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2. ɍɫɢɥɢɬɟɥɢ ɦɨɳɧɨɫɬɢ
2.3. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢ ɩɚɪɚɦɟɬɪɵ ɭɫɢɥɢɬɟɥɟɣ
ɦɨɳɧɨɫɬɢ
2.3.1. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɍɆ
Ⱦɥɹ ɨɰɟɧɤɢ ɤɚɱɟɫɬɜɚ ɭɫɢɥɢɬɟɥɟɣ ɦɨɳɧɨɫɬɢ ɢɫɩɨɥɶɡɭɸɬ ɞɜɟ ɨɫɧɨɜɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ:
ɚ) ɚɦɩɥɢɬɭɞɧɭɸ, ɬɨ ɟɫɬɶ ɡɚɜɢɫɢɦɨɫɬɶ ɜɵɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ ɤɨɥɟɛɚɧɢɣܲ
(ɥɢɛɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɢɥɟɧɢɹ ɦɨɳɧɨɫɬɢ ܭ
ɛ) ɚɦɩɥɢɬɭɞɧɨ-ɱɚɫɬɨɬɧɭɸ — ɡɚɜɢɫɢɦɨɫɬɶ ܭ
ɉɪɢɦɟɪɵ ɚɦɩɥɢɬɭɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 2.11 .
) ɨɬ ɜɯɨɞɧɨɣ ܲ˅˘ǡ
ɨɬ ɱɚɫɬɨɬɵ ɤɨɥɟɛɚɧɢɣ f.
˅˞˘
ɚ) ɡɚɜɢɫɢɦɨɫɬɶ ɜɵɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ ɨɬ ɜɯɨɞɧɨɣ
ɛ) ɡɚɜɢɫɢɦɨɫɬɶ ܭ
Ɋɢɫ. 2.11. Ⱥɦɩɥɢɬɭɞɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɭɫɢɥɢɬɟɥɹ ɦɨɳɧɨɫɬɢ.
ɨɬ ɜɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ
41
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
ȼɨɡɦɨɠɧɚɹ ɚɦɩɥɢɬɭɞɧɨ-ɱɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɭɫɢɥɢɬɟɥɹ ɩɪɟɞɫɬɚɜɥɟɧɚ
ɧɚ ɪɢɫ. 2. 12.
Ɋɢɫ. 2.12. Ⱥɦɩɥɢɬɭɞɧɨ-ɱɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɭɫɢɥɢɬɟɥɹ ɦɨɳɧɨɫɬɢ
2.3.2. ɉɚɪɚɦɟɬɪɵ ɍɆ
Ⱥ. Ɇɚɤɫɢɦɚɥɶɧɚɹ ɜɵɯɨɞɧɚɹ ɦɨɳɧɨɫɬɶ.
Ⱦɥɹ ɨɰɟɧɤɢ ɧɚɢɛɨɥɶɲɟɣ ɜɵɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ ɥɢɧɟɣɧɨɝɨ ɭɫɢɥɢɬɟɥɹ
ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɚɪɚɦɟɬɪ, ɧɚɡɵɜɟɦɵɣ ɦɨɳɧɨɫɬɶ ɨɞɧɨɞɟɰɢɛɟɥɶɧɨɣ ɤɨɦɩɪɟɫɫɢɢ
ࡼ
— ɷɬɨ ɜɵɯɨɞɧɚɹ ɦɨɳɧɨɫɬɶ ɭɫɢɥɢɬɟɥɹ, ɩɪɢ ɤɨɬɨɪɨɣ ɚɦɩɥɢɬɭɞɧɚɹ
ˇʐ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɨɬɤɥɨɧɢɥɚɫɶ ɧɚ — 1 ɞȻ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɥɢɧɟɣɧɨɣ ɟɟ
ɚɩɩɪɨɤɫɢɦɚɰɢɟɣ — ɪɢɫ. 2.11.
Ȼ. ɉɨɥɨɫɚ ɩɪɨɩɭɫɤɚɧɢɹ ɭɫɢɥɢɬɟɥɹ.
ɉɨɥɨɫɚ ɩɪɨɩɭɫɤɚɧɢɹ ο݂
݂
ˏ˃˘
Ȅ݂
, ɧɚ ɤɨɬɨɪɵɯ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɭɦɟɧɶɲɚɟɬɫɹ ɧɚ 3 ɞȻ, ɩɨ
ɫɪɚɜɧɟɧɢɸ ɫ ɦɚɤɫɢɦɚɥɶɧɵɦ ɡɧɚɱɟɧɢɟɦ — ɪɢɫ. 2.12.
ȼ. Ʉɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɦɨɳɧɨɫɬɢ.
˅˞˘
ܭ
=
˅˘
Ƚ. Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ ɞɨɛɚɜɥɟɧɧɨɣ ɦɨɳɧɨɫɬɢ (Power Added
Efficiency — PAE).
