
H {h[1 (1 / )]R}1(R 1) (2)= − −ε
Microstrip Lines
DESIGN FEATURE
1.0
4.0
3.0
2.0
0.1 0.2 0.4 0.6 0.8 1.0 2.0 4.0
(eef
f)0.5
e = 20
e = 15
e = 12e = 10e = 8e = 6e = 5e = 4e = 3e = 2
e = 1.5
W/h
2. The values of effective dielectric constant are shown fordifferent substrate relative dielectric constants as afunction of W/h.
H
l
a
h
15 25 35 45 550.51.0
2.0
3.0
4.0
5.0
2:2
2:1
1:2a = 24 mml = 30 mmh = 0.5 mmM = 1, N = 1
Heig
ht (H
)—m
m
Wavelength (l)—mm
H
a
h
3. Housing dimensions are selected for microstrip circuits (left) to minimize losses. The effects of unfavorable housingheight versus wavelength and different parasitic modes is shown (right).
Transmissionline
Microstrip(dielectric)(GaAs, Si)
Stripline
Suspended stripline
Slotline
Coplanarwaveguide
Finline
Q factor
250100 to 150
400
500
100
150
500
Radiaton
LowHigh
Low
Low
Medium
Medium
None
Dispersion
Low
None
None
High
Low
Low
Chipmounting
Difficult forshunt, easyfor series
Poor
Fair
Easy forshunt, diffi-cult forseries
Easy forseries andshunt
Fair
Impedancerange
20 to 120
35 to 250
40 to 150
60 to 200
20 to 250
10 to 400
A comparison of various transmission-line types
MICROWAVES & RF ■ MARCH 2000
82
and M and N = positive integers.From eq. 2, it is possible to obtain
the condition of absence of parasiticmodes:
R – 1 < 0 ; R < 1
or
or
Equation 4 is known as the condi-tion for wave propagation in awaveguide with dimensions l 2 a. Inthe case of this article, it can also beconsidered the condition for theabsence of parasitic modes in awaveguide of cross-section a 2 H orl 2 H. If eq. 4 is not satisfied, para-sitic modes can arise, and the heightH must be chosen to suppress thesemodes. Figure 3 (right) illustratesthe resulting graphs of unfavorableH versus l0 for housing dimensionsof a = 24 mm, l = 30 mm, and dielec-tric substrate with a dielectric con-stant of 9.8 and THK of 0.5 mm.
The top and side covers essentiallyredistribute the field of the more the-oretical microstrip and understand-ably have an influence on the effec-tive dielectric constant.
Figure 4 shows the relationshipbetween the effective dielectric con-stant and the physical dimensions ofthe shielded microstrip line for dif-ferent values of the relative dielec-tric constant of the substrate materi-al.2 In these curves, it has been
λ02 22/)[(M / ) (N / a) ] (4)< +l 0 5.
λ02 2 2[(M ) (N / a) ] (3)< +4 / / l
assumed that the side walls are suffi-ciently spaced so that they only seeweak fringing fields and, therefore,have a negligible effect on the effec-tive dielectric constant. The topcover tends to lower the effectivedielectric constant (which is consis-tent with intuition). The top wallenables electric fields in the air abovethe strip conductor thereby givingthe air more influence in determiningthe propagation characteristics.
The characteristic impedance of amicrostrip line may be approximate-ly calculated by assuming that theEM field in the line has a quasi trans-verse-EM (TEM) nature. The char-acteristic impedance of a microstripline can be calculated using theWheeler equations.3,4
Figure 5 shows the characteristicimpedance of microstrip lines for var-
ious geometries and substrates of dif-ferent relative dielectric constantswhile Fig. 6 illustrates the relation-ships between characteristic im-pedance and the physical dimensionsof shielded microstrip lines for twoexamples: substrates with low (2) andhigh (9.6) relative dielectric con-stants.2 The top cover tends to reducethe impedance. When the ratio of thedistance from the top cover to thedielectric substrate and the substratethickness [(H – h)/h] is greater than10, the enclosure effects can be con-sidered negligible. The characteristicimpedance range of a microstrip line is20 to 120 V. The upper limit is set byproduction tolerances while the lowerlimit is set by the appearance of high-er-order modes.
