David Jefferies
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Transmission line notes.
Waveguides and Cavity Resonators

What is microstrip transmission line?

Microstrip transmission line is a kind of "high grade" printed circuit construction, consisting of a track of copper or other conductor on an insulating substrate. There is a "backplane" on the other side of the insulating substrate, formed from similar conductor. A picture (37kB).

Looked at end on, there is a "hot" conductor which is the track on the top, and a "return" conductor which is the backplane on the bottom. Microstrip is therefore a variant of 2-wire transmission line.

If one solves the electromagnetic equations to find the field distributions, one finds very nearly a completely TEM (transverse electromagnetic) pattern. This means that there are only a few regions in which there is a component of electric or magnetic field in the direction of wave propagation. There is a picture of these field patterns (incomplete) in T C Edwards "Foundations for Microstrip Circuit Design" edition 2 page 45. See the booklist for further bibliographic details.

The field pattern is commonly referred to as a Quasi TEM pattern. Under some conditions one has to take account of the effects due to longitudinal fields. An example is geometrical dispersion, where different wave frequencies travel at different phase velocities, and the group and phase velocities are different.

The quasi TEM pattern arises because of the interface between the dielectric substrate and the surrounding air. The electric field lines have a discontinuity in direction at the interface. The boundary conditions for electric field are that the normal component (ie the component at right angles to the surface) of the electric field times the dielectric constant is continuous across the boundary; thus in the dielectric which may have dielectric constant 10, the electric field suddenly drops to 1/10 of its value in air. On the other hand, the tangential component (parallel to the interface) of the electric field is continuous across the boundary. In general then we observe a sudden change of direction of electric field lines at the interface, which gives rise to a longitudinal magnetic field component from the second Maxwell's equation, curl E = - dB/dt.

Since some of the electric energy is stored in the air and some in the dielectric, the effective dielectric constant for the waves on the transmission line will lie somewhere between that of the air and that of the dielectric. Typically the effective dielectric constant will be 50-85% of the substrate dielectric constant.

As an example, in (notionally) air spaced microstrip the velocity of waves would be c = 3 * 10^8 metres per second. We have to divide this figure by the square root of the effective dielectric constant to find the actual wave velocity for the real microstrip line. At 10 GHz the wavelength on notionally air spaced microstrip is therefore 3 cms; however on a substrate with effective dielectric constant of 7 the wavelength is 3/(sqrt{7}) = 1.13cms. Thus the maximum length for a stub to be used in stub matching, which is no more than half a wavelength, is about 5.6 mm.

A set of detailed design formulae and algorithms is presented in T C Edwards, Op Cit.

There is a rough and ready nomogram for calculating the impedance of microstrip from the dielectric properties and the geometry in this picture (37kB)

Substrate materials.

Important qualities of the dielectric substrate include

Types of substrate include plastics, sintered ceramics, glasses, and single crystal substrates (single crystals may have anisotropic dielectric constants; "anisotropic" means they are different along the different crystal directions with respect to the crystalline axes.)

Common substrate materials

The dielectric strength of ceramics and of single crystals far exceeds the strength of plastics, and so the power handling abilities are correspondingly higher, and the breakdown of high Q filter structures correspondingly less of a problem.

It is also a good idea to have a high dielectric constant substrate and a slow wave propagation velocity; this reduces the radiation loss from the circuits. However at the higher frequencies the circuits get impossible small, which restricts the power handling capability. For these applications one often choses fused quartz (dielectric constant 3.8).

Copyright D.Jefferies 1996, 2002.
D.Jefferies email
21st February 2002.