download searchable PDF of Circuit Design book - IEEE Global ...

308 Direct-Coupled Filters
Table 8.3. Overcoupled QL Values for N~3
Lp (dB) QLI Qu Qu QL Product QuFp
Lossless Source
om 2.542 2.427 1.0 6.169 0.3146
0.10 2.112 2.106 1.0 4.449 0.5158
0.2 1.939 1.937 1.0 3.756 0.6138
0.5 1.687 1.629 1.0 2.748 0.7981
1.0 1.491 l.318 1.0 1.965 1.012
2.0 1.307 0.940 1.0 1.229 1.355
3.0 1.213 0.7011 1.0 0.8501 1.674
6.0 1.087 0.3201 1.0 0.3479 2.708
9.5 1.035 0.1371 1.0 0.1420 4.296
• Lossy Source
0.01 1.0 1.5420 1.0 1.542 0.6292
0.1 1.0 1.1120 1.0 1.1120 1.0320
0.2 1.0 0.9389 1.0 0.9389 1.2280
0.5 1.0 0.6870 1.0 0.6870 1.5960
1.0 1.0 0.4913 1.0 0.4913 2.0240
2.0 1.0 0.3072 1.0 0.3072 2.711
3.0 1.0 0.2125 1.0 0.2125 3.3490
6.0 1.0 0.0870 1.0 0.0870 5.4150
9.5 1.0 0.0355 1.0 0.0355 8.5910
Example 8.5b. Reconsider the specifications in Section 8.2.4 for the
Chebyshev overcoupled shape (with perfect inverters): the N = 3 lossy-source
filter is tuned to 50 MHz, and a 60-dB attenuation is required at 90 MHz.
Find the loaded-Q values and Ihe passband width if the passband ripple is to
be 0.2 dB. First find output resonator Qu; (8.18) shows that the loaded-Q
product must be 1035.32. Then (8.21) and the normalized loaded-Q product of
0.9389 from Table 8.3 yield Q u = 10.3312. Therefore, QL2=0.9389 X 10.3312
=9.7000, and Qu = 10.3312. Since QuFO., = 1.2280, F 0 .2=0.1189; i.e., the
0.2-dB-ripple passband widlh is 11.89%.
8.4.2. The Buttenvorth Maximally Flat Response Shape. The Butterworth
response shape is defined by
L(f) = 10 10glO[ 1+ .,(:p(] dB; (8.71)
• was defined in (8.62), and L p
is shown in Figure 8.25. Butterworth response
Equation (8.71) can be solved for the number of resonators required for the
given slopband loss L, at fractional frequency F, and comparable values of L p