768 Chapter 22
22.1.1 Attenuator K Value
To simplify the design of complex attenuators, a K
value is used in the equation. K is the ratio of current,
voltage, or power corresponding to a given value of
attenuation expressed in decibels. The equation for K is
(22-1)
(22-2)
To simplify the calculation of attenuator networks,
the values of the most frequently used expressions as
tabulated by P. K. McElroy are given in Table 22-1. The
various values of the expressions are substituted in the
K (^10) equations, saving much time.
dB
= ------ -^20
K 10
dB
= ------ -^10
Table 22-1. K” Factors for Calculating Attenuator Loss Values
abcdef ghij l
n
(dB)
n
(dB)
0.2 0.97724 1.023292 1.047128 0.011512 86.866 21.713 0.046052 43.437 0.022762 33.933 32.933 0.2
0.5 0.94406 1.059254 1.12202 0.028774 34.754 8.6810 0.1 1519 17.391 0.055939 17.877 16.877 0.5
0.8 0.91201 1.096477 1.20227 0.046019 21.730 5.4209 0.18447 10.888 0.087988 11.365 10.365 0.8
1.0 0.89125 1.12202 1.25893 0.057502 17.391 4.3335 0.23077 8.7237 0.10875 9.1954 8.1954 1.0
1.2 0.87096 1.14815 1.31826 0.068968 14.499 3.6076 0.27719 7.2842 0.12904 7.7499 6.7499 1.2
1.4 0.85114 1.17490 1.38038 0.080418 12.435 3.0888 0.32376 6.2579 0.14886 6.7176 5.7176 1.4
1.5 0.84139 1.18850 1.41254 0.086132 11.610 2.8809 0.34711 5.8480 0.15861 6.3050 5.3050 1.5
1.8 0.81283 1.23027 1.51356 0.103249 9.6853 2.3956 0.41744 4.8944 0.18717 5.3427 4.3427 1.8
2.0 0.79433 1.25893 1.58489 0.11463 8.7241 2.1523 0.46460 4.4195 0.20567 4.8620 3.8620 2.0
2.2 0.77625 1.28825 1.65959 0.12597 7.9384 1.9531 0.51200 4.0322 0.22375 4.4692 3.4692 2.2
2.4 0.75858 1.31826 1.73780 0.13728 7.2842 1.7867 0.55968 3.7108 0.24142 4.1421 3.1421 2.4
2.5 0.74989 1.33352 1.77828 0.14293 6.9966 1.7133 0.58363 3.5698 0.25011 3.9983 2.9983 2.5
3.0 0.70795 1.41254 1.99526 0.17100 5.8480 1.4192 0.70459 3.0095 0.29205 3.4240 2.4240 3.0
3.5 0.66834 1.49623 2.2387 0.19879 5.0304 1.2079 0.82789 2.6147 0.33166 3.0152 2.0152 3.5
4.0 0.63096 1.58489 2.5119 0.22627 4.4194 1.0483 0.95393 2.3229 0.36904 2.7097 1.7097 4.0
4.5 0.59566 1.67880 2.8184 0.25340 3.9464 0.92323 1.08314 2.0999 0.40434 2.4732 1.4732 4.5
5.0 0.56234 1.77828 3.1623 0.28013 3.5698 0.82241 1.21594 1.9249 0.43766 2.2849 1.2849 5.0
5.5 0.53088 1.88365 3.5481 0.30643 3.2633 0.73922 1.35277 1.7849 0.46912 2.1317 1.1317 5.5
6.0 0.50119 1.99526 3.9811 0.33228 3.0095 0.66932 1.49407 1.6709 0.49881 2.0048 1.0048 6.0
6.5 0.47315 2.1135 4.4668 0.35764 2.7961 0.60964 1.6403 1.5769 0.52685 1.89807 0.89807 6.5
7.0 0.44668 2.2387 5.0119 0.38246 2.6146 0.55801 1.7920 1.4985 0.55332 1.80730 0.80730 7.0
7.5 0.42170 2.3714 5.6234 0.40677 2.4854 0.51291 1.9497 1.4326 0.57830 1.72918 0.72918 7.5
8.0 0.39811 2.5119 6.3096 0.43051 2.3228 0.47309 2.1138 1.3767 0.60180 1.66142 0.66142 8.0
8.5 0.37584 2.6607 7.0795 0.45366 2.2043 0.43765 2.2849 1.3290 0.62416 1.60216 0.60216 8.5
9.0 0.35481 2.8184 7.9433 0.47622 2.0999 0.40592 2.4636 1.2880 0.64519 1.54993 0.54993 9.0
9.5 0.33497 2.9854 8.9125 0.49817 2.0074 0.37730 2.6504 1.2528 0.66503 1.50368 0.50368 9.5
10.0 0.31623 3.1623 10.000 0.51950 1.9249 0.35137 2.8561 1.2222 0.68377 1.46247 0.46247 10.0
12.0 0.25119 3.9811 15.849 0.59848 1.6709 0.26811 3.7299 1.1347 0.74881 1.33545 0.33545 12.0
14.0 0.19953 5.0119 25.119 0.66733 1.4985 0.20780 4.8124 1.0829 0.80047 1.24926 0.24926 14.0
16.0 0.15849 6.3096 39.811 0.72639 1.3767 0.16257 6.1511 1.0515 0.84151 1.18834 0.18834 16.0
18.0 0.12589 7.9433 63.096 0.77637 1.2880 0.12792 7.8174 1.03220 0.87411 1.14402 0.14402 18.0
20.0 0.100000 10.0000 100.000 0.81818 1.2222 0.10101 9.9000 1.02020 0.90000 1.11111 0.11111 20.0
22:0 0.079433 12.589 158.49 0.85282 1.1726 0.079935 12.510 1.01270 0.92057 1.08629 0.086291 22.0
24.0 0.063096 15.849 251.19 0.88130 1.1347 0.063348 15.786 1.00799 0.93690 1.06734 0.067345 24.0
26.0 0.050119 19.953 398.11 0.90455 1.1055 0.050246 19.903 1.00504 0.94988 1.05276 0.052762 26.0
28.0 0.039811 25.119 630.96 0.92343 1.0829 0.039874 25.079 1.00317 0.96019 1.04146 0.041461 28.0
r^1
K
--- -= K K^2 K 1–
K 1+
------------- K 1+
K 1–
------------- K
K 2 1–
----------------- K^2 1–
K
Kr–=
K^2 1+
K^2 1–
K 1–
K
1 –= r
K
K 1–
1
1 – r
-----------=
1
K 1–