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ Ⱥɑɏ ɤɚɤ ɪɚɡɧɨɫɬɶ ɱɚɫɬɨɬ
ିଷˇʐ
ǡǡʑ˕
ǡʑ˕
, ɢɥɢ ܭ
ߟ
ˇˑ˄
=
ǡˇʐ
˅˞˘ି˅˘
= ܲ
బ
˅˞˘ǡˇʐˏ
,%
Ȅܲ
˅˘ǡˇʐˏ
42
2. ɍɫɢɥɢɬɟɥɢ ɦɨɳɧɨɫɬɢ
Ⱦ. Ʉɨɷɮɮɢɰɢɟɧɬ ɲɭɦɚ N.
Ʉɨɷɮɮɢɰɢɟɧɬ ɲɭɦɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɢ ɩɨɞɚɱɟ ɧɚ ɜɯɨɞ ɭɫɢɥɢɬɟɥɹ ɲɭɦɨɜɵɯ
ɤɨɥɟɛɚɧɢɣ ɦɨɳɧɨɫɬɶɸ ܲ
ɜɵɯɨɞɧɨɝɨ ɲɭɦɚ ɪɟɚɥɶɧɨɝɨܲ
ܰ
ൌͳͲܲ
ˇʐ
ɢ ɨɰɟɧɢɜɚɟɬɫɹ ɪɚɡɧɢɰɟɣ (ɜ ɞȻɦ) ɦɨɳɧɨɫɬɟɣ
˛˅˘
ɢ ɢɞɟɚɥɶɧɨɝɨ, ɧɟɲɭɦɹɳɟɝɨ, ɭɫɢɥɢɬɟɥɹ:
˛˅˞˘
, — ͳͲܲ
˛˅˞˘
ȄͳͲܭ
˛˅˘
ȿ. ɉɨɤɚɡɚɬɟɥɢ ɧɟɥɢɧɟɣɧɨɫɬɢ ɭɫɢɥɢɬɟɥɹ.
Ʉɚɤ ɛɵ ɧɢ ɦɚɥɚ ɛɵɥɚ ɦɨɳɧɨɫɬɶ ɜɯɨɞɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɩɨɫɬɭɩɚɸɳɚɹ ɧɚ
ɬɪɚɧɡɢɫɬɨɪ, ɜ ɫɨɫɬɚɜɟ ɜɵɯɨɞɧɨɝɨ ɬɨɤɚ ݅
ɧɚɩɪɹɠɟɧɢɢ ݑ
ɩɨɹɜɥɹɸɬɫɹ ɝɚɪɦɨɧɢɤɢ ɜɯɨɞɧɨɣ ɱɚɫɬɨɬɵ. ɗɬɨ ɜɢɞɧɨ ɢɡ
˅˘
ɪɚɡɥɨɠɟɧɢɹ ɟɝɨ ɨɫɧɨɜɧɨɣ ɧɟɥɢɧɟɣɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ݅
ɩɪɢ ɝɚɪɦɨɧɢɱɟɫɤɨɦ ɜɯɨɞɧɨɦ
˅˞˘
˅˞˘(ݑ˅˘
ሻɜ ɪɹɞ Ɍɷɣɥɨɪɚ.
Ʉɪɨɦɟ ɬɨɝɨ, ɝɚɪɦɨɧɢɤɢ ɩɨɹɜɥɹɸɬɫɹ ɢɡ-ɡɚ ɜɥɢɹɧɢɹ ɜɧɭɬɪɟɧɧɢɯ ɟɦɤɨɫɬɟɣ
ɬɪɚɧɡɢɫɬɨɪɚ, ɤɨɬɨɪɵɟ ɧɟɥɢɧɟɣɧɵ. Ƚɚɪɦɨɧɢɱɟɫɤɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɜɯɨɞɧɨɣ ɢ
ɩɪɨɯɨɞɧɨɣ ɟɦɤɨɫɬɹɯ ɜɵɡɵɜɚɸɬ ɤɨɥɟɛɚɧɢɹ ɡɚɪɹɞɨɜ ɧɚ ɧɢɯ, ɫɨɞɟɪɠɚɳɢɟ ɜɵɫɲɢɟ
ɝɚɪɦɨɧɢɤɢ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɹɜɥɹɸɬɫɹ ɝɚɪɦɨɧɢɤɢ ɜɵɯɨɞɧɨɝɨ ɬɨɤɚ. ɗɬɢ
ɝɚɪɦɨɧɢɤɢ ɦɨɝɭɬ ɨɤɚɡɚɬɶ ɦɟɲɚɸɳɟɟ ɞɟɣɫɬɜɢɟ ɧɚ ɪɚɛɨɬɭ ɞɪɭɝɢɯ ɪɚɞɢɨɫɢɫɬɟɦ ɢ
ɢɯ ɜɟɥɢɱɢɧɚ ɞɨɥɠɧɚ ɛɵɬɶ ɨɝɪɚɧɢɱɟɧɚ. ɇɚɢɛɨɥɟɟ ɡɧɚɱɢɬɟɥɶɧɚ ɚɦɩɥɢɬɭɞɚ
ɜɬɨɪɨɣ ɝɚɪɦɨɧɢɤɢ. Ⱦɥɹ ɨɰɟɧɤɢ ɟɟ ɜɟɥɢɱɢɧɵ ɩɪɢɦɟɧɹɟɬɫɹ ɩɚɪɚɦɟɬɪ ɭɫɢɥɢɬɟɥɹ,
ɧɚɡɵɜɚɟɦɵɣ ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ (IP 2- interception point 2).
