Microstrip

Updated May 2, 2008

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Click here to go to our page on calculating transmission line loss

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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 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!