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1. ɉɟɪɟɞɚɬɱɢɤɢ ɢ ɩɪɢɟɦɧɢɤɢ
1.1. Ɋɚɞɢɨɩɟɪɟɞɚɬɱɢɤ
Ɋɚɞɢɨɩɟɪɟɞɚɬɱɢɤ ɩɪɟɞɧɚɡɧɚɱɟɧ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɪɚɞɢɨɫɢɝɧɚɥɨɜ —
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɵ, ɫɨɞɟɪɠɚɳɢɯ ɫɜɟɞɟɧɢɹ,
ɤɨɬɨɪɵɟ ɧɟɨɛɯɨɞɢɦɨ ɩɟɪɟɞɚɬɶ ɩɨ ɪɚɞɢɨɥɢɧɢɢ. ɇɚ ɜɯɨɞ ɩɟɪɟɞɚɬɱɢɤɚ ɩɨɫɬɭɩɚɟɬ
ɢɧɮɨɪɦɚɰɢɹ ɜ ɚɧɚɥɨɝɨɜɨɦ ɢɥɢ ɰɢɮɪɨɜɨɦ ɜɢɞɟ, ɤɨɬɨɪɚɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ
ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɜɢɞɟɨɫɢɝɧɚɥ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɤɨɥɟɛɚɧɢɹ ɤɚɤɨɣ-ɥɢɛɨ
ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɋɩɟɤɬɪ ɦɨɳɧɨɫɬɢ ɜɢɞɟɨɫɢɝɧɚɥɚ ɫɨɫɪɟɞɨɬɨɱɟɧ ɜ
ɞɢɚɩɚɡɨɧɟ 0 …ܨ
ɞɟɫɹɬɤɢ ɢɥɢ ɫɨɬɧɢ ɤȽɰ.
ɉɟɪɟɞɚɸɳɚɹ ɚɧɬɟɧɧɚ ɢɡɥɭɱɚɟɬ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɤɨɥɟɛɚɧɢɹ ɜ ɬɨɦ ɫɥɭɱɚɟ,
ɤɨɝɞɚ ɟɟ ɝɟɨɦɟɬɪɢɱɟɫɤɢɣ ɪɚɡɦɟɪ ɫɨɢɡɦɟɪɢɦ ɫ ɞɥɢɧɨɣ ɜɨɥɧɵ Ȝ ɤɨɥɟɛɚɧɢɣ
ɢɡɥɭɱɚɟɦɵɯ ɱɚɫɬɨɬ (ɢɥɢ ɛɨɥɶɲɟ ɞɥɢɧɵ ɜɨɥɧɵ). ɋ ɰɟɥɶɸ ɷɮɮɟɤɬɢɜɧɨɝɨ
ɢɡɥɭɱɟɧɢɹ ɫɩɟɤɬɪ ɜɢɞɟɨɫɢɝɧɚɥɚ ɩɟɪɟɞɜɢɝɚɸɬ ɜɜɟɪɯ ɩɨ ɨɫɢ ɱɚɫɬɨɬ, ɨɛɪɚɡɭɹ
ɪɚɞɢɨɫɢɝɧɚɥ. ɗɮɮɟɤɬɢɜɧɨ ɢɡɥɭɱɚɸɬɫɹ ɪɚɞɢɨɫɢɝɧɚɥɵ, ɫɪɟɞɧɹɹ ɱɚɫɬɨɬɚ ɤɨɬɨɪɵɯ
ɫɨɫɬɚɜɥɹɟɬ ɞɟɫɹɬɤɢ ɢ ɫɨɬɧɢ ɦɟɝɚɝɟɪɰ
ɉɪɨɰɟɫɫ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɜɢɞɟɨɫɢɝɧɚɥɚ ɜ ɪɚɞɢɨɫɢɝɧɚɥ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɭɬɟɦ
ɦɨɞɭɥɹɰɢɢ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɤɨɥɟɛɚɧɢɣ.
Ⱦɥɹ ɫɨɡɞɚɧɢɹ ɪɚɞɢɨɫɢɝɧɚɥɚ ɜ ɩɟɪɟɞɚɬɱɢɤɟ ɨɫɭɳɟɫɬɜɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɟ
ɩɪɨɰɟɫɫɵ:
1) ɮɨɪɦɢɪɨɜɚɧɢɟ ɜɢɞɟɨɫɢɝɧɚɥɚ, 2) ɝɟɧɟɪɢɪɨɜɚɧɢɟ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɧɚɡɵɜɚɟɦɵɯ ɧɟɫɭɳɢɦɢ, 3) ɦɨɞɭɥɹɰɢɹ ɢɯ
ɜɢɞɟɨɫɢɝɧɚɥɨɦ, 4) ɭɫɢɥɟɧɢɟ ɦɨɳɧɨɫɬɢ ɪɚɞɢɨɫɢɝɧɚɥɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,
ɨɛɹɡɚɬɟɥɶɧɵɦɢ ɭɫɬɪɨɣɫɬɜɚɦɢ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ ɹɜɥɹɸɬɫɹ: ɮɨɪɦɢɪɨɜɚɬɟɥɶ
ɜɢɞɟɨɫɢɝɧɚɥɚ, ɝɟɧɟɪɚɬɨɪ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɦɨɞɭɥɹɬɨɪ ɢ ɭɫɢɥɢɬɟɥɶ
ɦɨɳɧɨɫɬɢ.
, ɝɞɟ ɦɚɤɫɢɦɚɥɶɧɚɹ ɱɚɫɬɨɬɚ ܨ
௫
, ɟɞɢɧɢɰɵ, ɞɟɫɹɬɤɢ ɢ ɫɨɬɧɢ ɝɢɝɚɝɟɪɰ.
ɨɛɵɱɧɨ ɫɨɫɬɚɜɥɹɟɬ
௫
1.1.1. Ɏɭɧɤɰɢɨɧɚɥɶɧɵɟ ɫɯɟɦɵ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɨɜ
Ɋɚɞɢɨɩɟɪɟɞɚɬɱɢɤ ɫ ɦɨɞɭɥɹɰɢɟɣ ɤɨɥɟɛɚɧɢɣ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ
Ȼɥɨɤ-ɫɯɟɦɚ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 1.1. ȼ ɰɢɮɪɨɜɵɯ
ɩɟɪɟɞɚɬɱɢɤɚɯ ɜɢɞɟɨɫɢɝɧɚɥ ɮɨɪɦɢɪɭɟɬɫɹ ɜ ɩɪɨɰɟɫɫɨɪɟ, ɫ ɩɨɦɨɳɶɸ ɰɢɮɪɨɚɧɚɥɨɝɨɜɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɚɧɚɥɨɝɨɜɭɸ ɮɨɪɦɭ ɢ ɩɨɫɬɭɩɚɟɬ
ɧɚ ɦɨɞɭɥɹɬɨɪ. ɋɮɨɪɦɢɪɨɜɚɧɧɵɣ ɜ ɦɨɞɭɥɹɬɨɪɟ ɪɚɞɢɨɫɢɝɧɚɥ ɭɫɢɥɢɜɚɟɬɫɹ ɩɨ
ɦɨɳɧɨɫɬɢ, ɩɪɨɯɨɞɢɬ ɱɟɪɟɡ ɩɨɥɨɫɧɨ-ɩɪɨɩɭɫɤɚɸɳɢɣ ɮɢɥɶɬɪ ɢ ɢɡɥɭɱɚɟɬɫɹ
ɩɟɪɟɞɚɸɳɟɣ ɚɧɬɟɧɧɨɣ.
11
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
Ɋɢɫ. 1.1. Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ
(Ƚ — ɝɟɧɟɪɚɬɨɪ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ)
ɋɩɟɤɬɪ ɦɨɳɧɨɫɬɢ ɤɨɥɟɛɚɧɢɣ ɜ ɪɚɡɥɢɱɧɵɯ ɬɨɱɤɚɯ ɫɯɟɦɵ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ. 1.2.
