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Microstrip is by far the most
popular transmission line used in microwave engineering for circuit
design.

History of microstrip

Microstrip is a planar transmission
line, similar to stripline and coplanar
waveguide. Microstrip was developed by ITT Federal Telecommunications Laboratories in Nutley New Jersey, as a
competitor to stripline (first published by Grieg and Engelmann
in the December 1952 IRE proceedings). According to Pozar,
early microstrip work used fat substrates, which allowed non-TEM
waves to propagate which makes results unpredictable. In the 1960s
the thin version of microstrip became popular.

By 1955 ITT had published a number of papers on microstrip in the IEEE transactions on microwave theory and technique. A paper by M. Arditi titled Characteristics and Applications of Microstrip for Microwave Wiring is a good one. The author seems to apologize for the inability of microstrip to support slotted line measurements, (as it is "rather unconventional") and concludes that it is dispersion-free but non-TEM mode but admits that he didn't analyze this, he bases his assumption on limited measured data. The "microstrip kit" shown below is a priceless artifact. Presumably it would be sent to customers to let them try out microstrip for themselves. Networks such as rat-races can somehow be clipped together to form a receiver or something useful. It has plenty of transitions to waveguide and coax (called "transducers" in the paper) so you can actually measure what you just made... if anyone has one of these gems, please tell us your address we will fly the Microwaves101 private jet there to take some proper pictures!

This kit is similar to the Raytheon "Lectron", which was an educational toy marketed starting in 1967 in which magnets held circuit elements imprinted with their schematic symbols together, it had everything you needed to build a simple transistor radio, including a tiny speaker. One of these days we'll go out to the garage, find our old Lectron and take some photos. Not long ago, a Raytheon lawyer warned us not to use their good name on this web site. To which we respond, "ptttthhhhh!" with extra ejected saliva.

In 1996, a serious crime against microwave history was committed when ITT Nutley tore down their 300 foot microwave tower to make way for some ugly condos. The video below is not great, we'll keep an eye out for a better one.

Overview of microstrip

Microstrip transmission lines
consist of a conductive strip of width "W" and thickness
"t" and a wider ground plane, separated by a dielectric
layer (a.k.a. the "substrate") of thickness "H"
as shown in the figure below. Microstrip is by far the most popular
microwave transmission line, especially for microwave integrated
circuits and MMICs. The major advantage
of microstrip over stripline is that all active components can be
mounted on top of the board. The disadvantages are that when high
isolation is required such as in a filter or switch, some external
shielding may have to be considered. Given the chance, microstrip
circuits can radiate, causing unintended circuit response. A minor
issue with microstrip is that it is dispersive,
meaning that signals of different frequencies travel at slightly
different speeds. Microstrip does not support a TEM
mode, because of its filling
factor. For coupled
lines, the even and odd
modes will not have the same phase velocity. This property is
what causes the asymmetric frequency of microstrip bandpass filters,
for example.

Variants of microstrip include
embedded microstrip and coated microstrip, both of which add some
dielectric above the microstrip conductor. Anyone care to donate
some material on these topics?

Effective
dielectric constant

Because part of the fields from
the microstrip conductor exist in air, the effective dielectric
constant "Keff" is
somewhat less than the substrate's dielectric
constant (also known as the relative permittivity). Thanks to
Brian KC2PIT for reminding us the term "relative dielectric
constant" is an oxymoron only used my microwave morons!) According
to Bahl and Trivedi[1], the effective dielectric
constant ε_{eff}
(a.k.a. Keff) of microstrip is calculated by:

All microstrip equations are
approximate. The above equations ignore strip thickness, so we wouldn't
recommend relying on them for critical designs on thick copper boards.

The effective dielectric constant
is a seen to be a function of the ratio of the width to the height
of a microstrip line (W/H), as well as the dielectric constant
of the substrate material. Be careful, the way it is expressed here
it is also a function of H/W!

We have a table of "hard"
substrate material properties here,
and "soft" substrate material properties here,
in case you want to look up the dielectric constant of a specific
material.

Note that there are separate
solutions for cases where W/H is less than 1, and when W/H is greater
than or equal to 1. These equations provide a reasonableapproximation for ε_{eff}
(effective dielectric constant). This calculation ignores strip
thickness and frequency dispersion, but their effects are usually
small.

Wavelength for any transmission
line can be calculated by dividing free space wavelength by the
square root of the effective dielectric constant, which is explained
above.

Characteristic
impedance

Characteristic
impedance Z_{0} of microstrip is also a function of the ratio of the height
to the width W/H (and ratio of width to height H/W) of the transmission
line, and also has separate solutions depending on the value of
W/H. According to Bahl
and Trivedi[1], the characteristic impedance Z_{0} of
microstrip is calculated by:

Again, these equations
are approximate, and don't take into account strip thickness.
When strip thickness is a substantial fraction of substrate
height, you should use a more accurate calculation. Suggestion:
use Agilent ADS's Linecalc. One of these days we'll post some more
accurate equations.

For pure alumina (ε_{R}=9.8),
the ratio of W/H for fifty-ohm microstrip is about 95%. That means
on ten mil (254 micron) alumina, the width for fifty ohm microstrip
will be about 9.5 mils (241 microns). On GaAs (ε_{R}=12.9),
the W/H ratio for fifty ohms is about 75%. Therefore on four mil
(100 micron) GaAs, fifty ohm microstrip will have a width of about
3 mils (75 microns). On PTFE-based soft board materials ε_{R}=2.2),
W/H to get fifty ohms is about 3. Remember these!

Effect of metal thickness on
calculations

Having a finite thickness of
metal for conductor strips tends to increase the capacitance
of the lines, which effects the ε_{eff}
and Z_{0} calculations. We'll add this correction factor
at a later date.

Effect of cover height on calculations

Having a lid in close proximity
raises the capacitance per length, and therefore lowers the impedance.
We suggest that if your impedance calculation is important, to use
EDA software to make the final calculation
on line widths!

Cutoff frequency

Below we present a microstrip rule of thumb,
based on experience and not theory. In order to prevent higher-order
transmission modes which might ruin your day, you should limit the
thickness of your microstrip substrate to 10% of a wavelength.
Examples of what this means: 15 mil alumina is good up to 25 GHz,
4 mil GaAs is good up to 82 GHz, and 5 mil quartz is good up to
121 GHz. There are formulas associated with calculating the exact cut-off frequencies, some day maybe we'll post them.

Note to MMIC designers: increasing the height of a microstrip substrate decreases metal loss proportionately. It also increases the parasitic inductance associated with via holes. You may find that a two-mil substrate gives more gain than a four-mil substrate for the same active device, because of reduced inductance, and in many cases that "extra" gain will offset the loss associated with reduced strip widths. For switch designs, reduced substrate height means reduced switch isolation.

Note to GaN fab operators: as GaN-on-SiC moves into mainstream and up into millimeter-waves, it seems like most fabs are trying to duplicate the 50 and 100um (2 and 4 mil) thicknesses of GaAs substrates. If you consider that SiC has DK=10 versus GaAs DK of 12.9, you can get away with a 75um (three mil) process to serve all the way to 110 GHz. You will get better heat spreading and lower metal loss to boot.

The effective dielectric constant (and therefore phase velocity and characteristic impedance) of microstrip is a slight function
of frequency. This effect is not a big deal in most
cases.

Our main discussion of microstrip dispersion is now here.

References

[1] Reference:
I. J. Bahl and D. K. Trivedi, "A Designer's Guide to Microstrip
Line", Microwaves, May 1977, pp. 174-182. Go to our
book section and buy a book on microstrip!