RF and Microwave Engineering: Fundamentals of Wireless Communications

5.2 Normalized Power Waves

Let us consider the two-port network in Figure 5.2. The network is connected to two transmission lines with characteristic impedances Z₀₁ and Z₀₂.

Figure 5.2 Definition of incident and outgoing power waves a_i and b_i at a two-port network attached to transmission lines with characteristic impedances Z₀₁ and Z₀₂.

In Section 3.1 we discussed transmission lines and propagating voltage and current waves. We introduced a forward propagating voltage wave U_f and a reflected (backward travelling) voltage wave U_r. Based on these voltage waves we now derive normalized power waves by dividing the voltage waves by the square-root of the characteristic line impedances [1].

We define a forward propagating normalized power wave as

5.6

where i is the port index (i ∈ [2, 3]). Furthermore, we define a backward propagating normalized power wave as

5.7

For loss-less transmission lines the characteristic impedances are real-valued.¹ The impedances are also referred to as port reference impedances. Most often we use port reference impedances that equal the common² system impedance of Z₀ = 50 Ω. Throughout this book we assume port reference impedances of 50 Ω, if not otherwise ...