Reviewing the Basics of Microstrip

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DESIGN FEATURE Microstrip Lines Reviewing The Basics Of Microstrip An understanding of the fundamentals of Lines microstrip transmission lines can guide high- frequency designers in the proper application of this venerable circuit technology.

Leo G. Maloratsky RINTED transmission lines are widely used, and for good reason. Principal Engineer They are broadband in frequency. They provide circuits that are Rockwell Collins, 2100 West Hibiscus Pcompact and light in weight. They are generally economical to pro- Blvd., Melbourne, FL 32901; (407) duce since they are readily adaptable to hybrid and monolithic inte- 953-1729, e-mail: lgmalora@ grated-circuit (IC) fabrication technologies at RF and microwave fre- mbnotes.collins.rockwell.com. quencies. To better appreciate printed transmission lines, and microstrip in particular, some of the basic principles of microstrip lines will be reviewed here. A number of different transmis- with respect to the others. In Fig. 1, sion lines are generally used for it should be noted that the substrate microwave ICs (MICs) as shown in materials are denoted by the dotted Fig. 1. Each type has its advantages areas and the conductors are indicat- ed by the bold lines. The microstrip line is a transmis- Basic lines Modifications sion-line geometry with a single con- W W t a ductor trace on one side of a dielectric H hhhW W substrate and a single ground plane

line a h Suspended Inverted on the opposite side. Since it is an Microstrip Microstrip line Shielded microstrip line microstrip line microstrip line open structure, microstrip line has a t W W1 major fabrication advantage over b b t stripline. It also features ease of a W

Stripline 2 Stripline Double-conductor stripline interconnections and adjustments. In a microstrip line, the wave- W W W t b h t b length, ⌳, is given by: d aaa Λ=λε 0.5 stripline Shielded suspended / (eff ) (1) Suspended Shielded high-Q Shielded suspended stripline suspended stripline double-substrate stripline where: t W ttS W ⑀ h h h eff = the effective dielectric con- aaa stant, which depends on the dielec- Slotline Slotline Antipodal slotline Bilateral finline tric constant of the substrate materi- S a S W H W b al and the physical dimensions of the b h microstrip line, and

Coplanar Symmetrical ␭ waveguide = the free-space wavelength. coplanar line Shielded coplanar waveguide In a microstrip line, the electro- hhhh magnetic (EM) fields exist partly in WWWbbb W b the air above the dielectric substrate aaaa and partly within the substrate itself. Finline Antipodal finline Antipodal overlapping Finline Bilateral slotline finline Intuitively, the effective dielectric constant of the line is expected to be 1. These are commonly used types of printed transmission lines for MICs. greater than the dielectric constant

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of air (1) and less open to the air and, in reality, it is than that of the desirable to have circuits that are 4.0 ⑀ = 20 dielectric sub- covered to protect them from the 1 ⑀ strate. Various environment as well as to prevent = 15 curves for effec- radiation and EM interference ⑀ = 12 tive dielectric con- (EMI). Also, the microstrip configu- 3.0 ⑀ = 10 stant are shown in rations that have been so far dis-

0.5 ⑀ ) = 8 Fig. 2 as a func- cussed are transversally infinite in

eff ⑀ = 6 ⑀ tion of physical extent, which deviates from reality. ( ⑀ = 5 dimensions and Covering the basic microstrip config- 2.0 ⑀ = 4 ⑀ = 3 relative dielectric uration with metal top plates on the ⑀ = 2 constant. top and on the sides leads to a more Referring again realistic circuit configuration, a ⑀ 1.0 = 1.5 to Fig. 1, it should shielded microstrip line with a hous- 0.1 0.2 0.4 0.6 0.8 1.0 2.0 4.0 be apparent that a ing (Fig. 1). W/h basic (unshielded) The main purposes of the housing 2. The values of effective dielectric constant are shown for microstrip line is or package are to provide mechanical different substrate relative dielectric constants as a not really a practi- strength, EM shielding, germetiza- function of W/h. cal structure. It is tion, and heat sinking in the case of high-power applications. Packaging A comparison of various transmission-line types must protect the circuitry from mois- ture, humidity, dust, salt spray, and Transmission Impedance Chip other environmental contaminants. line Q factor Radiaton Dispersion range mounting In order to protect the circuit, certain methods of sealing can be used: con- Microstrip ductive epoxy, solder, gasket materi- (dielectric) 250 Low Low 20 to 120 Difficult for als, and metallization tape. (GaAs, Si) 100 to 150 High shunt, easy An MIC mounted into a housing for series may be looked on as a dielectrically loaded cavity resonator (Fig. 3, left) Stripline 400 Low None 35 to 250 Poor with the following inner dimensions: a is the width, l is the length, and H is Suspended stripline 500 Low None 40 to 150 Fair the height of the enclosure. These Slotline 100 Medium High 60 to 200 Easy for dimensions should be selected in a shunt, diffi- way so that the waveguide modes are cult for below cutoff. series The parasitic modes appear in this resonator if: Coplanar 150 Medium Low 20 to 250 Easy for =−ε − waveguide series and H {h[1 (1 / )]R}1(R 1) (2) shunt where: =+λ 22 2 Finline 500 None Low 10 to 400 Fair R (0 // 2) [(Ml ) (N / a) ] (2a)