ȼ ɤɚɱɟɫɬɜɟ ɝɟɧɟɪɚɬɨɪɚ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ ɨɛɵɱɧɨ ɩɪɢɦɟɧɹɸɬ ɫɢɧɬɟɡɚɬɨɪ ɱɚɫɬɨɬ.
˓
—
Ɋɢɫ. 1 2. ɋɩɟɤɬɪɵ ɦɨɳɧɨɫɬɢ ɤɨɥɟɛɚɧɢɣ ɜ ɬɨɱɤɚɯ 1,2,3 ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ ɫɯɟɦɵ
ɩɟɪɟɞɚɬɱɢɤɚ (ܵ
— ɫɩɟɤɬɪɚɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɦɨɳɧɨɫɬɢ ɜɢɞɟɨɫɢɝɧɚɥɚ, ܵ
˅
ɫɩɟɤɬɪɚɥɶɧɚɹ ɩɥɨɬɧɨɫɬɶ ɦɨɳɧɨɫɬɢ ɪɚɞɢɨɫɢɝɧɚɥɚ, P — ɦɨɳɧɨɫɬɶ ɤɨɥɟɛɚɧɢɣ ɧɟɫɭɳɟɣ
ɱɚɫɬɨɬɵ ݂
ሻ.
ː
Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɩɟɪɟɞɚɬɱɢɤɚ ɫ ɩɨɜɵɲɚɸɳɢɦ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɦ
ɱɚɫɬɨɬɵ
ȼ ɧɟɤɨɬɨɪɵɯ ɩɟɪɟɞɚɬɱɢɤɚɯ ɪɚɞɢɨɫɢɝɧɚɥ ɮɨɪɦɢɪɭɟɬɫɹ ɧɟ ɧɚ ɧɟɫɭɳɟɣ, ɚ ɧɚ
ɩɨɧɢɠɟɧɧɨɣ ɱɚɫɬɨɬɟ, ɧɚɡɵɜɚɟɦɨɣ ɩɨɞɧɟɫɭɳɟɣ. Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɬɚɤɨɝɨ
ɩɟɪɟɞɚɬɱɢɤɚ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 1.3.
12
1. ɉɟɪɟɞɚɬɱɢɤɢ ɢ ɩɪɢɟɦɧɢɤɢ
Ɋɢɫ. 1.3. Ɏɨɪɦɢɪɨɜɚɧɢɟ ɪɚɞɢɨɫɢɝɧɚɥɚ ɩɪɢ ɦɨɞɭɥɹɰɢɢ ɧɚ ɩɨɞɧɟɫɭɳɟɣ ɱɚɫɬɨɬɟ
Ⱦɥɹ ɩɟɪɟɧɨɫɚ ɫɩɟɤɬɪɚ ɪɚɞɢɨɫɢɝɧɚɥɚ ɫ ɩɨɞɧɟɫɭɳɟɣ ɧɚ ɧɟɫɭɳɭɸ ɱɚɫɬɨɬɭ
ɩɪɢɦɟɧɹɟɬɫɹ ɩɨɜɵɲɚɸɳɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɱɚɫɬɨɬɵ (up –converter),
ɫɨɞɟɪɠɚɳɢɣ ɫɦɟɫɢɬɟɥɶ ɱɚɫɬɨɬ, ɝɟɧɟɪɚɬɨɪ ɤɨɥɟɛɚɧɢɣ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ ɢ
ɩɨɥɨɫɧɨ-ɩɪɨɩɭɫɤɚɸɳɢɣ ɮɢɥɶɬɪ. ɇɚ ɜɯɨɞɵ ɦɨɞɭɥɹɬɨɪɚ ɩɨɫɬɭɩɚɸɬ ɤɨɥɟɛɚɧɢɹ
ɜɢɞɟɨɫɢɝɧɚɥɚ 1 ɢ ɝɟɧɟɪɚɬɨɪɚ ɩɨɞɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ 2. ɋɮɨɪɦɢɪɨɜɚɧɧɵɣ ɧɚ
ɩɨɞɧɟɫɭɳɟɣ ɱɚɫɬɨɬɟ ɪɚɞɢɨɫɢɝɧɚɥ 3 ɩɨɞɚɟɬɫɹ ɧɚ ɜɯɨɞ ɫɦɟɫɢɬɟɥɹ ɩɨɜɵɲɚɸɳɟɝɨ
ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɹ ɱɚɫɬɨɬɵ, ɧɚ ɜɬɨɪɨɣ ɜɯɨɞ ɤɨɬɨɪɨɝɨ ɩɨɫɬɭɩɚɸɬ ɤɨɥɟɛɚɧɢɹ
ɝɟɧɟɪɚɬɨɪɚ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ 4. ɋɮɨɪɦɢɪɨɜɚɧɧɵɣ ɧɚ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɟ
ɪɚɞɢɨɫɢɝɧɚɥ 5 ɭɫɢɥɢɜɚɟɬɫɹ ɩɨ ɦɨɳɧɨɫɬɢ. ɇɚ ɜɵɯɨɞɟ ɩɟɪɟɞɚɬɱɢɤɚ ɭɫɬɚɧɨɜɥɟɧ
ɮɢɥɶɬɪ ɧɢɠɧɢɯ ɱɚɫɬɨɬ, ɩɪɟɩɹɬɫɬɜɭɸɳɢɣ ɩɪɨɯɨɠɞɟɧɢɸ ɜ ɚɧɬɟɧɧɭ ɤɨɥɟɛɚɧɢɣ
ɜɵɫɲɢɯ ɝɚɪɦɨɧɢɤ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ.
Ɋɚɞɢɨɩɟɪɟɞɚɬɱɢɤ, ɫɨɜɦɟɳɟɧɧɵɣ ɫ ɚɧɬɟɧɧɨɣ
Ⱦɥɹ ɭɜɟɥɢɱɟɧɢɹ ɜɵɯɨɞɧɨɣ ɦɨɳɧɨɫɬɢ ɢ ɫɨɡɞɚɧɢɹ ɧɨɜɵɯ ɮɭɧɤɰɢɨɧɚɥɶɧɵɯ
ɜɨɡɦɨɠɧɨɫɬɟɣ ɜɵɯɨɞɧɭɸ ɱɚɫɬɶ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ ɜɵɩɨɥɧɹɸɬ ɜ ɜɢɞɟ
ɫɨɜɨɤɭɩɧɨɫɬɢ ɩɟɪɟɞɚɸɳɢɯ ɦɨɞɭɥɟɣ, ɤɚɠɞɵɣ ɢɡ ɤɨɬɨɪɵɯ ɢɦɟɟɬ ɫɜɨɸ ɚɧɬɟɧɧɭ.
ɂɡɥɭɱɟɧɢɹ ɤɚɠɞɨɝɨ ɦɨɞɭɥɹ ɫɭɦɦɢɪɭɸɬɫɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ, ɩɪɢɱɟɦ ɢɦɟɟɬɫɹ
ɜɨɡɦɨɠɧɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɫɞɜɢɝɚ ɮɚɡ ɤɨɥɟɛɚɧɢɣ ɦɟɠɞɭ ɨɬɞɟɥɶɧɵɦɢ
ɢɡɥɭɱɚɬɟɥɹɦɢ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɫɨɡɞɚɜɚɬɶ ɞɢɚɝɪɚɦɦɵ ɧɚɩɪɚɜɥɟɧɧɨɫɬɢ
ɫɩɟɰɢɚɥɶɧɵɯ ɮɨɪɦ ɢ ɩɟɪɟɦɟɳɟɧɢɹ ɥɭɱɚ.
