RF and Microwave Engineering: Fundamentals of Wireless Communications

5.4 S-Parameter Representation of Network Properties

Networks may have special electric properties like reciprocity or loss-lessness. These properties can be directly identified by looking at the scattering parameters as we will show in the following sections.

5.4.1 Matching

A matched port has a zero-valued reflection coefficient. A network that is matched at all ports has only reflection coefficients equal to zero.

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According to Equation 5.17 a reflection coefficient that is zero means that there is no reflected wave b_i at that port. The input impedance Z_ini at port i equals the port reference impedance Z_0i. Matching (i.e. the absence of reflections) is generally desirable in RF circuits. Perfect matching is practically impossible, so we try to keep reflections under a certain limit depending on our application. Typical limits where we consider matching to be sufficient are s₁₁ ≤ − 20 dB (1% reflected power), s₁₁ ≤ − 10 dB (10% reflected power) or s₁₁ ≤ − 6 dB (25% reflected power). The frequency range where we find our requirements satisfied is called (impedance) bandwidth.

Figure 5.4 shows as an example a frequency dependent reflection coefficient of an antenna. In the frequency range from the lower frequency f_{L, 10 dB} to the upper frequency f_{U, 10 dB} the reflection coefficient is −10 dB or less (the return loss is +10 dB or more). So the bandwidth is referred to as 10 dB ...