2.9 Transmission Lines Applied to High Frequency Circuits
101
Now, referring back to Figure 2.9-1, let consider one last interesting length for the
transmission line, .
For , equation (2.9-1) becomes
(
)
(
)
( )
(
)
Now, if our line is terminated with a short circuit, i.e.
, equation (2.9-1) becomes
This
means that, if we measure the input impedance
of a line terminated with a short
circuit, its modulus will be equal to the characteristic impedance of our transmission line.
Also if there was an open circuit at the end of the line, i.e.
, then
So, yet again, the modulus of
gives us the characteristic impedance of the line.
This is a very useful trick when it comes to verifying the impedance of a transmission line. You may
for example design a line by using a formula to achieve a specific impedance value and then wish to
verify its actual impedance either by simulation or direct measurement. To this end you can choose
a frequency (
) at which your line appears long
where is the speed
of propagation along the line and is its actual physical length. By measuring
the input impedance of the line
and taking its modulus you can then verify the actual impedance
of your line.
(2.9-4)
Conquer Radio Frequency
101 www.cadence.com/go/awr