5.0 H H 4.0 h a 3.0 a = 24 mm 2:2 1:2 l = 30 mm 2.0 h = 0.5 mm Height (H)—mm h l 2:1 M = 1, N = 1 1.0 a 0.5 15 25 35 45 55 Wavelength (␭)—mm 3. Housing dimensions are selected for microstrip circuits (left) to minimize losses. The effects of unfavorable housing height versus wavelength and different parasitic modes is shown (right).

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and M and N = positive integers. 2.6 W/h = 2 From eq. 2, it is possible to obtain ⑀ = 9.6 W/h = 1 the condition of absence of parasitic 2.5 W/h = 0.6 W/h = 0.5 modes: W/h = 0.4 2.4 W/h = 0.3 R – 1 < 0 ; R < 1 W/h = 0.1, 0.2 2.3 or λ222<+ 0 4/[(M /l ) (N / a) ] (3) 1.3 W/h = 2 ⑀ = 2.0

or Effective dielectric constant W/h = 1 λ <+2/)[(M /l )22 (N / a) ]05. (4) W/h = 0.6 0 W/h = 0.3, 0.4, 0.5 1.2 W/h = 0.2 Equation 4 is known as the condi- W/h = 0.1 tion for wave propagation in a 123456789 (H – h)/h a. In ן waveguide with dimensions l the case of this article, it can also be 4. The effective dielectric constant is shown as a function of the relative considered the condition for the dielectric constant and physical dimensions for a shielded microstrip line. absence of parasitic modes in a -H or assumed that the side walls are suffi- ious geometries and substrates of dif ן waveguide of cross-section a H. If eq. 4 is not satisfied, para- ciently spaced so that they only see ferent relative dielectric constants ן l sitic modes can arise, and the height weak fringing fields and, therefore, while Fig. 6 illustrates the relation- H must be chosen to suppress these have a negligible effect on the effec- ships between characteristic im- modes. Figure 3 (right) illustrates tive dielectric constant. The top pedance and the physical dimensions the resulting graphs of unfavorable cover tends to lower the effective of shielded microstrip lines for two ␭ H versus 0 for housing dimensions dielectric constant (which is consis- examples: substrates with low (2) and of a = 24 mm, l = 30 mm, and dielec- tent with intuition). The top wall high (9.6) relative dielectric con- tric substrate with a dielectric con- enables electric fields in the air above stants.2 The top cover tends to reduce stant of 9.8 and THK of 0.5 mm. the strip conductor thereby giving the impedance. When the ratio of the The top and side covers essentially the air more influence in determining distance from the top cover to the redistribute the field of the more the- the propagation characteristics. dielectric substrate and the substrate oretical microstrip and understand- The characteristic impedance of a thickness [(H – h)/h] is greater than ably have an influence on the effec- microstrip line may be approximate- 10, the enclosure effects can be con- tive dielectric constant. ly calculated by assuming that the sidered negligible. The characteristic Figure 4 shows the relationship EM field in the line has a quasi trans- impedance range of a microstrip line is between the effective dielectric con- verse-EM (TEM) nature. The char- 20 to 120 ⍀. The upper limit is set by stant and the physical dimensions of acteristic impedance of a microstrip production tolerances while the lower the shielded microstrip line for dif- line can be calculated using the limit is set by the appearance of high- ferent values of the relative dielec- Wheeler equations.3,4 er-order modes. tric constant of the substrate materi- Figure 5 shows the characteristic There are three types of losses al.2 In these curves, it has been impedance of microstrip lines for var- that occur in microstrip lines: con-

140 ⑀ = 5 ⍀ ⍀

110 ⑀ = 7 100

⑀ = 10 80 ⑀ = 16 ⑀ = 1 50 ⑀ = 2 Characteristic impedance— Characteristic impedance— ⑀ = 4 20 10 0.1 0.2 0.3 0.4 0.5 0.6 1.0 0.1 1.0 10.0 W/h W/h (a) (b)

