Radio Frequency Integrated Circuit Design - Webs

90 Radio Frequency Integrated Circuit Design
S parameters are a way of calculating a two-port network in terms of
incident and reflected (or scattered) power. Referring to Figure 4.31, assuming
port 1 is the input, a1 is the input wave, b 1 is the reflected wave, and b 2 is
the transmitted wave. We note that if a transmission line is terminated in its
characteristic impedance, then the load absorbs all incident power traveling
along the transmission line and there is no reflection.
The S parameters can be used to describe the relationship between these
waves as follows:
b 1 = S 11a 1 + S 12a 2
b 2 = S 22a 2 + S 21a 1
This can also be written in a matrix as
(4.38)
(4.39)
�b 1
b 2� =� S11 S12 S21 S22��a1 = [b] = [S ][a] (4.40)
a2�
Thus, S parameters are reflection or transmission coefficients and are
usually normalized to a particular impedance. S11, S22, S21, and S12 will now
each be defined.
S11 = b 1
a1 | a2 =0
(4.41)
S11 is the input reflection coefficient measured with the output terminated
with Z o . This means the output is matched and all power is transmitted into
the load; thus a2 is zero.
S21 = b 2
a1 | a2 =0
(4.42)
S21, the forward transmission coefficient, is also measured with the output
terminated with Z o . S21 is equivalent to gain.
Figure 4.31 General two-port system with incident and reflected waves.