Microstrip is a type of electrical transmission line which can be
fabricated using printed circuit board technology, and is used to convey
microwave-frequency signals. It consists of a conducting strip separated from a
ground plane by a dielectric layer known as the substrate. 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.
The disadvantages of microstrip compared with waveguide are the generally lower
power handling capacity, and higher losses. Also, unlike waveguide,
microstrip is 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 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. On a smaller scale, microstrip
transmission lines are also built into monolithic microwave integrated
circuits. 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 very similar to stripline
and coplanar waveguide, and it is possible to integrate all three on the
same substrate. Inhomogeneity
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 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.
Further consequences of an inhomogeneous medium include:
The line will not support a true TEM wave; at non-zero frequencies, both the
E and H fields will have longitudinal components. The longitudinal components
are small however, and so the dominant mode is referred to as quasi-TEM.
The line is dispersive. With increasing frequency, the effective dielectric
constant gradually climbs towards that of the substrate, so that the phase
velocity gradually decreases. This is true even with a non-dispersive
substrate material. The characteristic impedance of the line
changes slightly with frequency. The characteristic impedance of non-TEM
modes is not uniquely defined, and depending on the precise definition
used, the impedance of microstrip either rises, falls, or falls then rises with
increasing frequency. The low-frequency limit of the characteristic impedance is
referred to as the quasi-static characteristic impedance, and is the
same for all definitions of characteristic impedance.
The wave impedance varies over the cross-section of the line.
Characteristic impedance A closed-form approximate expression for
the quasi-static characteristic impedance of a microstrip line was
developed by Wheeler: 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: 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 of substrate, and t is the thickness of the strip
metallization. This formula is asymptotic to an exact
solution in three different cases , any ,
, and ,
It is claimed that for most other cases, the error in impedance is less than 1%,
and is always less than 2%. By covering all aspect-ratios in one formula,
Wheeler 1977 improves on Wheeler 1965 which gives one formula for and another
for . Nevertheless, the 1965 paper is perhaps the more often cited. 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.
Curiously, Harold Wheeler disliked both the terms 'microstrip' and
'characteristic impedance', and avoided using them in his papers.
Bends 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. 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. They find that a good fit for
the optimum percentage mitre is given by 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 for any percentage mitre within 4% 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.
See also Distributed element filter
Spurline, a microstrip notch-filter References
External links Microstrip in Microwave Encyclopedia
Microstrip Analysis/Synthesis Calculator