ɇɟɥɢɧɟɣɧɨɫɬɶ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɚɦɩɥɢɬɭɞɧɨɣ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɭɫɢɥɢɬɟɥɹ ܲ
(ܲ˅˘ሻǤ ȿɫɥɢ ɧɚ ɝɪɚɮɢɤ ɚɦɩɥɢɬɭɞɧɨɣ
˅˞˘
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɧɚɧɟɫɬɢ ɡɚɜɢɫɢɦɨɫɬɶ ɜɵɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ ɜɬɨɪɨɣ ɝɚɪɦɨɧɢɤɢ
ɨɬ ɦɨɳɧɨɫɬɢ ɜɯɨɞɧɵɯ ɤɨɥɟɛɚɧɢɣ ܲ
), ɬɨ ɨɪɞɢɧɚɬɚ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ
ଶ(ܲ˅˘
ɥɢɧɟɣɧɵɯ ɱɚɫɬɟɣ ɷɬɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ ɟɫɬɶ ɩɚɪɚɦɟɬɪ IP 2 — ɪɢɫ. 2. 13.
Ɋɢɫ. 2.13. Ɂɚɜɢɫɢɦɨɫɬɶ ɦɨɳɧɨɫɬɢ ɜɵɯɨɞɧɵɯ ɤɨɥɟɛɚɧɢɣ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɢ (¨) ɢ
ɜɬɨɪɨɣ ɝɚɪɦɨɧɢɤɢ (Ƒ) ɨɬ ɜɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ (ɜ ɞȻɦ).
43
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
ɉɪɢ ɩɨɞɚɱɟ ɧɚ ɜɯɨɞ ɭɫɢɥɢɬɟɥɹ ɤɨɥɟɛɚɧɢɣ ɞɜɭɯ ɱɚɫɬɨɬ ݂ଵ ɢ ݂
ɩɨɹɜɥɹɸɬɫɹ ɤɨɥɟɛɚɧɢɹ ɤɨɦɛɢɧɚɰɢɨɧɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ݂݊
± m݂
ଵ
ɧɚ ɜɵɯɨɞɟ
ଶ
, ɝɞɟ n ɢ m —
ଶ
ɰɟɥɵɟ ɱɢɫɥɚ, ɱɬɨ ɨɛɭɫɥɨɜɥɟɧɨ ɧɟɥɢɧɟɣɧɨɫɬɶɸ ɜɨɥɶɬ-ɚɦɩɟɪɧɵɯ ɢ ɜɨɥɶɬɤɭɥɨɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɬɪɚɧɡɢɫɬɨɪɚ. ɇɚɢɛɨɥɟɟ ɛɥɢɡɤɢ ɤ ɜɯɨɞɧɵɦ ɱɚɫɬɨɬɚɦ ɢ
ɩɨɩɚɞɚɸɬ ɜ ɩɨɥɨɫɭ ɩɪɨɩɭɫɤɚɧɢɹ ɭɫɢɥɢɬɟɥɹ ɤɨɦɛɢɧɚɰɢɨɧɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ 3ɝɨ ɩɨɪɹɞɤɚ
(n + m = 3) 2݂
ǡ 2݂ଶ-݂ଵ ɢ 5-ɝɨ ɩɨɪɹɞɤɚ (n + m = 5) 3݂ଵ- 2݂ଶ, 3݂ଶ — 2݂
ଵ-݂ଶ
ଵ
—
ɪɢɫ. 2. 14.
Ɋɢɫ. 2.14. ɑɚɫɬɨɬɵ ɜɵɯɨɞɧɵɯ ɤɨɥɟɛɚɧɢɣ ɭɫɢɥɢɬɟɥɹ
ɉɪɢ ɞɜɭɯɱɚɫɬɨɬɧɨɦ ɜɨɡɞɟɣɫɬɜɢɢ ɧɟɥɢɧɟɣɧɨɫɬɶ ɭɫɢɥɢɬɟɥɹ ɨɰɟɧɢɜɚɸɬ
ɬɨɱɤɚɦɢ ɩɟɪɟɫɟɱɟɧɢɹ ɬɪɟɬɶɟɝɨ ɩɨɪɹɞɤɚ IP 3 ɢ ɩɹɬɨɝɨ ɩɨɪɹɞɤɚ IP 5. ɉɚɪɚɦɟɬɪ IP 3
ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɚɤɢɦ ɠɟ ɨɛɪɚɡɨɦ, ɤɚɤ ɢ IP 2: ɧɚ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ܲ
˅˞˘
(ܲ˅˘ሻ
ɧɚɧɨɫɢɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶ ɧɚɢɛɨɥɶɲɟɣ ɦɨɳɧɨɫɬɢ ɢɧɬɟɪɦɨɞɭɥɹɰɢɨɧɧɵɯ ɤɨɥɟɛɚɧɢɣ
3-ɝɨ ɩɨɪɹɞɤɚ ɨɬ ɦɨɳɧɨɫɬɢ ɜɯɨɞɧɵɯ ɤɨɥɟɛɚɧɢɣ ɢ ɨɪɞɢɧɚɬɚ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ
ɥɢɧɟɣɧɵɯ ɱɚɫɬɟɣ ɷɬɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɟɫɬɶ ɩɚɪɚɦɟɬɪ IP 3 — ɪɢɫ. 2.15.