5. The characteristic line impedance has been plotted for substrates with high (a) and low (b) dielectric constants.

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ground plane. The real benefit in hav- W/h = 0.1 ing a higher dielectric constant is W/h = 0.1 ⑀ = 9.6 ⑀ = 2 ⍀ W/h = 0.2 190 that the package size decreases by 90 ⍀ W/h = 0.2 approximately the square root of the W/h = 0.3 W/h = 0.4 160 W/h = 0.3 dielectric constant. This is an advan- 70 W/h = 0.5 W/h = 0.4 tage at lower frequencies but may be W/h = 0.5 W/h = 0.6 130 a problem at higher frequencies. 50 W/h = 0.6 In most conventional microstrip W/h = 1 100 designs with high substrate dielectric W/h = 1 constant, conductor losses in the strip 30 W/h = 2 70 conductor and the ground plane dom- Characteristic impedance— W/h = 2 Characteristic impedance— inate over dielectric and radiation 10 40 1234567 1234567 losses. Conductor losses are a result (H – h)/h (H – h)/h of several factors related to the metallic material composing the 6. These plots show the relationship between the characteristic impedance and ground plane and walls, among which the physical dimensions of microstrip lines using substrates with high (9.6, left) are conductivity, skin effects, and and low (2.0, right) dielectric constants. surface roughness. With finite conductivity, there is a non-uniform cur- ductor (or ohmic) losses, dielectric dielectric constant, the less the con- rent density starting at the surface losses, and radiation losses. An ideal- centration of energy is in the sub- and exponentially decaying into the ized microstrip line, being open to a strate region and, hence, the more bulk of the conductive metal. This is semi-infinite air space, acts similar to are the radiation losses. Radiation the alleged skin effect and its effects an antenna and tends to radiate ener- losses depend on the dielectric con- can be visualized by an approxima- gy. Substrate materials with low stant, the substrate thickness, and tion consisting of a uniform current dielectric constants (5 or less) are the circuit geometry. density flowing in a layer near the used when cost reduction is the pri- The use of high-dielectric-constant surface of the metallic elements to a ority. Similar materials are also used substrate materials reduces radia- uniform skin depth, ␦. The skin depth at millimeter-wave frequencies to tion losses because most of the EM of a conductor is defined as the dis- avoid excessively tight mechanical field is concentrated in the dielectric tance to the conductor (Fig. 7) where tolerances. However, the lower the between the conductive strip and the the current density drops to 1/e from a maximum current density of Imax, I(x) or 37 percent of its value at the surface of the conductor. Bottom of strip To minimize conductor loss while simultaneously minimizing the amount of metallic material flanking the dielectric, the conductor thick- Top of strip ness should be greater than approxi- t x mately three to five times the skin 0 depth. Au Au = 0.01 – 0.05 mil Ni Ni = 0.05 – 0.2 mil Microstrip In a microstrip line, conductor loss- Cu = 0.24 mil (f = 1.0 GHz) conductor es increase with increasing charac- I(t) Cu teristic impedance due to the greater I resistance of narrow strips. Conduc- max (1/e)I max tor losses follow a trend which is Substrate opposite to radiation loss with respect to W/h. I max (1/e)I max The fabrication process of real I(t) microstrip devices creates scratches Cu Cu Cu = 0.24 mil and bumps on the metal surfaces. A Ground Ni Ni = 0.05 – 0.2 mil plane cross-section of a microstrip line is Au = 0.01 – 0.05 mil shown in Fig. 7. The inside surfaces Au I(x) of the strip conductor and the ground Ground plane plane facing the substrate repeat the shape of the substrate. The current, 0 x concentrated in the metal surface next to the substrate, follows the 7. This cross-sectional view shows the current distribution across a microstrip uneven surface of the substrate and conductor and its ground plane. encounters a greater resistance com-

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overall EM wave propagation and, consequently, can D be combined linearly. To do so, it is convenient to 1.8 ␮ D1 = 1 m consider the total Q factor,

c0 which can be expressed by:

