Question

ou want to do Cet AaBbcel AaBbC AaBboct AaB AaBbCct AoBbocD Aab mal 1No Spac.. Heading 1 Heading 2 TitleSubtile Subtle Em... mphasis Intense E. Strong Quote Styles Radio Waves Through a Wall H&B model radio waves propagating through a wall as a sequence of three transmission lines as shown in the two figures below. In most practical cases Zs Zs Medin 08 07 06 0.5 04 03 02 Parallel Pol 0 500 1000 1500 2000 2500 Frequency in MHz Flgure 39 The reflectice coefficient of a wall as a function of the frequensy a) Locate an equation for the input impedance versus wavelength at the interface between medium 1 and medium 2. b) Explain why the reflection coefficient is O at the lowest frequencies c) The minimums and maximums of the reflection coefficient are periodic in de-/2. Why? d) Find an expression for de How is dedifferent than the thickness of the wall?

Answer 1

We are now ready to determine the input impedance of a transmission line of length r, attached to a load (antenna) with impedance 7A. Consider the following circuit: In low frequency circuit theory, the input impedance would simply be ZA. However, for high-frequency (or long) transmission lint's, we know that the voltage and the current are given by: For simplicity, assume the transmission line is lossless, so that the propagation constant is purely imaginary. If we define z = 0 to be at the terminals of the load or antenna, then we are interested in the ratio of the voltage to the current at location z = L: v(z) = v^+ (e6 - i beta + lambda^j beta z) Using the definition for gamma (the voltage reflection coefficient), the above equation can be manipulated algebraically, and when evaluated at z = -L, we obtain: This last equation is fundamnetal to understanding transmission lines. The input impedance of a load ZA is transformed by a transmission line as in the above equation. This equation can cause ZA to be transformed radically. An example will now be presented

2.