44
2. ɍɫɢɥɢɬɟɥɢ ɦɨɳɧɨɫɬɢ
Ɋɢɫ. 2.15. Ⱥɦɩɥɢɬɭɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɭɫɢɥɢɬɟɥɹ (¨) ɢ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɳɧɨɫɬɢ
ɤɨɥɟɛɚɧɢɣ ɦɚɤɫɢɦɚɥɶɧɨɣ ɢɧɬɟɪɦɨɞɭɥɹɰɢɨɧɧɨɣ ɱɚɫɬɨɬɵ ɬɪɟɬɶɟɝɨ ɩɨɪɹɞɤɚ (¸) ɨɬ
ɜɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ.
Ⱥɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ 5-ɝɨ ɩɨɪɹɞɤɚ — IP 5.
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɭɱɢɬɵɜɚɸɬɫɹ ɢɧɬɟɪɦɨɞɭɥɹɰɢɨɧɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ 3݂
3݂
— 2݂
ଶ
.
ଵ
— 2݂
ଵ
ɢ
ଶ
2.4. Ɋɟɠɢɦɵ ɪɚɛɨɬɵ ɚɤɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ
Ɋɚɫɫɦɨɬɪɢɦ ɪɚɛɨɬɭ ɚɤɬɢɜɧɨɝɨ ɷɥɟɦɟɧɬɚ ɜ ɭɫɢɥɢɬɟɥɟ ɦɨɳɧɨɫɬɢ ɧɚ ɩɪɢɦɟɪɟ
ɛɢɩɨɥɹɪɧɨɝɨ ɬɪɚɧɡɢɫɬɨɪɚ BJT. Ɋɟɠɢɦ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ ɩɨ ɩɨɫɬɨɹɧɧɨɦɭ
ɬɨɤɭ ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɱɟɧɢɹɦɢ ɩɨɫɬɨɹɧɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɩɢɬɚɧɢɹ ɢ ɫɦɟɳɟɧɢɹ,
ɩɨɞɜɟɞɟɧɧɵɯ ɤ ɬɪɚɧɡɢɫɬɨɪɭ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɫɯɟɦɨɣ ɪɢɫ. 2.9, ɛ. Ɋɟɠɢɦɵ
ɪɚɛɨɬɵ ɩɨ ɩɟɪɟɦɟɧɧɨɦɭ ɬɨɤɭ ɪɚɡɥɢɱɚɸɬɫɹ ɜɢɞɨɦ ɡɚɜɢɫɢɦɨɫɬɟɣ ɨɬ ɜɪɟɦɟɧɢ
ɧɚɩɪɹɠɟɧɢɣ ɢ ɬɨɤɨɜ ɧɚ ɷɥɟɤɬɪɨɞɚɯ ɬɪɚɧɡɢɫɬɨɪɚ ɢ ɱɢɫɥɟɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ
ɚɦɩɥɢɬɭɞ ɤɨɥɟɛɚɧɢɣ.
Ɉɫɧɨɜɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɬɪɚɧɡɢɫɬɨɪɚ ɹɜɥɹɟɬɫɹ ɩɟɪɟɯɨɞɧɚɹ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ, ɫɜɹɡɵɜɚɸɳɚɹ ɜɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɛɚɡɟݑ
ɤɨɥɥɟɤɬɨɪɧɵɦ ɬɨɤɨɦ ݅
ɧɚɩɪɹɠɟɧɢɹ ݑ
(t) ɧɚ ɩɟɪɟɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɪɚɡɥɢɱɚɸɬ ɥɢɧɟɣɧɵɣ ɢ
˄
— ɪɢɫ. 2.5, ɛ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɞɢɚɩɚɡɨɧɚ ɢɡɦɟɧɟɧɢɣ
ˍ
ɧɟɥɢɧɟɣɧɵɣ ɪɟɠɢɦɵ ɪɚɛɨɬɵ ȻɌ.
