20 log (IbRu/IaRL) = 20 log (Vb/Va)
Thus the insertion loss is
20 log (0.5V1/O.O479V1) = 20.37 dB
- 12 Propagation coefficient (Y) 229
9.12 PROPAGATION COEFFICIENT (y)
This is defined as the natural logarithm of the ratio of input to output currents
or voltages when the network is terminated in its characteristic impedance.
Thus
Y = In (11/12) (9.69)
Also
Y = In (V1/V2) (9.70)
As well as there being a change in level between I1 and I2 (or between V1 and
V2) there will in general be a change in phase between them, so that Y will be
complex. In general, therefore,
y = a + jfl (9.71)
From Equations (9.69) and (9.70) we see that
I /12 = e
and
Vl/V 2 -- e h
It follows that
11/12 = e ~+J~= e~e j~= e~Z_/3 (9.72)
SimilarlyV1/V2 = e~//3 (9.73)
where
a = In 111/121 nepers (= In IV1/Vzlnepers) (9.74)
and is called the attenuation coefficient because it is responsible for the change
in level between input and output quantities.
/3 (measured in radians or degrees) is called the phase change coefficient
because it gives the change in phase between the input and output quantities.