**Subject :**Microwave Engineering

## Microstrip Lines

**Introduction : -
**

Microwave integrated circuits with microstrip lines are commonly used with the chips. The microstrip line is also called an open-strip line. In engineering applications, MKS units have not been universally adopted for use in designing the microstrip line. In this section we use either English units or MKS units, depending on the application, for practical purposes.Modes on microstrip line are only quasi-transverse electric and magnetic (TEM). Thus the theory of TEM-coupled lines applies only approximately. Radiation loss in microstrip lines is a problem, particularly at such discontinuities as shortcircuit posts, corners, and so on. However, the use of thin, high-dielectric materials

considerably reduces the radiation loss of the open strip. A microstrip line has an advantage over the balanced-strip line because the open strip has better interconnection features and easier fabrication.

**Characteristic impedance of microstrip lines : -
**

Microstrip lines are used extensively to interconnect high-speed logic circuits in digital computers because they can be fabricated by automated techniques and they provide the required uniform signal paths. Figure shows cross sections of a microstrip line and a wire-over-ground line for purposes of comparison.

**Figure : Cross sections of (a) a microstripline and (b) a wire-over-ground line.**

In Figure above you can see that the characteristic impedance of a microstrip line is a function of the strip-line width, the strip-line thickness, the distance between the line and the ground plane, and the homogeneous dielectric constant of the board material.The well-known equation of the characteristic impedance of a wire-over-ground transmission line, as shown in Figure, is given by

where ε_{r} = dielectric constant of the ambient medium, h = the height from the center of the wire to the ground plane d = diameter of the wire.

If the effective or equivalent values of the relative dielectric constant e, of the ambient medium and the diameter d of the wire can be determined for the microstrip line, the characteristic impedance of the microstrip line can be calculated.

**Effective dielectric constant ε _{re} :**- For a homogeneous dielectric medium, the propagation-delay time per unit length is

where μ is the permeability of the medium and E is the permittivity of the medium. In free space, the propagation-delay time is

where

In transmission lines used for interconnections, the relative permeability is 1. Consequently, the propagation-delay time for a line in a nonmagnetic medium is :

The effective relative dielectric constant for a microstrip line can be related to the relative dielectric constant of the board material.