Ɍɚɤɢɟ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɢ, ɫɨɜɦɟɳɟɧɧɵɟ ɫ ɚɧɬɟɧɧɨɣ ɫɢɫɬɟɦɨɣ, ɧɚɡɵɜɚɸɬ
ɩɟɪɟɞɚɸɳɢɦɢ ɚɤɬɢɜɧɵɦɢ ɮɚɡɢɪɨɜɚɧɧɵɦɢ ɚɧɬɟɧɧɵɦɢ ɪɟɲɟɬɤɚɦɢ (ȺɎȺɊ).
Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɚɧɚɥɨɝɨɜɨɣ ȺɎȺɊ ɩɪɢɜɟɞɟɧɚ ɧɚ
ɪɢɫ. 1.4. Ʉɨɥɟɛɚɧɢɹ
ɝɟɧɟɪɚɬɨɪɚ ɫ ɩɨɦɨɳɶɸ ɞɟɥɢɬɟɥɟɣ ɦɨɳɧɨɫɬɢ ɩɨɫɬɭɩɚɸɬ ɧɚ N ɩɟɪɟɞɚɸɳɢɯ
ɦɨɞɭɥɟɣ, ɤɚɠɞɵɣ ɢɡ ɤɨɬɨɪɵɯ ɫɨɞɟɪɠɢɬ ɭɫɢɥɢɬɟɥɶ ɦɨɳɧɨɫɬɢ, ɭɩɪɚɜɥɹɟɦɵɣ
ɮɚɡɨɜɪɚɳɚɬɟɥɶ ɢ ɢɡɥɭɱɚɬɟɥɶ.
13
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
Ɋɢɫ. 1.4. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɩɟɪɟɞɚɸɳɟɣ ȺɎȺɊ
Ɋɚɞɢɨɩɟɪɟɞɚɬɱɢɤ ɫ ɰɢɮɪɨɜɵɦ ɮɨɪɦɢɪɨɜɚɧɢɟɦ ɪɚɞɢɨɫɢɝɧɚɥɚ
ȿɫɥɢ ɧɟɫɭɳɚɹ ɱɚɫɬɨɬɚ ɩɟɪɟɞɚɬɱɢɤɚ ɧɟɜɵɫɨɤɚ (ɧɟ ɛɨɥɶɲɟ ɧɟɫɤɨɥɶɤɢɯ ɫɨɬɟɧ
ɆȽɰ), ɞɥɹ ɤɨɬɨɪɨɣ ɞɨɫɬɭɩɧɨ ɩɪɢɦɟɧɟɧɢɟ ɫɨɜɪɟɦɟɧɧɵɯ Ⱥɐɉ, ɬɨ ɫɯɟɦɚ
ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ ɢɦɟɟɬ ɜɢɞ, ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɧɚ ɪɢɫ. 1.5.
Ɋɢɫ.1.5. ɋɯɟɦɚ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ ɫ ɰɢɮɪɨɜɵɦ ɮɨɪɦɢɪɨɜɚɧɢɟɦ ɪɚɞɢɨɫɢɝɧɚɥɚ
ȼ ɬɚɤɨɦ ɩɟɪɟɞɚɬɱɢɤɟ ɪɚɞɢɨɫɢɝɧɚɥ ɮɨɪɦɢɪɭɟɬɫɹ ɜ ɰɢɮɪɨɜɨɦ ɜɢɞɟ ɜ
ɩɪɨɰɟɫɫɨɪɟ, ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɚɧɚɥɨɝɨɜɭɸ ɮɨɪɦɭ, ɟɝɨ ɦɨɳɧɨɫɬɶ ɭɜɟɥɢɱɢɜɚɟɬɫɹ
ɢ ɝɚɪɦɨɧɢɤɢ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ ɨɬɮɢɥɶɬɪɨɜɵɜɚɸɬɫɹ ɮɢɥɶɬɪɨɦ ɧɢɠɧɢɯ ɱɚɫɬɨɬ,
ɜɤɥɸɱɟɧɧɵɦ ɩɟɪɟɞ ɚɧɬɟɧɧɨɣ.
ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɛɨɥɶɲɨɟ ɱɢɫɥɨ ɮɭɧɤɰɢɨɧɚɥɶɧɵɯ ɫɯɟɦ
ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɨɜ, ɤɨɬɨɪɵɟ ɪɚɡɥɢɱɚɸɬɫɹ ɫɩɨɫɨɛɚɦɢ ɜɵɩɨɥɧɟɧɢɹ
ɦɨɞɭɥɹɬɨɪɨɜ, ɝɟɧɟɪɚɬɨɪɨɜ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ, ɭɫɢɥɢɬɟɥɟɣ ɦɨɳɧɨɫɬɢ ɜɵɯɨɞɧɵɯ
ɤɨɥɟɛɚɧɢɣ.
1.1.2. Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɨɜ
Ⱦɢɚɩɚɡɨɧ ɱɚɫɬɨɬ, ɨɬɜɟɞɟɧɧɵɣ ɞɥɹ ɩɟɪɟɞɚɬɱɢɤɚ, ɜ ɫɢɫɬɟɦɚɯ ɫɜɹɡɢ ɪɚɡɞɟɥɹɟɬɫɹ
ɧɚ n ɤɚɧɚɥɨɜ, ɢɦɟɸɳɢɯ ɲɢɪɢɧɭ ɩɨɥɨɫɵ ɤɚɧɚɥɚ, ɧɟɧɚɦɧɨɝɨ ɩɪɟɜɵɲɚɸɳɭɸ
ɩɨɥɨɫɭ ɱɚɫɬɨɬ ɜɢɞɟɨɫɢɝɧɚɥɚ — ɪɢɫ.1.6.
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1. ɉɟɪɟɞɚɬɱɢɤɢ ɢ ɩɪɢɟɦɧɢɤɢ
Ɋɢɫ. 1.6. ɑɚɫɬɨɬɧɵɟ ɤɚɧɚɥɵ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ
Ɉɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ ɪɚɞɢɨɩɟɪɟɞɚɬɱɢɤɚ, ɜɨ-ɩɟɪɜɵɯ, ɨɩɪɟɞɟɥɹɸɬ ɟɝɨ
ɤɨɧɤɪɟɬɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ, ɚ ɜɨ-ɜɬɨɪɵɯ, ɭɤɚɡɵɜɚɸɬ ɧɚ ɬɪɟɛɨɜɚɧɢɹ ɫɬɚɧɞɚɪɬɨɜ
ɫɜɹɡɢ. Ʉ ɩɟɪɜɨɦɭ ɜɢɞɭ ɩɚɪɚɦɟɬɪɨɜ ɨɬɧɨɫɹɬɫɹ:
1) ɞɢɚɩɚɡɨɧ ɪɚɛɨɱɢɯ ɱɚɫɬɨɬ ο݂ൌ݂
௫
െf
min
,
2) ɱɢɫɥɨ ɤɚɧɚɥɨɜ n,
3) ɲɢɪɢɧɚ ɩɨɥɨɫɵ ɱɚɫɬɨɬ ɤɚɠɞɨɝɨ ɤɚɧɚɥɚ ο,
ο
4) ɞɨɥɝɨɜɪɟɦɟɧɧɚɹ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɧɟɫɬɚɛɢɥɶɧɨɫɬɶ ɱɚɫɬɨɬ
ౣ౮
బ
, ɝɞɟ ¨f
max
—
ɦɚɤɫɢɦɚɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɪɚɛɨɱɟɣ ɱɚɫɬɨɬɵ ɨɬ ɧɨɦɢɧɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ
ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɞɟɫɬɚɛɢɥɢɡɢɪɭɸɳɢɯ ɮɚɤɬɨɪɨɜ,
݂
5) ɜɵɯɨɞɧɚɹ ɦɨɳɧɨɫɬɶ P
6) ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɩɟɪɟɞɚɬɱɢɤɨɦ ɨɬ ɢɫɬɨɱɧɢɤɨɜ ɩɢɬɚɧɢɹ, P
7) ɩɪɨɦɵɲɥɟɧɧɵɣ ɄɉȾ Ș =
ɩɟɪ,
˒ˈ˓
.
