S-Parameters

S-parameters describe the input-output relationship between ports (or terminals) in an electrical system. For instance, if we have 2 ports (intelligently called Port 1 and Port 2), then S12 represents the power transferred from Port 1 to Port 2. S21 represents the power transferred from Port 2 to Port 1. In general, SNM represents the power transferred from Port N to Port M in a multi-port network. As an example, consider the following two-port network: In the above Figure, S21 represents the power received at antenna 2 relative to the power input to antenna 1. For instance, S21=0 dB implies that all the power delivered to antenna 1 ends up at the terminals of antenna 2 (which isn't physically possible). If S21=-10 dB, this implies that 1 Watt delivered to antenna 1 (or 0 dB), ends up as -10 dB at antenna 2, or 0.1 Watts. In practice, the most commonly quoted parameter in regards to antennas is S11. S11 represents how much power is reflected from the antenna. If S11=0 dB, then all the power is reflected from the antenna and nothing is radiated. If S11=-10 dB, this implies that if 3 dB of power is delivered to the antenna, -7 dB is the reflected power. The rest was "accepted" by the antenna. This accepted power is either radiated or absorbed as losses within an antenna. Since antennas are typically designed to be low loss, the majority of the power delivered to the antenna is radiated. As an example, consider the plot of S11 in the following figure: The above would typically be measured using a network analyzer, which can plot S11. The above figure shows that the antenna radiates best at 2.5 GHz, where S11=-10 dB. Further, at 1.5 GHz the antenna will radiate virtually nothing, as S11 is close to 0 dB. The bandwidth can also be determined from the above figure. If S11 is to be <-6 dB, then the bandwidth would be roughly 1 GHz, with 3 GHz the high end and 2 GHz the low end of the band.