Дискретизация сигналов. Учебное пособие
.pdfɉɨɝɪɟɲɧɨɫɬɢ 'ɫɥ ɢ 'ɪ ɜɯɨɞɹɬ ɜ ɜɵɪɚɠɟɧɢɟ (2.40) ɫ ɪɚɡɧɵɦɢ ɡɧɚɤɚɦɢ, ɩɨ-
ɷɬɨɦɭ ɩɪɢ ɧɟɤɨɬɨɪɵɯ ɡɧɚɱɟɧɢɹɯ W ɡ |
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R0 C ɢ ɜɪɟɦɟɧɢ ɪɚɡɦɵɤɚɧɢɹ ɤɥɸɱɚ tɩ ɷɬɢ |
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ɫɨɫɬɚɜɥɹɸɳɢɟ ɜɡɚɢɦɧɨ ɤɨɦɩɟɧɫɢɪɭɸɬɫɹ. |
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ɉɪɢ ɜɜɟɞɟɧɢɢ ɤɨɪɪɟɤɰɢɢ ɩɭɬɟɦ ɢɡɦɟɧɟɧɢɹ ɦɨɦɟɧɬɚ ɞɚɬɢɪɨɜɤɢ ɨɬɫɱɟɬɚ |
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( tɞ z 0 ) ɞɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ (2.40) ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɜɢɞɟ |
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ɜɪɟɦɹ ɡɚɞɟɪɠɤɢ ɨɬɫɱɟɬɚ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɬɨɥɶɤɨ ɩɚɪɚɦɟɬɪɚɦɢ ɍȼɏ.
Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɜɵɛɨɪɨɦ ɨɩɬɢɦɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɞɚɬɢɪɨɜɤɢ tɞ t ɡ
ɞɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɩɪɢ ɥɢɧɟɣɧɨ-ɢɡɦɟɧɹɸɳɟɦɫɹ ɜɯɨɞɧɨɦ ɫɢɝɧɚɥɟ ɦɨɠɟɬ ɛɵɬɶ ɩɨɥɧɨɫɬɶɸ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɚ ɩɪɢ ɥɸɛɵɯ ɡɧɚɱɟɧɢɹɯ Wɡ ɢ tɩ . Ɋɚɫɫɱɢ-
ɬɵɜɚɟɬɫɹ ɨɩɬɢɦɚɥɶɧɵɣ ɦɨɦɟɧɬ ɞɚɬɢɪɨɜɤɢ t0 ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ.
2.3.2. Ɋɚɫɱɟɬ ɨɩɬɢɦɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɞɢɫɤɪɟɬɢɡɚɰɢɢ (ɜɪɟɦɟɧɢ ɞɚɬɢɪɨɜɤɢ ɨɬɫɱɟɬɚ)
ȼɵɯɨɞɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɍȼɏ ɩɨɫɥɟ ɪɚɡɦɵɤɚɧɢɹ ɤɥɸɱɚ ɪɚɜɧɨ u2 (tɩ ) , ɫɥɟ-
ɞɨɜɚɬɟɥɶɧɨ, ɩɪɢ ɨɬɧɟɫɟɧɢɢ ɨɬɫɱɟɬɚ ɤ ɦɨɦɟɧɬɭ tɞ |
t0 ɞɨɥɠɧɨ ɜɵɩɨɥɧɹɬɶɫɹ ɪɚ- |
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ɜɟɧɫɬɜɨ 'ɞ(tɩ) |
0 . ɉɨɞɫɬɚɜɥɹɹ ɷɬɨ ɭɫɥɨɜɢɟ ɜ (2.40), ɩɨɥɭɱɢɦ |
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Ɂɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɥɸɱɚ |
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ɡɚɜɢɫɢɬ ɨɬ ɜɢɞɚ ɤɥɸɱɚ ɢ |
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ɮɨɪɦɵ ɭɩɪɚɜɥɹɸɳɢɯ ɢɦɩɭɥɶɫɨɜ. ɇɚɢɛɨɥɶɲɢɦ ɛɵɫɬɪɨɞɟɣɫɬɜɢɟɦ ɨɛɥɚɞɚɸɬ ɍȼɏ ɧɚ ɨɫɧɨɜɟ ɞɢɨɞɧɨ-ɦɨɫɬɨɜɨɝɨ ɤɥɸɱɚ ɢ ɭɩɪɚɜɥɹɟɦɨɝɨ ɷɦɢɬɬɟɪɧɨɝɨ ɩɨɜɬɨɪɢ-
41
ɬɟɥɹ. ɍɩɪɚɜɥɹɸɳɢɟ ɤɚɫɤɚɞɵ ɬɚɤɢɯ ɍȼɏ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɡɧɚɱɟɧɢɹ ɜɪɟɦɟɧɢ ɩɟɪɟɤɥɸɱɟɧɢɹ ɫɬɨɹɬ ɧɚ ɨɫɧɨɜɟ ɬɨɤɨɜɨɝɨ ɩɟɪɟɤɥɸɱɚɬɟɥɹ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɨɬɤɪɵɬɨɝɨ ɤɥɸɱɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɨɬɤɪɵɬɨɝɨ ɞɢɨɞɚ ɜ ɞɢɨɞɧɨ-ɦɨɫɬɨɜɨɦ ɤɥɸɱɟ ɢɥɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɷɦɢɬɬɟɪɧɨɝɨ ɩɟɪɟɯɨɞɚ ɜ ɭɩɪɚɜɥɹɟɦɨɦ ɩɨɜɬɨɪɢɬɟɥɟ, ɨɛ-
ɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɦ ɬɨɤɭ [6]: |
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, ɝɞɟ MT – ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɩɨɬɟɧɰɢ- |
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ɚɥ, i i ɭɩɪ iɜɯ – ɬɨɤ ɱɟɪɟɡ ɤɥɸɱ, |
ɩɪɢɱɟɦ ɬɨɤ iɭɩɪ , ɡɚɞɚɜɚɟɦɵɣ ɫɯɟɦɨɣ ɭɩɪɚɜ- |
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ɥɟɧɢɹ, ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɜɯɨɞɧɨɝɨ ɬɨɤɚ iɜɯ .
ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɡɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɬɨɤɚ iɭɩɪ ɩɪɢ ɪɚɡɦɵɤɚɧɢɢ ɤɥɸɱɚ ɫ ɞɨɫɬɚ-
ɬɨɱɧɨɣ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɨɝɪɟɲɧɨɫɬɢ ɪɚɡɦɵɤɚɧɢɹ ɬɨɱɧɨɫɬɶɸ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɥɢɧɟɣɧɵɦ:
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ȼ ɢɬɨɝɟ ɡɚɤɨɧ ɢɡɦɟɧɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɥɸɱɚ ɩɪɢ ɪɚɡɦɵɤɚɧɢɢ ɢɦɟɟɬ
ɜɢɞ:
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– ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɬɤɪɵɬɨɝɨ ɤɥɸɱɚ. |
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ɉɨɞɫɬɚɜɢɜ (2.47) ɜ (2.45) ɢ ɪɚɡɞɟɥɢɜ ɪɟɡɭɥɶɬɚɬ ɧɚ ɜɪɟɦɹ ɩɟɪɟɤɥɸɱɟɧɢɹ tɩ , |
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ɩɨɥɭɱɢɦ ɦɨɦɟɧɬ ɨɩɬɢɦɚɥɶɧɨɣ ɞɚɬɢɪɨɜɤɢ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ: |
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42
ȼ ɪɟɡɭɥɶɬɚɬɟ ɱɢɫɥɟɧɧɨɝɨ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ (2.48) ɩɨɥɭɱɟɧɨ, ɱɬɨ ɩɪɢ tɩ 1,78 Wɡ ɢ
ɞɚɬɢɪɨɜɤɟ ɦɨɦɟɧɬɨɦ ɧɚɱɚɥɚ ɪɚɡɦɵɤɚɧɢɹ ɤɥɸɱɚ (t0 0) ɩɪɨɢɫɯɨɞɢɬ ɜɡɚɢɦɧɚɹ ɤɨɦɩɟɧɫɚɰɢɹ ɩɨɝɪɟɲɧɨɫɬɟɣ ɫɥɟɠɟɧɢɹ ɢ ɪɚɡɦɵɤɚɧɢɹ. ɉɪɢ ɜɫɟɯ ɨɫɬɚɥɶɧɵɯ ɫɨɨɬ-
ɧɨɲɟɧɢɹɯ tɩ ɢ Wɡ ɞɥɹ ɤɨɦɩɟɧɫɚɰɢɢ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɬɪɟɛɭɟɬɫɹ ɧɟɧɭɥɟɜɨɣ ɦɨɦɟɧɬ ɞɚɬɢɪɨɜɤɢ, ɪɚɫɫɱɢɬɚɧɧɵɣ ɩɨ (2.48).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɵɛɨɪ ɨɩɬɢɦɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɞɚɬɢɪɨɜɤɢ ɩɨɡɜɨɥɹɟɬ ɩɨɥɧɨɫɬɶɸ ɫɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɩɨɝɪɟɲɧɨɫɬɢ ɫɥɟɠɟɧɢɹ ɢ ɪɚɡɦɵɤɚɧɢɹ ɩɪɢ ɥɢɧɟɣɧɨ-
ɢɡɦɟɧɹɸɳɟɦɫɹ ɫɢɝɧɚɥɟ. ɇɟɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ |
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0 , ɬ. ɟ. ɨɬɥɢɱɢɟ ɜɯɨɞɧɨɝɨ |
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ɫɢɝɧɚɥɚ ɨɬ ɥɢɧɟɣɧɨ-ɢɡɦɟɧɹɸɳɟɝɨɫɹ, ɩɪɢɜɨɞɢɬ ɤ ɩɨɹɜɥɟɧɢɸ ɫɨɫɬɚɜɥɹɸɳɟɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ, ɤɨɬɨɪɚɹ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɚ ɢɡɦɟɧɟɧɢɟɦ ɞɚɬɢɪɨɜɤɢ ɨɬɫɱɟɬɚ. Ɉɰɟɧɢɦ ɜɟɥɢɱɢɧɭ ɷɬɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɞɥɹ ɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ.
ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɧɚ ɜɯɨɞ ɍȼɏ ɩɨɫɬɭɩɚɟɬ ɫɢɝɧɚɥ u1(t) U sinZ t . ɉɨɞɫɬɚɜɥɹɹ ɟɝɨ ɜ ɩɪɚɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ (2.38), ɩɨɥɭɱɢɦ ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɜɵɯɨɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɍȼɏ:
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ɉɪɢ ɪɚɡɦɵɤɚɧɢɢ ɤɥɸɱɚ ɩɨ ɡɚɤɨɧɭ (2.47) ɧɚ ɧɚɤɨɩɢɬɟɥɶɧɨɣ ɟɦɤɨɫɬɢ C ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ tn ɮɨɪɦɢɪɭɟɬɫɹ ɧɚɩɪɹɠɟɧɢɟ
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Ɋɚɫɫɦɨɬɪɢɦ ɛɵɫɬɪɨɞɟɣɫɬɜɭɸɳɟɟ ɍȼɏ ɫ ɬɢɩɢɱɧɵɦɢ ɡɧɚɱɟɧɢɹɦ ɩɚɪɚɦɟɬɪɨɜ tn 3Wɡ, Wɡ RoC 1ɧɫ. ɉɪɢ ɱɚɫɬɨɬɟ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ 10 ɆȽɰ (ZWɡ
