Microstrip is a type of electrical transmission line which can be fabricated with any technology where a conductor is separated from a ground plane by a dielectric layer known as "substrate". Microstrip lines are used to convey microwave-frequency signals.
Typical realisation technologies are printed circuit board (PCB), alumina coated with a dielectric layer or sometimes silicon or some other similar technologies. Microwave components such as antennas, couplers, filters, power dividers etc. can be formed from microstrip, with the entire device existing as the pattern of metallization on the substrate. Microstrip is thus much less expensive than traditional waveguide technology, as well as being far lighter and more compact. Microstrip was developed by ITT laboratories as a competitor to stripline (first published by Grieg and Engelmann in the December 1952 IRE proceedings[1]).
The disadvantages of microstrip compared with waveguide are the generally lower power handling capacity, and higher losses. Also, unlike waveguide, microstrip is typically not enclosed, and is therefore susceptible to cross-talk and unintentional radiation.
For lowest cost, microstrip devices may be built on an ordinary FR-4 (standard PCB) substrate. However it is often found that the dielectric losses in FR4 are too high at microwave frequencies, and that the dielectric constant is not sufficiently tightly controlled. For these reasons, an alumina substrate is commonly used. From monolithic integration perspective microstrips with integrated circuit/monolithic microwave integrated circuit technologies might be feasible however their performance might be limited by the dielectric layer(s) and conductor thickness available.
Microstrip lines are also used in high-speed digital PCB designs, where signals need to be routed from one part of the assembly to another with minimal distortion, and avoiding high cross-talk and radiation.
Microstrip is one of many forms of planar transmission line, others include stripline and coplanar waveguide, and it is possible to integrate all of these on the same substrate.
A differential microstrip—a balanced signal pair of microstrip lines—is often used for high-speed signals such as DDR2 SDRAM clocks, USB Hi-Speed data lines, PCI Express data lines, LVDS data lines, etc., often all on the same PCB.[2] [3] [4] Most PCB design tools support such differential pairs.[5] [6]
The electromagnetic wave carried by a microstrip line exists partly in the dielectric substrate, and partly in the air above it. In general, the dielectric constant of the substrate will be different (and greater) than that of the air, so that the wave is travelling in an inhomogeneous medium. In consequence, the propagation velocity is somewhere between the speed of radio waves in the substrate, and the speed of radio waves in air. This behaviour is commonly described by stating the effective dielectric constant of the microstrip; this being the dielectric constant of an equivalent homogeneous medium (i.e., one resulting in the same propagation velocity).
Further consequences of an inhomogeneous medium include:
A closed-form approximate expression for the quasi-static characteristic impedance of a microstrip line was developed by Wheeler:[12] [13] [14]
Zrm{microstrip}=
| Z0 | |
| 2\pi\sqrt{2(1+\varepsilonr) |
where is the effective width, which is the actual width of the strip, plus a correction to account for the non-zero thickness of the metallization:
wrm{eff}=w+t
| 1+1/\varepsilonr | |
| 2\pi |
ln\left(
| 4e | ||||||||||
|
Here is the impedance of free space, is the relative permittivity of substrate, is the width of the strip, is the thickness ("height") of substrate, and is the thickness of the strip metallization.
This formula is asymptotic to an exact solution in three different cases:
It is claimed that for most other cases, the error in impedance is less than 1%, and is always less than 2%.[14] By covering all aspect-ratios in one formula, Wheeler 1977 improves on Wheeler 1965[13] which gives one formula for and another for (thus introducing a discontinuity in the result at).
Harold Wheeler disliked both the terms 'microstrip' and 'characteristic impedance', and avoided using them in his papers.
A number of other approximate formulae for the characteristic impedance have been advanced by other authors. However, most of these are applicable to only a limited range of aspect-ratios, or else cover the entire range piecewise.
In particular, the set of equations proposed by Hammerstad,[15] who modifies on Wheeler,[12] [13] are perhaps the most often cited:
Zrm{microstrip}= \begin{cases} \dfrac{Z0}{2\pi\sqrt{\varepsilonrm{eff}}}ln\left(8\dfrac{h}{w}+\dfrac{w}{4h}\right),&when\dfrac{w}{h}\leq1\\ \dfrac{Z0}{\sqrt{\varepsilonrm{eff}}\left[
| w | |
| h |
+1.393+0.667ln\left(
| w | |
| h |
+1.444\right)\right]},&when\dfrac{w}{h}\geq1 \end{cases}
where is the effective dielectric constant, approximated as:[16]
| \begin{align} \varepsilon | ||||
|
1}{2}+
| \varepsilonrm{r | |
| - |
1}{2}q\\ q&=
| 1 | |
| \sqrt{1+12(h/w) |
}+q2\\ q2&=\begin{cases}0.04(1-\dfrac{w}{h})2,&when\dfrac{w}{h}\leq1\ 0,&when\dfrac{w}{h}\geq1\\ \end{cases}.\\ \end{align}
Microstrip circuits may require a metallic enclosure, depending upon the application. If the top cover of the enclosure encroaches in the microstrip, the characteristic impedance of the microstrip may be reduced due to the additional path for plate and fringing capacitance. When this happens, equations have been developed to adjust the characteristic impedance in air (Er=1) of the microstrip,
\Delta
| a | |
| Z | |
| om |
| a | |
| Z | |
| om |
=
| a | |
| Z | |
| oinfty |
-\Delta
| a | |
| Z | |
| om |
| a | |
| Z | |
| oinfty |
\varepsilonre
Zom=
| a | |
| Z | |
| om |
/
| \sqrt{\varepsilon | |
| rem |
| \varepsilon | |
| rem |
\varepsilonre
wrm{eff}
w
\Delta
| a | |
| Z | |
| om |
| \varepsilon | |
| rem |
\varepsilon=1
\varepsilon=\varepsilonr
The equation for
| \varepsilon | |
| rem |
| \begin{align} \varepsilon | |
| rem |
&=
| \varepsilonr+1 | |
| 2 |
+
| \varepsilonr-1 | |
| 2 |
| q | |
| qC |
\\ q&isdefinedabove\\ qC&=tanh(1.043+.121
| c | |
| h |
-1.164
| h | |
| c |
)\\ \end{align}
The equation for
\Delta
| a | |
| Z | |
| om |
\begin{align} \Delta
| a | |
| Z | |
| om |
&=PQ\\ P&=270[1-tanhr(0.28+1.2\sqrt{
| c | |
| h |
\end.
