Page 346 - Maxwell House

326 Chapter 6

Therefore, the attenuation is proportional to the inverse function of the trace width. The minimal
thickness of trace must be greater than three to five skin depth. Evidently, the dissipation in
dielectric is proportional to its loss tangential and can be minimized choosing high-quality
materials with tan ≤ 0.001 like alumina, quartz, Teflon, etc. Meanwhile, the microstrip
monolithic integral circuits are fabricated on silicon or gallium arsenide substrate (see Table
6.1) that significantly increases dielectric losses and makes them dominant.
Looking back at Figure 6.6.16 we can see that the microstrip field structure above and below
the strip is rather different. If so, we can expect that such asymmetry in open line can be the
cause of the energy emission. The analysis shows [4] that this type of loss is rather low can be
practically neglected while ℎ ≪ 1 and drops almost linearly [4] as the ratio w/h grows, i.e.
⁄
as more energy is concentrated within the strip-ground plane gap.
The microstrip highest frequency of operation is limited not only by the attenuation but the
existence of higher and mainly hybrid modes propagating within the dielectric substrate and
only loosely coupled with the strip. Such modes are formed by the partial plane waves
sequentially reflected from the top dielectric-air and bottom dielectric-metal boundaries the
same way as in WR and shown in Figure 6.4.4. They are not guided by the strip anymore and
can propagate as surface waves in any direction over the substrate causing additional loss of
energy and parasitic coupling between various circuit parts printed on the same substrate. To
avoid this effect, the highest operation frequency must not exceed the cutoff frequency of the
−1
first surface mode [6], i.e. > or < = √2ℎ� − 1/tan ( ) ≅ √2ℎ √ (if >

10). Clearly, the cutoff frequency drops as the product ℎ √ increases meaning thicker

substrate, higher dielectric constant or all together. Typically, this cutoff frequency is in the
millimeter wave range. The effective way to suppress such modes is the vias usage.
The microstrip, as well as stripline, is not suitable as high power transmission feed like coaxial
line or waveguide. The average power handling is mainly limited by the temperature rise of the
dielectric substrate, its thermal conductivity (see Table 6.1), and maximum operating
temperature. That is typically in the range of several hundred Watts depending on substrate
thickness. The peak power is restricted by the electrical breakdown due to E-field concentration
around the sharp trace edges (so round them) and is primarily defined by the electric strength
of the dielectric substrate. Evidently, the usage of microstrip with wider trace and lower
characteristic impedance may improve both power handlings due to the E-field intensity
reduction. The limit of the peak power is typically around several kW depending on microstrip
design.

We refer the reader for more detail to [3 - 6]. The best way to get reliable data is the numerical
simulation using some commercial software like CST Microwave Studio.

6.6.8 Slotline
As we have mentioned before, this line refers to the class of planar open lines supporting DC
power transfer. As such, the frequency independent dominant mode is the TEM in lines without
dielectric layer and quasi-TEM (hybrid to be exact) if the strips are printed on the substrate. E-
and H-field pattern is demonstrated in Figure 6.6.18. The substrate dielectric was chosen as
Alumina ceramic ( = 10) and the medium surrounding the slotline is an air.