= 0,06) ɩɨɝɪɟɲɧɨɫɬɶ ɫɥɟɠɟɧɢɹ ɬɚɤɨɝɨ ɍȼɏ ɞɨɫɬɢɝɚɟɬ 6,3 %. ȼɜɟɞɟɧɢɟ ɤɨɪɪɟɤ-
ɰɢɢ ɩɭɬɟɦ ɢɡɦɟɧɟɧɢɹ ɞɚɬɢɪɨɜɤɢ ɨɬɫɱɟɬɚ ɧɚ ɜɪɟɦɹ t Wɡ ɭɦɟɧɶɲɚɟɬ ɩɨɝɪɟɲ-
43
ɧɨɫɬɶ ɫɥɟɠɟɧɢɹ ɞɨ ɜɟɥɢɱɢɧɵ Gɫɥ.ɤ 0,2 % . ɉɪɢɜɟɞɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɪɚɡɦɵɤɚ-
ɧɢɹ ɫ ɭɱɟɬɨɦ ɩɨɝɪɟɲɧɨɫɬɢ ɫɥɟɠɟɧɢɹ ɩɪɢ ɨɩɬɢɦɚɥɶɧɨɣ ɞɚɬɢɪɨɜɤɟ ɨɬɫɱɟɬɚ ɪɚɜɧɚ
G(to ) |
u2 (tn ) u1(to ) |
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(2.51) |
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U |
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Ɇɨɦɟɧɬ ɨɩɬɢɦɚɥɶɧɨɣ ɞɚɬɢɪɨɜɤɢ ɜ |
ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (2.20) |
ɪɚɜɟɧ |
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to 0,26tn 0,79 ɧɫ ɩɪɢ ɢɡɦɟɪɟɧɢɢ ɨɬ ɧɚɱɚɥɚ ɦɨɦɟɧɬɚ ɪɚɡɦɵɤɚɧɢɹ ɤɥɸɱɚ. |
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ɉɪɢ ɜɡɹɬɢɢ ɨɬɫɱɟɬɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ |
t 0, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɦɚɤɫɢ- |
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ɦɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɢɡɦɟɧɟɧɢɹ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ ɢ ɦɚɤɫɢɦɚɥɶɧɨɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ, ɩɨɝɪɟɲɧɨɫɬɶ (2.51) ɪɚɜɧɚ G1(to ) 0,03 % . ɉɪɢ ɫɞɜɢɝɟ ɦɨɦɟɧɬɚ
ɜɡɹɬɢɹ ɨɬɫɱɟɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ ɧɚ ɭɝɨɥ M |
S |
4 |
ɩɨɝɪɟɲɧɨɫɬɶ |
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(2.51) ɪɚɜɧɚ G2 (to ) 0,18 % , ɚ ɜ ɦɨɦɟɧɬ ɞɨɫɬɢɠɟɧɢɹ ɦɚɤɫɢɦɭɦɚ |
ɜɯɨɞɧɵɦ ɫɢɝ- |
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ɧɚɥɨɦ M |
S |
2 |
ɧɟɫɤɨɦɩɟɧɫɢɪɨɜɚɧɧɚɹ ɞɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɭɜɟɥɢɱɢɜɚɟɬ- |
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ɫɹ ɞɨ G3 (to ) |
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0,23 % . |
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Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɢɫɬɟɦɚɬɢɱɟɫɤɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɩɪɢ ɫɢɧɭɫɨɢɞɚɥɶɧɨɦ ɜɯɨɞɧɨɦ ɫɢɝɧɚɥɟ ɦɨɠɟɬ ɛɵɬɶ ɜ ɡɧɚɱɢɬɟɥɶɧɨɣ ɫɬɟɩɟɧɢ ɫɤɨɪɪɟɤɬɢɪɨɜɚɧɚ. ɇɚɩɪɢɦɟɪ, ɟɫɥɢ ɩɪɢ ɱɚɫɬɨɬɟ ɫɢɝɧɚɥɚ 10 ɆȽɰ ɩɨɝɪɟɲɧɨɫɬɶ ɛɟɡ ɤɨɪɪɟɤɰɢɢ ɫɨɫɬɚɜɥɹɟɬ 6,3 %, ɬɨ ɫ ɜɜɟɞɟɧɢɟɦ ɤɨɪɪɟɤɰɢɢ ɨɧɚ ɧɟ ɩɪɟɜɵɲɚɟɬ
0,23 %.
Ɋɟɚɥɶɧɵɟ ɭɫɬɪɨɣɫɬɜɚ ɨɬɥɢɱɚɸɬɫɹ ɨɬ ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɷɤɜɢɜɚɥɟɧɬɧɨɣ ɫɯɟɦɵ ɧɚɥɢɱɢɟɦ ɩɚɪɚɡɢɬɧɵɯ ɟɦɤɨɫɬɟɣ, ɧɟɥɢɧɟɣɧɨɫɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɹ Ro ɨɬɤɪɵɬɨɝɨ ɤɥɸɱɚ, ɧɟɥɢɧɟɣɧɵɦ ɡɚɤɨɧɨɦ ɢɡɦɟɧɟɧɢɹ ɭɩɪɚɜɥɹɸɳɟɝɨ ɬɨɤɚ, ɩɪɢɜɨɞɹɳɢɦ ɤ ɩɨɹɜɥɟɧɢɸ ɧɟɥɢɧɟɣɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ, ɤɨɬɨɪɭɸ ɧɟɜɨɡɦɨɠɧɨ ɫɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɢɡɦɟɧɟɧɢɟɦ ɞɚɬɢɪɨɜɤɢ ɨɬɫɱɟɬɨɜ. Ɍɟɦ ɧɟ ɦɟɧɟɟ, ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɜɨɡɦɨɠɧɨɫɬɶ ɭɱɟɫɬɶ ɢɥɢ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɭɦɟɧɶɲɢɬɶ ɷɬɭ ɩɨɝɪɟɲɧɨɫɬɶ ɨɫɬɚɟɬɫɹ, ɧɚɩɪɢɦɟɪ, ɩɨɫɥɟɞɭɸɳɟɣ ɰɢɮɪɨɜɨɣ ɮɢɥɶɬɪɚɰɢɟɣ.