The equation for
Zom
Zom=
| ||||||||||||||||
|
The equations are claimed to be accurate to within 1% for:
\begin{align} &1\le\varepsilonr\le30\\ &0.05\lew/h\le30.0\\ &t/h\le0.1\\ &c/h\ge1.0\\ \end{align}
When the dielectric layer is suspended over the lower ground plane by an air layer, the substrate is known as a suspended substrate, which is analogous to the layer D in the microstrip illustration at the top right of the page being nonzero. The advantages of using a suspended substrate over a traditional microstrip are reduced dispersion effects, increased design frequencies, wider strip geometries, reduced structural inaccuracies, more precise electrical properties, and a higher obtainable characteristic impedance. The disadvantage is that suspended substrates are larger than traditional microstrip substrates, and are more difficult to manufacture. When the conductor is placed below the dielectric layer, as opposed to above, the microstrip is known as an inverted microstrip.[18]
Pramanick and Bhartia documented a series of equations used to approximate the characteristic impedance (Zo) and effective dielectric constant (Ere) for suspended and inverted microstrips. The equations are accessible directly from the reference and are not repeated here.
John Smith worked out equations for the even and odd mode fringe capacitance for arrays of coupled microstrip lines in a suspended substrate using Fourier series expansion, and provides 1960s style Fortran code that performs the function. Single single microstrip lines behave like coupled microstrips with infinitely wide gaps, so Smith's equations may be used to compute fringe capacitance of single microstrip lines by entering a large number for the gap into the equations such that the other coupled microstrip no longer significantly effects the electrical characteristic of the single microstrip, which is typically a value of seven substrate heights or higher.[19] Inverted microstrips may be computed by swapping the cover height and suspended height variables. Microstrips with no metallic enclosure my be computed by entering a large variable into the metallic cover height such that the metallic cover no longer significantly effects the microstrip electrical characteristics. Inverted microstrips may be computed by swapping the metallic cover height and suspended height variables.
Smiths equations contain a bottleneck where the inverse of an Elliptic integral ratio must be solved,
F(1,k')/F(1,k)=X
X
k
To compute the Zo and Ere values for a suspended or inverted microstrip, the plate capacitance may added to the fringe capacitance for each side of the microstrip line to compute the total capacitance for both the dielectric case (Er) case and air case (Era), and the results may be used used to compute Zo and Ere, as shown.[20]
\begin{align} \varepsilonre&=
| |||||
| Cair |
\\ Zo&=
| 1 | ||||||||||
|
In order to build a complete circuit in microstrip, it is often necessary for the path of a strip to turn through a large angle. An abrupt 90° bend in a microstrip will cause a significant portion of the signal on the strip to be reflected back towards its source, with only part of the signal transmitted on around the bend. One means of effecting a low-reflection bend, is to curve the path of the strip in an arc of radius at least 3 times the strip-width.[21] However, a far more common technique, and one which consumes a smaller area of substrate, is to use a mitred bend.
To a first approximation, an abrupt un-mitred bend behaves as a shunt capacitance placed between the ground plane and the bend in the strip. Mitring the bend reduces the area of metallization, and so removes the excess capacitance. The percentage mitre is the cut-away fraction of the diagonal between the inner and outer corners of the un-mitred bend.
The optimum mitre for a wide range of microstrip geometries has been determined experimentally by Douville and James.[22] They find that a good fit for the optimum percentage mitre is given by
M=100
| x | |
| d |
\%=(52+65e-(27/20)(w/h))\%
subject to and with the substrate dielectric constant . This formula is entirely independent of . The actual range of parameters for which Douville and James present evidence is and . They report a VSWR of better than 1.1 (i.e., a return loss better than -26 dB) for any percentage mitre within 4% (of the original) of that given by the formula. At the minimum of 0.25, the percentage mitre is 98.4%, so that the strip is very nearly cut through.
For both the curved and mitred bends, the electrical length is somewhat shorter than the physical path-length of the strip.