Page 313 - Analog and Digital Filter Design

3 1 0 Analog and Digital Filter Design

For a short coaxial cable certain assumptions can be made, namely that it will
be loss-free. So letting G = 0 and R = 0, gives:

y= jm4F

In fact, there is an alternative expression, which may be more useful, in that the
equivalent reactance can be found:
[I 3
WC = Yo tan -.-

The ratio of operating frequency to quarter-wavelength frequency (duo)
can thus be used to find the equivalent capacitance. Y, is the characteristic
susceptance (l/ZJ.

Short-circuit Line

A short-circuit line has a different expression for its impedance:

Z,, = jZ, tan(yZ)

Again, y = jwm

SO z.,~ jz,tan(&/).
=
Again, there is a simple expression that can be used to find the equivalent induc-
tance directly. The ratio of operating frequency to quarter-wavelength frequency
(dmQ) can be used to find the inductive reactance.
[; ;

I
WL = 2, tan -.-

Use Of Misterminated Lines

Connecting short-circuited lines in the series path and open-circuit lines to shunt
the transmission path is equivalent to a ladder filter with series inductors and
shunt capacitors. A shorted-circuited line replaces each inductor, and an open-
circuit line replaces each capacitor. The difference between the two networks is
that the transnlission line filter has a periodic frequency response, because the