ȼɨ ɜɫɟɯ ɍȼɏ, ɤɚɤ ɢ ɜ Ⱥɐɉ ɛɟɡ ɍȼɏ, ɫɭɳɟɫɬɜɭɟɬ ɟɳɟ ɨɞɧɚ, ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɟɭɫɬɪɚɧɢɦɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ. ɗɬɨ ɫɥɭɱɚɣɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɩɨɝɪɟɲɧɨɫɬɢ ɪɚɡɦɵɤɚɧɢɹ, ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɜɪɟɦɟɧɧɨɣ ɧɟɫɬɚɛɢɥɶɧɨɫɬɶɸ ɭɩɪɚɜɥɹɸɳɢɯ ɢɦɩɭɥɶɫɨɜ, ɬ. ɟ. ɦɨɦɟɧɬɚ ɧɚɱɚɥɚ ɪɚɡɦɵɤɚɧɢɹ ɤɥɸɱɚ, ɧɟɫɬɚɛɢɥɶɧɨɫɬɶɸ ɡɚɤɨɧɚ ɢɡɦɟɧɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤɥɸɱɚ R(t) ɢ ɞɪɭɝɢɦɢ ɮɚɤɬɨɪɚ-
44
ɦɢ. ȼɨɡɧɢɤɚɸɳɚɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɷɬɨɝɨ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶ ɦɨɦɟɧɬɚ ɜɡɹɬɢɹ ɨɬɫɱɟɬɚ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɚɩɟɪɬɭɪɧɵɦ ɜɪɟɦɟɧɟɦ ɍȼɏ – ta .
Ɉɬɧɨɲɟɧɢɟ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ Wɡ ɤ ɚɩɟɪɬɭɪɧɨɦɭ ɜɪɟɦɟɧɢ ɫɨɜɪɟɦɟɧɧɵɯ ɛɵɫɬɪɨɞɟɣɫɬɜɭɸɳɢɯ ɍȼɏ ɤɨɥɟɛɥɟɬɫɹ ɜ ɲɢɪɨɤɢɯ ɩɪɟɞɟɥɚɯ: Wɡ ta = 10…100.
Ʉɪɨɦɟ ɬɨɝɨ, ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɨɛɳɟɩɪɢɧɹɬɨɣ ɦɟɬɨɞɢɤɢ ɢɡɦɟɪɟɧɢɹ ɢɥɢ ɪɚɫɱɟɬɚ ɷɬɢɯ ɩɚɪɚɦɟɬɪɨɜ, ɩɨɷɬɨɦɭ ɨɰɟɧɤɚ ɫɨɨɬɧɨɲɟɧɢɹ ɫɢɫɬɟɦɚɬɢɱɟɫɤɨɣ ɢ ɫɥɭɱɚɣɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɍȼɏ ɡɚɬɪɭɞɧɟɧɚ. ɉɪɢɛɥɢɠɟɧɧɚɹ ɨɰɟɧɤɚ ɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɍȼɏ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɚɩɟɪɬɭɪɧɨɟ ɜɪɟɦɹ ɛɵɫɬɪɨɞɟɣɫɬɜɭɸɳɢɯ ɞɢɨɞɧɨ-ɦɨɫɬɨɜɵɯ ɍȼɏ, ɜɵɩɨɥɧɟɧɧɵɯ ɧɚ ɞɢɫɤɪɟɬɧɵɯ ɷɥɟɦɟɧɬɚɯ, ~ ɜ 10 ɪɚɡ ɦɟɧɶɲɟ ɩɨɫɬɨɹɧɧɨɣ ɜɪɟɦɟɧɢ Wɡ. ɗɬɨ ɨɡɧɚɱɚ-
ɟɬ, ɱɬɨ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɪɚɧɟɟ ɡɧɚɱɟɧɢɹɯ Wɡ 1ɧɫ ɢ f 10 ɆȽɰ ɚɩɟɪɬɭɪɧɨɟ ɜɪɟɦɹ ta 0,1ɧɫ, ɚ ɦɚɤɫɢɦɚɥɶɧɨɟ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨ-
ɧɟɧɢɟ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ, ɨɛɭɫɥɨɜɥɟɧɧɨɣ ɧɚɥɢɱɢɟɦ ɚɩɟɪɬɭɪɧɨɝɨ ɜɪɟɦɟɧɢ, ɪɚɜɧɨ:
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X / |
t |
a |
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Va |
max |
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2S f ta |
0,63 % . |
(2.52) |
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ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɫɢɫɬɟɦɚɬɢɱɟɫɤɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɩɪɢ ɨɩɬɢɦɚɥɶɧɨɣ ɞɚɬɢɪɨɜɤɟ ɨɬɫɱɟɬɚ ɧɟ ɩɪɟɜɵɲɚɟɬ 0,23 %.
ɂɡ ɡɚɜɢɫɢɦɨɫɬɢ Va (ZWɡ) Z ta ɫɥɟɞɭɟɬ, ɱɬɨ ɩɪɢ ɭɦɟɧɶɲɟɧɢɢ ɱɚɫɬɨɬɵ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ Z ɨɬɧɨɲɟɧɢɟ ɫɥɭɱɚɣɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨ-
ɝɪɟɲɧɨɫɬɢ ɤ ɫɢɫɬɟɦɚɬɢɱɟɫɤɨɣ Va Gɫɥ.ɤ ɟɳɟ ɛɨɥɟɟ ɜɨɡɪɚɫɬɚɟɬ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ Ⱥɐɉ ɫ ɍȼɏ ɩɪɢ ɨɩɬɢɦɚɥɶɧɨɣ ɞɚɬɢɪɨɜɤɟ ɨɬɫɱɟɬɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ, ɝɥɚɜɧɵɦ ɨɛɪɚɡɨɦ, ɫɥɭɱɚɣɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ.
Ⱦɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ Ⱥɐɉ ɛɟɡ ɍȼɏ ɬɚɤɠɟ ɫɨɞɟɪɠɢɬ ɫɢɫɬɟɦɚɬɢɱɟɫɤɭɸ ɢ ɫɥɭɱɚɣɧɭɸ ɫɨɫɬɚɜɥɹɸɳɢɟ. Ⱦɥɹ ɩɚɪɚɥɥɟɥɶɧɨɝɨ Ⱥɐɉ, ɧɚɩɪɢɦɟɪ, ɪɚɛɨɬɚɸɳɟɝɨ ɜ ɪɟɠɢɦɟ «ɫɬɪɨɛɢɪɨɜɚɧɢɹ ɧɚ ɥɟɬɭ», ɫɢɫɬɟɦɚɬɢɱɟɫɤɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɪɟɦɟɧɟɦ ɪɚɡɪɟɲɟɧɢɹ ɬɪɢɝɝɟɪɨɜɡɚɳɟɥɨɤ, ɚ ɫɥɭɱɚɣɧɚɹ – ɚɩɟɪɬɭɪɧɵɦ ɜɪɟɦɟɧɟɦ. ɉɪɢɱɢɧɨɣ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɫɥɭɱɚɣɧɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɹɜɥɹɟɬɫɹ ɪɚɡɛɪɨɫ ɡɚɜɢɫɢɦɨɫɬɟɣ ɜɪɟɦɟɧɢ ɩɟɪɟɤɥɸɱɟɧɢɹ ɨɬ ɧɚɩɪɹɠɟɧɢɹ ɩɟɪɟɜɨɡɛɭɠɞɟɧɢɹ ɤɨɦɩɚɪɚɬɨɪɨɜ.
45
ɋɢɫɬɟɦɚɬɢɱɟɫɤɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɬɚɤɢɯ Ⱥɐɉ, ɩɪɨɹɜɥɹɸɳɚɹɫɹ ɤɚɤ ɱɚɫɬɨɬɧɵɟ ɢɫɤɚɠɟɧɢɹ, ɦɨɠɟɬ ɛɵɬɶ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɚ ɫ ɩɨɦɨɳɶɸ ɚɧɚɥɨɝɨɜɨɝɨ ɮɢɥɶɬɪɚ, ɫɨɡɞɚɸɳɟɝɨ ɩɪɟɞɵɫɤɚɠɟɧɢɹ ɧɚ ɜɯɨɞɟ Ⱥɐɉ, ɥɢɛɨ ɩɭɬɟɦ ɰɢɮɪɨɜɨɣ ɮɢɥɶɬɪɚɰɢɢ ɩɪɢ ɨɛɪɚɛɨɬɤɟ ɞɚɧɧɵɯ. ɉɨɫɥɟ ɩɪɨɜɟɞɟɧɢɹ ɬɚɤɨɣ ɤɨɪɪɟɤɰɢɢ ɨɩɪɟɞɟɥɹɸɳɟɟ ɜɥɢɹɧɢɟ ɛɭɞɟɬ ɢɦɟɬɶ ɫɥɭɱɚɣɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɫɬɚɜɥɹɸɳɚɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɛɵɫɬɪɨɞɟɣɫɬɜɭɸɳɢɯ Ⱥɐɉ, ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɤɨɧɟɱɧɵɦ ɚɩɟɪɬɭɪɧɵɦ ɜɪɟɦɟɧɟɦ, ɹɜɥɹɟɬɫɹ ɨɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɩɪɟɩɹɬɫɬɜɢɣ ɧɚ ɩɭɬɢ ɩɨɜɵɲɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɬɨɱɧɨɫɬɢ ɚɧɚ- ɥɨɝɨ-ɰɢɮɪɨɜɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ. ȼɨɡɦɨɠɧɵɦ ɦɟɬɨɞɨɦ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɹɜɥɹɟɬɫɹ ɩɪɢɦɟɧɟɧɢɟ ɨɩɟɪɚɰɢɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɜ ɩɪɨɰɟɫɫɟ ɨɛɪɚɛɨɬɤɢ ɩɨɥɭɱɟɧɧɵɯ ɨɬɫɱɟɬɨɜ.
2.3.3. Ⱥɧɚɥɢɡ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɜɟɫɨɜɨɣ ɮɭɧɤɰɢɢ
ɉɪɨɰɟɫɫ ɞɢɫɤɪɟɬɢɡɚɰɢɢ ɫɢɝɧɚɥɨɜ ɫ ɨɝɪɚɧɢɱɟɧɧɵɦ ɫɩɟɤɬɪɨɦ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɜɵɪɚɠɟɧɢɟɦ
|
n't W / 2 |
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y(n't) |
³x(t)M(n't t)dt , |
(2.53) |
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n't W / 2 |
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ɝɞɟ M(t) – ɜɟɫɨɜɚɹ ɮɭɧɤɰɢɹ, ɨɩɪɟɞɟɥɟɧɧɚɹ ɧɚ ɨɬɪɟɡɤɟ > W 2,W 2@. |
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ȿɫɥɢ M(t) =G(t) – ɞɟɥɶɬɚ-ɮɭɧɤɰɢɹ, ɬɨ y(n't) x(n't) , ɬ. |
ɟ. ɹɜɥɹɸɬɫɹ |
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ɦɝɧɨɜɟɧɧɵɦɢ ɨɬɫɱɟɬɚɦɢ ɫɢɝɧɚɥɚ ɢ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɟɨɪɟɦɨɣ Ʉɨɬɟɥɶɧɢɤɨɜɚ,
ɩɪɢ 't d S , ɝɞɟ Z c – ɝɪɚɧɢɱɧɚɹ ɱɚɫɬɨɬɚ ɫɩɟɤɬɪɚ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ, ɜɨɡɦɨɠɧɨ
Z c
ɬɨɱɧɨɟ ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɮɭɧɤɰɢɢ x(t) ɫ ɩɨɦɨɳɶɸ ɢɞɟɚɥɶɧɨɝɨ ɮɢɥɶɬɪɚ ɧɢɠɧɢɯ ɱɚɫɬɨɬ.
