A点より右側を見たインピーダンスを Z とすると,
Z | = | R1 + (R1 + R)//R2 = R1 + | |
= |
この状態の時,A点の電圧は,入力電圧の半分となります. これは,規定の負荷(= R)を接続しても生じる減衰なので, アッテネータの減衰としてはこれを除いて考え、 A点の電圧 Ea に対して出力電圧 Eo がどうなるかを考えます. すなわち,アッテネータの減衰率を K (1)とすると,
Ea = KEo | (20) |
図2より,
Eo | = | . Ea | |
= | . Ea | ||
= | . Ea | ||
= | Ea |
R1 の部分を-Y変換すると,
図3 (b)の回路となります.
この値について,
式(21), (22)の関係が成立すればよいので,
A点より右側を見たインピーダンスを Z とすると,
Z | = | R2//(R1 + R2//R) = R2//R1 + | |
= | = |
R | = | ||
R2R1 +2R2R2 + RR1R2 + RR22 | = | RR1R2 + RR22 + R1R22 | |
R2R1 +2R2R2 | = | R1R22 | |
(R22 - R2)R1 | = | 2R2R2 | |
R1 | = | (27) |
図4より,
= | |||
K | = | = +1 = R1 + 1 |
K | = | . +1 = . + 1 | |
= | +1 = = | ||
KR2 - KR | = | R2 + R | |
(K - 1)R2 | = | (K + 1)R | |
R2 | = | R | (28) |
R1 | = | = R | |
= | R = R | ||
= | R | (29) |
表1に,各種アッテネータの抵抗の係数を示します.
抵抗値は,アッテネータのインピーダンス R にこの表の係数を掛けた値になります。
減衰率 | 減衰率 | T型 | 橋絡T型 | 型 | |||
(dB) | K | R1 | R2 | R1 | R2 | R1 | R2 |
0.1 | 1.0116 | 0.0057564 | 86.857 | 0.011579 | 86.360 | 0.011513 | 173.72 |
0.2 | 1.0233 | 0.011512 | 43.426 | 0.023293 | 42.931 | 0.023028 | 86.863 |
0.3 | 1.0351 | 0.017268 | 28.947 | 0.035142 | 28.456 | 0.034546 | 57.912 |
0.4 | 1.0471 | 0.023022 | 21.707 | 0.047129 | 21.219 | 0.046068 | 43.437 |
0.5 | 1.0593 | 0.028774 | 17.362 | 0.059254 | 16.877 | 0.057596 | 34.753 |
0.6 | 1.0715 | 0.034525 | 14.465 | 0.071519 | 13.982 | 0.069133 | 28.964 |
0.7 | 1.0839 | 0.040273 | 12.395 | 0.083927 | 11.915 | 0.080678 | 24.830 |
0.8 | 1.0965 | 0.046019 | 10.842 | 0.096478 | 10.365 | 0.092234 | 21.730 |
0.9 | 1.1092 | 0.051762 | 9.6337 | 0.10917 | 9.1596 | 0.10380 | 19.319 |
1 | 1.1220 | 0.057501 | 8.6667 | 0.12202 | 8.1955 | 0.11538 | 17.391 |
2 | 1.2589 | 0.11462 | 4.3048 | 0.25893 | 3.8621 | 0.23230 | 8.7242 |
3 | 1.4125 | 0.17100 | 2.8385 | 0.41254 | 2.4240 | 0.35230 | 5.8480 |
4 | 1.5849 | 0.22627 | 2.0966 | 0.58489 | 1.7097 | 0.47697 | 4.4194 |
5 | 1.7783 | 0.28013 | 1.6448 | 0.77828 | 1.2849 | 0.60797 | 3.5698 |
6 | 1.9953 | 0.33228 | 1.3386 | 0.99526 | 1.0048 | 0.74704 | 3.0095 |
7 | 2.2387 | 0.38247 | 1.1160 | 1.2387 | 0.80728 | 0.89602 | 2.6146 |
8 | 2.5119 | 0.43051 | 0.94617 | 1.5119 | 0.66143 | 1.0569 | 2.3229 |
9 | 2.8184 | 0.47622 | 0.81183 | 1.8184 | 0.54994 | 1.2318 | 2.0999 |