There are three types of lossesthat occur in microstrip lines: con-
Microstrip Lines
DESIGN FEATURE
(H – h)/h
e = 9.6
e = 2.0
W/h = 2
W/h = 2
1 2 3 4 5 6 7 8 9Ef
fect
ive
diel
ectri
c co
nsta
nt1.2
1.3
2.3
2.4
2.5
2.6W/h = 1W/h = 0.6W/h = 0.5W/h = 0.4W/h = 0.3W/h = 0.1, 0.2
W/h = 1W/h = 0.6W/h = 0.3, 0.4, 0.5W/h = 0.2W/h = 0.1
4. The effective dielectric constant is shown as a function of the relativedielectric constant and physical dimensions for a shielded microstrip line.
(a) (b)
Char
acte
ristic
impe
danc
e—V
Char
acte
ristic
impe
danc
e—V
W/h W/h0.1 0.1 1.0 10.00.2 0.3 0.4 0.5 0.6 1.0
140
110 100
10
80
50
20
e = 1
e = 5
e = 7
e = 10
e = 16
e = 2
e = 4
5. The characteristic line impedance has been plotted for substrates with high (a) and low (b) dielectric constants.
MICROWAVES & RF ■ MARCH 2000
84
ductor (or ohmic) losses, dielectriclosses, and radiation losses. An ideal-ized microstrip line, being open to asemi-infinite air space, acts similar toan antenna and tends to radiate ener-gy. Substrate materials with lowdielectric constants (5 or less) areused when cost reduction is the pri-ority. Similar materials are also usedat millimeter-wave frequencies toavoid excessively tight mechanicaltolerances. However, the lower the
dielectric constant, the less the con-centration of energy is in the sub-strate region and, hence, the moreare the radiation losses. Radiationlosses depend on the dielectric con-stant, the substrate thickness, andthe circuit geometry.
The use of high-dielectric-constantsubstrate materials reduces radia-tion losses because most of the EMfield is concentrated in the dielectricbetween the conductive strip and the
ground plane. The real benefit in hav-ing a higher dielectric constant isthat the package size decreases byapproximately the square root of thedielectric constant. This is an advan-tage at lower frequencies but may bea problem at higher frequencies.
In most conventional microstripdesigns with high substrate dielectricconstant, conductor losses in the stripconductor and the ground plane dom-inate over dielectric and radiationlosses. Conductor losses are a resultof several factors related to themetallic material composing theground plane and walls, among whichare conductivity, skin effects, andsurface roughness. With finite con-ductivity, there is a non-uniform cur-rent density starting at the surfaceand exponentially decaying into thebulk of the conductive metal. This isthe alleged skin effect and its effectscan be visualized by an approxima-tion consisting of a uniform currentdensity flowing in a layer near thesurface of the metallic elements to auniform skin depth, d. The skin depthof a conductor is defined as the dis-tance to the conductor (Fig. 7) wherethe current density drops to 1/e froma maximum current density of Imax,or 37 percent of its value at the sur-face of the conductor.
To minimize conductor loss whilesimultaneously minimizing theamount of metallic material flankingthe dielectric, the conductor thick-ness should be greater than approxi-mately three to five times the skindepth.
In a microstrip line, conductor loss-es increase with increasing charac-teristic impedance due to the greaterresistance of narrow strips. Conduc-tor losses follow a trend which isopposite to radiation loss withrespect to W/h.
The fabrication process of realmicrostrip devices creates scratchesand bumps on the metal surfaces. Across-section of a microstrip line isshown in Fig. 7. The inside surfacesof the strip conductor and the groundplane facing the substrate repeat theshape of the substrate. The current,concentrated in the metal surfacenext to the substrate, follows theuneven surface of the substrate andencounters a greater resistance com-
Microstrip Lines
DESIGN FEATURE
1 2 3 4 5 6 73 4 5 6 740
190
160
130
100
70
Char
acte
ristic
impe
danc
e—V
Char
acte
ristic
impe
danc
e—V
(H – h)/h(H – h)/h
90
70
50
30
101 2
W/h = 0.1
W/h = 1
W/h = 0.2
W/h = 0.3W/h = 0.4
W/h = 0.5
W/h = 0.6
e = 2
W/h = 2W/h = 2
W/h = 1
W/h = 0.6
W/h = 0.3
W/h = 0.2
W/h = 0.4
e = 9.6W/h = 0.1
W/h = 0.5
6. These plots show the relationship between the characteristic impedance andthe physical dimensions of microstrip lines using substrates with high (9.6, left)and low (2.0, right) dielectric constants.
