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WHAT ARE "S" PARAMETERS? "S" parameters are measured so easily that obtaining accurate
"S" parameters are reflection and transmission coefficients, phase information is no longer a problem. Measurements like elec-
familiar concepts to RF and microwave designers. Transmission co- trical length or dielectric coefficient can be determined readily from
efficients are commonly called gains or attenuations; reflection co- the phase of a transmission coefficient. Phase is the difference be-
efficients are directly related to VSWR's and impedances. tween only knowing a VSWR and knowing the exact impedance.
VSWR's have been useful in calculating mismatch uncertainty, but
Conceptually they are like "h," "y," or "z" parameters because
they describe the inputs and outputs of a black box. The inputs and when components are characterized with "s" parameters there is no
outputs are in terms of power for "s" parameters, while they are mismatch uncertainty. The mismatch error can be precisely calcu-
voltages and currents for "h," "y," and "z" parameters. Using the lated.
convention that "a" is a signal into a port and "b" is a signal out
of a port, the figure below will help to explain "s" parameters.
Easy To Measure
Two-port "s" parameters are easy to measure at high frequencies
TEST DEVICE because the device under test is terminated in the characteristic
impedance of the measuring system. The characteristic impedance
i s"
i termination has the following advantages:
S2|
S |2
s 22 i1
02
1. The termination is accurate at high frequencies . . . it is
possible to build an accurate characteristic impedance load. "Open"
or "short" terminations are required to determine "h," "y," or "z"
In this figure, "a" and "b" are the square roots of power; (a,)J is parameters, but lead inductance and capacitance make these termi-
the power incident at port 1, and (b2)2 is the power leaving port 2. nations unrealistic at high frequencies.
The diagram shows the relationship between the "s" parameters
2. No tuning is required to terminate a device in the characteristic
and the "a's" and "b's." For example, a signal a, is partially re-
impedance . . . positioning an "open" or "short" at the terminals of
flected at port 1 and the rest of the signal is transmitted through
a test device requires precision tuning. A "short" is placed at the
the device and out of port 2. The fraction of a, that is reflected at
end of a transmission line, and the line length is precisely varied un-
port 1 is Sn, and the fraction of a, that is transmitted is s,(. Simi-
til an "open" or "short" is reflected to the device terminals. On the
larly, the fraction of az that is reflected at port 2 is $32, and the
other hand, if a characteristic impedance load is placed at the end
fraction 5u is transmitted.
of the line, the device will see the characteristic impedance regard-
The signal bi leaving port 1 is the sum of the fraction of a, that
was reflected at port 1 and the fraction of a? that was transmitted less of line length.
from port 2.
3. Broadband swept frequency measurements are possible . . .
Thus, the outputs can be related to the inputs by the equations:
because the device will remain terminated in the characteristic im-
bi = SM 3, -f Su 3i pedance as frequency changes. However, a carefully reflected "open"
j = Si. a, -f s