ɫ ɜɵɯɨɞɧɵɦ
˄
45
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
2.4.1. Ʌɢɧɟɣɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ
Ʌɢɧɟɣɧɨɦɭ ɪɟɠɢɦɭ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɢɡɦɟɧɟɧɢɟ ݑ
ɭɱɚɫɬɤɟ ɩɟɪɟɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɝɪɚɮɢɤ ɤɨɬɨɪɨɝɨ ɦɨɠɧɨ
ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɬɶ ɩɪɹɦɨɣ ɥɢɧɢɟɣ. ɋɱɢɬɚɹ ɜɯɨɞɧɵɦ ɜɨɡɞɟɣɫɬɜɢɟɦ ɧɚ
ɬɪɚɧɡɢɫɬɨɪ ɧɚɩɪɹɠɟɧɢɟ
ݑ
ɝɞɟ ܷ
– ɩɨɫɬɨɹɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɛɚɡɟ, ܷ
ʐ
ɧɚɩɪɹɠɟɧɢɹ ɱɚɫɬɨɬɵ ߱ǡ ɢ ɪɚɡɥɚɝɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ݅
ɨɤɪɟɫɬɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɹ ܷ
= ܫˍ(ܷ
݅
ˍ
) + ݀݅ˍȀ݀ݑ˄ (ܷ˄߱ݐሻ +
ʐ
…
= ܷ
˄
, ɡɚɩɢɲɟɦ
ʐ
ଵ
݀
݅
ˍ
Ǩ
+ ܷ˄߱ݐ, (2.9)
ʐ
— ɚɦɩɥɢɬɭɞɚ ɩɟɪɟɦɟɧɧɨɝɨ
˄
(ݑ˄ሻ ɜ ɪɹɞ Ɍɷɣɥɨɪɚ ɜ
ˍ
ଶ
ଵ
݀
൘
݀ݑ
݅
ˍ
൘
݀ݑ
+ …
ଶ
˄
(ܷ
߱ݐሻ
˄
ଶ
߱ݐሻ
ሺܷ
˄
˄
ଶ
+ …
(t) ɧɚ
˄
Ɂɞɟɫɶ ɩɪɨɢɡɜɨɞɧɵɟ ɜɡɹɬɵ ɜ ɬɨɱɤɟ ܷ
ɂɡɜɟɫɬɧɨ, ɱɬɨ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɟ ɪɚɡɥɨɠɟɧɢɹ ɮɭɧɤɰɢɣ (߱ݐ)
ɝɚɪɦɨɧɢɱɟɫɤɢɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɱɚɫɬɨɬ ݊߱ݐǤ ȼ ɫɨɫɬɚɜɟ ɬɨɤɚ ɛɭɞɭɬ ɤɨɥɟɛɚɧɢɹ
ɬɨɥɶɤɨ ɜɯɨɞɧɨɣ ɱɚɫɬɨɬɵ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɪɹɞɚ
, n — ɰɟɥɨɟ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɱɢɫɥɨ.
ʐ
Ǩ
ଵ
݀
݅
ˍ
൘
݀ݑ
n
ɩɪɢ n 2
ܷ
˄
˄
ɫɨɞɟɪɠɚɬ
ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ, ɱɟɦ ɩɪɢ n = 1. ȼ ɷɬɨɦ ɫɥɭɱɚɟ, ɪɟɠɢɦ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ
ɥɢɧɟɣɧɵɣ. ɍɫɢɥɢɬɟɥɶ ɦɨɳɧɨɫɬɢ, ɬɪɚɧɡɢɫɬɨɪ ɤɨɬɨɪɨɝɨ ɪɚɛɨɬɚɟɬ ɜ ɥɢɧɟɣɧɨɦ
ɪɟɠɢɦɟ, ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɟ ɨɫɨɛɟɧɧɨɫɬɢ:
- ɩɪɢ ɝɚɪɦɨɧɢɱɟɫɤɨɦ ɜɯɨɞɧɨɦ ɜɨɡɞɟɣɫɬɜɢɢ ɤɨɥɟɛɚɧɢɹ ɜɫɟɯ ɮɢɡɢɱɟɫɤɢɯ
ɜɟɥɢɱɢɧ ɜ ɥɸɛɨɣ ɬɨɱɤɟ ɰɟɩɢ — ɝɚɪɦɨɧɢɱɟɫɤɢɟ,
- ɩɚɪɚɦɟɬɪɵ — ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ, ɜɯɨɞɧɵɟ ɢ ɜɵɯɨɞɧɵɟ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɩɚɪɚɦɟɬɪɵ ɦɚɬɪɢɰ ɪɚɫɫɟɹɧɢɹ ɢ ɜɫɟ ɞɪɭɝɢɟ ɧɟ ɡɚɜɢɫɹɬ ɨɬ
ɜɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ.
ɇɚ ɪɢɫ. 2.16 ɢɡɨɛɪɚɠɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɪɟɦɟɧɢ ɜɯɨɞɧɨɝɨ ݑ
ɜɵɯɨɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ݑ
(t), ɚ ɬɚɤɠɟ ɜɵɯɨɞɧɨɝɨ ɬɨɤɚ ݅
ˍ
(t) ɬɪɚɧɡɢɫɬɨɪɚ ɩɪɢ
ˍ
(t) ɢ
˄
ɝɚɪɦɨɧɢɱɟɫɤɨɦ ɜɯɨɞɧɨɦ ɜɨɡɞɟɣɫɬɜɢɢ ɜ ɥɢɧɟɣɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ.
46
ݑ
7
݅
ݑ
2. ɍɫɢɥɢɬɟɥɢ ɦɨɳɧɨɫɬɢ
, ȼ
˄
1.0525
1.052
1.0515
1.051
1.0505
1.05
1.0495
1.049
1.0485
1.048
1.0475
0 0.2 0.4 0.6 0.66
t, ɧɫ
ɚ)
, ɦȺ
ˍ
1.65
1.645
1.64
1.635
1.63
1.625
1.62
1.615
1.61
1.605
1.6
0 0.2 0.4 0.6 0.667
t, ɧɫ
ɛ)
, ȼ
ˍ
4.5
p1
p1
4
3.5
3
2.5
2
1.5
0 0.2 0.4 0.6 0.667
p1
t, ɧɫ
ɜ)
Ɋɢɫ. 2.16. Ɂɚɜɢɫɢɦɨɫɬɶ ɨɬ ɜɪɟɦɟɧɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɛɚɡɟ (ɚ),
ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ (ɛ) ɢ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ (ɜ) ɜ ɥɢɧɟɣɧɨɦ ɭɫɢɥɢɬɟɥɟ.