బ
0 .
Ʉɪɨɦɟ ɬɨɝɨ, ɧɭɠɧɨ ɡɚɞɚɬɶ ɜɢɞ ɦɨɞɭɥɹɰɢɢ ɢ ɩɚɪɚɦɟɬɪɵ ɦɨɞɭɥɢɪɭɸɳɢɯ
ɜɢɞɟɨɫɢɝɧɚɥɨɜ.
ɉɟɪɟɞɚɬɱɢɤ ɞɨɥɠɟɧ ɨɛɟɫɩɟɱɢɜɚɬɶ ɮɨɪɦɢɪɨɜɚɧɢɟ ɪɚɞɢɨɫɢɝɧɚɥɚ ɫ ɡɚɞɚɧɧɵɦɢ
ɪɚɛɨɱɢɦɢ ɢ ɷɤɫɩɥɭɚɬɚɰɢɨɧɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɩɪɢ ɨɞɧɨɜɪɟɦɟɧɧɨɦ
ɜɵɩɨɥɧɟɧɢɢ ɬɪɟɛɨɜɚɧɢɣ ɫɬɚɧɞɚɪɬɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɫɨɜɦɟɫɬɢɦɨɫɬɢ (ɗɆɋ). Ʉ
ɨɫɧɨɜɧɵɦ ɬɪɟɛɨɜɚɧɢɹɦ ɫɬɚɧɞɚɪɬɚ ɗɆɋ, ɜ ɧɚɢɛɨɥɶɲɟɣ ɫɬɟɩɟɧɢ ɜɥɢɹɸɳɢɦ ɧɚ
ɮɭɧɤɰɢɨɧɚɥɶɧɭɸ ɫɯɟɦɭ ɩɟɪɟɞɚɬɱɢɤɚ, ɨɬɧɨɫɹɬɫɹ ɞɜɚ ɩɚɪɚɦɟɬɪɚ.
• Mɨɳɧɨɫɬɶ ɢɡɥɭɱɟɧɢɹ ɜ ɫɨɫɟɞɧɟɦ ɤɚɧɚɥɟ. ɋɩɟɤɬɪ ɥɸɛɨɝɨ
ɦɨɞɭɥɢɪɨɜɚɧɧɨɝɨ ɫɢɝɧɚɥɚ ɞɨɥɠɟɧ ɛɵɬɶ ɨɝɪɚɧɢɱɟɧ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ
ɨɫɬɚɬɨɱɧɚɹ ɦɨɳɧɨɫɬɶ ɦɨɞɭɥɢɪɨɜɚɧɧɨɝɨ ɫɢɝɧɚɥɚ ɜ ɩɨɥɨɫɟ ɱɚɫɬɨɬ
ɫɨɫɟɞɧɟɝɨ ɤɚɧɚɥɚ ɧɟ ɩɪɟɜɵɲɚɥɚ ɡɚɞɚɧɧɨɣ ɫɬɚɧɞɚɪɬɨɦ ɜɟɥɢɱɢɧɵ, ɤɚɤ
ɩɪɚɜɢɥɨ, ɧɟ ɛɨɥɟɟ ɦɢɧɭɫ 70 ɞȻ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɨɳɧɨɫɬɢ ɜ ɨɫɧɨɜɧɨɦ
(ɪɚɛɨɱɟɦ) ɤɚɧɚɥɟ.
• Mɨɳɧɨɫɬɶ ɜɧɟɩɨɥɨɫɧɨɝɨ ɢɡɥɭɱɟɧɢɹ ɜ ɲɢɪɨɤɨɣ ɩɨɥɨɫɟ ɱɚɫɬɨɬ. Ɇɨɳɧɨɫɬɶ
ɢɡɥɭɱɟɧɢɹ ɩɟɪɟɞɚɬɱɢɤɚ ɧɚ ɜɫɟɯ ɱɚɫɬɨɬɚɯ ɞɨɥɠɧɚ ɛɵɬɶ ɨɝɪɚɧɢɱɟɧɚ
ɜɟɥɢɱɢɧɨɣ, ɨɩɪɟɞɟɥɟɧɧɨɣ ɫɬɚɧɞɚɪɬɨɦ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ ɛɨɥɟɟ ɦɢɧɭɫ 70 ɞȻ
ɨɬɧɨɫɢɬɟɥɶɧɨɫɬɢ ɦɨɳɧɨɫɬɢ ɩɟɪɟɞɚɬɱɢɤɚ ɧɚ ɨɫɧɨɜɧɨɣ (ɪɚɛɨɱɟɣ) ɱɚɫɬɨɬɟ.
ȼ ɫɨɫɬɚɜ ɚɧɚɥɨɝɨɜɨɣ ɱɚɫɬɢ ɩɟɪɟɞɚɬɱɢɤɚ ɦɨɝɭɬ ɜɯɨɞɢɬɶ ɫɥɟɞɭɸɳɢɟ
ɪɚɞɢɨɬɟɯɧɢɱɟɫɤɢɟ ɭɫɬɪɨɣɫɬɜɚ:
- ɭɫɢɥɢɬɟɥɶ ɦɨɳɧɨɫɬɢ,
15
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
- ɚɜɬɨɝɟɧɟɪɚɬɨɪ,
- ɫɢɧɬɟɡɚɬɨɪ ɱɚɫɬɨɬ,
- ɦɨɞɭɥɹɬɨɪ,
- ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɱɚɫɬɨɬɵ.
ɉɨɦɢɦɨ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɭɫɬɪɨɣɫɬɜ, ɩɟɪɟɞɚɬɱɢɤ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ
ɭɦɧɨɠɢɬɟɥɢ ɢ ɞɟɥɢɬɟɥɢ ɱɚɫɬɨɬɵ, ɮɚɡɨɜɪɚɳɚɬɟɥɢ, ɜɟɧɬɢɥɢ, ɩɟɪɟɤɥɸɱɚɬɟɥɢ ɢ
ɞɪ. Ɉɛɹɡɚɬɟɥɶɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ ɰɢɮɪɨɜɵɯ ɩɟɪɟɞɚɬɱɢɤɨɜ ɹɜɥɹɸɬɫɹ ɐȺɉ, Ⱥɐɉ
ɢ ɩɪɨɰɟɫɫɨɪɵ.
1.2. Ɋɚɞɢɨɩɪɢɟɦɧɢɤ
Ɋɚɞɢɨɩɪɢɟɦɧɢɤ ɩɪɟɞɧɚɡɧɚɱɟɧ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ ɫɥɟɞɭɸɳɢɯ ɮɭɧɤɰɢɣ:
- ɜɵɞɟɥɟɧɢɹ ɩɪɢɧɢɦɚɟɦɨɝɨ ɪɚɞɢɨɫɢɝɧɚɥɚ ɢɡ ɩɨɦɟɯ ɢ ɫɢɝɧɚɥɨɜ ɞɪɭɝɢɯ
ɪɚɞɢɨɫɬɚɧɰɢɣ,
- ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɪɚɞɢɨɫɢɝɧɚɥɚ ɜ ɜɢɞɟɨɫɢɝɧɚɥ,
- ɢɡɜɥɟɱɟɧɢɹ ɩɟɪɟɞɚɜɚɟɦɨɣ ɢɧɮɨɪɦɚɰɢɢ ɢɡ ɜɢɞɟɨɫɢɝɧɚɥɚ .
