Microstrip
Updated May 2,
2008
Click
here to go to our page on microstrip loss
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here to go to our page on bends in transmission lines
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here to go to our main page on microwave transmission lines
Click
here to go to our microwave calculators
Click
here to go to our page on calculating transmission line loss
Click
here to go to our page on microstrip patch antennas (new for
September 2007!)
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 laboratories 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.
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 (usually
not a big deal, but this property is what causes the asymmetric
frequency of 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 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 eff
of microstrip is calculated by:

The effective dielectric constant
is a seen to be a function of the ratio of the width to the height
of the 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 reasonable
approximation for eff
(effective dielectric constant). This calculation ignores strip
thickness and frequency dispersion, but their effects are usually
small.
Go to our microwave
calculator page, our microstrip calculator does this calculation
for you!
Here's calculator
that was suggested to us that takes into account the metal thickness
effect:
(link fixed May
1, 2008 thanks to Brian...)
http://emclab.mst.edu/pcbtlc2/microstrip.html
Let us know if you
find it accurate (or not!)
Wavelength
Wavelength for any transmission
line can be calculated by dividing free space wavelength by the
squareroot of the effective dielectric constant, which is explained
above.
Characteristic
impedance
The characteristic
impedance Z0 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 Z0 of
microstrip is calculated by:

Go to our microwave
calculator page, our microstrip calculator does this calculation
for you!
It's time for a
Microwaves101 Rule of Thumb!
For pure alumina ( 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 ( 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 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 the conductor strips tends to increase the capacitance
of the lines, which effects the eff
and Z0 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 will ruin your day, you should limit the
thickness of the 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.
Microstrip loss calculations
This topic now has it's own
page! Also, check out our page on transmission
line loss calculations page.
Dispersion
Someday we'll add the calculation
that shows that effective dielectric constant is a slight function
of frequency for microstrip. This effect is not a big deal in most
cases. Here's our page on the topic of
dispersion!
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!
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