Читать книгу Handbook of Microwave Component Measurements - Joel P. Dunsmore - Страница 53

Certainly the most widespread transmission line must be the microstrip line, shown in Figure 1.30. This is found in planar structures such as PC boards and micro‐circuits. Consisting of a thin strip of metal on a dielectric substrate, over a ground plane, it is used for connection between components as well as creating transmission line components such as couplers and filters (Hong and Lancaster 2001).

Figure 1.30 Planer transmission lines: microstrip (a), coplanar waveguide (b), strip line (c).

The computation of the transmission parameters has been fully documented in many forms, but for measurement purposes these lines are typically 50 Ω (or the equivalent system impedance) even though as a design element they can take on any value. For most applications, the dielectric constant is 10 or less, so the w/h ratio is greater than 1 for 50 Ω. The approximate impedance can be computed as (Pozar 1990)

(1.86)

where ε_re is the effective relative‐dielectric‐constant, found from

(1.87)

The effective relative‐dielectric constant sets the velocity factor of the transmission line, but in microstrip, some of the fields travel in the substrate and some in air. Therefore, the transmission is not purely transverse‐electromagnetic (TEM), and some structures become more difficult to design, particularly coupled lines, the even and odd mode velocity factors of which are not the equal. Since the line is not pure TEM, at high frequency, dispersion effects will become apparent where the effective delay of the line is not constant with frequency.

The loss of microstrip lines is difficult to compute accurately because it depends upon many factors including the conductivity of the microstrip line and the ground plan, the dielectric loss of the substrate, radiated loss to the housing or shield, and losses related to both surface roughness and edge roughness. These roughness losses can be significant in PC board and low‐temperature cofired‐ceramic (LTCC) applications and are dependent upon the particular processes used. While there are high‐quality PC board materials (Duriod™ or GTEK™ are common trade names), the material known as FR4 is most common, and the dielectric constant and loss of this PC board material can be uncertain. The finished substrate can be comprised of layers of board material sandwiched together with glue, and the final thickness can depend upon processing steps, so it is best when evaluating microstrip transmission lines to produce sample structures that can help determine the exact nature of the material.

One high‐performance material used is single‐crystal sapphire, and it has the unusual property of having a dielectric constant that has a directionality, with a higher constant of 10.4 in one of the three dimensions, and a lower constant of 9.8 in the other two. A second, common high‐performance dielectric is ceramic found in thin‐film, thick‐film, and LTCC applications. It has a uniform dielectric constant typically between 9.6 and 9.8 depending upon the purity and grain structure of the ceramic.