47
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
Ⱥɦɩɥɢɬɭɞɚ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ
= Sܷ
ܫ
ˍ
.
˄
Ⱥɦɩɥɢɬɭɞɚ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ
ܷ
= ܫˍܼ
ˍ
— ɜɯɨɞɧɨɣ ɢɦɩɟɞɚɧɫ ɜɵɯɨɞɧɨɣ ɫɨɝɥɚɫɭɸɳɟɣ ɰɟɩɢ ɭɫɢɥɢɬɟɥɹ.
ɝɞɟ ܼ
ˍ
,
ˍ
Ɏɚɡɚ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɩɪɨɬɢɜɨɩɨɥɨɠɧɚ ɮɚɡɚɦ ɤɨɥɥɟɤɬɨɪɧɨɝɨ
ɬɨɤɚ ɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɛɚɡɟ.
Ɉɰɟɧɢɦ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɜɨɡɦɨɠɧɨɫɬɢ ɥɢɧɟɣɧɨɝɨ ɭɫɢɥɢɬɟɥɹ ɦɨɳɧɨɫɬɢ.
ɋ ɷɬɨɣ ɰɟɥɶɸ ɪɚɫɫɱɢɬɚɟɦ ɫɪɟɞɧɸɸ ɡɚ ɩɟɪɢɨɞ ɤɨɥɟɛɚɧɢɣ ɦɨɳɧɨɫɬɶ ɧɚ
ɤɨɥɥɟɤɬɨɪɟ ɬɪɚɧɡɢɫɬɨɪɚ
்
ܲ
ଵ
=
݅
(t )ݑ
ˍ
ˍ
்
(t) dt, (2.10)
ˍ
ɝɞɟ ɤɨɥɥɟɤɬɨɪɧɵɣ ɬɨɤ
݅
(t) = ܫˍ + ܫˍ߱ݐ, (2.11)
ˍ
ɤɨɥɥɟɤɬɨɪɧɨɟ ɧɚɩɪɹɠɟɧɢɟ
ݑ
ܫ
ˋܷˍ — ɩɨɫɬɨɹɧɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ, ܫˍǡǡܷ
ˍ
ɩɟɪɢɨɞɚ T=
ʹߨ
ൗ
— ɮɚɡɨɜɵɣ ɫɞɜɢɝ ɦɟɠɞɭ ɤɨɥɟɛɚɧɢɹɦɢ ݅ˍ(t) ɢݑ
ǡ߮
ˍ
߱
(t) =ܷˍ+ܷˍሺ߱ݐ+߮ˍሻ (2.12)
ˍ
— ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ
ˍ
(t).
ˍ
ɉɨɞɫɬɚɜɥɹɹ (2.11) ɢ (2.12) ɜ (2.10), ɩɨɥɭɱɢɦ ɩɨɫɥɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ
ଵ
+
ଶ
ܫˍܷˍ ߮
,
ˍ
ɝɞɟ
ܲ
ˍ
= ܲ
ܲ = ܫˍܷ
- ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɬɪɚɧɡɢɫɬɨɪɨɦ ɨɬ ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ, ܲ
ଵ
ܫˍܷˍ ߮
ଶ
— ɦɨɳɧɨɫɬɶ ɤɨɥɟɛɚɧɢɣ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɬɪɚɧɡɢɫɬɨɪ ɧɟ
ˍ
(2.13)
ˍ
> 0,
ɩɨɬɪɟɛɥɹɥ ɦɨɳɧɨɫɬɶ ɤɨɥɟɛɚɧɢɣ, ɚ ɨɬɞɚɜɚɥ ɟɟ ɜ ɧɚɝɪɭɡɤɭ, ɧɭɠɧɨ ɜɵɩɨɥɧɟɧɢɟ
ɭɫɥɨɜɢɹ ߮
= ߨ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ
ɩɪɢ ߮
ˍ
< 0, ɢɥɢ
ˍ
గ
<߮
ଶ
ଷగ
<
ɪɚɞɢɚɧ. Ɉɬɞɚɜɚɟɦɚɹ ɦɨɳɧɨɫɬɶ ɦɚɤɫɢɦɚɥɶɧɚ
ˍ
ଶ
ܲ
= ܲȄܲ
ˍ
ɝɞɟ
ܲ
ଵ
=
ܫˍܷ
(2.14)
ˍ
ଶ
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ ɬɪɚɧɡɢɫɬɨɪɚ, ɤɚɤ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ
ɷɧɟɪɝɢɣ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
48
2. ɍɫɢɥɢɬɟɥɢ ɦɨɳɧɨɫɬɢ
ܲ
ߟ =
.
