Antennas. Yi Huang

Medium 2

      Similarly, we can apply other three Maxwell’s equations to this boundary to obtain:

      (1.39)

      where J_s is the surface current density and ρ_s is the surface charge density. These results can be interpreted as

       The change in tangential component of the magnetic field across a boundary is equal to the surface current density on the boundary;

       The change in the normal component of the electric flux density across a boundary is equal to the surface charge density on the boundary;

       The normal component of the magnetic flux density is continuous across the boundary between two media, while the normal component of the magnetic field is not continuous unless μ1 = μ2.

      Applying these boundary conditions on a perfect conductor (which means no electric and magnetic field inside and the conductivity σ = ∞) in the air, we have

      (1.40)

We can also use these results to illustrate, for example, the field distribution around a two‐wire transmission line as shown in Figure 1.15, where the electric fields are plotted as the solid lines and the magnetic fields are shown in broken lines. As expected, the electric field is from positive charges to the negative charges, while the magnetic field forms loops around the current.

Figure 1.15 Electromagnetic field distribution around a two‐wire transmission line

1.5 Summary

      In this chapter, we have introduced the concept of antennas, briefly reviewed antenna history, and laid down the mathematical foundations for further study. The focus has been on the basics of EMs, which include electric and magnetic fields, EM properties of materials, Maxwell’s equations, and boundary conditions. Maxwell’s equations have revealed how electric fields, magnetic fields, and sources (currents and charges) are interlinked. They are the foundation of EMs and antennas.

References

      1 1. 1. R. E. Collin, Antennas and Radiowave Propagation, McGraw‐Hill, Inc., 1985.

      2 2. 2. J. D. Kraus and D. A. Fleisch, Electromagnetics with Applications, 5th edition, McGraw‐Hill, Inc., 1999.

Problems

      1 Q1.1. What wireless communication experiment did H. Hertz conduct in 1887? Use a diagram to illustrate your answer.

      2 Q1.2. Use an example to explain what a complex number means in our daily life.

      3 Q1.3. Vector and . Findthe amplitude of vector A;the angle between vectors A and B;the dot product of these two vectors;a vector which is orthogonal to A and B.

      4 Q1.4. Vector . Find∇ • A;∇ × A;(∇ • ∇)A;∇ ∇ • A

      5 Q1.5. Vector . FindThe amplitude of E;Plot the real part of E as a function of t;Plot the real part of E as a function of z;What this vector means.

      6 Q1.6. Explain why mobile phone service providers have to pay license fees to us the spectrum. Who is responsible for the spectrum allocation in your country?

      7 Q1.7. Cellular mobile communications have become part of our daily life. Explain the major differences between the 2nd, 3rd, and 4th generations of cellular mobile systems in terms of the frequency, data rate, and bandwidth. Further explain why their operational frequencies have increased.

      8 Q1.8. Which frequency bands have been used for radar applications? Give an example.

      9 Q1.9. Express 1 kW in dB, 10 kV in dBV, 0.5 dB in W, and 40 dBμV/m in V/m and μV/m.

      10 Q1.10. Explain the concepts of the electric field and magnetic field, how are they linked to the electric and magnetic flux density functions?

      11 Q1.11. What are the material properties of interest to our electromagnetic and antenna engineers?

      12 Q1.12. What is the Lorentz force? Name an application of the Lorentz force in our daily life.

      13 Q1.13. If a magnetic field on a conducting surface z = 0 is , find the surface current density Js.

      14 Q1.14. Use Maxwell’s equations to explain the major differences between the static EM fields and time‐varying EM fields.

      15 Q1.15. Express the boundary conditions for the electric and magnetic fields on the surface of a perfect conductor.