ȿɫɥɢ ɜ ɤɚɱɟɫɬɜɟ M(t) ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɪɹɦɨɭɝɨɥɶɧɵɣ ɢɦɩɭɥɶɫ ɤɨɧɟɱɧɨɣ ɞɥɢɬɟɥɶɧɨɫɬɢ
M(t) |
1, |
W 2 d t dW |
2 |
, |
(2.54) |
® |
t W 2, t |
!W 2 |
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¯0, |
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46
ɬɨ y(n 't) ɹɜɥɹɸɬɫɹ ɞɢɫɤɪɟɬɧɵɦɢ ɨɬɫɱɟɬɚɦɢ ɫɤɨɥɶɡɹɳɟɝɨ ɢɧɬɟɝɪɚɥɚ, ɪɚɫɫɦɨɬɪɟɧɧɨɝɨ ɜ ɩɚɪɚɝɪɚɮɟ 1.1.2.1. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɥɹ ɬɨɱɧɨɝɨ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɮɭɧɤɰɢɢ x(t) ɩɨ ɡɧɚɱɟɧɢɹɦ y(n ' t) ɧɟɨɛɯɨɞɢɦ ɫɩɟɰɢɚɥɶɧɵɣ ɤɨɪɪɟɤɬɢɪɭɸɳɢɣ ɮɢɥɶɬɪ.
ɂɧɬɟɝɪɢɪɭɸɳɢɟ ɍȼɏ (ɂɍȼɏ) ɫ ɩɪɹɦɨɭɝɨɥɶɧɵɦɢ ɜɟɫɨɜɵɦɢ ɮɭɧɤɰɢɹɦɢ ɦɨɝɭɬ ɨɫɭɳɟɫɬɜɥɹɬɶ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ ɜ ɧɚɤɨɩɢɬɟɥɶɧɨɣ ɟɦɤɨɫɬɢ, ɫɬɪɨɛɢɪɭɟɦɨɣ ɛɵɫɬɪɨɞɟɣɫɬɜɭɸɳɢɦ ɩɟɪɟɤɥɸɱɚɬɟɥɟɦ ɬɨɤɚ.
Ⱥɩɟɪɬɭɪɧɨɟ ɜɪɟɦɹ ɬɚɤɨɝɨ ɂɍȼɏ, ɪɚɫɫɱɢɬɚɧɧɨɟ ɩɨ ɫɤɨɪɨɫɬɢ ɩɟɪɟɤɥɸɱɟɧɢɹ ɤɥɸɱɚ, ɫɨɫɬɚɜɥɹɟɬ 0,2…0,4 ɧɫ. Ȼɨɥɟɟ ɬɨɱɧɵɣ ɚɧɚɥɢɡ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɚɩɟɪɬɭɪɧɨɟ ɜɪɟɦɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡɦɟɧɟɧɢɟɦ ɢɧɬɟɪɜɚɥɚ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ, ɜɵɡɜɚɧɧɵɦ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɨɛɴɟɦɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɛɚɡ ɬɪɚɧɡɢɫɬɨɪɨɜ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɤɚɫɤɚɞɚ. ɗɬɢ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɫɨɡɞɚɸɬɫɹ ɟɦɤɨɫɬɧɵɦɢ ɬɨɤɚɦɢ ɩɪɢ ɩɟɪɟɤɥɸɱɟɧɢɢ ɬɪɚɧɡɢɫɬɨɪɨɜ.
Ⱥɩɟɪɬɭɪɧɨɟ ɜɪɟɦɹ ɂɍȼɏ ɢɦɟɟɬ ɬɭ ɠɟ ɜɟɥɢɱɢɧɭ, ɱɬɨ ɢ ɞɥɹ ɛɵɫɬɪɨɞɟɣɫɬɜɭɸɳɢɯ ɍȼɏ ɦɝɧɨɜɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ. Ɉɞɧɚɤɨ ɞɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ, ɨɛɭɫɥɨɜɥɟɧɧɚɹ ɢɡɦɟɧɟɧɢɟɦ ɫɢɝɧɚɥɚ ɜ ɬɟɱɟɧɢɟ ɚɩɟɪɬɭɪɧɨɝɨ ɜɪɟɦɟɧɢ, ɞɥɹ ɷɬɢɯ ɞɜɭɯ ɜɢɞɨɜ ɍȼɏ ɦɨɠɟɬ ɫɢɥɶɧɨ ɪɚɡɥɢɱɚɬɶɫɹ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ ɞɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟ ɚɛɫɨɥɸɬɧɵɦ ɩɪɢɪɚɳɟɧɢɟɦ ɫɢɝɧɚɥɚ ɜ ɬɟɱɟɧɢɟ ɚɩɟɪɬɭɪɧɨɝɨ ɜɪɟɦɟɧɢ, ɤɚɤ ɜ ɍȼɏ ɦɝɧɨɜɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɚ ɨɬɧɨɲɟɧɢɟɦ ɷɬɨɝɨ ɩɪɢɪɚɳɟɧɢɹ ɤɨ ɜɫɟɦɭ ɢɧɬɟɝɪɚɥɭ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ ɩɨ ɞɥɢɬɟɥɶɧɨɫɬɢ ɫɬɪɨɛɢɦɩɭɥɶɫɚ. ɉɨɷɬɨɦɭ ɞɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɂɍȼɏ ɭɦɟɧɶɲɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɭɜɟɥɢɱɟɧɢɸ ɢɧɬɟɪɜɚɥɚ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ.
Ⱦɥɹ ɨɰɟɧɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɂɍȼɏ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɚ ɮɨɪɦɭɥɚ
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G ɞ = |
W h21ɛ rɛ' |
(iɜɯ.ɧ iɜɯ.ɤ) , |
(2.55) |
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W ho |
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ɝɞɟ Wh 21ɛ = |
1 |
– ɜɪɟɦɹ ɩɪɨɥɟɬɚ ɧɟɨɫɧɨɜɧɵɯ ɧɨɫɢɬɟɥɟɣ ɱɟɪɟɡ ɛɚɡɭ ɬɪɚɧɡɢɫɬɨɪɚ; |
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2Sfɝɪ |
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rɛ' – ɭɫɪɟɞɧɟɧɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɛɚɡɨɜɨɣ ɰɟɩɢ; ho – ɬɟɦɩɟɪɚɬɭɪɧɵɣ ɩɨɬɟɧɰɢɚɥ;
iɜɯ.ɧ, iɜɯ.ɤ. – ɜɯɨɞɧɵɟ ɬɨɤɢ ɜ ɧɚɱɚɥɟ ɢ ɜ ɤɨɧɰɟ ɢɧɬɟɪɜɚɥɚ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ.