ȼɵɞɟɥɟɧɢɟ ɩɨɥɟɡɧɨɝɨ ɪɚɞɢɨɫɢɝɧɚɥɚ ɢɡ ɩɨɦɟɯ ɢ ɞɪɭɝɢɯ, ɦɟɲɚɸɳɢɯ,
ɫɢɝɧɚɥɨɜ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɭɬɟɦ ɮɢɥɶɬɪɚɰɢɢ, ɫɨɫɬɨɹɳɟɣ ɢɡ ɞɜɭɯ ɷɬɚɩɨɜ:
ɚ) ɩɪɟɞɜɚɪɢɬɟɥɶɧɚɹ,
ɛ) ɨɫɧɨɜɧɚɹ.
ɉɪɟɞɜɚɪɢɬɟɥɶɧɚɹ ɮɢɥɶɬɪɚɰɢɹ (ɫɟɥɟɤɰɢɹ) ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɭɬɟɦ ɜɵɞɟɥɟɧɢɹ
ɪɚɞɢɨɫɢɝɧɚɥɚ ɜɯɨɞɧɵɦ ɮɢɥɶɬɪɨɦ ɩɪɢɟɦɧɢɤɚ — ɩɪɟɫɟɥɟɤɬɨɪɨɦ,
ɭɫɬɚɧɨɜɥɟɧɧɵɦ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɨɫɥɟ ɩɪɢɟɦɧɨɣ ɚɧɬɟɧɧɵ. ɉɪɨɰɟɫɫ
ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɪɚɞɢɨɫɢɝɧɚɥɚ ɜ ɜɢɞɟɨɫɢɝɧɚɥ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɭɬɟɦ
ɞɟɦɨɞɭɥɹɰɢɢ. Ɉɫɧɨɜɧɚɹ ɫɟɥɟɤɰɢɹ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɢɦɟɧɟɧɢɟɦ ɚɧɚɥɨɝɨɜɨɝɨ ɢɥɢ
ɰɢɮɪɨɜɨɝɨ ɮɢɥɶɬɪ
ɜɢɞɟɨɫɢɝɧɚɥ ɩɨɫɬɭɩɚɟɬ ɧɚ ɨɤɨɧɟɱɧɨɟ ɭɫɬɪɨɣɫɬɜɨ (ɧɚɩɪɢɦɟɪ,
ɝɪɨɦɤɨɝɨɜɨɪɢɬɟɥɶ) ɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɢɡɜɥɟɱɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɧɟ ɬɪɟɛɭɟɬɫɹ.
ȼ ɩɪɢɟɦɧɢɤɚɯ ɰɢɮɪɨɜɵɯ ɫɢɝɧɚɥɨɜ ɜɢɞɟɨɫɢɝɧɚɥ ɩɪɟɨɛɪɚɡɭɟɬɫɹ ɜ ɰɢɮɪɨɜɭɸ
ɮɨɪɦɭ ɢ ɞɥɹ ɢɡɜɥɟɱɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɫɥɭɠɢɬ ɰɢɮɪɨɜɨɣ ɞɟɬɟɤɬɨɪ.
ɚ ɩɨɫɥɟ ɞɟɦɨɞɭɥɹɰɢɢ. ȼ ɩɪɢɟɦɧɢɤɚɯ ɚɧɚɥɨɝɨɜɵɯ ɫɢɝɧɚɥɨɜ
1.2.1. Ɏɭɧɤɰɢɨɧɚɥɶɧɵɟ ɫɯɟɦɵ ɪɚɞɢɨɩɪɢɟɦɧɢɤɨɜ
Ɋɚɞɢɨɩɪɢɟɦɧɢɤ ɩɪɹɦɨɝɨ ɭɫɢɥɟɧɢɹ
ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɩɪɢɟɦɧɢɤɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 1.7. Ɋɚɞɢɨɩɪɢɟɦɧɢɤ ɫɨɫɬɨɢɬ
ɢɡ ɚɧɚɥɨɝɨɜɨɣ ɢ ɰɢɮɪɨɜɨɣ ɱɚɫɬɟɣ. Ⱥɧɚɥɨɝɨɜɚɹ ɱɚɫɬɶ ɜɤɥɸɱɚɟɬ:
í ɩɪɟɫɟɥɟɤɬɨɪ,
í ɭɫɢɥɢɬɟɥɶ ɪɚɞɢɨɱɚɫɬɨɬɵ, ɤɨɬɨɪɵɣ ɞɨɥɠɟɧ ɢɦɟɬɶ ɧɢɡɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ
ɲɭɦɚ ɢ ɜɵɫɨɤɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɭɫɢɥɟɧɢɹ ɦɨɳɧɨɫɬɢ (ɟɝɨ ɧɚɡɵɜɚɸɬ
ɦɚɥɨɲɭɦɹɳɢɣ ɭɫɢɥɢɬɟɥɶ — Ɇɒɍ),
í ɞɟɦɨɞɭɥɹɬɨɪ,
í ɮɢɥɶɬɪ ɨɫɧɨɜɧɨɣ ɫɟɥɟɤɰɢɢ,
16
1. ɉɟɪɟɞɚɬɱɢɤɢ ɢ ɩɪɢɟɦɧɢɤɢ
í ɭɫɢɥɢɬɟɥɢ ɧɢɡɤɨɣ ɱɚɫɬɨɬɵ (ɍɇɑ),
í Ⱥɐɉ.
ɐɢɮɪɨɜɚɹ ɱɚɫɬɶ ɫɨɞɟɪɠɢɬ ɩɪɨɰɟɫɫɨɪ, ɜɵɩɨɥɧɹɸɳɢɣ ɪɨɥɶ ɰɢɮɪɨɜɨɝɨ
ɞɟɬɟɤɬɨɪɚ.
Ɋɢɫ. 1.7. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɪɚɞɢɨɩɪɢɟɦɧɢɤɚ
Ʉɚɤ ɜɢɞɢɦ, ɜ ɩɪɢɟɦɧɢɤɟ ɨɫɭɳɟɫɬɜɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɨɫɧɨɜɧɵɟ ɩɪɨɰɟɫɫɵ:
ɚ) ɮɢɥɶɬɪɚɰɢɹ ɜɵɫɨɤɨɱɚɫɬɨɬɧɵɯ ɤɨɥɟɛɚɧɢɣ,
ɛ) ɭɫɢɥɟɧɢɟ ɦɨɳɧɨɫɬɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɤɨɥɟɛɚɧɢɣ,
ɜ) ɞɟɦɨɞɭɥɹɰɢɹ,
ɝ) ɞɟɬɟɤɬɢɪɨɜɚɧɢɟ (ɜɵɞɟɥɟɧɢɟ ɢɧɮɨɪɦɚɰɢɢ ɢɡ ɜɢɞɟɨɫɢɝɧɚɥɚ).
ɋɩɟɤɬɪɵ ɦɨɳɧɨɫɬɢ ɫɢɝɧɚɥɨɜ ɜ ɪɚɡɥɢɱɧɵɯ ɬɨɱɤɚɯ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɵ
ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 1.8.
