RF and Microwave Engineering: Fundamentals of Wireless Communications

4.3 Microstrip Line

4.3.1 Characteristic Impedance and Effective Permittivity

Figure 4.6 shows the cross-section of a microstrip line. A microstrip line consists of a dielectric (or semiconductor) substrate with a continuous ground plane on one side and a metallic strip on the other side. An electromagnetic wave that propagates on a microstrip line exists in two different media: air (above the metallic trace) and substrate (between strip and ground plane). At the air–substrate interface the fields have to meet electromagnetic boundary conditions. These boundary conditions lead to (small) longitudinal electric and magnetic field components. Since the longitudial components are small compared to the transversal field components the fundamental wave mode is referred to as quasi-TEM.

Figure 4.6 Geometry of a microstrip line and electric and magnetic field distribution of a quasi-TEM wave.

Electromagnetic waves in air (with a relative permittivity of one) and in substrate (with a relative permittivity of ε_r) have different phase velocities. The resultant velocity c on a microstrip line is given somewhere in between these two velocities and can be expressed by the definition of an effective relative permittivity.

4.24

The effective relative permittivity is in the range 1 ≤ ε_r,eff ≤ ε ...