RF and Microwave Engineering: Fundamentals of Wireless Communications

7.8 Problems

7.1. We consider a communication standard with a maximum transmit power of 100 mW (EIRP). Transmitter and receiver amplifiers are connected via low-loss transmission lines (attenuation a₁ = 2.5 dB) to antennas with a gain of G₁ = 5 dBi.

In order to extend the range of the wireless system the transmission lines are substituted by shorter transmission lines with an attenuation of a₂ = 1 dB. Furthermore, antennas with larger gain are used G₂ = 15 dBi. What is the maximum permissible transmit power of the transmitter amplifier before and after the system modification? Why is there a range extension at all?

7.2. Investigate some of the ideas to reduce the height of monopole antennas shown in Section 7.4.3 by using an EM simulator of your choice. Select an operating frequency of f = 2.45 GHz.

7.3. Design a coaxial-feed patch antenna for a frequency of f = 4 GHz. The substrate has a relative permittivity of ε_r = 3.38 and a height of h = 1.6 mm. The width shall be W = 1.5L, where L is the resonant length of the patch. Check the performance of your design with an EM simulator of your choice.

7.4. Demonstrate that the electric and magnetic field strength of a Hertzian dipole given in Equation 7.34 can be derived from Equation 7.29 by using Equations 7.23 and 7.24.

7.5. Derive the relation in Equation 7.62 that determines the phase of antenna elements of a group antenna in order to steer the direction of the main lobe.