Ɋɢɫ.1.8. ɋɩɟɤɬɪɵ ɪɚɞɢɨɫɢɝɧɚɥɚ (ɬɨɱɤɚ 1) ɢ ɜɢɞɟɨɫɢɝɧɚɥɚ (ɬɨɱɤɚ 2)
ɋɩɟɤɬɪ ɪɚɞɢɨɫɢɝɧɚɥɚ ɫɨɫɪɟɞɨɬɨɱɟɧ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɵ
ɩɟɪɟɞɚɬɱɢɤɚ݂
. ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɟɦɨɞɭɥɹɰɢɢ ɢ ɮɢɥɶɬɪɚɰɢɢ ɨɛɪɚɡɭɟɬɫɹ ɫɩɟɤɬɪ
ːˈ˔
ɦɨɳɧɨɫɬɢ ɜɢɞɟɨɫɢɝɧɚɥɚ, ɡɚɧɢɦɚɸɳɢɣ ɩɨɥɨɫɭ ɱɚɫɬɨɬ ɨɬ 0 ɞɨ ɦɚɤɫɢɦɚɥɶɧɨɣ
ɱɚɫɬɨɬɵ ܨ
. Ɉɫɧɨɜɧɚɹ ɫɟɥɟɤɰɢɹ ɜɢɞɟɨɫɢɝɧɚɥɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨɥɨɫɧɨ-
௫
ɩɪɨɩɭɫɤɚɸɳɢɦ ɮɢɥɶɬɪɨɦ (ɉɉɎ) ɧɚ ɜɵɯɨɞɟ ɞɟɦɨɞɭɥɹɬɨɪɚ. Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ
ɜɟɥɢɱɢɧɵ ɜɢɞɟɨɫɢɝɧɚɥɚ, ɞɨɫɬɚɬɨɱɧɨɣ ɞɥɹ ɪɚɛɨɬɵ Ⱥɐɉ, ɩɪɢɦɟɧɟɧ ɭɫɢɥɢɬɟɥɶ
ɧɢɡɤɢɯ ɱɚɫɬɨɬ (ɍɇɑ). Ⱦɟɦɨɞɭɥɹɬɨɪ ɬɚɤɨɝɨ ɩɪɢɟɦɧɢɤɚ ɦɨɠɟɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧ
ɧɚ ɞɢɨɞɟ ɢɥɢ ɬɪɚɧɡɢɫɬɨɪɟ ɜ ɜɢɞɟ ɚɜɬɨɧɨɦɧɨɝɨ ɧɟɥɢɧɟɣɧɨɝɨ ɭɫɬɪɨɣɫɬɜɚ.
Ƚɟɬɟɪɨɞɢɧɧɵɣ ɪɚɞɢɨɩɪɢɟɦɧɢɤ
ȼ ɞɪɭɝɨɦ ɜɚɪɢɚɧɬɟ ɞɟɦɨɞɭɥɹɬɨɪ ɪɚɞɢɨɩɪɢɟɦɧɢɤɚ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɫɯɟɦɟ, ɬɚɤ
ɧɚɡɵɜɚɟɦɨɝɨ, ɫɢɧɯɪɨɧɧɨɝɨ ɞɟɬɟɤɬɨɪɚ. ȼ ɫɨɫɬɚɜ ɬɚɤɨɝɨ ɩɪɢɟɦɧɢɤɚ ɜɤɥɸɱɚɸɬ
17
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
ɦɟɫɬɧɵɣ ɝɟɧɟɪɚɬɨɪ (LO — Local Oscillator), ɧɚɡɵɜɚɟɦɵɣ ɝɟɬɟɪɨɞɢɧɨɦ. ɋɯɟɦɚ
ɝɟɬɟɪɨɞɢɧɧɨɝɨ ɪɚɞɢɨɩɪɢɟɦɧɢɤɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 1.9.
Ɋɢɫ. 1.9. ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɝɟɬɟɪɨɞɢɧɧɨɝɨ ɩɪɢɟɦɧɢɤɚ
ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɞɟɦɨɞɭɥɹɬɨɪ ɫɨɫɬɨɢɬ ɢɡ ɫɦɟɫɢɬɟɥɹ ɱɚɫɬɨɬ, ɝɟɬɟɪɨɞɢɧɚ ɢ
Ɏɇɑ. ɑɚɫɬɨɬɚ ɤɨɥɟɛɚɧɢɣ ɧɚɩɪɹɠɟɧɢɹ ɝɟɬɟɪɨɞɢɧɚ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɪɚɜɧɨɣ
ɱɚɫɬɨɬɟ ɫɢɝɧɚɥɚ, ɬɨ ɟɫɬɶ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɟ ɩɟɪɟɞɚɬɱɢɤɚ ݂
ɱɚɫɬɨɬ ɜɵɩɨɥɧɹɟɬɫɹ ɩɟɪɟɦɧɨɠɟɧɢɟ ɧɚɩɪɹɠɟɧɢɣ ɫɢɝɧɚɥɚݑ
߮ሺݐሻ) ɢ ɝɟɬɟɪɨɞɢɧɚ ݑ
= ܷˆ߱
ˆ
ɧɚɩɪɹɠɟɧɢɣ ɫɭɦɦɚɪɧɨɣ ݑ
ሺሺ߱ -߱ˆ) t – ߮ሺݐሻሻɱɚɫɬɨɬ. Ʉɨɥɟɛɚɧɢɹ ɫɭɦɦɚɪɧɨɣ ɱɚɫɬɨɬɵ ɧɟ
ܷ
ο
t. ɇɚ ɜɵɯɨɞɟ ɫɦɟɫɢɬɟɥɹ ɩɨɹɜɥɹɸɬɫɹ ɤɨɥɟɛɚɧɢɹ
ˆ
ൌܷσሺሺ߱ +߱ˆ)t + ߮ሺݐሻሻ ɢ ɪɚɡɧɨɫɬɧɨɣ ݑ
σ
= ݂
. . ȼ ɫɦɟɫɢɬɟɥɟ
ˆ
=ܷ(t)ሺ߱
˔
t +
ο
=
ɩɪɨɩɭɫɤɚɸɬɫɹ Ɏɇɑ. ɉɪɢ ɪɚɜɟɧɫɬɜɟ ɱɚɫɬɨɬ ɫɢɝɧɚɥɚ ɢ ɝɟɬɟɪɨɞɢɧɚ ɫɩɟɤɬɪ
ɤɨɥɟɛɚɧɢɣ ɪɚɡɧɨɫɬɧɨɣ ɱɚɫɬɨɬɵ ɩɨɜɬɨɪɹɟɬ ɫɩɟɤɬɪ ɜɢɞɟɨɫɢɝɧɚɥɚ ɢ ɱɟɪɟɡ ɍɇɑ
ɩɨɫɬɭɩɚɟɬ ɜ ɭɫɬɪɨɣɫɬɜɨ ɜɵɞɟɥɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ. ɋɩɟɤɬɪɵ ɦɨɳɧɨɫɬɢ ɫɢɝɧɚɥɨɜ
ɜ ɪɚɡɥɢɱɧɵɯ ɬɨɱɤɚɯ ɝɟɬɟɪɨɞɢɧɧɨɝɨ ɩɪɢɟɦɧɢɤɚ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 1.10.
Ɋɢɫ. 1.10. ɋɩɟɤɬɪɵ ɦɨɳɧɨɫɬɢ ɫɢɝɧɚɥɨɜ ɜ ɝɟɬɟɪɨɞɢɧɧɨɦ ɩɪɢɟɦɧɢɤɟ
Ɉɫɧɨɜɧɚɹ ɫɟɥɟɤɰɢɹ ɩɪɢɧɹɬɨɝɨ ɜɢɞɟɨɫɢɝɧɚɥɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɰɢɮɪɨɜɵɦ
ɮɢɥɶɬɪɨɦ ɜ ɭɫɬɪɨɣɫɬɜɟ ɞɟɬɟɤɬɢɪɨɜɚɧɢɹ.