Bottom of strip
Top of strip
Au = 0.01 – 0.05 milNi = 0.05 – 0.2 milCu = 0.24 mil (f = 1.0 GHz)
Ground planeI(x)
I(t)
I(t)
I(x)
Cu
Cu
Ni0
0
AuMicrostrip conductor
Ni = 0.05 – 0.2 milAu = 0.01 – 0.05 mil
Cu = 0.24 mil
Substrate
Ground plane
I max
I max (1/e)I max
(1/e)I max
Cu
AuNi
t x
x
7. This cross-sectional view shows the current distribution across a microstripconductor and its ground plane.
MICROWAVES & RF ■ MARCH 2000
86
pared to the case of a smooth sub-strate. As the roughness of the sur-face increases, the length of the cur-rent path increases and, therefore,the losses increase.
Consider a substrate surfacewhich, for example, coincides withthe shape of the diamond abrasivematerial that is used to polish thesubstrate. The path of the current inconductor segment a-d (Fig. 8a) isshown by the line abcd. For an ideal-ly smooth surface, the length of thecurrent path AB is: IAB = Dnwhere:
n = the number of diamond abra-sives within segment AB.
The ratio of conductor losses in thecase of an uneven surface,a cr, to loss-es in the case of a perfectly smoothsurface, a c0),2 is:
Using eq. 5, acr/ac0 can be plottedas a function of ra for D1 = 1 mm andD 2 = 3 mm (Fig. 8b). Analysis of theresulting functions shows that forsmaller diameters, conductor lossesin the microstrip line are moredependent on the unevenness of thesubstrate roughness because theextra path length a surface (or skin)current sees is less. For example,consider a copper (Cu) microstripline with sapphire substrate wheretypically the roughness is 1 mm.5 Theskin depth at a few gigahertz is 1 mmand the loss is increased approxi-mately 60 percent when the surfaceroughness is taken into account.
α αcr co a
a a0.5
1 arccos [1 (4r / D)]
2{[(2r / D)[1 (2r / D)]} (5)
/ = + −
− −
To minimize dielectric losses, high-quality, low-loss dielectric sub-strates, such as alumina, quartz, andsapphire, are typically used in hybridICs. For most microstrip lines, con-ductor losses greatly exceed dielec-tric losses. However, in monolithicmicrowave ICs (MMICs), silicon (Si)or GaAs substrates result in muchlarger dielectric losses (approximate-ly 0.04 dB/mm).5
The preceding sections have con-sidered the individual contributionsto losses in microstrip by radiation,ohmic, and dielectric effects. Theseindividual loss components are atmost first-order perturbations in the
overall EM wave propaga-tion and, consequently, canbe combined linearly. Todo so, it is convenient toconsider the total Q factor,which can be expressed by:
1/Q = (1/Qc) + (1/Qd) +(1/Q r)
where:Qc, Qd, and Qr are the
quality factors corre-sponding to the conductor,dielectric, and radiationlosses, respectively. Theunloaded Q factor of the
microstrip line is typically on theorder of 250.
CHOOSING DIMENSIONSFor all circuit considerations, a
basic approach involves starting withthe particular ranges of dimensionratios required to achieve a desiredcharacteristic impedance. Followingthat, the strip width should be mini-mized to decrease the overall dimen-sions, as well as to suppress higher-order modes. It is important toremember, however, that a smallerstrip width leads to higher losses.
Factors that affect the choice of sub-strate thickness are the most contro-
Microstrip Lines
DESIGN FEATURE
(a) (b)ra—mm
a cr/a
c0
1.2
1.4
1.6
1.8
0.2 0.4 0.6
D1 = 1 mm
D2 = 3 mm
D
A B
ra
ba c d2f
8. The profile of a substrate’s uneven surface (a) shows how surface roughness affectsnormalized conductor losses (b).
ML 1
ML 2
Slot
s
S
Ground
HousingDielectricsubstrate
Via
SS
Ground plane
l
Cover
ML
ML
SLL CPW
Overlap
Vias
(a)
(c) (d)
(b)
ML
9. Various transitions between microstrip and other circuit structures arepossible: microstrip to microstrip (a), microstrip to suspended stripline (b),microstrip to slotted line (c), and microstrip to coplanar waveguide (d).
