Page 284 - Complete Wireless Design

Filter Design

Filter Design 283

Figure 6.19 Joining two half-
sections by adding series
inductors.

Figure 6.20 Joining two half-
sections by adding shunt
capacitors.

To design a low-pass filter, a half-section (as depicted in Fig. 6.16) can be cal-
culated by:

R

1
0

f
f R
L and C
C
0
C
2 2
where R impedance at the filter’s input and output and f filter’s 3-dB
0 C
cutoff frequency.
After the L and C values are calculated, the actual number of poles can be
increased from the present half-section’s two, to any number desired. This is
accomplished by combining half-sections as shown in Fig. 6.21, adding the
capacitances, or by combining them as shown in Fig. 6.22 and adding the
inductances.
However, combining half-sections as shown in Fig. 6.23 would be incorrect,
and would result in a filter that not only has too many components, but also
will not function as designed. This is because only shunt elements are allowed
to “blend” with shunt elements, and only series elements can “blend” with
series elements.
As the number of filter sections increases, the actual cutoff frequency will
begin to decrease. This is referred to as the cascade effect. If this is not taken
into account, the cutoff frequency will drop, especially when three or more sec-
tions are combined. Table 6.1 is a list of the correction factors that must be
used to obtain an accurate cutoff frequency when cascading multiple sections.
To utilize this table in low-pass filter design: If f of the lowpass filter is to
C
be 200 MHz, and a 2-section filter is required, then first multiply the adjust-
ment factor of 1.15 times the f . This would be equal to 230 MHz. Now design
C
the 2-section low-pass filter as if the f will be 230 MHz, and a filter with a
C
true f at the desired frequency of 200 MHz will now be the result.
C

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