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Model X3C19E2-20S
REV C
P In P Out (RL)
P Out (DC)
Input Port
Pin 1
Direct Port
Coupled Port Pin 4
P Out (CPL)
Isolated Port
P Out (ISO)
Figure 1
The coupler is excited at the input port with P in (watts) of power. Assuming the coupler is not ideal, and that there are
no radiation losses, power will exit the coupler at all four ports. Symbolically written, P out(RL) is the power that is
returned to the source because of impedance mismatch, P out(ISO) is the power at the isolated port, P out(CPL) is the
power at the coupled port, and P out(DC) is the power at the direct port.
At Anaren, insertion loss is defined as the log of the input power divided by the sum of the power at the coupled and
direct ports:
Note: in this document, insertion loss is taken to be a positive number. In many places, insertion loss is written as a
negative number. Obviously, a mere sign change equates the two quantities.
? ?
IL = 10 ? log 10 ?
?
? out ( CPL ) + P out ( DC ) ?
? P ?
In terms of S-parameters, IL can be computed as follows:
P in
( dB )
(2)
IL = ? 10 ? log 10 ? ? S 31 + S 41
?
?
2
2 ?
?
( dB )
(3)
We notice that this insertion loss value includes the power lost because of return loss as well as power lost to the
isolated port.
For thermal calculations, we are only interested in the power lost “inside” the coupler. Since P out(RL) is lost in the
source termination and P out(ISO) is lost in an external termination, they are not be included in the insertion loss for
thermal calculations. Therefore, we define a new insertion loss value solely to be used for thermal calculations:
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