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-lin '"
1 +jOn : c, 3L, L,
I
)
r
Some Lumped-Element Transfonnations 365
L" c,
r
1\
"
g,
L 12
=--
-h FAr
Figure 9.28. Two·pole bandpass equivalent network using L 12
.
Another useful set of equivalent networks is available by using the Norton
transformations described in Section 6.53, Consider the bandpass prototype
network in Figure 9.27. Parameter FM is the passband fractional frequency,
and the g; are the corresponding lowpass prototype element values for a
I-ohm source resistance. An inductive Norton transformer replacement produces
the network in Figure 9,28, which is equivalent at all frequencies. Note
that the impedance-scaling parameter r must be greater than unity. A capacitive
Norton transformer replacement produces the network in Figure 9.29,
A more flexible transformation applies to a three-pole bandpass prototype
network that is modified by an inductive and a capacitive Norton transformation,
The results appear to be direct-coupled filters, but they are not, because
all the L's and C's touching each node are not resonant. Two possible
topologies appear in Figures 9,30 and 93\. Now there are two impedance
scaling parameters, N, and r; their ranges and relationships may be seen in
the equations included in the figures, Various combinations of Figures 9.28
through 9,31 may be employed to obtain suitable element values,
"1 + jD n
c"
"
: :: C, L, : _ C, g,
~FAr
c I2 =-­
g,
Figure 9.29. Two-pole bandpass equivalent network using C 12
.