ൗ
ܲ
ɍɱɢɬɵɜɚɹ (2.13) ɢ (2.14), ɡɚɩɢɲɟɦ
ܫ
ܷ
ˍ
ߟ = Ͳǡͷ
ˍ
ൗ
ܫ
ˍ
(2.15)
ൗ
ܷ
ˍ
Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɬɪɚɧɡɢɫɬɨɪ ɧɟ ɡɚɯɨɞɢɥ ɜ ɢɧɜɟɪɫɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ ɩɪɢ
ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɹɯ, ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɣ ܫ
ˋܷˍܷˍ. ɉɪɢ ɷɬɨɦ, ɦɚɤɫɢɦɚɥɶɧɵɟ ܫ
ܫ
ˍ
ˍ௫
=ܫˍ, ܷ
ˍ௫
= ܷ
ˍ
ˍ
ɢ
ɦɚɤɫɢɦɚɥɶɧɵɣ ɄɉȾ ɧɟ ɦɨɠɟɬ ɩɪɟɜɵɲɚɬɶ 50%.
Ⱦɨɫɬɨɢɧɫɬɜɨ ɥɢɧɟɣɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ ɜ ɜɨɡɦɨɠɧɨɫɬɢ
ɭɫɢɥɢɜɚɬɶ ɤɨɥɟɛɚɧɢɹ ɫ ɢɡɦɟɧɹɸɳɟɣɫɹ ɚɦɩɥɢɬɭɞɨɣ ɩɪɢ ɦɢɧɢɦɚɥɶɧɵɯ
ɡɧɚɱɟɧɢɹɯ ɜɵɫɲɢɯ ɝɚɪɦɨɧɢɤ. ɇɟɞɨɫɬɚɬɨɤ — ɧɢɡɤɢɣ ɄɉȾ.
2.4.2. ɇɟɥɢɧɟɣɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ
ɉɪɢ ɛɨɥɶɲɢɯ ɚɦɩɥɢɬɭɞɚɯ ɤɨɥɟɛɚɧɢɣ ɧɚ ɜɯɨɞɟ ɬɪɚɧɡɢɫɬɨɪɚ ɪɟɚɥɢɡɭɟɬɫɹ
ɧɟɥɢɧɟɣɧɵɣ ɪɟɠɢɦ ɟɝɨ ɪɚɛɨɬɵ, ɜ ɤɨɬɨɪɨɦ ɪɚɛɨɱɚɹ ɬɨɱɤɚ ɧɚ ɩɟɪɟɯɨɞɧɨɣ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ (ɪɢɫ. 2.5, ɛ) ɡɚɯɨɞɢɬ ɜ ɧɟɥɢɧɟɣɧɭɸ ɨɛɥɚɫɬɶ. ɋ ɰɟɥɶɸ
ɭɜɟɥɢɱɟɧɢɹ ɄɉȾ ɬɪɚɧɡɢɫɬɨɪɚ ɩɪɟɞɩɪɢɧɹɬɚ ɩɨɩɵɬɤɚ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɟ ɬɨɥɶɤɨ
ɚɤɬɢɜɧɭɸ ɨɛɥɚɫɬɶ ɬɪɚɧɡɢɫɬɨɪɚ, ɝɞɟ ɤɨɥɥɟɤɬɨɪɧɵɣ ɬɨɤ ɨɬɥɢɱɟɧ ɨɬ 0, ɧɨ ɢ
ɨɛɥɚɫɬɶ ɨɬɫɟɱɤɢ, ɝɞɟ ݅
ɄɉȾ ɬɪɚɧɡɢɫɬɨɪɚ ɜ ɧɟɥɢɧɟɣɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ, ɡɧɚɹ
ɡɚɜɢɫɢɦɨɫɬɢ ݅
(t) ɢ ݑ
ˍ
ɢɫɩɨɥɶɡɭɹ ɩɟɪɟɯɨɞɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɢ ɜɵɛɢɪɚɹ ɩɨɫɬɨɹɧɧɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ
, ɩɨɥɭɱɢɦ ɡɚɜɢɫɢɦɨɫɬɶ ݅
ܷ
˄
ൎͲ.
ˍ
(t). ȿɫɥɢ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɛɚɡɟ ɝɚɪɦɨɧɢɱɟɫɤɨɟ (2.9), ɬɨ
ˍ
(t) ɜ ɜɢɞɟ ɢɦɩɭɥɶɫɨɜ — ɪɢɫ. 2.17, ɛ.
ˍ
ɚ)
49
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
ɛ)
Ɋɢɫ. 2. 17. Ɂɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɪɟɦɟɧɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɛɚɡɟ ݑ
(ɛ) ɜ ɪɟɠɢɦɚɯ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ ɫ ɨɬɫɟɱɤɨɣ ɜɵɯɨɞɧɨɝɨ ɬɨɤɚ.