ɋɭɩɟɪɝɟɬɟɪɨɞɢɧɧɵɣ ɪɚɞɢɨɩɪɢɟɦɧɢɤ
ɇɟɞɨɫɬɚɬɤɨɦ ɩɪɢɟɦɧɢɤɨɜ ɩɪɹɦɨɝɨ ɭɫɢɥɟɧɢɹ ɢ ɝɟɬɟɪɨɞɢɧɧɨɝɨ ɹɜɥɹɟɬɫɹ
ɫɥɨɠɧɨɫɬɶ ɜɵɞɟɥɟɧɢɹ ɩɨɥɟɡɧɨɝɨ ɪɚɞɢɨɫɢɝɧɚɥɚ ɢɡ ɦɧɨɠɟɫɬɜɚ ɩɪɢɧɢɦɚɟɦɵɯ
ɫɢɝɧɚɥɨɜ ɞɪɭɝɢɯ ɫɬɚɧɰɢɣ. Ⱦɥɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɜɵɞɟɥɟɧɢɹ ɩɨɥɟɡɧɨɝɨ
ɪɚɞɢɨɫɢɝɧɚɥɚ ɩɪɢɦɟɧɹɟɬɫɹ ɩɪɟɫɟɥɟɤɬɨɪ, ɬɨ ɟɫɬɶ ɩɨɥɨɫɧɨ-ɩɪɨɩɭɫɤɚɸɳɢɣ
18
1. ɉɟɪɟɞɚɬɱɢɤɢ ɢ ɩɪɢɟɦɧɢɤɢ
ɮɢɥɶɬɪ. Ɉɫɧɨɜɨɣ ɥɸɛɨɝɨ ɮɢɥɶɬɪɚ ɹɜɥɹɟɬɫɹ ɪɟɡɨɧɚɬɨɪ, ɞɨɛɪɨɬɧɨɫɬɶ ɤɨɬɨɪɨɝɨ
݂
˓
൘
ܳൌ
ɨɩɪɟɞɟɥɹɟɬ ɟɝɨ ɮɢɥɶɬɪɭɸɳɢɟ ɜɨɡɦɨɠɧɨɫɬɢ.
ο݂
ȿɫɥɢ ɜ ɩɪɢɟɦɧɨɣ ɚɧɬɟɧɧɟ ɢɦɟɸɬɫɹ ɫɢɝɧɚɥɵ ɞɪɭɝɢɯ ɫɬɚɧɰɢɣ, ɱɚɫɬɨɬɵ
ɤɨɬɨɪɵɯ ɛɥɢɡɤɢ ɤ ݂
ǡɬɨ ɩɨɥɨɫɚ ɩɪɨɩɭɫɤɚɧɢɹ ɩɪɟɫɟɥɟɤɬɨɪɚ ɞɨɥɠɧɚ ɛɵɬɶ ɧɟ
ɛɨɥɶɲɟ ɞɢɚɩɚɡɨɧɚ ɱɚɫɬɨɬ, ɡɚɧɢɦɚɟɦɵɯ ɜɢɞɟɨɫɢɝɧɚɥɨɦ. Ʌɟɝɤɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ
ɩɪɢ ɧɚɫɬɪɨɣɤɟ ɪɟɡɨɧɚɬɨɪɚ ɧɚ ɱɚɫɬɨɬɭ ɩɪɢɧɢɦɚɟɦɵɯ ɤɨɥɟɛɚɧɢɣ ɢ
ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜɵɞɟɥɢɬɶ ɩɨɥɟɡɧɵɣ ɫɢɝɧɚɥ, ɞɨɛɪɨɬɧɨɫɬɶ ɪɟɡɨɧɚɬɨɪɚ ɞɨɥɠɧɚ
ɛɵɬɶ ɱɪɟɡɜɵɱɚɣɧɨ ɜɵɫɨɤɨɣ. ɇɚɩɪɢɦɟɪ, ɩɪɢ ɧɟɫɭɳɟɣ ɱɚɫɬɨɬɟ ɪɚɞɢɨɫɢɝɧɚɥɚ
ɫɢɝɧɚɥɚ 2 ȽȽɰ ɢ ɩɨɥɨɫɟ ɱɚɫɬɨɬ ɜɢɞɟɨɫɢɝɧɚɥɚ 200 ɤȽɰ ɞɨɛɪɨɬɧɨɫɬɶ ɪɟɡɨɧɚɬɨɪɚ
ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ 10000, ɱɬɨ ɧɟɪɟɚɥɢɡɭɟɦɨ ɧɚ ɬɚɤɨɣ ɱɚɫɬɨɬɟ ɩɪɢɟɦɚ
. Ⱦɥɹ
ɜɨɡɦɨɠɧɨɫɬɢ ɮɢɥɶɬɪɚɰɢɢ ɩɨɥɟɡɧɨɝɨ ɪɚɞɢɨɫɢɝɧɚɥɚ ɢɡ ɫɢɝɧɚɥɨɜ ɫɨɫɟɞɧɢɯ
ɤɚɧɚɥɨɜ ɩɪɢɦɟɧɹɟɬɫɹ ɫɯɟɦɚ ɪɚɞɢɨɩɪɢɟɦɧɢɤɚ ɫ ɩɨɧɢɠɟɧɢɟɦ ɱɚɫɬɨɬɵ
ɩɪɢɧɢɦɚɟɦɵɯ ɤɨɥɟɛɚɧɢɣ.
Ɋɚɞɢɨɩɪɢɟɦɧɢɤ ɫ ɩɨɧɢɠɚɸɳɢɦ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɦ ɱɚɫɬɨɬɵ (down —
converter) ɧɚɡɵɜɚɸɬ ɫɭɩɟɪɝɟɬɟɪɨɞɢɧɨɦ, ɟɝɨ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɩɨɤɚɡɚɧɚ ɧɚ
ɪɢɫ. 1.11.
Ɋɢɫ. 1.11. Ɏɭɧɤɰɢɨɧɚɥɶɧɚɹ ɫɯɟɦɚ ɫɭɩɟɪɝɟɬɟɪɨɞɢɧɧɨɝɨ ɩɪɢɟɦɧɢɤɚ
ɋɭɩɟɪɝɟɬɟɪɨɞɢɧɧɵɣ ɪɚɞɢɨɩɪɢɟɦɧɢɤ ɫɨɞɟɪɠɢɬ ɩɨɧɢɠɚɸɳɢɣ
ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɱɚɫɬɨɬɵ, ɫɨɫɬɨɹɳɢɣ ɢɡ ɫɦɟɫɢɬɟɥɹ, ɝɟɬɟɪɨɞɢɧɚ ɢ ɮɢɥɶɬɪɚ
ɧɢɠɧɢɯ ɱɚɫɬɨɬ. ɉɪɟɨɛɪɚɡɨɜɚɬɟɥɶ ɱɚɫɬɨɬɵ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɫɢɧɯɪɨɧɧɨɝɨ
ɞɟɬɟɤɬɨɪɚ ɬɟɦ, ɱɬɨ ɱɚɫɬɨɬɚ ɤɨɥɟɛɚɧɢɣ ɧɚɩɪɹɠɟɧɢɹ ɝɟɬɟɪɨɞɢɧɚ ݂
ǡ(݂
ɱɚɫɬɨɬɟ ɫɢɝɧɚɥɚ ݂
ɦɨɠɟɬ ɛɵɬɶ ɦɟɧɶɲɟ ɢɥɢ ɛɨɥɶɲɟ ɱɚɫɬɨɬɵ ɫɢɝɧɚɥɚ).
ˆ
ɧɟ ɪɚɜɧɚ
ˆ
Ɋɚɡɧɨɫɬɶ ɦɟɠɞɭ ɧɢɦɢ
݂
= ݂ˆ- ݂˔ (ɢɥɢ ݂˒˓=݂˔-݂ˆሻ
˒˓
ɧɚɡɵɜɚɟɬɫɹ ɩɪɨɦɟɠɭɬɨɱɧɨɣ ɱɚɫɬɨɬɨɣ. ɉɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫɩɟɤɬɪɨɜ ɱɚɫɬɨɬ
ɫɢɝɧɚɥɨɜ ɜ ɪɚɡɥɢɱɧɵɯ ɬɨɱɤɚɯ ɫɭɩɟɪɝɟɬɟɪɨɞɢɧɧɨɝɨ ɩɪɢɟɦɧɢɤɚ ɩɨɤɚɡɚɧɵ ɧɚ
ɪɢɫ. 1.12.
