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Stripline

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Early electronic transmission line medium
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Cross-section diagram of stripline geometry. Centralconductor (A) is sandwiched betweenground planes (B and D). Structure is supported bydielectric (C).

Inelectronics,stripline is atransverse electromagnetic (TEM)transmission line medium invented by Robert M. Barrett of theAir Force Cambridge Research Centre in the 1950s. Stripline is the earliest form ofplanar transmission line.

Description

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A striplinecircuit uses a flat strip of metal which is sandwiched between twoparallelground planes. The insulating material of thesubstrate forms adielectric. The width of the strip, the thickness of the substrate and therelative permittivity of the substrate determine thecharacteristic impedance of the strip which is atransmission line. As shown in the diagram, the central conductor need not be equally spaced between the ground planes. In the general case, the dielectric material may be different above and below the central conductor. A stripline that uses air as the dielectric material is known as anair stripline.

To prevent the propagation of unwanted modes, the two ground planes must be shorted together. This is commonly achieved by arow of vias running parallel to the strip on each side.

Likecoaxial cable, stripline is non-dispersive, and has nocutoff frequency. Good isolation between adjacent traces can be achieved more easily than withmicrostrip.Stripline provides for enhanced noise immunity against the propagation of radiated RF emissions, at the expense of slower propagation speeds when compared to microstrip lines. The effective permittivity of striplines equals the relative permittivity of the dielectric substrate because of wave propagation only in the substrate. Hence striplines have higher effective permittivity in comparison to microstrip lines, which in turn reduces wave propagation speed (see alsovelocity factor) according to

vp=c0ϵr,eff.{\displaystyle v_{\mathrm {p} }={\frac {c_{0}}{\sqrt {\epsilon _{\mathrm {r,eff} }}}}.}

History

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Stripline, now used as a generic term, was originally a proprietary brand of Airborne Instruments Laboratory Inc. (AIL). The version as produced by AIL was essentially air insulated (air stripline) with just a thin layer of dielectric material - just enough to support the conducting strip. The conductor was printed on both sides of the dielectric. The more familiar version with the space between the two plates completely filled with dielectric was originally produced bySanders Associates who marketed it under the brand name oftriplate.[1]

Stripline was initially preferred to its rival, microstrip, made byITT. Transmission in stripline is purelyTEM mode and consequently there is nodispersion (provided that the dielectric of substrate is not itself dispersive). Also, discontinuity elements on the line (gaps,stubs, posts etc) present a purelyreactive impedance. This is not the case with microstrip; the differing dielectrics above and below the strip result in longitudinal non-TEM components to the wave. This results in dispersion and discontinuity elements have aresistive component causing them to radiate. In the 1950sEugene Fubini, at the time working for AIL, jokingly suggested that a microstrip dipole would make a good antenna. This was intended to highlight the drawbacks of microstrip, but themicrostrip patch antenna has become the most popular design of antenna in mobile devices.[2] Stripline remained in the ascendent for its performance advantages through the 1950s and 1960s but eventually microstrip won out, especially in mass produced items, because it was easier to assemble and the lack of an upper dielectric meant that components were easier to access and adjust. As the complexity of printed circuits increased, this convenience issue became more important until today microstrip is the dominant planar technology. Miniaturisation also leads to favouring microstrip because its disadvantages are not so severe in a miniaturised circuit. However, stripline is still chosen where operation over a wide band is required.[3]

Comparison to microstrip

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Microstrip is similar to stripline transmission line except that the microstrip is not sandwiched, it is on a surface layer, above a ground plane.Stripline is more expensive to fabricate than microstrip, and because of the second groundplane, the strip widths are much narrower for a given impedance and board thickness than for microstrip.

Characteristic Impedance

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An accurate closed form equation for thecharacteristic impedance of a stripline with a thin centered conductor has been reported as[4]

Zstripline=30πEr1TWeff+CfCf=2πln(11T+1)Tπln(1(1T)21){\displaystyle {\begin{aligned}Z_{stripline}&={\frac {30\pi }{\sqrt {E_{r}}}}{\frac {1-T}{W_{eff}+C_{f}}}\\C_{f}&={\frac {2}{\pi }}ln{\biggr (}{\frac {1}{1-T}}+1{\biggr )}-{\frac {T}{\pi }}ln{\biggr (}{\frac {1}{(1-T)^{2}}}-1{\biggr )}\\\end{aligned}}}

Where:

Weff={W(0.35W)21+12T,W<0.35W,W0.35T=thW=whw=width of the stripline conductort=thickness of the stripline conductorh=thickness of the substrate from the top ground plate to the bottom ground plateEr=dielectric constant of the substrate dielectric material{\displaystyle {\begin{aligned}W_{eff}&={\begin{cases}W-{\frac {(0.35-W)^{2}}{1+12T}},&W<0.35\\W,&W\geq 0.35\end{cases}}\\T&={\frac {t}{h}}\\W&={\frac {w}{h}}\\w&={\text{width of the stripline conductor}}\\t&={\text{thickness of the stripline conductor}}\\h&={\text{thickness of the substrate from the top ground plate to the bottom ground plate}}\\E_{r}&={\text{dielectric constant of the substrate dielectric material}}\end{aligned}}}

Note that when the conductor thickness is small, T<<1 or t<<h, the equations simplify significantly.

Zstripline=30πEr1Weff+0.441271{\displaystyle {\begin{aligned}Z_{stripline}&={\frac {30\pi }{\sqrt {Er}}}{\frac {1}{W_{eff}+0.441271}}\\\end{aligned}}}

Where:

Weff={W(0.35W)2,W<0.35W,W0.35{\displaystyle {\begin{aligned}W_{eff}&={\begin{cases}W-(0.35-W)^{2},&W<0.35\\W,&W\geq 0.35\end{cases}}\\\end{aligned}}}

The accuracy of the formula is claimed to be at least 1% for W/(H-T) > .05 and T< 0.025.