MICROWAVES & RF ■ MARCH 2000
88
versial. The positive effects of decreas-ing substrate thickness are compactcircuits, ease of integration, less ten-dency to launch higher-order modes orradiation, and via holes drilled throughthe dielectric substrate will contributesmaller parasitic inductances to theoverall performance.
However, a decrease in the sub-strate thickness (h) while maintain-
ing a constant characteristic im-pedance, Z0, must be accompanied bya narrowing of the conductor width,W. Narrowing W leads to higher con-ductor losses along with a lower Q.Also, for smaller W and h, the fabri-cation tolerances become moresevere. Careless handing of thin sub-strates can cause stress and strainwhich can modify the performance of
the substrate.Microstrip circuit dimensions
decrease with increasing substratedielectric constant. Losses then usu-ally increase because higher dielec-tric constant materials usually havehigher loss tangents, tan d, and alsobecause for the same characteristicimpedance, reduced conductor linewidths have higher ohmic losses.This is a typical conflicting situationbetween the necessary requirementsfor small dimensions and low loss.For many applications, lower dielec-tric constants are preferred sincelosses are reduced, conductor geome-tries are larger (and, therefore, moreproducible), and the cutoff frequencyof the circuit increases.
MICROSTRIP TRANSITIONSThe rapid development of high-
density modules requires the designof interconnects and transitions,especially for multilayer circuits.Consider useful transitions frommicrostrip to other printed transitionlines. A transition between twomicrostrip lines (Fig. 9a) can be real-ized through a slot in the groundplane.
A transition between a microstripline and a suspended stripline circuitis shown in Fig. 9b.
A transition between a slotline anda microstrip line can be seen in Fig.9c.7,8
An overlay transition between amicrostrip line and coplanar waveg-uide (CPW) is shown (Fig. 9d).9,10
AcknowledgmentThe author would like to thank Dr. Paul Chorney who
reviewed these materials and provided valuable sugges-tions.
References1. H. Sobol, “Application of Integrated Circuit Technolo-
gy to Microwave Frequencies,” Proceedings of the IEEE,Vol. 59, 1971, pp. 1200-1211.
2. L.G. Maloratsky, Miniaturization of Microwave Ele-ments and Devices, Soviet Radio, Moscow, 1976.
3. H.A. Wheeler, “Transmission-Line Properties of aStrip on a Dielectric Sheet on a Plane,” IEEE Transactionson Microwave Theory & Techniques, Vol. 25, No. 8, August1977, pp. 631-647.
4. H.A. Wheeler, “Transmission-Line Properties of Par-allel Strips Separated by a Dielectric Sheet,” IEEE Trans-actions on Microwave Theory & Techniques, Vol. 3, No. 3,March 1965, pp. 172-185.
5. T.C. Edwards, Foundations for Microstrip CircuitDesign, Wiley, New York, 1981.
6. K.J. Herrick, J.G. Yook, and P.B. Katehi, “Microtech-nology in the Development of Three-Dimensional Circuits,”IEEE Transactions on Microwave Theory & Techniques,Vol. 46, No. 11, November 1998.
7. S.B. Cohn, “Slot-Line on a Dielectric Substrate,”IEEE Transactions on Microwave Theory & Techniques,Vol. 17, 1969, pp. 768-778.
8. J.S. Izadian and S.M. Izadian, Microwave TransitionDesign, Artech House, Norwood, MA, 1988.
9. M. Hougart and C. Aury, “Various Excitation of Copla-nar Waveguides,” IEEE MTT-S International MicrowaveSymposium Digest, 1979.
10. J. Burke and R.W. Jackson, “Surface-to-Surface Tran-sition via Electromagnetic Coupling of Microstrip andCoplanar Waveguide,” IEEE Transactions on MicrowaveTheory & Techniques, Vol. 37, No. 3, March 1989, pp. 519-525.
Microstrip Lines
DESIGN FEATURE
••