47
ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɬɪɚɧɡɢɫɬɨɪɨɜ ɫ fɝɪ = 1 ȽȽɰ, W = 50 ɧɫ ɢ ɚɦɩɥɢɬɭɞɟ ɜɯɨɞɧɨɝɨ ɬɨɤɚ iɜɯ = 1 ɦȺ G ɞ d 1 %. Ⱦɚɧɧɨɟ ɂɍȼɏ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɟɨɛɪɚɡɨɜɵɜɚɬɶ ɜ ɰɢɮɪɨɜɨɣ ɤɨɞ ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɟɞɢɧɢɰɵ 7-ɝɨ ɪɚɡɪɹɞɚ ɫɢɝɧɚɥ ɫ ɩɨɥɨɫɨɣ
10 ɆȽɰ.
ɂɧɬɟɝɪɢɪɭɸɳɢɟ ɍȼɏ ɫ ɩɪɹɦɨɭɝɨɥɶɧɵɦɢ ɫɬɪɨɛɢɦɩɭɥɶɫɚɦɢ (ɜɟɫɨɜɨɣ ɮɭɧɤɰɢɟɣ M(t) ) ɹɜɥɹɸɬɫɹ ɩɪɨɫɬɟɣɲɢɦ ɜɢɞɨɦ ɍȼɏ ɞɚɧɧɨɝɨ ɤɥɚɫɫɚ. ȿɝɨ ɛɵɫɬɪɨ-
ɞɟɣɫɬɜɢɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɞɥɢɬɟɥɶɧɨɫɬɶɸ ɮɪɨɧɬɚ ɢɦɩɭɥɶɫɚ M(t) ɢ ɫɤɨɪɨɫɬɶɸ ɩɟ-
ɪɟɤɥɸɱɟɧɢɹ ɬɨɤɨɜɨɝɨ ɤɥɸɱɚ. ȼ ɫɜɹɡɢ ɫ ɷɬɢɦ ɚɤɬɭɚɥɶɧɚ ɡɚɞɚɱɚ ɩɨɢɫɤɚ ɛɨɥɟɟ ɝɥɚɞɤɨɣ ɜɟɫɨɜɨɣ ɮɭɧɤɰɢɢ, ɩɪɟɞɫɬɚɜɥɹɸɳɟɣ ɦɟɧɟɟ ɠɟɫɬɤɢɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɛɵɫɬɪɨɞɟɣɫɬɜɢɸ ɤɨɦɦɭɬɢɪɭɸɳɢɯ ɭɫɬɪɨɣɫɬɜ.
2.3.4. ɋɪɚɜɧɢɬɟɥɶɧɵɣ ɚɧɚɥɢɡ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɢɧɬɟɝɪɢɪɭɸɳɢɯ ɭɫɬɪɨɣɫɬɜ ɞɢɫɤɪɟɬɢɡɚɰɢɢ
ȼɨɡɧɢɤɧɨɜɟɧɢɟ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɜ ɢɧɬɟɝɪɢɪɭɸɳɢɯ ɍȼɏ ɫɜɹɡɚɧɨ ɫ ɢɫɤɚɠɟɧɢɹɦɢ ɮɨɪɦɵ ɜɟɫɨɜɨɣ ɞɢɫɤɪɟɬɢɡɢɪɭɸɳɟɣ ɮɭɧɤɰɢɢ ɢ ɛɵɫɬɪɨɦɟɧɹɸɳɟɝɨɫɹ ɜɯɨɞɧɨɝɨ ɫɢɝɧɚɥɚ, ɜɨɡɧɢɤɚɸɳɢɦɢ ɜɫɥɟɞɫɬɜɢɟ ɢɧɟɪɰɢɨɧɧɨɫɬɢ ɢɫɩɨɥɶɡɭɟɦɵɯ ɷɥɟɦɟɧɬɨɜ. ɇɚɩɪɢɦɟɪ, ɜ ɂɍȼɏ ɫ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɜɟɫɨɜɨɣ ɮɭɧɤɰɢɟɣ ɩɪɢɱɢɧɨɣ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɹɜɥɹɟɬɫɹ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɨɬ ɟɦɤɨɫɬɧɵɯ ɬɨɤɨɜ ɧɚ ɛɚɡɨɜɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɤɚɫɤɚɞɚ. ɉɪɢ ɪɟɚɥɢɡɚɰɢɢ ɫɜɟɪɬɤɢ ɫɢɝɧɚɥɚ ɢ ɜɟɫɨɜɨɣ ɮɭɧɤɰɢɢ ɫ ɩɨɦɨɳɶɸ ɩɟɪɟɦɧɨɠɢɬɟɥɹ ɜɨɡɧɢɤɚɸɬ ɚɧɚɥɨɝɢɱɧɵɟ ɢɫɤɚɠɟɧɢɹ, ɨɛɭɫɥɨɜɥɟɧɧɵɟ ɢɧɟɪɰɢɨɧɧɨɫɬɶɸ ɫɯɟɦɵ.
Ⱥɦɩɥɢɬɭɞɧɨ-ɱɚɫɬɨɬɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɟɪɟɦɧɨɠɢɬɟɥɹ ɧɚ ɝɪɚɧɢɰɟ ɪɚɛɨɱɟɝɨ ɞɢɚɩɚɡɨɧɚ ɱɚɫɬɨɬ ɢɦɟɟɬ ɫɩɚɞ ɫ ɤɪɭɬɢɡɧɨɣ 20 ɞȻ/ɞɟɤ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɚɧɚɥɢɡɚ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɷɤɜɢɜɚɥɟɧɬɧɭɸ ɫɯɟɦɭ, ɜ ɤɨɬɨɪɨɣ ɱɚɫɬɨɬɧɵɟ ɫɜɨɣɫɬɜɚ ɩɟɪɟɦɧɨɠɢɬɟɥɹ ɨɩɢɫɵɜɚɸɬɫɹ ɢɧɟɪɰɢɨɧɧɵɦɢ ɡɜɟɧɶɹɦɢ ɩɟɪɜɨɝɨ ɩɨɪɹɞɤɚ, ɜɤɥɸɱɟɧɧɵɦɢ ɧɚ ɜɯɨɞɟ ɢɞɟɚɥɶɧɨɝɨ ɦɧɨɠɢɬɟɥɶɧɨɝɨ ɭɫɬɪɨɣɫɬɜɚ.