19
Ɋɨɦɚɧɸɤ ȼ.Ⱥ. Ⱥɧɚɥɨɝɨɜɵɟ ɭɫɬɪɨɣɫɬɜɚ ɩɪɢɟɦɨɩɟɪɟɞɚɬɱɢɤɨɜ
Ɋɢɫ. 1.12. ɋɩɟɤɬɪɵ ɦɨɳɧɨɫɬɢ ɫɢɝɧɚɥɨɜ ɜ ɫɭɩɟɪɝɟɬɟɪɨɞɢɧɧɨɦ ɩɪɢɟɦɧɢɤɟ.
ɇɚ ɜɵɯɨɞɟ ɫɦɟɫɢɬɟɥɹ ɨɛɪɚɡɭɸɬɫɹ ɤɨɥɟɛɚɧɢɹ ɱɚɫɬɨɬ ݂˒˓ ɢ ݂ఀ = ݂ˆ+ ݂
ɧɢɠɧɢɯ ɱɚɫɬɨɬ ɩɪɨɩɭɫɤɚɟɬ ɤɨɥɟɛɚɧɢɹ ɩɪɨɦɟɠɭɬɨɱɧɨɣ ɱɚɫɬɨɬɵ ݂
. Ɏɢɥɶɬɪ
˔
, ɤɨɬɨɪɵɟ
˒˓
ɭɫɢɥɢɜɚɸɬɫɹ ɭɫɢɥɢɬɟɥɟɦ ɩɪɨɦɟɠɭɬɨɱɧɨɣ ɱɚɫɬɨɬɵ (ɍɉɑ) ɢ ɩɨɫɬɭɩɚɸɬ ɧɚ
ɩɨɥɨɫɧɨ- ɩɪɨɩɭɫɤɚɸɳɢɣ ɮɢɥɶɬɪ, ɝɞɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɨɫɧɨɜɧɚɹ ɮɢɥɶɬɪɚɰɢɹ
ɩɪɢɧɢɦɚɟɦɨɝɨ ɪɚɞɢɨɫɢɝɧɚɥɚ. ɉɪɨɦɟɠɭɬɨɱɧɚɹ ɱɚɫɬɨɬɚ ɦɨɠɟɬ ɛɵɬɶ ɜɵɛɪɚɧɚ
ɞɨɫɬɚɬɨɱɧɨ ɧɢɡɤɨɣ, ɱɬɨ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɫɨɡɞɚɬɶ ɮɢɥɶɬɪ, ɫɩɨɫɨɛɧɵɣ
ɨɫɭɳɟɫɬɜɢɬɶ ɜɵɫɨɤɨɤɚɱɟɫɬɜɟɧɧɭɸ ɮɢɥɶɬɪɚɰɢɸ ɤɨɥɟɛɚɧɢɣ ɪɚɞɢɨɤɚɧɚɥɚ.
ɋɭɩɟɪɝɟɬɟɪɨɞɢɧɧɵɣ ɪɚɞɢɨɩɪɢɟɦɧɢɤ ɢɦɟɟɬ ɫɭɳɟɫɬɜɟɧɧɵɣ ɧɟɞɨɫɬɚɬɨɤ. ȿɫɥɢ
ɧɚ ɜɵɯɨɞɟ ɩɪɢɟɦɧɨɣ ɚɧɬɟɧɧɵ ɨɤɚɠɟɬɫɹ ɦɨɳɧɵɣ ɪɚɞɢɨɫɢɝɧɚɥ ɞɪɭɝɨɣ
ɪɚɞɢɨɫɬɚɧɰɢɢ, ɱɚɫɬɨɬɚ ɤɨɬɨɪɨɝɨ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɱɚɫɬɨɬɵ ɝɟɬɟɪɨɞɢɧɚ ɧɚ
ɩɪɨɦɟɠɭɬɨɱɧɭɸ ɱɚɫɬɨɬɭ, ɧɨ ɫɩɟɤɬɪ ɷɬɨɝɨ ɫɢɝɧɚɥɚ ɡɟɪɤɚɥɟɧ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɫɩɟɤɬɪɚ ɝɟɬɟɪɨɞɢɧɚ, ɬɨ ɧɚ ɜɵɯɨɞɟ ɫɦɟɫɢɬɟɥɹ ɩɨɹɜɹɬɫɹ ɤɨɥɟɛɚɧɢɹ ɱɚɫɬɨɬɵ ݂
˒˓
. ȼ
ɪɟɡɭɥɶɬɚɬɟ ɩɪɢɧɢɦɚɟɦɵɣ ɪɚɞɢɨɫɢɝɧɚɥ ɦɨɠɟɬ ɛɵɬɶ ɧɟ ɨɛɧɚɪɭɠɟɧ. ɉɨɞɨɛɧɵɣ
ɦɟɲɚɸɳɢɣ ɪɚɞɢɨɫɢɝɧɚɥ ɧɚɡɵɜɚɸɬ ɡɟɪɤɚɥɶɧɵɦ.
Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɡɟɪɤɚɥɶɧɵɣ ɫɢɝɧɚɥ ɧɟ ɩɨɩɚɥ ɜ ɩɨɫɥɟɞɭɸɳɢɟ ɤɚɫɤɚɞɵ
ɪɚɞɢɨɩɪɢɟɦɧɢɤɚ, ɬɪɟɛɭɟɬɫɹ ɜɵɫɨɤɨɤɚɱɟɫɬɜɟɧɧɚɹ ɮɢɥɶɬɪɚɰɢɹ ɤɨɥɟɛɚɧɢɣ,
ɩɨɫɬɭɩɚɸɳɢɯ ɢɡ ɚɧɬɟɧɧɵ, ɩɪɟɫɟɥɟɤɬɨɪɨɦ, ɤɨɬɨɪɵɣ ɧɚɫɬɪɨɟɧ ɧɚ ɱɚɫɬɨɬɭ
ɫɢɝɧɚɥɚ ݂
݂
ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɚ .
ˊ
. ɗɬɨ ɜɨɡɦɨɠɧɨ, ɟɫɥɢ ɪɚɡɧɢɰɚ ɱɚɫɬɨɬ ɦɟɠɞɭ ݂
˔
ɢ ɡɟɪɤɚɥɶɧɨɣ ɱɚɫɬɨɬɨɣ
˔
Ɋɚɞɢɨɩɪɢɟɦɧɢɤ ɫ ɩɪɹɦɵɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟɦ ɩɪɢɧɹɬɨɝɨ ɪɚɞɢɨɫɢɝɧɚɥɚ ɜ
ɰɢɮɪɨɜɭɸ ɮɨɪɦɭ.
ȿɫɥɢ ɱɚɫɬɨɬɚ ɧɟɫɭɳɢɯ ɤɨɥɟɛɚɧɢɣ ɧɟ ɨɱɟɧɶ ɜɵɫɨɤɚɹ, ɩɪɢ ɤɨɬɨɪɨɣ
ɫɭɳɟɫɬɜɭɸɳɢɟ Ⱥɐɉ ɫɩɨɫɨɛɧɵ ɫɪɚɡɭ ɩɪɟɨɛɪɚɡɨɜɚɬɶ ɚɧɚɥɨɝɨɜɵɣ ɫɢɝɧɚɥ ɜ
ɰɢɮɪɨɜɭɸ ɮɨɪɦɭ, ɬɨ ɫɯɟɦɚ ɪɚɞɢɨɩɪɢɟɦɧɢɤɚ ɢɦɟɟɬ ɜɢɞ, ɩɨɤɚɡɚɧɧɵɣ ɧɚ
ɪɢɫ. 1.13.
20
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