1106 
MONITORING 
becoming widely accepted is that they are easy 
to measure, because the required terminations 
are not open or short circuits as is true of the 
z- or y-parameters. The use of a finite terminat- 
ing impedance for measurement helps to sta- 
bilize the device whose parameters are being 
measured; whereas the device may become 
unstable when an attempt to short or open one 
port is made. This advantage is especially evi- 
dent at frequencies above 100 MHz where valid 
open or short circuits are difficult to obtain. 
In system design the transfer of power is 
generally of primary interest and mating net- 
works are often used so that power transfer 
is optimized. The s-parameters provide infor- 
mation that is closely related to power transfer ; 
therefore, circuit design is simplified, because 
the required matching networks are easy to 
describe. 
Numerous papers have defined and discussed 
the generalized scattering parameters and, 
therefore, a detailed description is not given 
here.^-^ Material sufficient for understanding 
how the parameters are used for the present 
application is included. 
Figure 1 shows a 2-port network to be de- 
scribed by s-parameters. The equations that are 
generally used are 
bi = Siiai + Si2a2 
b2 = S2iai -\- 8228.2 
(1) 
where the a's and b's are the incident and re- 
flected voltage waves normalized to V^o- The 
characteristic impedance is designed by Z„. The 
incident and reflected waves are closely related 
to power flow, since \sLi\^ is the power incident 
on the i"" port and \hi\^ is the power reflected 
from or leaving the i*'' port. 
If a2 is set to 0, Sn and S21 may be determined ; 
and if ai is 0, then S12 and S22 may be determined. 
Either ai or a2 is made 0 by terminating the 
port of interest in Zo. This termination absorbs 
all the incident power, so there is no reflected 
wave. 
If V+ and V- are defined as the incident 
and reflected voltage waves, respectively, then 
the following definitions hold and can be used 
to find the s-parameters. 
Sn = V1-/V1+ 
S21 = V2-/V1+ 
V2+= 0 
S12 = V1-/V2+ 
V2+=0 
S22 = V2-/V2+ 
Vi+ = 0 
(2) 
Vi+ = 0 
The incident and reflected voltages are easily 
measured. The parameters Sn and S22 are simply 
reflection coefficients and are measured under 
the condition that both ports are terminated 
in the characteristic impedance of the system, 
Z„ They provide sufficient information for de- 
termining the input and output impedances of 
a 2-port system, when Zo terminations are used. 
Likewise, the parameters S21 and S12 are the 
forward and reverse transmission gains with 
the input and output ports terminated in Zo. 
Eq. (1) shows that like other parameter sets, 
s-parameters relate two input and two output 
quantities, and Eq. (2) indicates the conditions 
that must be satisfied to measure the four 
parameters. Figure 2 shows that the terminals 
of the 2-port device connected to a system that 
has a characteristic impedance of 50 ohms. The 
50-ohm terminations insure that no reflections 
will occur at the load or generator. By applying 
a signal to one of the ports, 3 measurements will 
define 2 of the parameters. If, for example, the 
input is on the left in Figure 2, then V2+ = 
a2 = 0. Under this condition, measurements of 
Vi+, Vi" and V2~ will specify Sn and S21 as 
indicated by Eq. (2). If the input and output 
ports are reversed, then Vi+ = ai = 0 and meas- 
FiGURE 1. — Two-port network. Biotelemetry transmitter 
design methods. Figure 2. — Simplified measurement circuit. 
