Microstrip

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 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 is the generally lower power handling capacity, and higher losses.

For lowest cost, microstrip devices may be built on an ordinary FR-4 (standard PCB) substrate.

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.

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.

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] where weff 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: Here Z0 is the impedance of free space, εr is the relative permittivity of substrate, w is the width of the strip, h is the thickness ("height") of substrate, and t is the thickness of the strip metallization.

In particular, the set of equations proposed by Hammerstad,[15] who modifies on Wheeler,[12][13] are perhaps the most often cited: where εeff is the effective dielectric constant, approximated as:[16] Microstrip circuits may require a metallic enclosure, depending upon the application.

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.

[18][19] 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.

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 of the charge distribution, and provides 1960s style Fortran code that performs the function.

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 (εr) case and air case (εra), and the results may be used to compute Zo and Ere, as shown:[22][21] 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.

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.

The optimum mitre for a wide range of microstrip geometries has been determined experimentally by Douville and James.

[24] They find that a good fit for the optimum percentage mitre is given by subject to w/h ≥ 0.25 and with the substrate dielectric constant εr ≤ 25.

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 d) of that given by the formula.

Extensive work has been performed developing models for these types of junctions, and are documented in publicly available literature, such as Quite universal circuit simulator (QUCS).

This may come about inadvertently as lines are laid out, or intentionally to shape a desired transfer function, or design a distributed filter.

Closed form expressions for even and odd mode characteristic impedance (Zoe, Zoo) and effective dielectric constant (εree, εreo) have been developed with defined accuracy under stated conditions.

John Smith worked out equations for the even and odd mode fringe capacitance for arrays of coupled microstrip lines with a metallic cover including suspended microstrips using Fourier series expansion of the charge distribution, and provides 1960s style Fortran code that performs the function.

Although Smith provides an elaborate search algorithm to find k, faster and more accurate convergence may be achieved with Newton's method, or interpolation tables may be employed.

Smith compares the accuracy of his Fourier series capacitance solutions to published tables of the times.

However, a more modern approach is to compare the even and odd mode impedance and effective dielectric constants results to those obtains from electromagnetic simulations such as Sonnet.

The example begins by computing the value of log(k), then k, and goes on to use k, εr, substrate geometry, and conductor geometry to compute the capacitances and subsequently the even and odd mode impedance and effective dielectric constant (Zoe, Zoo, εre and εro).

of 0.5 mm approximated with 7 mm with dielectric with air Ceven Codd When two microstrip lines exist close enough in proximity for coupling to occur but are not symmetrical in width, even and odd mode analysis is not directly applicable to characterize the lines.

Nonadjacent microstrip capacitance may be accurately calculated using the Finite element method (FEM).

When the microstrip characteristic impedance (Zo), effective dielectric constant (Ere), and total losses (

[42] Welch and Pratt, and Schneider proposed the following expressions for attenuation due to dielectric losses.

Coupled microstrip losses may be estimated using the same even and odd mode analysis as is used for characteristic impedance, dielectric constant.