10 | 3.1623 | 0.51949 | 0.70273 | 2.1623 | 0.46248 | 1.4230 | 1.9250 |
11 | 3.5481 | 0.56026 | 0.61231 | 2.5481 | 0.39244 | 1.6331 | 1.7849 |
12 | 3.9811 | 0.59848 | 0.53621 | 2.9811 | 0.33545 | 1.8649 | 1.6709 |
13 | 4.4668 | 0.63416 | 0.47137 | 3.4668 | 0.28845 | 2.1215 | 1.5769 |
14 | 5.0119 | 0.66732 | 0.41560 | 4.0119 | 0.24926 | 2.4062 | 1.4985 |
15 | 5.6234 | 0.69804 | 0.36727 | 4.6234 | 0.21629 | 2.7228 | 1.4326 |
16 | 6.3096 | 0.72639 | 0.32515 | 5.3096 | 0.18834 | 3.0755 | 1.3767 |
17 | 7.0795 | 0.75246 | 0.28826 | 6.0795 | 0.16449 | 3.4691 | 1.3290 |
18 | 7.9433 | 0.77637 | 0.25584 | 6.9433 | 0.14402 | 3.9087 | 1.2880 |
19 | 8.9125 | 0.79823 | 0.22726 | 7.9125 | 0.12638 | 4.4002 | 1.2528 |
20 | 10.000 | 0.81818 | 0.20202 | 9.0000 | 0.11111 | 4.9500 | 1.2222 |
22 | 12.589 | 0.85282 | 0.15987 | 11.589 | 0.086287 | 6.2549 | 1.1726 |
24 | 15.849 | 0.88130 | 0.12670 | 14.849 | 0.067345 | 7.8929 | 1.1347 |
26 | 19.953 | 0.90455 | 0.10049 | 18.953 | 0.052763 | 9.9513 | 1.1055 |
28 | 25.119 | 0.92343 | 0.079748 | 24.119 | 0.041461 | 12.540 | 1.0829 |
30 | 31.623 | 0.93869 | 0.063309 | 30.623 | 0.032655 | 15.796 | 1.0653 |
32 | 39.811 | 0.95099 | 0.050269 | 38.811 | 0.025766 | 19.893 | 1.0515 |
34 | 50.119 | 0.96088 | 0.039921 | 49.119 | 0.020359 | 25.049 | 1.0407 |
36 | 63.096 | 0.96880 | 0.031706 | 62.096 | 0.016104 | 31.540 | 1.0322 |
38 | 79.433 | 0.97513 | 0.025182 | 78.433 | 0.012750 | 39.710 | 1.0255 |
40 | 100.00 | 0.98020 | 0.020002 | 99.000 | 0.010101 | 49.995 | 1.0202 |
42 | 125.89 | 0.98424 | 0.015888 | 124.89 | 0.0080069 | 62.942 | 1.0160 |
44 | 158.49 | 0.98746 | 0.012620 | 157.49 | 0.0063496 | 79.242 | 1.0127 |
46 | 199.53 | 0.99003 | 0.010024 | 198.53 | 0.0050371 | 99.761 | 1.0101 |
48 | 251.19 | 0.99207 | 0.0079623 | 250.19 | 0.0039970 | 125.59 | 1.0080 |
50 | 316.23 | 0.99370 | 0.0063246 | 315.23 | 0.0031723 | 158.11 | 1.0063 |
52 | 398.11 | 0.99499 | 0.0050238 | 397.11 | 0.0025182 | 199.05 | 1.0050 |
54 | 501.19 | 0.99602 | 0.0039905 | 500.19 | 0.0019993 | 250.59 | 1.0040 |
56 | 630.96 | 0.99684 | 0.0031698 | 629.96 | 0.0015874 | 315.48 | 1.0032 |
58 | 794.33 | 0.99749 | 0.0025179 | 793.33 | 0.0012605 | 397.16 | 1.0025 |
60 | 1000.0 | 0.99800 | 0.0020000 | 999.00 | 0.0010010 | 500.00 | 1.0020 |