For thick conductors, Wheeler provides the following more accurate equations[5]

Zstripline=30Erln(1+C2(C+C2+6.27)){\displaystyle {\begin{aligned}Z_{stripline}={\frac {30}{\sqrt {E_{r}}}}ln{\biggr (}1+{\frac {C}{2}}{\big (}C+{\sqrt {C^{2}+6.27}}{\big )}{\biggr )}\\\end{aligned}}}

Where:

C=8(1T)π(W+ΔW)ΔW=Tπ(1T){112ln[(T2T)2+(.0796TW+1.1T)M]}M=31.5+T(1T){\displaystyle {\begin{aligned}C&={\frac {8(1-T)}{\pi (W+\Delta W)}}\\\Delta W&={\frac {T}{\pi (1-T)}}{\biggr \{}1-{\frac {1}{2}}ln{\biggr [}{\bigg (}{\frac {T}{2-T}}{\biggr )}^{2}+{\biggr (}{\frac {.0796T}{W+1.1T}}{\biggr )}^{M}{\biggr ]}{\biggr \}}\\M&={\frac {3}{1.5+{\frac {T}{(1-T)}}}}\\\end{aligned}}}

Where T and W are as defined the same as the above expression.

The accuracy is claimed to be at least 0.5% for C>0.25.

Non-centered conductor

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For stripline conductors that are not centered, that is, the distance to the upper ground plane is not the same as to the lower ground plane, strategies exist to estimate the characteristic impedance in at least one of two ways.

Zo estimation using upper and lower capacitance

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If the asymmetry of the conductor placement is not large, the lower and upper capacitance per unit length may be estimated for the upper ground plane and the lower ground plane using centered stripline equations and standardtransmission line equations for homogeneous lines,Vc2/εr=1/LC{\displaystyle V_{c}^{2}/\varepsilon _{r}=1/LC}, andZo2=L/C{\displaystyle Z_{o}^{2}=L/C} whereVc{\displaystyle V_{c}} is the sped of light.

TheZo{\displaystyle Z_{o}} of each stripline may be evaluated independently, and the results used to estimate theZo{\displaystyle Z_{o}} of the asymmetric stripline. Small errors are introduced in theZo{\displaystyle Z_{o}} estimation due to the slightly differing capacitance paths to the ground planes between the asymmetric case being estimated and the symmetric cases used to make the estimation, so only small asymmetric placement of the strip will be expected to produce an acceptable estimation forZo{\displaystyle Z_{o}} of the asymmetrically placed strip.

To summarize:

ZoL=Zo of a stripline of height 2HLZoU=Zo of a stripline of height 2HUCoL=εrVcZoLCoU=εrVcZoUCo=CoL/2+CoU/2Lo=εrCoVc2Zo=LoCo{\displaystyle {\begin{aligned}Z_{oL}&=Z_{o}{\text{ of a stripline of height }}2H_{L}\\Z_{oU}&=Z_{o}{\text{ of a stripline of height }}2H_{U}\\C_{oL}&={\frac {\sqrt {\varepsilon _{r}}}{V_{c}Z_{oL}}}\\C_{oU}&={\frac {\sqrt {\varepsilon _{r}}}{V_{c}Z_{oU}}}\\C_{o}&=C_{oL}/2+C_{oU}/2\\L_{o}&={\frac {\varepsilon _{r}}{C_{o}V_{c}^{2}}}\\Z_{o}&={\sqrt {\frac {L_{o}}{C_{o}}}}\\\end{aligned}}}.

Where:

Vc{\displaystyle V_{c}} is the speed of light in a vacuum.

HL{\displaystyle H_{L}} andHU{\displaystyle H_{U}} are measured from center of the conductor to the lower and upper ground plane, respectively.

Co and Lo are the capacitance and inductance per unit length of the associated transmission line.

Zo estimation using microstrip metallic cover

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If there is no dielectric in the asymmetric stripline, then the stripline looks like a microstrip with a dielectric of air,ε=1{\displaystyle \varepsilon =1}, inside a metallic enclosure. This permits the air characteristic impedance,Zoa{\displaystyle Z_{o}^{a}}, to be calculated usingmicrostrip metallic enclosure equations. WhenZoa{\displaystyle Z_{o}^{a}} is known,Zo{\displaystyle Z_{o}} may be calculated usingZo=Zoa/εr{\displaystyle Z_{o}=Z_{o}^{a}/{\sqrt {\varepsilon _{r}}}}. The accuracy of thisZo{\displaystyle Z_{o}} estimation is quantified and listed in the microstrip metallic enclosure equations.

Losses

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Since microstrip loss calculation are not directly a function of dielectric constant and geometry or metallic cover height,microstrip loss equations may also be used for stripline losses by treating εre as a constant equal to εr.[6]

See also

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References

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  1. ^Oliner, pp.556-559
  2. ^Yarman, p. 67
  3. ^Oliner, pp. 558-562
  4. ^Steer, Michael (October 21, 2020)."3.7: Stripline - Engineering LibreTexts".Engineering LibreTexts.
  5. ^Rhea, Randall W. (1995).HF Filter Design and Computer Simulation. New York, NY, US: McGraw-Hill. pp. 106, 107.ISBN 0-07-052055-0.
  6. ^Garg, Ramesh; Bahl, Inder; Bozzi, Maurizio (2013).Microstrip Lines and Slotlines (3rd ed.). Boston, London: Artech House. pp. 469–473.ISBN 978-1-60807-535-5.{{cite book}}: CS1 maint: date and year (link)

Bibliography

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External links

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