݅
ˍ
(ɚ) ɢ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ
˄
Ⱦɥɢɬɟɥɶɧɨɫɬɶ ɢɦɩɭɥɶɫɨɜ ɬɨɤɚ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɧɨɣ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ
ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ܷ
ɢ ɚɦɩɥɢɬɭɞɵ ܷ
˄
. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (2.15), ɄɉȾ
˄
ɡɚɜɢɫɢɬ ɨɬ ɨɬɧɨɲɟɧɢɣ ɚɦɩɥɢɬɭɞ ɤ ɩɨɫɬɨɹɧɧɵɦ ɫɨɫɬɚɜɥɹɸɳɢɦ ɬɨɤɚ ɢ
ɧɚɩɪɹɠɟɧɢɹ ɤɨɥɥɟɤɬɨɪɚ. ɉɪɢ ɪɚɛɨɬɟ ɬɪɚɧɡɢɫɬɨɪɚ ɫ ɨɬɫɟɱɤɨɣ ɜɵɯɨɞɧɨɝɨ ɬɨɤɚ
ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɤɨɥɥɟɤɬɨɪɟ ɨɫɬɚɟɬɫɹ ɝɚɪɦɨɧɢɱɟɫɤɢɦ, ɤɚɤ ɢ ɜ ɥɢɧɟɣɧɨɦ ɪɟɠɢɦɟ
(2. 12). ɗɬɨ ɞɨɫɬɢɝɚɟɬɫɹ ɬɟɦ, ɱɬɨ ɜɵɯɨɞɧɚɹ ɫɨɝɥɚɫɭɸɳɚɹ ɰɟɩɶ ɭɫɢɥɢɬɟɥɹ
ɢɡɛɢɪɚɬɟɥɶɧɚ ɢ ɜɵɞɟɥɹɟɬ ɢɡ ɫɩɟɤɬɪɚ ɬɨɤɚ ɫɨɫɬɚɜɥɹɸɳɭɸ ɜɯɨɞɧɨɣ ɱɚɫɬɨɬɵ. ȼ
ܷ
ɷɬɨɦ ɫɥɭɱɚɟ, ɨɬɧɨɲɟɧɢɟ
ˍ
, ɤɚɤ ɢ ɪɚɧɟɟ, ɧɟ ɩɪɟɜɵɲɚɟɬ 1.
ൗ
ܷ
ˍ
ȼɨɡɦɨɠɧɨɫɬɶ ɭɜɟɥɢɱɟɧɢɹ ɄɉȾ ɩɨɹɜɥɹɟɬɫɹ ɩɨ ɬɨɣ ɩɪɢɱɢɧɟ, ɱɬɨ ɜ ɪɟɠɢɦɚɯ ɫ
ܫ
ɨɬɫɟɱɤɨɣ ɤɨɥɥɟɤɬɨɪɧɨɝɨ ɬɨɤɚ ɨɬɧɨɲɟɧɢɟ
ˍ
ɫɬɚɧɨɜɢɬɫɹ ɛɨɥɶɲɟ 1. ɗɬɨ
ൗ
ܫ
ˍ
ɨɬɧɨɲɟɧɢɟ, ɚ ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɄɉȾ ɡɚɜɢɫɢɬ ɨɬ ɞɥɢɬɟɥɶɧɨɫɬɢ ɢɦɩɭɥɶɫɨɜ ɬɨɤɚ.
2.4.3. ɄɉȾ ɬɪɚɧɡɢɫɬɨɪɚ ɜ ɭɫɢɥɢɬɟɥɟ
ɉɪɢ ɪɚɛɨɬɟ ɬɪɚɧɡɢɫɬɨɪɚ ɜ ɧɟɥɢɧɟɣɧɨɦ ɪɟɠɢɦɟ ɜɵɯɨɞɧɨɣ ɬɨɤ ɬɟɨɪɟɬɢɱɟɫɤɢ
ɢɦɟɟɬ ɛɟɫɤɨɧɟɱɧɨɟ ɱɢɫɥɨ ɫɩɟɤɬɪɚɥɶɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɱɚɫɬɨɬ n߱, ɩ =
0,1,2,3…, ɩɨɷɬɨɦɭ ɜɵɯɨɞɧɚɹ ɦɨɳɧɨɫɬɶ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ ɝɚɪɦɨɧɢɤɢ ɜɯɨɞɧɨɣ
ɱɚɫɬɨɬɵ. Ⱦɥɹ ɭɫɢɥɢɬɟɥɹ ɜɚɠɧɵ ɜɵɯɨɞɧɵɟ ɤɨɥɟɛɚɧɢɹ ɱɚɫɬɨɬɵ ߱ǡɩɨɷɬɨɦɭ
ɢɧɬɟɪɟɫɟɧ ɄɉȾ ɬɪɚɧɡɢɫɬɨɪɚ ɩɨ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɟ
ܲ
ଵ
ߟ
ɝɞɟ ܲ
— ɦɨɳɧɨɫɬɶ ɜɵɯɨɞɧɵɯ ɤɨɥɟɛɚɧɢɣ ɩɟɪɜɨɣ ɝɚɪɦɨɧɢɤɢ.
ଵ
ɋ ɰɟɥɶɸ ɢɡɭɱɟɧɢɹ ɜɨɡɦɨɠɧɨɫɬɟɣ ɞɨɫɬɢɠɟɧɢɹ ɧɚɢɛɨɥɶɲɢɯ ߟ
ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɬɪɚɧɡɢɫɬɨɪɚ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɩɪɨɫɬɨɣ ɚɧɚɥɢɬɢɱɟɫɤɨɣ
=
ଵ
, (2.16)
ൗ
ܲ
ɜ ɧɟɥɢɧɟɣɧɨɦ
ଵ
50
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