␣ 1.6 / cr ␣ 1.4 ␮ 1/Q = (1/Qc) + (1/Qd) + D2 = 3 m ␾ (1/Q r) 1.2 2 a b c d ABwhere: 0.2 0.4 0.6 Q , Q , and Q are the ␮ r c d r ra— m a (a) (b) quality factors corre- sponding to the conductor, 8. The profile of a substrate’s uneven surface (a) shows how surface roughness affects dielectric, and radiation normalized conductor losses (b). losses, respectively. The unloaded Q factor of the pared to the case of a smooth sub- To minimize dielectric losses, high- microstrip line is typically on the strate. As the roughness of the sur- quality, low-loss dielectric sub- order of 250. face increases, the length of the cur- strates, such as alumina, quartz, and rent path increases and, therefore, sapphire, are typically used in hybrid CHOOSING DIMENSIONS the losses increase. ICs. For most microstrip lines, con- For all circuit considerations, a Consider a substrate surface ductor losses greatly exceed dielec- basic approach involves starting with which, for example, coincides with tric losses. However, in monolithic the particular ranges of dimension the shape of the diamond abrasive microwave ICs (MMICs), silicon (Si) ratios required to achieve a desired material that is used to polish the or GaAs substrates result in much characteristic impedance. Following substrate. The path of the current in larger dielectric losses (approximate- that, the strip width should be mini- conductor segment a-d (Fig. 8a) is ly 0.04 dB/mm).5 mized to decrease the overall dimen- shown by the line abcd. For an ideal- The preceding sections have con- sions, as well as to suppress higher- ly smooth surface, the length of the sidered the individual contributions order modes. It is important to current path AB is: IAB = Dn to losses in microstrip by radiation, remember, however, that a smaller where: ohmic, and dielectric effects. These strip width leads to higher losses. n = the number of diamond abra- individual loss components are at Factors that affect the choice of sub- sives within segment AB. most first-order perturbations in the strate thickness are the most contro- The ratio of conductor losses in the case of an uneven surface,␣ , to loss- cr ML 2 Cover es in the case of a perfectly smooth surface, ␣ ),2 is: c0 ML 1 l SS αα=+ − cr/ co1 arccos [1 (4r a / D)] ML Ground −−0.5 s Via 2{[(2raa / D)[1 (2r / D)]} (5) Dielectric Housing substrate ␣ ␣ Slot S Using eq. 5, cr/ c0 can be plotted Ground plane ␮ as a function of ra for D1 = 1 m and ␮ (a) (b) D 2 = 3 m (Fig. 8b). Analysis of the resulting functions shows that for ML smaller diameters, conductor losses Vias in the microstrip line are more ML dependent on the unevenness of the substrate roughness because the extra path length a surface (or skin) current sees is less. For example, Overlap consider a copper (Cu) microstrip line with sapphire substrate where ␮ 5 typically the roughness is 1 m. The (c) (d) CPW skin depth at a few gigahertz is 1 ␮m SLL and the loss is increased approxi- 9. Various transitions between microstrip and other circuit structures are mately 60 percent when the surface possible: microstrip to microstrip (a), microstrip to suspended stripline (b), roughness is taken into account. microstrip to slotted line (c), and microstrip to coplanar waveguide (d).

MICROWAVES & RF ■ MARCH 2000 86 DESIGN FEATURE Microstrip Lines versial. The positive effects of decreas- ing a constant characteristic im- the substrate. ing substrate thickness are compact pedance, Z0, must be accompanied by Microstrip circuit dimensions circuits, ease of integration, less ten- a narrowing of the conductor width, decrease with increasing substrate dency to launch higher-order modes or W. Narrowing W leads to higher con- dielectric constant. Losses then usu- radiation, and via holes drilled through ductor losses along with a lower Q. ally increase because higher dielec- the dielectric substrate will contribute Also, for smaller W and h, the fabri- tric constant materials usually have smaller parasitic inductances to the cation tolerances become more higher loss tangents, tan ␦, and also overall performance. severe. Careless handing of thin sub- because for the same characteristic However, a decrease in the substrates can cause stress and strain impedance, reduced conductor line strate thickness (h) while maintain- which can modify the performance of widths have higher ohmic losses. This is a typical conflicting situation between the necessary requirements for small dimensions and low loss. For many applications, lower dielectric constants are preferred since losses are reduced, conductor geometries are larger (and, therefore, more producible), and the cutoff frequency of the circuit increases. MICROSTRIP TRANSITIONS The rapid development of high- density modules requires the design of interconnects and transitions, especially for multilayer circuits. Consider useful transitions from microstrip to other printed transition lines. A transition between two microstrip lines (Fig. 9a) can be real- ized through a slot in the ground plane. A transition between a microstrip line and a suspended stripline circuit is shown in Fig. 9b. A transition between a slotline and a microstrip line can be seen in Fig. 9c.7,8 An overlay transition between a microstrip line and coplanar waveguide (CPW) is shown (Fig. 9d).9,10 •• Acknowledgment The author would like to thank Dr. Paul Chorney who reviewed these materials and provided valuable sugges- tions. References 1. 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 a Strip on a Dielectric Sheet on a Plane,” IEEE Transactions on Microwave Theory & Techniques, Vol. 25, No. 8, August 1977, 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 Circuit Design, 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 Transition Design, Artech House, Norwood, MA, 1988. 9. M. Hougart and C. Aury, “Various Excitation of Copla- nar Waveguides,” IEEE MTT-S International Microwave Symposium Digest, 1979. 10. J. Burke and R.W. Jackson, “Surface-to-Surface Tran- sition via Electromagnetic Coupling of Microstrip and Coplanar Waveguide,” IEEE Transactions on Microwave Theory & Techniques, Vol. 37, No. 3, March 1989, pp. 519- 525.

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