Ⱦɢɧɚɦɢɱɟɫɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɧɚ ɫɢɧɭɫɨɢɞɚɥɶɧɨɦ ɜɯɨɞɧɨɦ ɫɢɝɧɚɥɟ, ɜɧɨɫɢɦɚɹ ɷɤɜɢɜɚɥɟɧɬɧɨɣ RC-ɰɟɩɶɸ, ɦɨɠɟɬ ɛɵɬɶ ɜ ɡɧɚɱɢɬɟɥɶɧɨɣ ɦɟɪɟ ɫɤɨɦɩɟɧɫɢɪɨɜɚɧɚ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɜ ɩɚɪɚɝɪɚɮɟ 2.3.2, ɢɡɦɟɧɟɧɢɟɦ ɞɚɬɢɪɨɜɤɢ ɨɬɫɱɟɬɨɜ. ɂɦɩɭɥɶɫɵ ɞɢɫɤɪɟɬɢɡɢɪɭɸɳɟɣ ɮɭɧɤɰɢɢ M(t) ɢɦɟɸɬ ɝɨɪɚɡɞɨ ɛɨɥɟɟ ɲɢɪɨɤɢɣ, ɩɨ ɫɪɚɜɧɟ-
48
ɧɢɸ ɫ ɜɯɨɞɧɵɦ ɫɢɝɧɚɥɨɦ, ɧɟɨɝɪɚɧɢɱɟɧɧɵɣ ɫɩɟɤɬɪ ɢ ɩɨɞɜɟɪɝɚɸɬɫɹ ɛɨɥɶɲɢɦ ɢɫɤɚɠɟɧɢɹɦ. ɗɬɨ ɢ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɵɦ ɢɫɬɨɱɧɢɤɨɦ ɞɢɧɚɦɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɜ ɢɧɬɟɝɪɢɪɭɸɳɢɯ ɍȼɏ.
ɉɪɨɜɟɞɟɦ ɤɨɥɢɱɟɫɬɜɟɧɧɨɟ ɫɪɚɜɧɟɧɢɟ ɞɢɧɚɦɢɱɟɫɤɢɯ ɩɨɝɪɟɲɧɨɫɬɟɣ ɂɍȼɏ ɫ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɢ ɤɨɫɢɧɭɫɨɢɞɚɥɶɧɨɣ ɜɟɫɨɜɵɦɢ ɮɭɧɤɰɢɹɦɢ.
ɉɭɫɬɶ ɧɚ ɜɯɨɞ ɩɟɪɟɦɧɨɠɢɬɟɥɹ ɩɨɫɬɭɩɚɟɬ ɫɢɧɭɫɨɢɞɚɥɶɧɵɣ ɫɢɝɧɚɥ f (t) Asin 2TS t , ɚ ɧɚ ɞɪɭɝɨɣ ɟɝɨ ɜɯɨɞ ɩɨɞɚɟɬɫɹ ɥɢɛɨ ɤɨɫɢɧɭɫɨɢɞɚɥɶɧɚɹ ɥɢɛɨ ɩɪɹɦɨɭɝɨɥɶɧɚɹ ɜɟɫɨɜɚɹ ɮɭɧɤɰɢɹ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵɟ:
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ɇɚ ɜɯɨɞɵ ɢɞɟɚɥɶɧɨɝɨ ɩɟɪɟɦɧɨɠɢɬɟɥɹ ɩɨɫɬɭɩɚɸɬ ɫɢɝɧɚɥɵ
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ɩɪɢ T2 t T2 ;
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ȼɵɯɨɞɧɨɣ ɫɢɝɧɚɥ ɢɞɟɚɥɶɧɨɝɨ ɛɟɡɵɧɟɪɰɢɨɧɧɨɝɨ ɂɍȼɏ, ɨɬɧɟɫɟɧɧɵɣ ɤ ɦɨɦɟɧɬɭ ɜɪɟɦɟɧɢ t = 0, ɪɚɜɟɧ
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ɉɨɷɬɨɦɭ ɜɵɯɨɞɧɨɣ ɫɢɝɧɚɥ ɪɟɚɥɶɧɨɝɨ ɂɍȼɏ, ɨɬɧɟɫɟɧɧɵɣ ɤ ɷɬɨɦɭ ɠɟ ɦɨɦɟɧɬɭ ɜɪɟɦɟɧɢ, ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɫɢɫɬɟɦɚɬɢɱɟɫɤɭɸ ɞɢɧɚɦɢɱɟɫɤɭɸ ɩɨɝɪɟɲɧɨɫɬɶ
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Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɨɝɪɟɲɧɨɫɬɢ (2.61) ɧɟɨɛɯɨɞɢɦɨ ɡɚɞɚɬɶ ɨɬɧɨɲɟɧɢɟ T . ɉɨ-
W
ɝɪɟɲɧɨɫɬɶ ɩɟɪɟɞɚɱɢ ɫɢɧɭɫɨɢɞɚɥɶɧɨɝɨ ɫɢɝɧɚɥɚ ɢɧɬɟɝɪɢɪɭɸɳɟɣ RC-ɰɟɩɶɸ ɩɪɢ ɨɩ-
ɬɢɦɚɥɶɧɨɣ ɞɚɬɢɪɨɜɤɟ ɨɬɫɱɟɬɚ ɧɟ ɩɪɟɜɵɲɚɟɬ 0,5 % ɩɪɢ ZW |
0,1, ɬ. ɟ. ɩɪɢ T 10S, |
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ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɜɟɫɨɜɨɣ ɮɭɧɤɰɢɢ ɧɚ ɜɯɨɞ ɢɞɟɚɥɶɧɨɝɨ ɩɟɪɟɦɧɨɠɢɬɟɥɹ ɩɨɫɬɭɩɚɟɬ ɫɢɝɧɚɥ
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50